Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE PAGES

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; ...

2017-10-17

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Zuwei; Zhao, Haibo, E-mail: klinsmannzhb@163.com; Zheng, Chuguang

2015-01-15

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule providesmore » a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.« less

On spatial mutation-selection models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

Application of Markov Models for Analysis of Development of Psychological Characteristics

ERIC Educational Resources Information Center

Kuravsky, Lev S.; Malykh, Sergey B.

2004-01-01

A technique to study combined influence of environmental and genetic factors on the base of changes in phenotype distributions is presented. Histograms are exploited as base analyzed characteristics. A continuous time, discrete state Markov process with piece-wise constant interstate transition rates is associated with evolution of each histogram.…

SAChES: Scalable Adaptive Chain-Ensemble Sampling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swiler, Laura Painton; Ray, Jaideep; Ebeida, Mohamed Salah

We present the development of a parallel Markov Chain Monte Carlo (MCMC) method called SAChES, Scalable Adaptive Chain-Ensemble Sampling. This capability is targed to Bayesian calibration of com- putationally expensive simulation models. SAChES involves a hybrid of two methods: Differential Evo- lution Monte Carlo followed by Adaptive Metropolis. Both methods involve parallel chains. Differential evolution allows one to explore high-dimensional parameter spaces using loosely coupled (i.e., largely asynchronous) chains. Loose coupling allows the use of large chain ensembles, with far more chains than the number of parameters to explore. This reduces per-chain sampling burden, enables high-dimensional inversions and the usemore » of computationally expensive forward models. The large number of chains can also ameliorate the impact of silent-errors, which may affect only a few chains. The chain ensemble can also be sampled to provide an initial condition when an aberrant chain is re-spawned. Adaptive Metropolis takes the best points from the differential evolution and efficiently hones in on the poste- rior density. The multitude of chains in SAChES is leveraged to (1) enable efficient exploration of the parameter space; and (2) ensure robustness to silent errors which may be unavoidable in extreme-scale computational platforms of the future. This report outlines SAChES, describes four papers that are the result of the project, and discusses some additional results.« less

[Prediction method of rural landscape pattern evolution based on life cycle: a case study of Jinjing Town, Hunan Province, China].

PubMed

Ji, Xiang; Liu, Li-Ming; Li, Hong-Qing

2014-11-01

Taking Jinjing Town in Dongting Lake area as a case, this paper analyzed the evolution of rural landscape patterns by means of life cycle theory, simulated the evolution cycle curve, and calculated its evolution period, then combining CA-Markov model, a complete prediction model was built based on the rule of rural landscape change. The results showed that rural settlement and paddy landscapes of Jinjing Town would change most in 2020, with the rural settlement landscape increased to 1194.01 hm2 and paddy landscape greatly reduced to 3090.24 hm2. The quantitative and spatial prediction accuracies of the model were up to 99.3% and 96.4%, respectively, being more explicit than single CA-Markov model. The prediction model of rural landscape patterns change proposed in this paper would be helpful for rural landscape planning in future.

Entanglement revival can occur only when the system-environment state is not a Markov state

NASA Astrophysics Data System (ADS)

Sargolzahi, Iman

2018-06-01

Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will call strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the whole system-environment is a Markov state, then each localized dynamics of the whole system-environment reduces to a localized subdynamics of the system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system-environment state is not a Markov state. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system-environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.

A flowgraph model for bladder carcinoma

PubMed Central

2014-01-01

Background Superficial bladder cancer has been the subject of numerous studies for many years, but the evolution of the disease still remains not well understood. After the tumor has been surgically removed, it may reappear at a similar level of malignancy or progress to a higher level. The process may be reasonably modeled by means of a Markov process. However, in order to more completely model the evolution of the disease, this approach is insufficient. The semi-Markov framework allows a more realistic approach, but calculations become frequently intractable. In this context, flowgraph models provide an efficient approach to successfully manage the evolution of superficial bladder carcinoma. Our aim is to test this methodology in this particular case. Results We have built a successful model for a simple but representative case. Conclusion The flowgraph approach is suitable for modeling of superficial bladder cancer. PMID:25080066

The algebra of the general Markov model on phylogenetic trees and networks.

PubMed

Sumner, J G; Holland, B R; Jarvis, P D

2012-04-01

It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.

The Jukes-Cantor Model of Molecular Evolution

ERIC Educational Resources Information Center

Erickson, Keith

2010-01-01

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Amini, Hadis, E-mail: nhamini@stanford.edu

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, whichmore » extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.« less

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

PubMed

Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C

2014-04-01

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

Driving style recognition method using braking characteristics based on hidden Markov model

PubMed Central

Wu, Chaozhong; Lyu, Nengchao; Huang, Zhen

2017-01-01

Since the advantage of hidden Markov model in dealing with time series data and for the sake of identifying driving style, three driving style (aggressive, moderate and mild) are modeled reasonably through hidden Markov model based on driver braking characteristics to achieve efficient driving style. Firstly, braking impulse and the maximum braking unit area of vacuum booster within a certain time are collected from braking operation, and then general braking and emergency braking characteristics are extracted to code the braking characteristics. Secondly, the braking behavior observation sequence is used to describe the initial parameters of hidden Markov model, and the generation of the hidden Markov model for differentiating and an observation sequence which is trained and judged by the driving style is introduced. Thirdly, the maximum likelihood logarithm could be implied from the observable parameters. The recognition accuracy of algorithm is verified through experiments and two common pattern recognition algorithms. The results showed that the driving style discrimination based on hidden Markov model algorithm could realize effective discriminant of driving style. PMID:28837580

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic amplitude versus angle (AVA) and controlled source electromagnetic (CSEM) data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo (MCMC) sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis (DREAM) and Adaptive Metropolis (AM) samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and CSEM data. The multi-chain MCMC is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration,more » the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic AVA and CSEM joint inversion provides better estimation of reservoir saturations than the seismic AVA-only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated – reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Handling target obscuration through Markov chain observations

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Wu, Biao

2008-04-01

Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.

PubMed

Djordjevic, Ivan B

2015-08-24

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

PubMed Central

Djordjevic, Ivan B.

2015-01-01

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled. PMID:26305258

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method

PubMed Central

Kim, Kyungmok; Lee, Jaewook

2016-01-01

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones. PMID:28773359

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Walker, Anthony; Safta, Cosmin; Munger, William

2017-09-01

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

Differential Equation Models for Sharp Threshold Dynamics

DTIC Science & Technology

2012-08-01

dynamics, and the Lanchester model of armed conflict, where the loss of a key capability drastically changes dynamics. We derive and demonstrate a step...dynamics using differential equations. 15. SUBJECT TERMS Differential Equations, Markov Population Process, S-I-R Epidemic, Lanchester Model 16...infection, where a detection event drastically changes dynamics, and the Lanchester model of armed conflict, where the loss of a key capability

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Advancing X-ray scattering metrology using inverse genetic algorithms.

PubMed

Hannon, Adam F; Sunday, Daniel F; Windover, Donald; Kline, R Joseph

2016-01-01

We compare the speed and effectiveness of two genetic optimization algorithms to the results of statistical sampling via a Markov chain Monte Carlo algorithm to find which is the most robust method for determining real space structure in periodic gratings measured using critical dimension small angle X-ray scattering. Both a covariance matrix adaptation evolutionary strategy and differential evolution algorithm are implemented and compared using various objective functions. The algorithms and objective functions are used to minimize differences between diffraction simulations and measured diffraction data. These simulations are parameterized with an electron density model known to roughly correspond to the real space structure of our nanogratings. The study shows that for X-ray scattering data, the covariance matrix adaptation coupled with a mean-absolute error log objective function is the most efficient combination of algorithm and goodness of fit criterion for finding structures with little foreknowledge about the underlying fine scale structure features of the nanograting.

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

Bykova, Nadezda A; Favorov, Alexander V; Mironov, Andrey A

2013-01-01

The problem of reconstruction of ancestral states given a phylogeny and data from extant species arises in a wide range of biological studies. The continuous-time Markov model for the discrete states evolution is generally used for the reconstruction of ancestral states. We modify this model to account for a case when the states of the extant species are uncertain. This situation appears, for example, if the states for extant species are predicted by some program and thus are known only with some level of reliability; it is common for bioinformatics field. The main idea is formulation of the problem as a hidden Markov model on a tree (tree HMM, tHMM), where the basic continuous-time Markov model is expanded with the introduction of emission probabilities of observed data (e.g. prediction scores) for each underlying discrete state. Our tHMM decoding algorithm allows us to predict states at the ancestral nodes as well as to refine states at the leaves on the basis of quantitative comparative genomics. The test on the simulated data shows that the tHMM approach applied to the continuous variable reflecting the probabilities of the states (i.e. prediction score) appears to be more accurate then the reconstruction from the discrete states assignment defined by the best score threshold. We provide examples of applying our model to the evolutionary analysis of N-terminal signal peptides and transcription factor binding sites in bacteria. The program is freely available at http://bioinf.fbb.msu.ru/~nadya/tHMM and via web-service at http://bioinf.fbb.msu.ru/treehmmweb.

Reverse engineering a social agent-based hidden markov model--visage.

PubMed

Chen, Hung-Ching Justin; Goldberg, Mark; Magdon-Ismail, Malik; Wallace, William A

2008-12-01

We present a machine learning approach to discover the agent dynamics that drives the evolution of the social groups in a community. We set up the problem by introducing an agent-based hidden Markov model for the agent dynamics: an agent's actions are determined by micro-laws. Nonetheless, We learn the agent dynamics from the observed communications without knowing state transitions. Our approach is to identify the appropriate micro-laws corresponding to an identification of the appropriate parameters in the model. The model identification problem is then formulated as a mixed optimization problem. To solve the problem, we develop a multistage learning process for determining the group structure, the group evolution, and the micro-laws of a community based on the observed set of communications among actors, without knowing the semantic contents. Finally, to test the quality of our approximations and the feasibility of the approach, we present the results of extensive experiments on synthetic data as well as the results on real communities, such as Enron email and Movie newsgroups. Insight into agent dynamics helps us understand the driving forces behind social evolution.

Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.; Kuvshinov, Alexey V.

2016-05-01

This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.

Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant

NASA Astrophysics Data System (ADS)

Aggarwal, Anil Kr.; Kumar, Sanjeev; Singh, Vikram; Garg, Tarun Kr.

2015-12-01

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth-death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman-Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga-Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the urea synthesis system of the fertilizer plant.

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-06-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R}^d. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^-, ɛ > 0. Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+, where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^-. We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^-. Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^-. In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on {Γ}^+ associated with the averaged Markov birth-and-death operator {\\overline{L}} = \\int _{Γ}^- L^+(γ ^-)d μ _{inv}(γ ^-).

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-04-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R^d . Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^- , ɛ > 0 . Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+ , where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^- . We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^- . Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^- . In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on Γ^+ associated with the averaged Markov birth-and-death operator \\overline{L} = \\int _{Γ}^-}L^+(γ ^-)d μ _{inv}(γ ^-).

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Identifying differentially expressed genes in cancer patients using a non-parameter Ising model.

PubMed

Li, Xumeng; Feltus, Frank A; Sun, Xiaoqian; Wang, James Z; Luo, Feng

2011-10-01

Identification of genes and pathways involved in diseases and physiological conditions is a major task in systems biology. In this study, we developed a novel non-parameter Ising model to integrate protein-protein interaction network and microarray data for identifying differentially expressed (DE) genes. We also proposed a simulated annealing algorithm to find the optimal configuration of the Ising model. The Ising model was applied to two breast cancer microarray data sets. The results showed that more cancer-related DE sub-networks and genes were identified by the Ising model than those by the Markov random field model. Furthermore, cross-validation experiments showed that DE genes identified by Ising model can improve classification performance compared with DE genes identified by Markov random field model. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

PSEMA: An Algorithm for Pattern Stimulated Evolution of Music

NASA Astrophysics Data System (ADS)

Mavrogianni, A. N.; Vlachos, D. S.; Harvalias, G.

2008-11-01

An algorithm for pattern stimulating evolution of music is presented in this work (PSEMA). The system combines a pattern with a genetic algorithm for automatic music composition in order to create a musical phrase uniquely characterizing the pattern. As an example a musical portrait is presented. The initialization of the musical phrases is done with a Markov Chain process. The evolution is dominated by an arbitrary correspondence between the pattern (feature extraction of the pattern may be used in this step) and the esthetic result of the musical phrase.

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

DOE PAGES

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.; ...

2017-09-27

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Two fundamental questions about protein evolution.

PubMed

Penny, David; Zhong, Bojian

2015-12-01

Two basic questions are considered that approach protein evolution from different directions; the problems arising from using Markov models for the deeper divergences, and then the origin of proteins themselves. The real problem for the first question (going backwards in time) is that at deeper phylogenies the Markov models of sequence evolution must lose information exponentially at deeper divergences, and several testable methods are suggested that should help resolve these deeper divergences. For the second question (coming forwards in time) a problem is that most models for the origin of protein synthesis do not give a role for the very earliest stages of the process. From our knowledge of the importance of replication accuracy in limiting the length of a coding molecule, a testable hypothesis is proposed. The length of the code, the code itself, and tRNAs would all have prior roles in increasing the accuracy of RNA replication; thus proteins would have been formed only after the tRNAs and the length of the triplet code are already formed. Both questions lead to testable predictions. Copyright © 2014 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

SMURFLite: combining simplified Markov random fields with simulated evolution improves remote homology detection for beta-structural proteins into the twilight zone.

PubMed

Daniels, Noah M; Hosur, Raghavendra; Berger, Bonnie; Cowen, Lenore J

2012-05-01

One of the most successful methods to date for recognizing protein sequences that are evolutionarily related has been profile hidden Markov models (HMMs). However, these models do not capture pairwise statistical preferences of residues that are hydrogen bonded in beta sheets. These dependencies have been partially captured in the HMM setting by simulated evolution in the training phase and can be fully captured by Markov random fields (MRFs). However, the MRFs can be computationally prohibitive when beta strands are interleaved in complex topologies. We introduce SMURFLite, a method that combines both simplified MRFs and simulated evolution to substantially improve remote homology detection for beta structures. Unlike previous MRF-based methods, SMURFLite is computationally feasible on any beta-structural motif. We test SMURFLite on all propeller and barrel folds in the mainly-beta class of the SCOP hierarchy in stringent cross-validation experiments. We show a mean 26% (median 16%) improvement in area under curve (AUC) for beta-structural motif recognition as compared with HMMER (a well-known HMM method) and a mean 33% (median 19%) improvement as compared with RAPTOR (a well-known threading method) and even a mean 18% (median 10%) improvement in AUC over HHPred (a profile-profile HMM method), despite HHpred's use of extensive additional training data. We demonstrate SMURFLite's ability to scale to whole genomes by running a SMURFLite library of 207 beta-structural SCOP superfamilies against the entire genome of Thermotoga maritima, and make over a 100 new fold predictions. Availability and implementaion: A webserver that runs SMURFLite is available at: http://smurf.cs.tufts.edu/smurflite/

Lifting the Markov blankets of socio-cultural evolution. A comment on "Answering Schrödinger's question: A free-energy formulation" by Maxwell James Désormeau Ramstead et al.

NASA Astrophysics Data System (ADS)

Leydesdorff, Loet

2018-03-01

Ramstead et al. [8] claim an encompassing ontology which can be used as a heuristics for studying life, mind, and society both empirically and in terms of computer simulations. The systems levels are self-organizing into a hierarchy; "Markov blankets" close the various levels for one another. Homo sapiens sapiens is placed at the top of this hierarchy as "the world's most complex living systems." Humans are said to generate "(epi)genetically-specified expectations that have been shaped by selection to guide action-perception cycles toward adaptive or unsurprising states."

Vulnerability of networks of interacting Markov chains.

PubMed

Kocarev, L; Zlatanov, N; Trajanov, D

2010-05-13

The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.

Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module

NASA Astrophysics Data System (ADS)

Martinez, Gregory D.; McKay, James; Farmer, Ben; Scott, Pat; Roebber, Elinore; Putze, Antje; Conrad, Jan

2017-11-01

We introduce ScannerBit, the statistics and sampling module of the public, open-source global fitting framework GAMBIT. ScannerBit provides a standardised interface to different sampling algorithms, enabling the use and comparison of multiple computational methods for inferring profile likelihoods, Bayesian posteriors, and other statistical quantities. The current version offers random, grid, raster, nested sampling, differential evolution, Markov Chain Monte Carlo (MCMC) and ensemble Monte Carlo samplers. We also announce the release of a new standalone differential evolution sampler, Diver, and describe its design, usage and interface to ScannerBit. We subject Diver and three other samplers (the nested sampler MultiNest, the MCMC GreAT, and the native ScannerBit implementation of the ensemble Monte Carlo algorithm T-Walk) to a battery of statistical tests. For this we use a realistic physical likelihood function, based on the scalar singlet model of dark matter. We examine the performance of each sampler as a function of its adjustable settings, and the dimensionality of the sampling problem. We evaluate performance on four metrics: optimality of the best fit found, completeness in exploring the best-fit region, number of likelihood evaluations, and total runtime. For Bayesian posterior estimation at high resolution, T-Walk provides the most accurate and timely mapping of the full parameter space. For profile likelihood analysis in less than about ten dimensions, we find that Diver and MultiNest score similarly in terms of best fit and speed, outperforming GreAT and T-Walk; in ten or more dimensions, Diver substantially outperforms the other three samplers on all metrics.

Evolving autonomous learning in cognitive networks.

PubMed

Sheneman, Leigh; Hintze, Arend

2017-12-01

There are two common approaches for optimizing the performance of a machine: genetic algorithms and machine learning. A genetic algorithm is applied over many generations whereas machine learning works by applying feedback until the system meets a performance threshold. These methods have been previously combined, particularly in artificial neural networks using an external objective feedback mechanism. We adapt this approach to Markov Brains, which are evolvable networks of probabilistic and deterministic logic gates. Prior to this work MB could only adapt from one generation to the other, so we introduce feedback gates which augment their ability to learn during their lifetime. We show that Markov Brains can incorporate these feedback gates in such a way that they do not rely on an external objective feedback signal, but instead can generate internal feedback that is then used to learn. This results in a more biologically accurate model of the evolution of learning, which will enable us to study the interplay between evolution and learning and could be another step towards autonomously learning machines.

Patchwork sampling of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kürsten, Rüdiger; Behn, Ulrich

2016-03-01

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Delay chemical master equation: direct and closed-form solutions

PubMed Central

Leier, Andre; Marquez-Lago, Tatiana T.

2015-01-01

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616

Delay chemical master equation: direct and closed-form solutions.

PubMed

Leier, Andre; Marquez-Lago, Tatiana T

2015-07-08

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

PyDREAM: high-dimensional parameter inference for biological models in python.

PubMed

Shockley, Erin M; Vrugt, Jasper A; Lopez, Carlos F; Valencia, Alfonso

2018-02-15

Biological models contain many parameters whose values are difficult to measure directly via experimentation and therefore require calibration against experimental data. Markov chain Monte Carlo (MCMC) methods are suitable to estimate multivariate posterior model parameter distributions, but these methods may exhibit slow or premature convergence in high-dimensional search spaces. Here, we present PyDREAM, a Python implementation of the (Multiple-Try) Differential Evolution Adaptive Metropolis [DREAM(ZS)] algorithm developed by Vrugt and ter Braak (2008) and Laloy and Vrugt (2012). PyDREAM achieves excellent performance for complex, parameter-rich models and takes full advantage of distributed computing resources, facilitating parameter inference and uncertainty estimation of CPU-intensive biological models. PyDREAM is freely available under the GNU GPLv3 license from the Lopez lab GitHub repository at http://github.com/LoLab-VU/PyDREAM. c.lopez@vanderbilt.edu. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

Optimal satisfaction degree in energy harvesting cognitive radio networks

NASA Astrophysics Data System (ADS)

Li, Zan; Liu, Bo-Yang; Si, Jiang-Bo; Zhou, Fu-Hui

2015-12-01

A cognitive radio (CR) network with energy harvesting (EH) is considered to improve both spectrum efficiency and energy efficiency. A hidden Markov model (HMM) is used to characterize the imperfect spectrum sensing process. In order to maximize the whole satisfaction degree (WSD) of the cognitive radio network, a tradeoff between the average throughput of the secondary user (SU) and the interference to the primary user (PU) is analyzed. We formulate the satisfaction degree optimization problem as a mixed integer nonlinear programming (MINLP) problem. The satisfaction degree optimization problem is solved by using differential evolution (DE) algorithm. The proposed optimization problem allows the network to adaptively achieve the optimal solution based on its required quality of service (Qos). Numerical results are given to verify our analysis. Project supported by the National Natural Science Foundation of China (Grant No. 61301179), the Doctorial Programs Foundation of the Ministry of Education of China (Grant No. 20110203110011), and the 111 Project (Grant No. B08038).

Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

NASA Astrophysics Data System (ADS)

Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

2015-03-01

We present Π4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes

NASA Astrophysics Data System (ADS)

Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.

2016-06-01

We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.

Estimation in a semi-Markov transformation model

PubMed Central

Dabrowska, Dorota M.

2012-01-01

Multi-state models provide a common tool for analysis of longitudinal failure time data. In biomedical applications, models of this kind are often used to describe evolution of a disease and assume that patient may move among a finite number of states representing different phases in the disease progression. Several authors developed extensions of the proportional hazard model for analysis of multi-state models in the presence of covariates. In this paper, we consider a general class of censored semi-Markov and modulated renewal processes and propose the use of transformation models for their analysis. Special cases include modulated renewal processes with interarrival times specified using transformation models, and semi-Markov processes with with one-step transition probabilities defined using copula-transformation models. We discuss estimation of finite and infinite dimensional parameters of the model, and develop an extension of the Gaussian multiplier method for setting confidence bands for transition probabilities. A transplant outcome data set from the Center for International Blood and Marrow Transplant Research is used for illustrative purposes. PMID:22740583

Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

PubMed

Sumner, Jeremy G

2017-03-01

We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.

Exact Markov chains versus diffusion theory for haploid random mating.

PubMed

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

Modelling Evolutionary Algorithms with Stochastic Differential Equations.

PubMed

Heredia, Jorge Pérez

2017-11-20

There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

NASA Astrophysics Data System (ADS)

Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben

2017-08-01

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.

Animal vocal sequences: not the Markov chains we thought they were

PubMed Central

Kershenbaum, Arik; Bowles, Ann E.; Freeberg, Todd M.; Jin, Dezhe Z.; Lameira, Adriano R.; Bohn, Kirsten

2014-01-01

Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the ‘renewal process’ (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Markov state modeling of sliding friction

NASA Astrophysics Data System (ADS)

Pellegrini, F.; Landes, François P.; Laio, A.; Prestipino, S.; Tosatti, E.

2016-11-01

Markov state modeling (MSM) has recently emerged as one of the key techniques for the discovery of collective variables and the analysis of rare events in molecular simulations. In particular in biochemistry this approach is successfully exploited to find the metastable states of complex systems and their evolution in thermal equilibrium, including rare events, such as a protein undergoing folding. The physics of sliding friction and its atomistic simulations under external forces constitute a nonequilibrium field where relevant variables are in principle unknown and where a proper theory describing violent and rare events such as stick slip is still lacking. Here we show that MSM can be extended to the study of nonequilibrium phenomena and in particular friction. The approach is benchmarked on the Frenkel-Kontorova model, used here as a test system whose properties are well established. We demonstrate that the method allows the least prejudiced identification of a minimal basis of natural microscopic variables necessary for the description of the forced dynamics of sliding, through their probabilistic evolution. The steps necessary for the application to realistic frictional systems are highlighted.

MCMC genome rearrangement.

PubMed

Miklós, István

2003-10-01

As more and more genomes have been sequenced, genomic data is rapidly accumulating. Genome-wide mutations are believed more neutral than local mutations such as substitutions, insertions and deletions, therefore phylogenetic investigations based on inversions, transpositions and inverted transpositions are less biased by the hypothesis on neutral evolution. Although efficient algorithms exist for obtaining the inversion distance of two signed permutations, there is no reliable algorithm when both inversions and transpositions are considered. Moreover, different type of mutations happen with different rates, and it is not clear how to weight them in a distance based approach. We introduce a Markov Chain Monte Carlo method to genome rearrangement based on a stochastic model of evolution, which can estimate the number of different evolutionary events needed to sort a signed permutation. The performance of the method was tested on simulated data, and the estimated numbers of different types of mutations were reliable. Human and Drosophila mitochondrial data were also analysed with the new method. The mixing time of the Markov Chain is short both in terms of CPU times and number of proposals. The source code in C is available on request from the author.

Dynamic Noise and its Role in Understanding Epidemiological Processes

NASA Astrophysics Data System (ADS)

Stollenwerk, Nico; Aguiar, Maíra

2010-09-01

We investigate the role of dynamic noise in understanding epidemiological systems, such as influenza or dengue fever by deriving stochastic ordinary differential equations from markov processes for discrete populations. This approach allows for an easy analysis of dynamical noise transitions between co-existing attractors.

Error modeling for differential GPS. M.S. Thesis - MIT, 12 May 1995

NASA Technical Reports Server (NTRS)

Blerman, Gregory S.

1995-01-01

Differential Global Positioning System (DGPS) positioning is used to accurately locate a GPS receiver based upon the well-known position of a reference site. In utilizing this technique, several error sources contribute to position inaccuracy. This thesis investigates the error in DGPS operation and attempts to develop a statistical model for the behavior of this error. The model for DGPS error is developed using GPS data collected by Draper Laboratory. The Marquardt method for nonlinear curve-fitting is used to find the parameters of a first order Markov process that models the average errors from the collected data. The results show that a first order Markov process can be used to model the DGPS error as a function of baseline distance and time delay. The model's time correlation constant is 3847.1 seconds (1.07 hours) for the mean square error. The distance correlation constant is 122.8 kilometers. The total process variance for the DGPS model is 3.73 sq meters.

Analyzing a stochastic time series obeying a second-order differential equation.

PubMed

Lehle, B; Peinke, J

2015-06-01

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.

A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

PubMed

Hui, David Shui Wing; Chen, Yi-Chao; Zhang, Gong; Wu, Weijie; Chen, Guanrong; Lui, John C S; Li, Yingtao

2017-06-16

This paper establishes a Markov chain model as a unified framework for describing the evolution processes in complex networks. The unique feature of the proposed model is its capability in addressing the formation mechanism that can reflect the "trichotomy" observed in degree distributions, based on which closed-form solutions can be derived. Important special cases of the proposed unified framework are those classical models, including Poisson, Exponential, Power-law distributed networks. Both simulation and experimental results demonstrate a good match of the proposed model with real datasets, showing its superiority over the classical models. Implications of the model to various applications including citation analysis, online social networks, and vehicular networks design, are also discussed in the paper.

Monogamy has a fixation advantage based on fitness variance in an ideal promiscuity group.

PubMed

Garay, József; Móri, Tamás F

2012-11-01

We consider an ideal promiscuity group of females, which implies that all males have the same average mating success. If females have concealed ovulation, then the males' paternity chances are equal. We find that male-based monogamy will be fixed in females' promiscuity group when the stochastic Darwinian selection is described by a Markov chain.We point out that in huge populations the relative advantage (difference between average fitness of different strategies) determines primarily the end of evolution; in the case of neutrality (means are equal) the smallest variance guarantees fixation (absorption) advantage; when the means and variances are the same, then the higher third moment determines which types will be fixed in the Markov chains.

STDP Installs in Winner-Take-All Circuits an Online Approximation to Hidden Markov Model Learning

PubMed Central

Kappel, David; Nessler, Bernhard; Maass, Wolfgang

2014-01-01

In order to cross a street without being run over, we need to be able to extract very fast hidden causes of dynamically changing multi-modal sensory stimuli, and to predict their future evolution. We show here that a generic cortical microcircuit motif, pyramidal cells with lateral excitation and inhibition, provides the basis for this difficult but all-important information processing capability. This capability emerges in the presence of noise automatically through effects of STDP on connections between pyramidal cells in Winner-Take-All circuits with lateral excitation. In fact, one can show that these motifs endow cortical microcircuits with functional properties of a hidden Markov model, a generic model for solving such tasks through probabilistic inference. Whereas in engineering applications this model is adapted to specific tasks through offline learning, we show here that a major portion of the functionality of hidden Markov models arises already from online applications of STDP, without any supervision or rewards. We demonstrate the emergent computing capabilities of the model through several computer simulations. The full power of hidden Markov model learning can be attained through reward-gated STDP. This is due to the fact that these mechanisms enable a rejection sampling approximation to theoretically optimal learning. We investigate the possible performance gain that can be achieved with this more accurate learning method for an artificial grammar task. PMID:24675787

Animal vocal sequences: not the Markov chains we thought they were.

PubMed

Kershenbaum, Arik; Bowles, Ann E; Freeberg, Todd M; Jin, Dezhe Z; Lameira, Adriano R; Bohn, Kirsten

2014-10-07

Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the 'renewal process' (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Recognizing Chromospheric Objects via Markov Chain Monte Carlo

NASA Technical Reports Server (NTRS)

Mukhtar, Saleem; Turmon, Michael J.

1997-01-01

The solar chromosphere consists of three classes which contribute differentially to ultraviolet radiation reaching the earth. We describe a data set of solar images, means of segmenting the images into the constituent classes, and a novel high-level representation for compact objects based on a triangulated spatial membership function.

Analysis of a Delayed Delta Modulator.

DTIC Science & Technology

1983-05-01

parallels that of Janardhanan [10] for DPCM with matched integra- tion of stationary first-order Gauss-Markov input. In Subsection A the limiting...181, 1978. [10] JANARDHANAN , E., "Differential PCM -ystems", IEEE Trans. Conmmun., vol. Com-27, pp. 82-93, 1979. [111 KANTOROVICI, L.V. and KRYLOV, V.I

Global dynamics of a stochastic neuronal oscillator

NASA Astrophysics Data System (ADS)

Yamanobe, Takanobu

2013-11-01

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

Global dynamics of a stochastic neuronal oscillator.

PubMed

Yamanobe, Takanobu

2013-11-01

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

Bayesian experimental design for models with intractable likelihoods.

PubMed

Drovandi, Christopher C; Pettitt, Anthony N

2013-12-01

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables. © 2013, The International Biometric Society.

Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-01-01

We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.

A Modern Take on the RV Classics: N-body Analysis of GJ 876 and 55 Cnc

NASA Astrophysics Data System (ADS)

Nelson, Benjamin E.; Ford, E. B.; Wright, J.

2013-01-01

Over the past two decades, radial velocity (RV) observations have uncovered a diverse population of exoplanet systems, in particular a subset of multi-planet systems that exhibit strong dynamical interactions. To extract the model parameters (and uncertainties) accurately from these observations, one requires self-consistent n-body integrations and must explore a high-dimensional 7 x number of planets) parameter space, both of which are computationally challenging. Utilizing the power of modern computing resources, we apply our Radial velocity Using N-body Differential Evolution Markov Chain Monte Carlo code (RUN DEMCMC) to two landmark systems from early exoplanet surveys: GJ 876 and 55 Cnc. For GJ 876, we analyze the Keck HIRES (Rivera et al. 2010) and HARPS (Correia et al. 2010) data and constrain the distribution of the Laplace argument. For 55 Cnc, we investigate the orbital architecture based on a cumulative 1086 RV observations from various sources and transit constraints from Winn et al. 2011. In both cases, we also test for long-term orbital stability.

Bayesian Inference for Source Reconstruction: A Real-World Application

PubMed Central

Yee, Eugene; Hoffman, Ian; Ungar, Kurt

2014-01-01

This paper applies a Bayesian probabilistic inferential methodology for the reconstruction of the location and emission rate from an actual contaminant source (emission from the Chalk River Laboratories medical isotope production facility) using a small number of activity concentration measurements of a noble gas (Xenon-133) obtained from three stations that form part of the International Monitoring System radionuclide network. The sampling of the resulting posterior distribution of the source parameters is undertaken using a very efficient Markov chain Monte Carlo technique that utilizes a multiple-try differential evolution adaptive Metropolis algorithm with an archive of past states. It is shown that the principal difficulty in the reconstruction lay in the correct specification of the model errors (both scale and structure) for use in the Bayesian inferential methodology. In this context, two different measurement models for incorporation of the model error of the predicted concentrations are considered. The performance of both of these measurement models with respect to their accuracy and precision in the recovery of the source parameters is compared and contrasted. PMID:27379292

Evolution properties of online user preference diversity

NASA Astrophysics Data System (ADS)

Guo, Qiang; Ji, Lei; Liu, Jian-Guo; Han, Jingti

2017-02-01

Detecting the evolution properties of online user preference diversity is of significance for deeply understanding online collective behaviors. In this paper, we empirically explore the evolution patterns of online user rating preference, where the preference diversity is measured by the variation coefficient of the user rating sequence. The statistical results for four real systems show that, for movies and reviews, the user rating preference would become diverse and then get centralized finally. By introducing the empirical variation coefficient, we present a Markov model, which could regenerate the evolution properties of two online systems regarding to the stable variation coefficients. In addition, we investigate the evolution of the correlation between the user ratings and the object qualities, and find that the correlation would keep increasing as the user degree increases. This work could be helpful for understanding the anchoring bias and memory effects of the online user collective behaviors.

On the distribution of interspecies correlation for Markov models of character evolution on Yule trees.

PubMed

Mulder, Willem H; Crawford, Forrest W

2015-01-07

Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule process, in which new species are "born" from existing lineages at a constant rate. Recent work has illuminated some of the structural properties of Yule trees, but it remains mostly unknown how these properties affect sequence and trait patterns observed at the tips of the phylogenetic tree. Understanding the interplay between speciation and mutation under simple models of evolution is essential for deriving valid phylogenetic inference methods and gives insight into the optimal design of phylogenetic studies. In this work, we derive the probability distribution of interspecies covariance under Brownian motion and Ornstein-Uhlenbeck models of phenotypic change on a Yule tree. We compute the probability distribution of the number of mutations shared between two randomly chosen taxa in a Yule tree under discrete Markov mutation models. Our results suggest summary measures of phylogenetic information content, illuminate the correlation between site patterns in sequences or traits of related organisms, and provide heuristics for experimental design and reconstruction of phylogenetic trees. Copyright © 2014 Elsevier Ltd. All rights reserved.

Characterizing and Differentiating Brain State Dynamics via Hidden Markov Models

PubMed Central

Ou, Jinli; Xie, Li; Jin, Changfeng; Li, Xiang; Zhu, Dajiang; Jiang, Rongxin; Chen, Yaowu

2014-01-01

Functional connectivity measured from resting state fMRI (R-fMRI) data has been widely used to examine the brain’s functional activities and has been recently used to characterize and differentiate brain conditions. However, the dynamical transition patterns of the brain’s functional states have been less explored. In this work, we propose a novel computational framework to quantitatively characterize the brain state dynamics via hidden Markov models (HMMs) learned from the observations of temporally dynamic functional connectomics, denoted as functional connectome states. The framework has been applied to the R-fMRI dataset including 44 post-traumatic stress disorder (PTSD) patients and 51 normal control (NC) subjects. Experimental results show that both PTSD and NC brains were undergoing remarkable changes in resting state and mainly transiting amongst a few brain states. Interestingly, further prediction with the best-matched HMM demonstrates that PTSD would enter into, but could not disengage from, a negative mood state. Importantly, 84 % of PTSD patients and 86 % of NC subjects are successfully classified via multiple HMMs using majority voting. PMID:25331991

Markov Model of Accident Progression at Fukushima Daiichi

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cuadra A.; Bari R.; Cheng, L-Y

2012-11-11

On March 11, 2011, a magnitude 9.0 earthquake followed by a tsunami caused loss of offsite power and disabled the emergency diesel generators, leading to a prolonged station blackout at the Fukushima Daiichi site. After successful reactor trip for all operating reactors, the inability to remove decay heat over an extended period led to boil-off of the water inventory and fuel uncovery in Units 1-3. A significant amount of metal-water reaction occurred, as evidenced by the quantities of hydrogen generated that led to hydrogen explosions in the auxiliary buildings of the Units 1 & 3, and in the de-fuelled Unitmore » 4. Although it was assumed that extensive fuel damage, including fuel melting, slumping, and relocation was likely to have occurred in the core of the affected reactors, the status of the fuel, vessel, and drywell was uncertain. To understand the possible evolution of the accident conditions at Fukushima Daiichi, a Markov model of the likely state of one of the reactors was constructed and executed under different assumptions regarding system performance and reliability. The Markov approach was selected for several reasons: It is a probabilistic model that provides flexibility in scenario construction and incorporates time dependence of different model states. It also readily allows for sensitivity and uncertainty analyses of different failure and repair rates of cooling systems. While the analysis was motivated by a need to gain insight on the course of events for the damaged units at Fukushima Daiichi, the work reported here provides a more general analytical basis for studying and evaluating severe accident evolution over extended periods of time. This work was performed at the request of the U.S. Department of Energy to explore 'what-if' scenarios in the immediate aftermath of the accidents.« less

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

Scaling properties of multiscale equilibration

NASA Astrophysics Data System (ADS)

Detmold, W.; Endres, M. G.

2018-04-01

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on nontopological long-distance observables in pure S U (3 ) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

A systematic review of models used in cost-effectiveness analyses of preventing osteoporotic fractures.

PubMed

Si, L; Winzenberg, T M; Palmer, A J

2014-01-01

This review was aimed at the evolution of health economic models used in evaluations of clinical approaches aimed at preventing osteoporotic fractures. Models have improved, with medical continuance becoming increasingly recognized as a contributor to health and economic outcomes, as well as advancements in epidemiological data. Model-based health economic evaluation studies are increasingly used to investigate the cost-effectiveness of osteoporotic fracture preventions and treatments. The objective of this study was to carry out a systematic review of the evolution of health economic models used in the evaluation of osteoporotic fracture preventions. Electronic searches within MEDLINE and EMBASE were carried out using a predefined search strategy. Inclusion and exclusion criteria were used to select relevant studies. References listed of included studies were searched to identify any potential study that was not captured in our electronic search. Data on country, interventions, type of fracture prevention, evaluation perspective, type of model, time horizon, fracture sites, expressed costs, types of costs included, and effectiveness measurement were extracted. Seventy-four models were described in 104 publications, of which 69% were European. Earlier models focused mainly on hip, vertebral, and wrist fracture, but later models included multiple fracture sites (humerus, pelvis, tibia, and other fractures). Modeling techniques have evolved from simple decision trees, through deterministic Markov processes to individual patient simulation models accounting for uncertainty in multiple parameters. Treatment continuance has been increasingly taken into account in the models in the last decade. Models have evolved in their complexity and emphasis, with medical continuance becoming increasingly recognized as a contributor to health and economic outcomes. This evolution may be driven in part by the desire to capture all the important differentiating characteristics of medications under scrutiny, as well as the advancement in epidemiological data relevant to osteoporosis fractures.

Catching Galactic open clusters in advanced stages of dynamical evolution

NASA Astrophysics Data System (ADS)

Angelo, M. S.; Piatti, A. E.; Dias, W. S.; Maia, F. F. S.

2018-04-01

During their dynamical evolution, Galactic open clusters (OCs) gradually lose their stellar content mainly because of internal relaxation and tidal forces. In this context, the study of dynamically evolved OCs is necessary to properly understand such processes. We present a comprehensive Washington CT1 photometric analysis of six sparse OCs, namely: ESO 518-3, Ruprecht 121, ESO 134-12, NGC 6573, ESO 260-7 and ESO 065-7. We employed Markov chain Monte-Carlo simulations to robustly determine the central coordinates and the structural parameters and T1 × (C - T1) colour-magnitude diagrams (CMDs) cleaned from field contamination were used to derive the fundamental parameters. ESO 518-03, Ruprecht 121, ESO 134-12 and NGC 6573 resulted to be of nearly the same young age (8.2 ≤log(t yr-1) ≤ 8.3); ESO 260-7 and ESO065-7 are of intermediate age (9.2 ≤log(t yr-1) ≤ 9.4). All studied OCs are located at similar Galactocentric distances (RG ˜ 6 - 6.9 kpc), considering uncertainties, except for ESO 260-7 (RG = 8.9 kpc). These OCs are in a tidally filled regime and are dynamically evolved, since they are much older than their half-mass relaxation times (t/trh ≳ 30) and present signals of low-mass star depletion. We distinguished two groups: those dynamically evolving towards final disruptions and those in an advanced dynamical evolutionary stage. Although we do not rule out that the Milky Way potential could have made differentially faster their dynamical evolutions, we speculate here with the possibility that they have been mainly driven by initial formation conditions.

Catching Galactic open clusters in advanced stages of dynamical evolution

NASA Astrophysics Data System (ADS)

Angelo, M. S.; Piatti, A. E.; Dias, W. S.; Maia, F. F. S.

2018-07-01

During their dynamical evolution, Galactic open clusters (OCs) gradually lose their stellar content mainly because of internal relaxation and tidal forces. In this context, the study of dynamically evolved OCs is necessary to properly understand such processes. We present a comprehensive Washington CT1 photometric analysis of six sparse OCs, namely ESO 518-3, Ruprecht 121, ESO 134-12, NGC 6573, ESO 260-7, and ESO 065-7. We employed Markov chain Monte Carlo simulations to robustly determine the central coordinates and the structural parameters and T1 × (C - T1) colour-magnitude diagrams cleaned from field contamination were used to derive the fundamental parameters. ESO 518-03, Ruprecht 121, ESO 134-12, and NGC 6573 resulted to be of nearly the same young age [8.2 ≤log(t yr-1) ≤ 8.3]; ESO 260-7 and ESO065-7 are of intermediate age [9.2 ≤log(t yr-1) ≤ 9.4]. All studied OCs are located at similar Galactocentric distances (RG ˜6-6.9 kpc), considering uncertainties, except for ESO 260-7 (RG = 8.9 kpc). These OCs are in a tidally filled regime and are dynamically evolved, since they are much older than their half-mass relaxation times (t/trh ≳ 30) and present signals of low-mass star depletion. We distinguished two groups: those dynamically evolving towards final disruptions and those in an advanced dynamical evolutionary stage. Although we do not rule out that the Milky Way potential could have made differentially faster their dynamical evolutions, we speculate here with the possibility that they have been mainly driven by initial formation conditions.

Toward a comprehensive phylogenetic reconstruction of the evolutionary history of mitogen-activated protein kinases in the plant kingdom.

PubMed

Janitza, Philipp; Ullrich, Kristian Karsten; Quint, Marcel

2012-01-01

The mitogen-activated protein kinase (MAPK) pathway is a three-tier signaling cascade that transmits cellular information from the plasma membrane to the cytoplasm where it triggers downstream responses. The MAPKs represent the last step in this cascade and are activated when both tyrosine and threonine residues in a conserved TxY motif are phosphorylated by MAPK kinases, which in turn are themselves activated by phosphorylation by MAPK kinase kinases. To understand the molecular evolution of MAPKs in the plant kingdom, we systematically conducted a Hidden-Markov-Model based screen to identify MAPKs in 13 completely sequenced plant genomes. In this analysis, we included green algae, bryophytes, lycophytes, and several mono- and eudicotyledonous species covering >800 million years of evolution. The phylogenetic relationships of the 204 identified MAPKs based on Bayesian inference facilitated the retraction of the sequence of emergence of the four major clades that are characterized by the presence of a TDY or TEY-A/TEY-B/TEY-C type kinase activation loop. We present evidence that after the split of TDY- and TEY-type MAPKs, initially the TEY-C clade emerged. This was followed by the TEY-B clade in early land plants until the TEY-A clade finally emerged in flowering plants. In addition to these well characterized clades, we identified another highly conserved clade of 45 MAPK-likes, members of which were previously described as Mak-homologous kinases. In agreement with their essential functions, molecular population genetic analysis of MAPK genes in Arabidopsis thaliana accessions reveal that purifying selection drove the evolution of the MAPK family, implying strong functional constraints on MAPK genes. Closely related MAPKs most likely subfunctionalized, a process in which differential transcriptional regulation of duplicates may be involved.

A Mixture Rasch Model with a Covariate: A Simulation Study via Bayesian Markov Chain Monte Carlo Estimation

ERIC Educational Resources Information Center

Dai, Yunyun

2013-01-01

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…

Lord's Wald Test for Detecting Dif in Multidimensional Irt Models: A Comparison of Two Estimation Approaches

ERIC Educational Resources Information Center

Lee, Soo; Suh, Youngsuk

2018-01-01

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

Rotational evolution of slow-rotator sequence stars

NASA Astrophysics Data System (ADS)

Lanzafame, A. C.; Spada, F.

2015-12-01

Context. The observed relationship between mass, age and rotation in open clusters shows the progressive development of a slow-rotator sequence among stars possessing a radiative interior and a convective envelope during their pre-main sequence and main-sequence evolution. After 0.6 Gyr, most cluster members of this type have settled on this sequence. Aims: The observed clustering on this sequence suggests that it corresponds to some equilibrium or asymptotic condition that still lacks a complete theoretical interpretation, and which is crucial to our understanding of the stellar angular momentum evolution. Methods: We couple a rotational evolution model, which takes internal differential rotation into account, with classical and new proposals for the wind braking law, and fit models to the data using a Monte Carlo Markov chain (MCMC) method tailored to the problem at hand. We explore to what extent these models are able to reproduce the mass and time dependence of the stellar rotational evolution on the slow-rotator sequence. Results: The description of the evolution of the slow-rotator sequence requires taking the transfer of angular momentum from the radiative core to the convective envelope into account. We find that, in the mass range 0.85-1.10 M⊙, the core-envelope coupling timescale for stars in the slow-rotator sequence scales as M-7.28. Quasi-solid body rotation is achieved only after 1-2 Gyr, depending on stellar mass, which implies that observing small deviations from the Skumanich law (P ∝ √{t}) would require period data of older open clusters than is available to date. The observed evolution in the 0.1-2.5 Gyr age range and in the 0.85-1.10 M⊙ mass range is best reproduced by assuming an empirical mass dependence of the wind angular momentum loss proportional to the convective turnover timescale and to the stellar moment of inertia. Period isochrones based on our MCMC fit provide a tool for inferring stellar ages of solar-like main-sequence stars from their mass and rotation period that is largely independent of the wind braking model adopted. These effectively represent gyro-chronology relationships that take the physics of the two-zone model for the stellar angular momentum evolution into account.

Acquisition Management for System of Systems: Requirement Evolution and Acquisition Strategy Planning

DTIC Science & Technology

2013-01-29

of modern portfolio and control theory . The reformulation allows for possible changes in estimated quantities (e.g., due to market shifts in... Portfolio Theory (MPT). Final Report: NPS award N00244-11-1-0003 5 Extending CEM and Markov: Agent-Based Modeling Approach Research conducted in the...integration and acquisition from a robust portfolio theory standpoint. Robust portfolio management methodologies have been widely used by financial

Continuously growing rodent molars result from a predictable quantitative evolutionary change over 50 million years

PubMed Central

Mushegyan, Vagan; Eronen, Jussi T.; Lawing, A. Michelle; Sharir, Amnon; Janis, Christine; Jernvall, Jukka; Klein, Ophir D.

2015-01-01

Summary The fossil record is widely informative about evolution, but fossils are not systematically used to study the evolution of stem cell-driven renewal. Here, we examined evolution of the continuous growth (hypselodonty) of rodent molar teeth, which is fuelled by the presence of dental stem cells. We studied occurrences of 3500 North American rodent fossils, ranging from 50 million years ago (mya) to 2 mya. We examined changes in molar height to determine if evolution of hypselodonty shows distinct patterns in the fossil record, and we found that hypselodont taxa emerged through intermediate forms of increasing crown height. Next, we designed a Markov simulation model, which replicated molar height increases throughout the Cenozoic, and, moreover, evolution of hypselodonty. Thus, by extension, the retention of the adult stem-cell niche appears to be a predictable quantitative rather than a stochastic qualitative process. Our analyses predict that hypselodonty will eventually become the dominant phenotype. PMID:25921530

Passive Acoustic Leak Detection for Sodium Cooled Fast Reactors Using Hidden Markov Models

NASA Astrophysics Data System (ADS)

Marklund, A. Riber; Kishore, S.; Prakash, V.; Rajan, K. K.; Michel, F.

2016-06-01

Acoustic leak detection for steam generators of sodium fast reactors have been an active research topic since the early 1970s and several methods have been tested over the years. Inspired by its success in the field of automatic speech recognition, we here apply hidden Markov models (HMM) in combination with Gaussian mixture models (GMM) to the problem. To achieve this, we propose a new feature calculation scheme, based on the temporal evolution of the power spectral density (PSD) of the signal. Using acoustic signals recorded during steam/water injection experiments done at the Indira Gandhi Centre for Atomic Research (IGCAR), the proposed method is tested. We perform parametric studies on the HMM+GMM model size and demonstrate that the proposed method a) performs well without a priori knowledge of injection noise, b) can incorporate several noise models and c) has an output distribution that simplifies false alarm rate control.

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

NASA Astrophysics Data System (ADS)

Sun, L.; Melatos, A.; Suvorova, S.; Moran, W.; Evans, R. J.

2018-02-01

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semicoherent search based on a hidden Markov model tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the F statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semicoherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by 2 to 3 orders of magnitude.

Microscopic theory of energy dissipation and decoherence in open systems: A quantum Fermi's golden rule

NASA Astrophysics Data System (ADS)

Taj, D.; Iotti, R. C.; Rossi, F.

2009-11-01

We shall revisit the conventional adiabatic or Markov approximation, which — contrary to the semiclassical case- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally addressed by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, able to provide a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, our procedure guarantees a positive evolution for a variety of physical subsystem (including the common partial trace), and quantum scattering rates are well defined even for subsystems with internal structure/ continuous energy spectrum. We shall compare the proposed Markov dissipation model with the conventional one also through basic simulations of energy-relaxation versus decoherence channels in prototypical semiconductor nanodevices.

A discrete Markov metapopulation model for persistence and extinction of species.

PubMed

Thompson, Colin J; Shtilerman, Elad; Stone, Lewi

2016-09-07

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Markovian model of evolving world input-output network

PubMed Central

Isacchini, Giulio

2017-01-01

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money. PMID:29065145

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

NASA Astrophysics Data System (ADS)

Li, Zhiqiang; Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-04-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

A new class of accelerated kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bulatov, V V; Oppelstrup, T; Athenes, M

2011-11-30

Kinetic (aka dynamic) Monte Carlo (KMC) is a powerful method for numerical simulations of time dependent evolution applied in a wide range of contexts including biology, chemistry, physics, nuclear sciences, financial engineering, etc. Generally, in a KMC the time evolution takes place one event at a time, where the sequence of events and the time intervals between them are selected (or sampled) using random numbers. While details of the method implementation vary depending on the model and context, there exist certain common issues that limit KMC applicability in almost all applications. Among such is the notorious 'flicker problem' where themore » same states of the systems are repeatedly visited but otherwise no essential evolution is observed. In its simplest form the flicker problem arises when two states are connected to each other by transitions whose rates far exceed the rates of all other transitions out of the same two states. In such cases, the model will endlessly hop between the two states otherwise producing no meaningful evolution. In most situation of practical interest, the trapping cluster includes more than two states making the flicker somewhat more difficult to detect and to deal with. Several methods have been proposed to overcome or mitigate the flicker problem, exactly [1-3] or approximately [4,5]. Of the exact methods, the one proposed by Novotny [1] is perhaps most relevant to our research. Novotny formulates the problem of escaping from a trapping cluster as a Markov system with absorbing states. Given an initial state inside the cluster, it is in principle possible to solve the Master Equation for the time dependent probabilities to find the walker in a given state (transient or absorbing) of the cluster at any time in the future. Novotny then proceeds to demonstrate implementation of his general method to trapping clusters containing the initial state plus one or two transient states and all of their absorbing states. Similar methods have been subsequently proposed in [refs] but applied in a different context. The most serious deficiency of the earlier methods is that size of the trapping cluster size is fixed and often too small to bring substantial simulation speedup. Furthermore, the overhead associated with solving for the probability distribution on the trapping cluster sometimes makes such simulations less efficient than the standard KMC. Here we report on a general and exact accelerated kinetic Monte Carlo algorithm generally applicable to arbitrary Markov models1. Two different implementations are attempted both based on incremental expansion of trapping sub-set of Markov states: (1) numerical solution of the Master Equation with absorbing states and (2) incremental graph reduction followed by randomization. Of the two implementations, the 2nd one performs better allowing, for the first time, to overcome trapping basins spanning several million Markov states. The new method is used for simulations of anomalous diffusion on a 2D substrate and of the kinetics of diffusive 1st order phase transformations in binary alloys. Depending on temperature and (alloy) super-saturation conditions, speedups of 3 to 7 orders of magnitude are demonstrated, with no compromise of simulation accuracy.« less

Probability distributions of molecular observables computed from Markov models. II. Uncertainties in observables and their time-evolution

NASA Astrophysics Data System (ADS)

Chodera, John D.; Noé, Frank

2010-09-01

Discrete-state Markov (or master equation) models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic (such as the correlation function) of the equilibrium dynamics of a single molecule. Without meaningful error bars (which arise from both approximation and statistical error), there is no way to determine whether the deviations between model and experiment are statistically meaningful. Previous work has demonstrated that a Bayesian method that enforces microscopic reversibility can be used to characterize the statistical component of correlated uncertainties in state-to-state transition probabilities (and functions thereof) for a model inferred from molecular simulation data. Here, we extend this approach to include the uncertainty in observables that are functions of molecular conformation (such as surrogate spectroscopic signals) characterizing each state, permitting the full statistical uncertainty in computed spectroscopic experiments to be assessed. We test the approach in a simple model system to demonstrate that the computed uncertainties provide a useful indicator of statistical variation, and then apply it to the computation of the fluorescence autocorrelation function measured for a dye-labeled peptide previously studied by both experiment and simulation.

Background Adjusted Alignment-Free Dissimilarity Measures Improve the Detection of Horizontal Gene Transfer.

PubMed

Tang, Kujin; Lu, Yang Young; Sun, Fengzhu

2018-01-01

Horizontal gene transfer (HGT) plays an important role in the evolution of microbial organisms including bacteria. Alignment-free methods based on single genome compositional information have been used to detect HGT. Currently, Manhattan and Euclidean distances based on tetranucleotide frequencies are the most commonly used alignment-free dissimilarity measures to detect HGT. By testing on simulated bacterial sequences and real data sets with known horizontal transferred genomic regions, we found that more advanced alignment-free dissimilarity measures such as CVTree and [Formula: see text] that take into account the background Markov sequences can solve HGT detection problems with significantly improved performance. We also studied the influence of different factors such as evolutionary distance between host and donor sequences, size of sliding window, and host genome composition on the performances of alignment-free methods to detect HGT. Our study showed that alignment-free methods can predict HGT accurately when host and donor genomes are in different order levels. Among all methods, CVTree with word length of 3, [Formula: see text] with word length 3, Markov order 1 and [Formula: see text] with word length 4, Markov order 1 outperform others in terms of their highest F 1 -score and their robustness under the influence of different factors.

Markov-chain model of classified atomistic transition states for discrete kinetic Monte Carlo simulations.

PubMed

Numazawa, Satoshi; Smith, Roger

2011-10-01

Classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The scheme is then used to determine transitions that can be applied in a lattice-based kinetic Monte Carlo (KMC) atomistic simulation model. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multidimensional Boolean valued functions in three-dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology-dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. Excellent agreement with observed experimental results is obtained.

Active contour-based visual tracking by integrating colors, shapes, and motions.

PubMed

Hu, Weiming; Zhou, Xue; Li, Wei; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen

2013-05-01

In this paper, we present a framework for active contour-based visual tracking using level sets. The main components of our framework include contour-based tracking initialization, color-based contour evolution, adaptive shape-based contour evolution for non-periodic motions, dynamic shape-based contour evolution for periodic motions, and the handling of abrupt motions. For the initialization of contour-based tracking, we develop an optical flow-based algorithm for automatically initializing contours at the first frame. For the color-based contour evolution, Markov random field theory is used to measure correlations between values of neighboring pixels for posterior probability estimation. For adaptive shape-based contour evolution, the global shape information and the local color information are combined to hierarchically evolve the contour, and a flexible shape updating model is constructed. For the dynamic shape-based contour evolution, a shape mode transition matrix is learnt to characterize the temporal correlations of object shapes. For the handling of abrupt motions, particle swarm optimization is adopted to capture the global motion which is applied to the contour in the current frame to produce an initial contour in the next frame.

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species.

PubMed

Wang, Xueying; Walton, Jay R; Parshad, Rana D

2016-01-01

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vrugt, Jasper A; Robinson, Bruce A; Ter Braak, Cajo J F

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented usingmore » the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.« less

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

A bioinformatic analysis of ribonucleotide reductase genes in phage genomes and metagenomes

PubMed Central

2013-01-01

Background Ribonucleotide reductase (RNR), the enzyme responsible for the formation of deoxyribonucleotides from ribonucleotides, is found in all domains of life and many viral genomes. RNRs are also amongst the most abundant genes identified in environmental metagenomes. This study focused on understanding the distribution, diversity, and evolution of RNRs in phages (viruses that infect bacteria). Hidden Markov Model profiles were used to analyze the proteins encoded by 685 completely sequenced double-stranded DNA phages and 22 environmental viral metagenomes to identify RNR homologs in cultured phages and uncultured viral communities, respectively. Results RNRs were identified in 128 phage genomes, nearly tripling the number of phages known to encode RNRs. Class I RNR was the most common RNR class observed in phages (70%), followed by class II (29%) and class III (28%). Twenty-eight percent of the phages contained genes belonging to multiple RNR classes. RNR class distribution varied according to phage type, isolation environment, and the host’s ability to utilize oxygen. The majority of the phages containing RNRs are Myoviridae (65%), followed by Siphoviridae (30%) and Podoviridae (3%). The phylogeny and genomic organization of phage and host RNRs reveal several distinct evolutionary scenarios involving horizontal gene transfer, co-evolution, and differential selection pressure. Several putative split RNR genes interrupted by self-splicing introns or inteins were identified, providing further evidence for the role of frequent genetic exchange. Finally, viral metagenomic data indicate that RNRs are prevalent and highly dynamic in uncultured viral communities, necessitating future research to determine the environmental conditions under which RNRs provide a selective advantage. Conclusions This comprehensive study describes the distribution, diversity, and evolution of RNRs in phage genomes and environmental viral metagenomes. The distinct distributions of specific RNR classes amongst phages, combined with the various evolutionary scenarios predicted from RNR phylogenies suggest multiple inheritance sources and different selective forces for RNRs in phages. This study significantly improves our understanding of phage RNRs, providing insight into the diversity and evolution of this important auxiliary metabolic gene as well as the evolution of phages in response to their bacterial hosts and environments. PMID:23391036

Differential-Evolution Control Parameter Optimization for Unmanned Aerial Vehicle Path Planning

PubMed Central

Kok, Kai Yit; Rajendran, Parvathy

2016-01-01

The differential evolution algorithm has been widely applied on unmanned aerial vehicle (UAV) path planning. At present, four random tuning parameters exist for differential evolution algorithm, namely, population size, differential weight, crossover, and generation number. These tuning parameters are required, together with user setting on path and computational cost weightage. However, the optimum settings of these tuning parameters vary according to application. Instead of trial and error, this paper presents an optimization method of differential evolution algorithm for tuning the parameters of UAV path planning. The parameters that this research focuses on are population size, differential weight, crossover, and generation number. The developed algorithm enables the user to simply define the weightage desired between the path and computational cost to converge with the minimum generation required based on user requirement. In conclusion, the proposed optimization of tuning parameters in differential evolution algorithm for UAV path planning expedites and improves the final output path and computational cost. PMID:26943630

Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

PubMed

Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

2013-07-01

Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

Can discrete event simulation be of use in modelling major depression?

PubMed Central

Le Lay, Agathe; Despiegel, Nicolas; François, Clément; Duru, Gérard

2006-01-01

Background Depression is among the major contributors to worldwide disease burden and adequate modelling requires a framework designed to depict real world disease progression as well as its economic implications as closely as possible. Objectives In light of the specific characteristics associated with depression (multiple episodes at varying intervals, impact of disease history on course of illness, sociodemographic factors), our aim was to clarify to what extent "Discrete Event Simulation" (DES) models provide methodological benefits in depicting disease evolution. Methods We conducted a comprehensive review of published Markov models in depression and identified potential limits to their methodology. A model based on DES principles was developed to investigate the benefits and drawbacks of this simulation method compared with Markov modelling techniques. Results The major drawback to Markov models is that they may not be suitable to tracking patients' disease history properly, unless the analyst defines multiple health states, which may lead to intractable situations. They are also too rigid to take into consideration multiple patient-specific sociodemographic characteristics in a single model. To do so would also require defining multiple health states which would render the analysis entirely too complex. We show that DES resolve these weaknesses and that its flexibility allow patients with differing attributes to move from one event to another in sequential order while simultaneously taking into account important risk factors such as age, gender, disease history and patients attitude towards treatment, together with any disease-related events (adverse events, suicide attempt etc.). Conclusion DES modelling appears to be an accurate, flexible and comprehensive means of depicting disease progression compared with conventional simulation methodologies. Its use in analysing recurrent and chronic diseases appears particularly useful compared with Markov processes. PMID:17147790

Can discrete event simulation be of use in modelling major depression?

PubMed

Le Lay, Agathe; Despiegel, Nicolas; François, Clément; Duru, Gérard

2006-12-05

Depression is among the major contributors to worldwide disease burden and adequate modelling requires a framework designed to depict real world disease progression as well as its economic implications as closely as possible. In light of the specific characteristics associated with depression (multiple episodes at varying intervals, impact of disease history on course of illness, sociodemographic factors), our aim was to clarify to what extent "Discrete Event Simulation" (DES) models provide methodological benefits in depicting disease evolution. We conducted a comprehensive review of published Markov models in depression and identified potential limits to their methodology. A model based on DES principles was developed to investigate the benefits and drawbacks of this simulation method compared with Markov modelling techniques. The major drawback to Markov models is that they may not be suitable to tracking patients' disease history properly, unless the analyst defines multiple health states, which may lead to intractable situations. They are also too rigid to take into consideration multiple patient-specific sociodemographic characteristics in a single model. To do so would also require defining multiple health states which would render the analysis entirely too complex. We show that DES resolve these weaknesses and that its flexibility allow patients with differing attributes to move from one event to another in sequential order while simultaneously taking into account important risk factors such as age, gender, disease history and patients attitude towards treatment, together with any disease-related events (adverse events, suicide attempt etc.). DES modelling appears to be an accurate, flexible and comprehensive means of depicting disease progression compared with conventional simulation methodologies. Its use in analysing recurrent and chronic diseases appears particularly useful compared with Markov processes.

Using hidden Markov models and observed evolution to annotate viral genomes.

PubMed

McCauley, Stephen; Hein, Jotun

2006-06-01

ssRNA (single stranded) viral genomes are generally constrained in length and utilize overlapping reading frames to maximally exploit the coding potential within the genome length restrictions. This overlapping coding phenomenon leads to complex evolutionary constraints operating on the genome. In regions which code for more than one protein, silent mutations in one reading frame generally have a protein coding effect in another. To maximize coding flexibility in all reading frames, overlapping regions are often compositionally biased towards amino acids which are 6-fold degenerate with respect to the 64 codon alphabet. Previous methodologies have used this fact in an ad hoc manner to look for overlapping genes by motif matching. In this paper differentiated nucleotide compositional patterns in overlapping regions are incorporated into a probabilistic hidden Markov model (HMM) framework which is used to annotate ssRNA viral genomes. This work focuses on single sequence annotation and applies an HMM framework to ssRNA viral annotation. A description of how the HMM is parameterized, whilst annotating within a missing data framework is given. A Phylogenetic HMM (Phylo-HMM) extension, as applied to 14 aligned HIV2 sequences is also presented. This evolutionary extension serves as an illustration of the potential of the Phylo-HMM framework for ssRNA viral genomic annotation. The single sequence annotation procedure (SSA) is applied to 14 different strains of the HIV2 virus. Further results on alternative ssRNA viral genomes are presented to illustrate more generally the performance of the method. The results of the SSA method are encouraging however there is still room for improvement, and since there is overwhelming evidence to indicate that comparative methods can improve coding sequence (CDS) annotation, the SSA method is extended to a Phylo-HMM to incorporate evolutionary information. The Phylo-HMM extension is applied to the same set of 14 HIV2 sequences which are pre-aligned. The performance improvement that results from including the evolutionary information in the analysis is illustrated.

The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks.

PubMed

Sainudiin, Raazesh; Welch, David

2016-12-07

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network - three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of "meme" evolution in online social media networks through transmission events that can be distilled from observable actions such as "likes", "mentions", "retweets" and "+1s" along with any concomitant comments. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Treatment evolution and new standards of care: implications for cost-effectiveness analysis.

PubMed

Shechter, Steven M

2011-01-01

Traditional approaches to cost-effectiveness analysis have not considered the downstream possibility of a new standard of care coming out of the research and development pipeline. However, the treatment landscape for patients may change significantly over the course of their lifetimes. To present a Markov modeling framework that incorporates the possibility of treatment evolution into the incremental cost-effectiveness ratio (ICER) that compares treatments available at the present time. . Markov model evaluated by matrix algebra. Measurements. The author evaluates the difference between the new and traditional ICER calculations for patients with chronic diseases facing a lifetime of treatment. The bias of the traditional ICER calculation may be substantial, with further testing revealing that it may be either positive or negative depending on the model parameters. The author also performs probabilistic sensitivity analyses with respect to the possible timing of a new treatment discovery and notes the increase in the magnitude of the bias when the new treatment is likely to appear sooner rather than later. Limitations. The modeling framework is intended as a proof of concept and therefore makes simplifying assumptions such as time stationarity of model parameters and consideration of a single new drug discovery. For diseases with a more active research and development pipeline, the possibility of a new treatment paradigm may be at least as important to consider in sensitivity analysis as other parameters that are often considered.

A novel multilayer model for missing link prediction and future link forecasting in dynamic complex networks

NASA Astrophysics Data System (ADS)

Yasami, Yasser; Safaei, Farshad

2018-02-01

The traditional complex network theory is particularly focused on network models in which all network constituents are dealt with equivalently, while fail to consider the supplementary information related to the dynamic properties of the network interactions. This is a main constraint leading to incorrect descriptions of some real-world phenomena or incomplete capturing the details of certain real-life problems. To cope with the problem, this paper addresses the multilayer aspects of dynamic complex networks by analyzing the properties of intrinsically multilayered co-authorship networks, DBLP and Astro Physics, and presenting a novel multilayer model of dynamic complex networks. The model examines the layers evolution (layers birth/death process and lifetime) throughout the network evolution. Particularly, this paper models the evolution of each node's membership in different layers by an Infinite Factorial Hidden Markov Model considering feature cascade, and thereby formulates the link generation process for intra-layer and inter-layer links. Although adjacency matrixes are useful to describe the traditional single-layer networks, such a representation is not sufficient to describe and analyze the multilayer dynamic networks. This paper also extends a generalized mathematical infrastructure to address the problems issued by multilayer complex networks. The model inference is performed using some Markov Chain Monte Carlo sampling strategies, given synthetic and real complex networks data. Experimental results indicate a tremendous improvement in the performance of the proposed multilayer model in terms of sensitivity, specificity, positive and negative predictive values, positive and negative likelihood ratios, F1-score, Matthews correlation coefficient, and accuracy for two important applications of missing link prediction and future link forecasting. The experimental results also indicate the strong predictivepower of the proposed model for the application of cascade prediction in terms of accuracy.

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

PubMed Central

Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-01-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit. PMID:29765629

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

PubMed

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation.

PubMed

Slater, Graham J; Harmon, Luke J; Wegmann, Daniel; Joyce, Paul; Revell, Liam J; Alfaro, Michael E

2012-03-01

In recent years, a suite of methods has been developed to fit multiple rate models to phylogenetic comparative data. However, most methods have limited utility at broad phylogenetic scales because they typically require complete sampling of both the tree and the associated phenotypic data. Here, we develop and implement a new, tree-based method called MECCA (Modeling Evolution of Continuous Characters using ABC) that uses a hybrid likelihood/approximate Bayesian computation (ABC)-Markov-Chain Monte Carlo approach to simultaneously infer rates of diversification and trait evolution from incompletely sampled phylogenies and trait data. We demonstrate via simulation that MECCA has considerable power to choose among single versus multiple evolutionary rate models, and thus can be used to test hypotheses about changes in the rate of trait evolution across an incomplete tree of life. We finally apply MECCA to an empirical example of body size evolution in carnivores, and show that there is no evidence for an elevated rate of body size evolution in the pinnipeds relative to terrestrial carnivores. ABC approaches can provide a useful alternative set of tools for future macroevolutionary studies where likelihood-dependent approaches are lacking. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Dissipation and decoherence in nanodevices: a generalized Fermi's golden rule

NASA Astrophysics Data System (ADS)

Taj, D.; Iotti, R. C.; Rossi, F.

2009-06-01

We shall revisit the conventional adiabatic or Markov approximation, which—in contrast to the semiclassical case—does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that includes the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in the case the subsystem is infinitely extended/has a continuous spectrum.

Passive acoustic leak detection for sodium cooled fast reactors using hidden Markov models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riber Marklund, A.; Kishore, S.; Prakash, V.

2015-07-01

Acoustic leak detection for steam generators of sodium fast reactors have been an active research topic since the early 1970's and several methods have been tested over the years. Inspired by its success in the field of automatic speech recognition, we here apply hidden Markov models (HMM) in combination with Gaussian mixture models (GMM) to the problem. To achieve this, we propose a new feature calculation scheme, based on the temporal evolution of the power spectral density (PSD) of the signal. Using acoustic signals recorded during steam/water injection experiments done at the Indira Gandhi Centre for Atomic Research (IGCAR), themore » proposed method is tested. We perform parametric studies on the HMM+GMM model size and demonstrate that the proposed method a) performs well without a priori knowledge of injection noise, b) can incorporate several noise models and c) has an output distribution that simplifies false alarm rate control. (authors)« less

Multiobjective Optimization Using a Pareto Differential Evolution Approach

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

Deep 3 GHz number counts from a P(D) fluctuation analysis

NASA Astrophysics Data System (ADS)

Vernstrom, T.; Scott, Douglas; Wall, J. V.; Condon, J. J.; Cotton, W. D.; Fomalont, E. B.; Kellermann, K. I.; Miller, N.; Perley, R. A.

2014-05-01

Radio source counts constrain galaxy populations and evolution, as well as the global star formation history. However, there is considerable disagreement among the published 1.4-GHz source counts below 100 μJy. Here, we present a statistical method for estimating the μJy and even sub-μJy source count using new deep wide-band 3-GHz data in the Lockman Hole from the Karl G. Jansky Very Large Array. We analysed the confusion amplitude distribution P(D), which provides a fresh approach in the form of a more robust model, with a comprehensive error analysis. We tested this method on a large-scale simulation, incorporating clustering and finite source sizes. We discuss in detail our statistical methods for fitting using Markov chain Monte Carlo, handling correlations, and systematic errors from the use of wide-band radio interferometric data. We demonstrated that the source count can be constrained down to 50 nJy, a factor of 20 below the rms confusion. We found the differential source count near 10 μJy to have a slope of -1.7, decreasing to about -1.4 at fainter flux densities. At 3 GHz, the rms confusion in an 8-arcsec full width at half-maximum beam is ˜ 1.2 μJy beam-1, and a radio background temperature ˜14 mK. Our counts are broadly consistent with published evolutionary models. With these results, we were also able to constrain the peak of the Euclidean normalized differential source count of any possible new radio populations that would contribute to the cosmic radio background down to 50 nJy.

Single-Molecule Test for Markovianity of the Dynamics along a Reaction Coordinate.

PubMed

Berezhkovskii, Alexander M; Makarov, Dmitrii E

2018-05-03

In an effort to answer the much-debated question of whether the time evolution of common experimental observables can be described as one-dimensional diffusion in the potential of mean force, we propose a simple criterion that allows one to test whether the Markov assumption is applicable to a single-molecule trajectory x( t). This test does not involve fitting of the data to any presupposed model and can be applied to experimental data with relatively low temporal resolution.

SPOTting model parameters using a ready-made Python package

NASA Astrophysics Data System (ADS)

Houska, Tobias; Kraft, Philipp; Breuer, Lutz

2015-04-01

The selection and parameterization of reliable process descriptions in ecological modelling is driven by several uncertainties. The procedure is highly dependent on various criteria, like the used algorithm, the likelihood function selected and the definition of the prior parameter distributions. A wide variety of tools have been developed in the past decades to optimize parameters. Some of the tools are closed source. Due to this, the choice for a specific parameter estimation method is sometimes more dependent on its availability than the performance. A toolbox with a large set of methods can support users in deciding about the most suitable method. Further, it enables to test and compare different methods. We developed the SPOT (Statistical Parameter Optimization Tool), an open source python package containing a comprehensive set of modules, to analyze and optimize parameters of (environmental) models. SPOT comes along with a selected set of algorithms for parameter optimization and uncertainty analyses (Monte Carlo, MC; Latin Hypercube Sampling, LHS; Maximum Likelihood, MLE; Markov Chain Monte Carlo, MCMC; Scuffled Complex Evolution, SCE-UA; Differential Evolution Markov Chain, DE-MCZ), together with several likelihood functions (Bias, (log-) Nash-Sutcliff model efficiency, Correlation Coefficient, Coefficient of Determination, Covariance, (Decomposed-, Relative-, Root-) Mean Squared Error, Mean Absolute Error, Agreement Index) and prior distributions (Binomial, Chi-Square, Dirichlet, Exponential, Laplace, (log-, multivariate-) Normal, Pareto, Poisson, Cauchy, Uniform, Weibull) to sample from. The model-independent structure makes it suitable to analyze a wide range of applications. We apply all algorithms of the SPOT package in three different case studies. Firstly, we investigate the response of the Rosenbrock function, where the MLE algorithm shows its strengths. Secondly, we study the Griewank function, which has a challenging response surface for optimization methods. Here we see simple algorithms like the MCMC struggling to find the global optimum of the function, while algorithms like SCE-UA and DE-MCZ show their strengths. Thirdly, we apply an uncertainty analysis of a one-dimensional physically based hydrological model build with the Catchment Modelling Framework (CMF). The model is driven by meteorological and groundwater data from a Free Air Carbon Enrichment (FACE) experiment in Linden (Hesse, Germany). Simulation results are evaluated with measured soil moisture data. We search for optimal parameter sets of the van Genuchten-Mualem function and find different equally optimal solutions with some of the algorithms. The case studies reveal that the implemented SPOT methods work sufficiently well. They further show the benefit of having one tool at hand that includes a number of parameter search methods, likelihood functions and a priori parameter distributions within one platform independent package.

Active heat pulse sensing of 3-D-flow fields in streambeds

NASA Astrophysics Data System (ADS)

Banks, Eddie W.; Shanafield, Margaret A.; Noorduijn, Saskia; McCallum, James; Lewandowski, Jörg; Batelaan, Okke

2018-03-01

Profiles of temperature time series are commonly used to determine hyporheic flow patterns and hydraulic dynamics in the streambed sediments. Although hyporheic flows are 3-D, past research has focused on determining the magnitude of the vertical flow component and how this varies spatially. This study used a portable 56-sensor, 3-D temperature array with three heat pulse sources to measure the flow direction and magnitude up to 200 mm below the water-sediment interface. Short, 1 min heat pulses were injected at one of the three heat sources and the temperature response was monitored over a period of 30 min. Breakthrough curves from each of the sensors were analysed using a heat transport equation. Parameter estimation and uncertainty analysis was undertaken using the differential evolution adaptive metropolis (DREAM) algorithm, an adaption of the Markov chain Monte Carlo method, to estimate the flux and its orientation. Measurements were conducted in the field and in a sand tank under an extensive range of controlled hydraulic conditions to validate the method. The use of short-duration heat pulses provided a rapid, accurate assessment technique for determining dynamic and multi-directional flow patterns in the hyporheic zone and is a basis for improved understanding of biogeochemical processes at the water-streambed interface.

Solar flare impulsive phase emission observed with SDO/EVE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kennedy, Michael B.; Milligan, Ryan O.; Mathioudakis, Mihalis

2013-12-10

Differential emission measures (DEMs) during the impulsive phase of solar flares were constructed using observations from the EUV Variability Experiment (EVE) and the Markov-Chain Monte Carlo method. Emission lines from ions formed over the temperature range log T{sub e} = 5.8-7.2 allow the evolution of the DEM to be studied over a wide temperature range at 10 s cadence. The technique was applied to several M- and X-class flares, where impulsive phase EUV emission is observable in the disk-integrated EVE spectra from emission lines formed up to 3-4 MK and we use spatially unresolved EVE observations to infer the thermalmore » structure of the emitting region. For the nine events studied, the DEMs exhibited a two-component distribution during the impulsive phase, a low-temperature component with peak temperature of 1-2 MK, and a broad high-temperature component from 7 to 30 MK. A bimodal high-temperature component is also found for several events, with peaks at 8 and 25 MK during the impulsive phase. The origin of the emission was verified using Atmospheric Imaging Assembly images to be the flare ribbons and footpoints, indicating that the constructed DEMs represent the spatially average thermal structure of the chromospheric flare emission during the impulsive phase.« less

End-to-End QoS for Differentiated Services and ATM Internetworking

NASA Technical Reports Server (NTRS)

Su, Hongjun; Atiquzzaman, Mohammed

2001-01-01

The Internet was initially design for non real-time data communications and hence does not provide any Quality of Service (QoS). The next generation Internet will be characterized by high speed and QoS guarantee. The aim of this paper is to develop a prioritized early packet discard (PEPD) scheme for ATM switches to provide service differentiation and QoS guarantee to end applications running over next generation Internet. The proposed PEPD scheme differs from previous schemes by taking into account the priority of packets generated from different application. We develop a Markov chain model for the proposed scheme and verify the model with simulation. Numerical results show that the results from the model and computer simulation are in close agreement. Our PEPD scheme provides service differentiation to the end-to-end applications.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Machine health prognostics using the Bayesian-inference-based probabilistic indication and high-order particle filtering framework

NASA Astrophysics Data System (ADS)

Yu, Jianbo

2015-12-01

Prognostics is much efficient to achieve zero-downtime performance, maximum productivity and proactive maintenance of machines. Prognostics intends to assess and predict the time evolution of machine health degradation so that machine failures can be predicted and prevented. A novel prognostics system is developed based on the data-model-fusion scheme using the Bayesian inference-based self-organizing map (SOM) and an integration of logistic regression (LR) and high-order particle filtering (HOPF). In this prognostics system, a baseline SOM is constructed to model the data distribution space of healthy machine under an assumption that predictable fault patterns are not available. Bayesian inference-based probability (BIP) derived from the baseline SOM is developed as a quantification indication of machine health degradation. BIP is capable of offering failure probability for the monitored machine, which has intuitionist explanation related to health degradation state. Based on those historic BIPs, the constructed LR and its modeling noise constitute a high-order Markov process (HOMP) to describe machine health propagation. HOPF is used to solve the HOMP estimation to predict the evolution of the machine health in the form of a probability density function (PDF). An on-line model update scheme is developed to adapt the Markov process changes to machine health dynamics quickly. The experimental results on a bearing test-bed illustrate the potential applications of the proposed system as an effective and simple tool for machine health prognostics.

A Detailed History of Intron-rich Eukaryotic Ancestors Inferred from a Global Survey of 100 Complete Genomes

PubMed Central

Csuros, Miklos; Rogozin, Igor B.; Koonin, Eugene V.

2011-01-01

Protein-coding genes in eukaryotes are interrupted by introns, but intron densities widely differ between eukaryotic lineages. Vertebrates, some invertebrates and green plants have intron-rich genes, with 6–7 introns per kilobase of coding sequence, whereas most of the other eukaryotes have intron-poor genes. We reconstructed the history of intron gain and loss using a probabilistic Markov model (Markov Chain Monte Carlo, MCMC) on 245 orthologous genes from 99 genomes representing the three of the five supergroups of eukaryotes for which multiple genome sequences are available. Intron-rich ancestors are confidently reconstructed for each major group, with 53 to 74% of the human intron density inferred with 95% confidence for the Last Eukaryotic Common Ancestor (LECA). The results of the MCMC reconstruction are compared with the reconstructions obtained using Maximum Likelihood (ML) and Dollo parsimony methods. An excellent agreement between the MCMC and ML inferences is demonstrated whereas Dollo parsimony introduces a noticeable bias in the estimations, typically yielding lower ancestral intron densities than MCMC and ML. Evolution of eukaryotic genes was dominated by intron loss, with substantial gain only at the bases of several major branches including plants and animals. The highest intron density, 120 to 130% of the human value, is inferred for the last common ancestor of animals. The reconstruction shows that the entire line of descent from LECA to mammals was intron-rich, a state conducive to the evolution of alternative splicing. PMID:21935348

Differences in Cell Division Rates Drive the Evolution of Terminal Differentiation in Microbes

PubMed Central

Matias Rodrigues, João F.; Rankin, Daniel J.; Rossetti, Valentina; Wagner, Andreas; Bagheri, Homayoun C.

2012-01-01

Multicellular differentiated organisms are composed of cells that begin by developing from a single pluripotent germ cell. In many organisms, a proportion of cells differentiate into specialized somatic cells. Whether these cells lose their pluripotency or are able to reverse their differentiated state has important consequences. Reversibly differentiated cells can potentially regenerate parts of an organism and allow reproduction through fragmentation. In many organisms, however, somatic differentiation is terminal, thereby restricting the developmental paths to reproduction. The reason why terminal differentiation is a common developmental strategy remains unexplored. To understand the conditions that affect the evolution of terminal versus reversible differentiation, we developed a computational model inspired by differentiating cyanobacteria. We simulated the evolution of a population of two cell types –nitrogen fixing or photosynthetic– that exchange resources. The traits that control differentiation rates between cell types are allowed to evolve in the model. Although the topology of cell interactions and differentiation costs play a role in the evolution of terminal and reversible differentiation, the most important factor is the difference in division rates between cell types. Faster dividing cells always evolve to become the germ line. Our results explain why most multicellular differentiated cyanobacteria have terminally differentiated cells, while some have reversibly differentiated cells. We further observed that symbioses involving two cooperating lineages can evolve under conditions where aggregate size, connectivity, and differentiation costs are high. This may explain why plants engage in symbiotic interactions with diazotrophic bacteria. PMID:22511858

A novel image encryption algorithm based on chaos maps with Markov properties

NASA Astrophysics Data System (ADS)

Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang

2015-02-01

In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.

Evidence of correlated evolution and adaptive differentiation of stem and leaf functional traits in the herbaceous genus, Helianthus.

PubMed

Pilote, Alex J; Donovan, Lisa A

2016-12-01

Patterns of plant stem traits are expected to align with a "fast-slow" plant economic spectrum across taxa. Although broad patterns support such tradeoffs in field studies, tests of hypothesized correlated trait evolution and adaptive differentiation are more robust when taxa relatedness and environment are taken into consideration. Here we test for correlated evolution of stem and leaf traits and their adaptive differentiation across environments in the herbaceous genus, Helianthus. Stem and leaf traits of 14 species of Helianthus (28 populations) were assessed in a common garden greenhouse study. Phylogenetically independent contrasts were used to test for evidence of correlated evolution of stem hydraulic and biomechanical properties, correlated evolution of stem and leaf traits, and adaptive differentiation associated with source habitat environments. Among stem traits, there was evidence for correlated evolution of some hydraulic and biomechanical properties, supporting an expected tradeoff between stem theoretical hydraulic efficiency and resistance to bending stress. Population differentiation for suites of stem and leaf traits was found to be consistent with a "fast-slow" resource-use axis for traits related to water transport and use. Associations of population traits with source habitat characteristics supported repeated evolution of a resource-acquisitive "drought-escape" strategy in arid environments. This study provides evidence of correlated evolution of stem and leaf traits consistent with the fast-slow spectrum of trait combinations related to water transport and use along the stem-to-leaf pathway. Correlations of traits with source habitat characteristics further indicate that the correlated evolution is associated, at least in part, with adaptive differentiation of Helianthus populations among native habitats differing in climate. © 2016 Botanical Society of America.

Pyvolve: A Flexible Python Module for Simulating Sequences along Phylogenies.

PubMed

Spielman, Stephanie J; Wilke, Claus O

2015-01-01

We introduce Pyvolve, a flexible Python module for simulating genetic data along a phylogeny using continuous-time Markov models of sequence evolution. Easily incorporated into Python bioinformatics pipelines, Pyvolve can simulate sequences according to most standard models of nucleotide, amino-acid, and codon sequence evolution. All model parameters are fully customizable. Users can additionally specify custom evolutionary models, with custom rate matrices and/or states to evolve. This flexibility makes Pyvolve a convenient framework not only for simulating sequences under a wide variety of conditions, but also for developing and testing new evolutionary models. Pyvolve is an open-source project under a FreeBSD license, and it is available for download, along with a detailed user-manual and example scripts, from http://github.com/sjspielman/pyvolve.

MuSE: accounting for tumor heterogeneity using a sample-specific error model improves sensitivity and specificity in mutation calling from sequencing data.

PubMed

Fan, Yu; Xi, Liu; Hughes, Daniel S T; Zhang, Jianjun; Zhang, Jianhua; Futreal, P Andrew; Wheeler, David A; Wang, Wenyi

2016-08-24

Subclonal mutations reveal important features of the genetic architecture of tumors. However, accurate detection of mutations in genetically heterogeneous tumor cell populations using next-generation sequencing remains challenging. We develop MuSE ( http://bioinformatics.mdanderson.org/main/MuSE ), Mutation calling using a Markov Substitution model for Evolution, a novel approach for modeling the evolution of the allelic composition of the tumor and normal tissue at each reference base. MuSE adopts a sample-specific error model that reflects the underlying tumor heterogeneity to greatly improve the overall accuracy. We demonstrate the accuracy of MuSE in calling subclonal mutations in the context of large-scale tumor sequencing projects using whole exome and whole genome sequencing.

Biology-Culture Co-evolution in Finite Populations.

PubMed

de Boer, Bart; Thompson, Bill

2018-01-19

Language is the result of two concurrent evolutionary processes: biological and cultural inheritance. An influential evolutionary hypothesis known as the moving target problem implies inherent limitations on the interactions between our two inheritance streams that result from a difference in pace: the speed of cultural evolution is thought to rule out cognitive adaptation to culturally evolving aspects of language. We examine this hypothesis formally by casting it as as a problem of adaptation in time-varying environments. We present a mathematical model of biology-culture co-evolution in finite populations: a generalisation of the Moran process, treating co-evolution as coupled non-independent Markov processes, providing a general formulation of the moving target hypothesis in precise probabilistic terms. Rapidly varying culture decreases the probability of biological adaptation. However, we show that this effect declines with population size and with stronger links between biology and culture: in realistically sized finite populations, stochastic effects can carry cognitive specialisations to fixation in the face of variable culture, especially if the effects of those specialisations are amplified through cultural evolution. These results support the view that language arises from interactions between our two major inheritance streams, rather than from one primary evolutionary process that dominates another.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

Bayesian Analysis of Biogeography when the Number of Areas is Large

PubMed Central

Landis, Michael J.; Matzke, Nicholas J.; Moore, Brian R.; Huelsenbeck, John P.

2013-01-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a “data-augmentation” approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea. [ancestral area analysis; Bayesian biogeographic inference; data augmentation; historical biogeography; Markov chain Monte Carlo.] PMID:23736102

On Markov parameters in system identification

NASA Technical Reports Server (NTRS)

Phan, Minh; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.

Activation rates for nonlinear stochastic flows driven by non-Gaussian noise

NASA Astrophysics Data System (ADS)

van den Broeck, C.; Hänggi, P.

1984-11-01

Activation rates are calculated for stochastic bistable flows driven by asymmetric dichotomic Markov noise (a two-state Markov process). This noise contains as limits both a particular type of non-Gaussian white shot noise and white Gaussian noise. Apart from investigating the role of colored noise on the escape rates, one can thus also study the influence of the non-Gaussian nature of the noise on these rates. The rate for white shot noise differs in leading order (Arrhenius factor) from the corresponding rate for white Gaussian noise of equal strength. In evaluating the rates we demonstrate the advantage of using transport theory over a mean first-passage time approach for cases with generally non-white and non-Gaussian noise sources. For white shot noise with exponentially distributed weights we succeed in evaluating the mean first-passage time of the corresponding integro-differential master-equation dynamics. The rate is shown to coincide in the weak noise limit with the inverse mean first-passage time.

Nonlinear Markov Control Processes and Games

DTIC Science & Technology

2012-11-15

the analysis of a new class of stochastic games , nonlinear Markov games , as they arise as a ( competitive ) controlled version of nonlinear Markov... competitive interests) a nonlinear Markov game that we are investigating. I 0. :::tUt::JJt:.l.. I I t:t11VI;:, nonlinear Markov game , nonlinear Markov...corresponding stochastic game Γ+(T, h). In a slightly different setting one can assume that changes in a competitive control process occur as a

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

Cost Analysis of Ceramic Heads in Primary Total Hip Arthroplasty.

PubMed

Carnes, Keith J; Odum, Susan M; Troyer, Jennifer L; Fehring, Thomas K

2016-11-02

The advent of adverse local tissue reactions seen in metal-on-metal bearings, and the recent recognition of trunnionosis, have led many surgeons to recommend ceramic-on-polyethylene articulations for primary total hip arthroplasty. However, to our knowledge, there has been little research that has considered whether the increased cost of ceramic provides enough benefit over cobalt-chromium to justify its use. The primary purpose of this study was to compare the cost-effectiveness of ceramic-on-polyethylene implants and metal-on-polyethylene implants in patients undergoing total hip arthroplasty. Markov decision modeling was used to determine the ceramic-on-polyethylene implant revision rate necessary to be cost-effective compared with the revision rate of metal-on-polyethylene implants across a range of patient ages and implant costs. A different set of Markov models was used to estimate the national cost burden of choosing ceramic-on-polyethylene implants over metal-on-polyethylene implants for primary total hip arthroplasties. The Premier Research Database was used to identify 20,398 patients who in 2012 were ≥45 years of age and underwent a total hip arthroplasty with either a ceramic-on-polyethylene implant or a metal-on-polyethylene implant. The cost-effectiveness of ceramic heads is highly dependent on the cost differential between ceramic and metal femoral heads and the age of the patient. At a cost differential of $325, ceramic-on-polyethylene bearings are cost-effective for patients <85 years of age. At a cost differential of $600, it is cost-effective to utilize ceramic-on-polyethylene bearings in patients <65 years of age, and, at a differential of $1,003, ceramic-on-polyethylene bearings are not cost-effective at any age. The ability to recoup the initial increased expenditure of ceramic heads through a diminished lifetime revision cost is dependent on the price premium for ceramic and the age of the patient. A wholesale switch to ceramic bearings regardless of age or cost differential may result in an economic burden to the health system. Economic and decision analysis, Level III. See Instructions for Authors for a complete description of levels of evidence. Copyright © 2016 by The Journal of Bone and Joint Surgery, Incorporated.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes

ERIC Educational Resources Information Center

Kapland, David

2008-01-01

This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…

Higher-Order Corrections to Timelike Jets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giele, W.T.; /Fermilab; Kosower, D.A.

2011-02-01

We present a simple formalism for the evolution of timelike jets in which tree-level matrix element corrections can be systematically incorporated, up to arbitrary parton multiplicities and over all of phase space, in a way that exponentiates the matching corrections. The scheme is cast as a shower Markov chain which generates one single unweighted event sample, that can be passed to standard hadronization models. Remaining perturbative uncertainties are estimated by providing several alternative weight sets for the same events, at a relatively modest additional overhead. As an explicit example, we consider Z {yields} q{bar q} evolution with unpolarized, massless quarksmore » and include several formally subleading improvements as well as matching to tree-level matrix elements through {alpha}{sub s}{sup 4}. The resulting algorithm is implemented in the publicly available VINCIA plugin to the PYTHIA8 event generator.« less

Markov stochasticity coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

An informational transition in conditioned Markov chains: Applied to genetics and evolution.

PubMed

Zhao, Lei; Lascoux, Martin; Waxman, David

2016-08-07

In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states. Copyright © 2016 Elsevier Ltd. All rights reserved.

Alcohol Use Among American Indian High School Youths From Adolescence and Young Adulthood: A Latent Markov Model*

PubMed Central

Mitchell, Christina M.; Beals, Janette; Whitesell, Nancy Rumbaugh

2008-01-01

Objective: We explored patterns of alcohol use among American Indian youths as well as concurrent predictors and developmental outcomes 6 years later. Method: This study used six semi-annual waves of data collected across 3 years from 861 American Indian youths, ages 14-20 initially, from two western tribes. Using a latent Markov model, we examined patterns of change in latent states of adolescent alcohol use in the past 6 months, combining these states of alcohol use into three latent statuses that described patterns of change across the 3 years: abstainers, inconsistent drinkers, and consistent drinkers. We then explored how the latent statuses differed, both initially and in young adulthood (ages 20-26). Results: Both alcohol use and nonuse were quite stable across time, although we also found evidence of change. Despite some rather troubling drinking patterns as teens, especially among consistent drinkers, most of the youths had achieved important tasks of young adulthood. But patterns of use during adolescence were related to greater levels of substance use in young adulthood. Conclusions: Latent Markov modeling provided a useful categorization of alcohol use that more finely differentiated those youths who would otherwise have been considered inconsistent drinkers. Findings also suggest that broad-based interventions during adolescence may not be the most important ones; instead, programs targeting later alcohol and other drug use may be a more strategic use of often limited resources. PMID:18781241

On Markov modelling of near-wall turbulent shear flow

NASA Astrophysics Data System (ADS)

Reynolds, A. M.

1999-11-01

The role of Reynolds number in determining particle trajectories in near-wall turbulent shear flow is investigated in numerical simulations using a second-order Lagrangian stochastic (LS) model (Reynolds, A.M. 1999: A second-order Lagrangian stochastic model for particle trajectories in inhomogeneous turbulence. Quart. J. Roy. Meteorol. Soc. (In Press)). In such models, it is the acceleration, velocity and position of a particle rather than just its velocity and position which are assumed to evolve jointly as a continuous Markov process. It is found that Reynolds number effects are significant in determining simulated particle trajectories in the viscous sub-layer and the buffer zone. These effects are due almost entirely to the change in the Lagrangian integral timescale and are shown to be well represented in a first-order LS model by Sawford's correction footnote Sawford, B.L. 1991: Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys Fluids, 3, 1577-1586). This is found to remain true even when the Taylor-Reynolds number R_λ ~ O(0.1). This is somewhat surprising because the assumption of a Markovian evolution for velocity and position is strictly applicable only in the large Reynolds number limit because then the Lagrangian acceleration autocorrelation function approaches a delta function at the origin, corresponding to an uncorrelated component in the acceleration, and hence a Markov process footnote Borgas, M.S. and Sawford, B.L. 1991: The small-scale structure of acceleration correlations and its role in the statistical theory of turbulent dispersion. J. Fluid Mech. 288, 295-320.

Solving SAT Problem Based on Hybrid Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan

Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.

Shape Optimization of Rubber Bushing Using Differential Evolution Algorithm

PubMed Central

2014-01-01

The objective of this study is to design rubber bushing at desired level of stiffness characteristics in order to achieve the ride quality of the vehicle. A differential evolution algorithm based approach is developed to optimize the rubber bushing through integrating a finite element code running in batch mode to compute the objective function values for each generation. Two case studies were given to illustrate the application of proposed approach. Optimum shape parameters of 2D bushing model were determined by shape optimization using differential evolution algorithm. PMID:25276848

Postcopulatory sexual selection influences baculum evolution in primates and carnivores.

PubMed

Brindle, Matilda; Opie, Christopher

2016-12-14

The extreme morphological variability of the baculum across mammals is thought to be the result of sexual selection (particularly, high levels of postcopulatory selection). However, the evolutionary trajectory of the mammalian baculum is little studied and evidence for the adaptive function of the baculum has so far been elusive. Here, we use Markov chain Monte Carlo methods implemented in a Bayesian phylogenetic framework to reconstruct baculum evolution across the mammalian class and investigate the rate of baculum length evolution within the primate order. We then test the effects of testes mass (postcopulatory sexual selection), polygamy, seasonal breeding and intromission duration on the baculum in primates and carnivores. The ancestral mammal did not have a baculum, but both ancestral primates and carnivores did. No relationship was found between testes mass and baculum length in either primates or carnivores. Intromission duration correlated with baculum presence over the course of primate evolution, and prolonged intromission predicts significantly longer bacula in extant primates and carnivores. Both polygamous and seasonal breeding systems predict significantly longer bacula in primates. These results suggest the baculum plays an important role in facilitating reproductive strategies in populations with high levels of postcopulatory sexual selection. © 2016 The Authors.

Postcopulatory sexual selection influences baculum evolution in primates and carnivores

PubMed Central

Brindle, Matilda

2016-01-01

The extreme morphological variability of the baculum across mammals is thought to be the result of sexual selection (particularly, high levels of postcopulatory selection). However, the evolutionary trajectory of the mammalian baculum is little studied and evidence for the adaptive function of the baculum has so far been elusive. Here, we use Markov chain Monte Carlo methods implemented in a Bayesian phylogenetic framework to reconstruct baculum evolution across the mammalian class and investigate the rate of baculum length evolution within the primate order. We then test the effects of testes mass (postcopulatory sexual selection), polygamy, seasonal breeding and intromission duration on the baculum in primates and carnivores. The ancestral mammal did not have a baculum, but both ancestral primates and carnivores did. No relationship was found between testes mass and baculum length in either primates or carnivores. Intromission duration correlated with baculum presence over the course of primate evolution, and prolonged intromission predicts significantly longer bacula in extant primates and carnivores. Both polygamous and seasonal breeding systems predict significantly longer bacula in primates. These results suggest the baculum plays an important role in facilitating reproductive strategies in populations with high levels of postcopulatory sexual selection. PMID:27974519

A compositional framework for Markov processes

NASA Astrophysics Data System (ADS)

Baez, John C.; Fong, Brendan; Pollard, Blake S.

2016-03-01

We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.

Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xiaoying; Liu, Chongxuan; Hu, Bill X.

2014-01-01

A multi-rate expression for uranyl [U(VI)] surface complexation reactions has been proposed to describe diffusion-limited U(VI) sorption/desorption in heterogeneous subsurface sediments. An important assumption in the rate expression is that its rate constants follow a certain type probability distribution. In this paper, a Bayes-based, Differential Evolution Markov Chain method was used to assess the distribution assumption and to analyze parameter and model structure uncertainties. U(VI) desorption from a contaminated sediment at the US Hanford 300 Area, Washington was used as an example for detail analysis. The results indicated that: 1) the rate constants in the multi-rate expression contain uneven uncertaintiesmore » with slower rate constants having relative larger uncertainties; 2) the lognormal distribution is an effective assumption for the rate constants in the multi-rate model to simualte U(VI) desorption; 3) however, long-term prediction and its uncertainty may be significantly biased by the lognormal assumption for the smaller rate constants; and 4) both parameter and model structure uncertainties can affect the extrapolation of the multi-rate model with a larger uncertainty from the model structure. The results provide important insights into the factors contributing to the uncertainties of the multi-rate expression commonly used to describe the diffusion or mixing-limited sorption/desorption of both organic and inorganic contaminants in subsurface sediments.« less

A process of rumour scotching on finite populations.

PubMed

de Arruda, Guilherme Ferraz; Lebensztayn, Elcio; Rodrigues, Francisco A; Rodríguez, Pablo Martín

2015-09-01

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible-infected-recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation.

A process of rumour scotching on finite populations

PubMed Central

de Arruda, Guilherme Ferraz; Lebensztayn, Elcio; Rodrigues, Francisco A.; Rodríguez, Pablo Martín

2015-01-01

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible–infected–recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation. PMID:26473048

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.

PubMed

Kapfer, Sebastian C; Krauth, Werner

2017-12-15

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

NASA Astrophysics Data System (ADS)

Kapfer, Sebastian C.; Krauth, Werner

2017-12-01

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Adaptive hidden Markov model with anomaly States for price manipulation detection.

PubMed

Cao, Yi; Li, Yuhua; Coleman, Sonya; Belatreche, Ammar; McGinnity, Thomas Martin

2015-02-01

Price manipulation refers to the activities of those traders who use carefully designed trading behaviors to manually push up or down the underlying equity prices for making profits. With increasing volumes and frequency of trading, price manipulation can be extremely damaging to the proper functioning and integrity of capital markets. The existing literature focuses on either empirical studies of market abuse cases or analysis of particular manipulation types based on certain assumptions. Effective approaches for analyzing and detecting price manipulation in real time are yet to be developed. This paper proposes a novel approach, called adaptive hidden Markov model with anomaly states (AHMMAS) for modeling and detecting price manipulation activities. Together with wavelet transformations and gradients as the feature extraction methods, the AHMMAS model caters to price manipulation detection and basic manipulation type recognition. The evaluation experiments conducted on seven stock tick data from NASDAQ and the London Stock Exchange and 10 simulated stock prices by stochastic differential equation show that the proposed AHMMAS model can effectively detect price manipulation patterns and outperforms the selected benchmark models.

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

NASA Astrophysics Data System (ADS)

Seid, Abdu Mohammed; Berhane, Tesfahun; Roininen, Lassi; Nigussie, Melessew

2018-03-01

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia (11.6 °N, 37.4 °E) . We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled Inv -χ2 hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.

Cloud computing task scheduling strategy based on improved differential evolution algorithm

NASA Astrophysics Data System (ADS)

Ge, Junwei; He, Qian; Fang, Yiqiu

2017-04-01

In order to optimize the cloud computing task scheduling scheme, an improved differential evolution algorithm for cloud computing task scheduling is proposed. Firstly, the cloud computing task scheduling model, according to the model of the fitness function, and then used improved optimization calculation of the fitness function of the evolutionary algorithm, according to the evolution of generation of dynamic selection strategy through dynamic mutation strategy to ensure the global and local search ability. The performance test experiment was carried out in the CloudSim simulation platform, the experimental results show that the improved differential evolution algorithm can reduce the cloud computing task execution time and user cost saving, good implementation of the optimal scheduling of cloud computing tasks.

Semi-Markov adjunction to the Computer-Aided Markov Evaluator (CAME)

NASA Technical Reports Server (NTRS)

Rosch, Gene; Hutchins, Monica A.; Leong, Frank J.; Babcock, Philip S., IV

1988-01-01

The rule-based Computer-Aided Markov Evaluator (CAME) program was expanded in its ability to incorporate the effect of fault-handling processes into the construction of a reliability model. The fault-handling processes are modeled as semi-Markov events and CAME constructs and appropriate semi-Markov model. To solve the model, the program outputs it in a form which can be directly solved with the Semi-Markov Unreliability Range Evaluator (SURE) program. As a means of evaluating the alterations made to the CAME program, the program is used to model the reliability of portions of the Integrated Airframe/Propulsion Control System Architecture (IAPSA 2) reference configuration. The reliability predictions are compared with a previous analysis. The results bear out the feasibility of utilizing CAME to generate appropriate semi-Markov models to model fault-handling processes.

Modeling Protoplanetary Disks to Characterize the Evolution of their Structure

NASA Astrophysics Data System (ADS)

Allen, Magdelena; van der Marel, Nienke; Williams, Jonathan

2018-01-01

Stars form from gravitationally collapsing clouds of gas and dust. Most young stars retain a protoplanetary disk for a few million years. This disk’s dust reemits stellar flux in the infrared, producing a spectral energy distribution (SED) observable by Spitzer and other telescopes. To understand the inner clearing of dust cavities and evolution in the SED, we used the Chiang & Goldreich two-layer approximation. We first wrote a python script based on refinements by Dullemond that includes a hot, puffed inner rim, shadowed mid region, flaring outer disk, and a variable inner cavity. This was then coupled with a Markov Chain Monte Carlo procedure to fit the observed SEDs of disks in the star forming Lupus region. The fitting procedure recovers physical characteristics of the disk including temperature, size, mass, and surface density. We compare the characteristics of circumstellar disks without holes and more evolved transition disks with cleared inner regions.

Open Markov Processes and Reaction Networks

ERIC Educational Resources Information Center

Swistock Pollard, Blake Stephen

2017-01-01

We begin by defining the concept of "open" Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain "boundary" states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow…

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

The explicit form of the rate function for semi-Markov processes and its contractions

NASA Astrophysics Data System (ADS)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

Communication: Introducing prescribed biases in out-of-equilibrium Markov models

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-03-01

Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

A mathematical description of the inclusive fitness theory.

PubMed

Wakano, Joe Yuichiro; Ohtsuki, Hisashi; Kobayashi, Yutaka

2013-03-01

Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. This paper aims to provide a mathematical description of the inclusive fitness theory. Specifically, we provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. Our framework is based on the probability distribution of "offspring-to-parent map", from which the key concepts of the theory, such as fitness function, relatedness and inclusive fitness, are derived in a straightforward manner. We prove theorems showing that inclusive fitness always provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in the Wright's island model with recurrent mutations. We also show the existence of the critical mutation rate, which does not depend on the number of islands and below which a positive dispersal rate evolves. Our framework can also be applied to lattice or network structured populations. Copyright © 2012 Elsevier Inc. All rights reserved.

Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains.

PubMed

Tataru, Paula; Hobolth, Asger

2011-12-05

Continuous time Markov chains (CTMCs) is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes) are unaccessible and the past must be inferred from DNA sequence data observed in the present. We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD), the second on uniformization (UNI), and the third on integrals of matrix exponentials (EXPM). The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.

AEOLUS: A MARKOV CHAIN MONTE CARLO CODE FOR MAPPING ULTRACOOL ATMOSPHERES. AN APPLICATION ON JUPITER AND BROWN DWARF HST LIGHT CURVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karalidi, Theodora; Apai, Dániel; Schneider, Glenn

Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of amore » giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR.« less

On a Result for Finite Markov Chains

ERIC Educational Resources Information Center

Kulathinal, Sangita; Ghosh, Lagnojita

2006-01-01

In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

The Markov blankets of life: autonomy, active inference and the free energy principle

PubMed Central

Palacios, Ensor; Friston, Karl; Kiverstein, Julian

2018-01-01

This work addresses the autonomous organization of biological systems. It does so by considering the boundaries of biological systems, from individual cells to Home sapiens, in terms of the presence of Markov blankets under the active inference scheme—a corollary of the free energy principle. A Markov blanket defines the boundaries of a system in a statistical sense. Here we consider how a collective of Markov blankets can self-assemble into a global system that itself has a Markov blanket; thereby providing an illustration of how autonomous systems can be understood as having layers of nested and self-sustaining boundaries. This allows us to show that: (i) any living system is a Markov blanketed system and (ii) the boundaries of such systems need not be co-extensive with the biophysical boundaries of a living organism. In other words, autonomous systems are hierarchically composed of Markov blankets of Markov blankets—all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment. PMID:29343629

Continuous-Time Semi-Markov Models in Health Economic Decision Making: An Illustrative Example in Heart Failure Disease Management.

PubMed

Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe

2016-01-01

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.

Competition drives trait evolution and character displacement between Mimulus species along an environmental gradient.

PubMed

Kooyers, Nicholas J; James, Brooke; Blackman, Benjamin K

2017-05-01

Closely related species may evolve to coexist stably in sympatry through niche differentiation driven by in situ competition, a process termed character displacement. Alternatively, past evolution in allopatry may have already sufficiently reduced niche overlap to permit establishment in sympatry, a process called ecological sorting. The relative importance of each process to niche differentiation is contentious even though they are not mutually exclusive and are both mediated via multivariate trait evolution. We explore how competition has impacted niche differentiation in two monkeyflowers, Mimulus alsinoides and M. guttatus, which often co-occur. Through field observations, common gardens, and competition experiments, we demonstrate that M. alsinoides is restricted to marginal habitats in sympatry and that the impacts of character displacement on niche differentiation are complex. Competition with M. guttatus alters selection gradients and has favored taller M. alsinoides with earlier seasonal flowering at low elevation and floral shape divergence at high elevation. However, no trait exhibits the pattern typically associated with character displacement, higher divergence between species in sympatry than allopatry. Thus, although character displacement was unlikely the process driving initial divergence along niche axes necessary for coexistence, we conclude that competition in sympatry has likely driven trait evolution along additional niche axes. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Skin cancer texture analysis of OCT images based on Haralick, fractal dimension, Markov random field features, and the complex directional field features

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2016-10-01

In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Discovering Beaten Paths in Collaborative Ontology-Engineering Projects using Markov Chains

PubMed Central

Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A.; Noy, Natalya F.

2014-01-01

Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50, 000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology-engineering projects and tools in the biomedical domain. PMID:24953242

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Giorgos, E-mail: garab@math.uoc.gr; Katsoulakis, Markos A., E-mail: markos@math.umass.edu; Plechac, Petr, E-mail: plechac@math.udel.edu

2012-10-01

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decompositionmore » corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.« less

Discovering beaten paths in collaborative ontology-engineering projects using Markov chains.

PubMed

Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A; Noy, Natalya F

2014-10-01

Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50,000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology-engineering projects and tools in the biomedical domain. Copyright © 2014 Elsevier Inc. All rights reserved.

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Application of differential evolution algorithm on self-potential data.

PubMed

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods.

Application of Differential Evolution Algorithm on Self-Potential Data

PubMed Central

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods. PMID:23240004

Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

PubMed Central

Newton, Paul K; Mason, Jeremy; Venkatappa, Neethi; Jochelson, Maxine S; Hurt, Brian; Nieva, Jorge; Comen, Elizabeth; Norton, Larry; Kuhn, Peter

2015-01-01

Background: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. Aims: Develop a Markov based model of breast cancer progression that has predictive capability. Methods: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. Results: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as “sponges” or “spreaders” with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. Conclusions: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease. PMID:28721371

Wrinkling pattern evolution of cylindrical biological tissues with differential growth.

PubMed

Jia, Fei; Li, Bo; Cao, Yan-Ping; Xie, Wei-Hua; Feng, Xi-Qiao

2015-01-01

Three-dimensional surface wrinkling of soft cylindrical tissues induced by differential growth is explored. Differential volumetric growth can cause their morphological stability, leading to the formation of hexagonal and labyrinth wrinkles. During postbuckling, multiple bifurcations and morphological transitions may occur as a consequence of continuous growth in the surface layer. The physical mechanisms underpinning the morphological evolution are examined from the viewpoint of energy. Surface curvature is found to play a regulatory role in the pattern evolution. This study may not only help understand the morphogenesis of soft biological tissues, but also inspire novel routes for creating desired surface patterns of soft materials.

Automatic Clustering Using FSDE-Forced Strategy Differential Evolution

NASA Astrophysics Data System (ADS)

Yasid, A.

2018-01-01

Clustering analysis is important in datamining for unsupervised data, cause no adequate prior knowledge. One of the important tasks is defining the number of clusters without user involvement that is known as automatic clustering. This study intends on acquiring cluster number automatically utilizing forced strategy differential evolution (AC-FSDE). Two mutation parameters, namely: constant parameter and variable parameter are employed to boost differential evolution performance. Four well-known benchmark datasets were used to evaluate the algorithm. Moreover, the result is compared with other state of the art automatic clustering methods. The experiment results evidence that AC-FSDE is better or competitive with other existing automatic clustering algorithm.

Evolution of tuf genes: ancient duplication, differential loss and gene conversion.

PubMed

Lathe, W C; Bork, P

2001-08-03

The tuf gene of eubacteria, encoding the EF-tu elongation factor, was duplicated early in the evolution of the taxon. Phylogenetic and genomic location analysis of 20 complete eubacterial genomes suggests that this ancient duplication has been differentially lost and maintained in eubacteria.

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

Lee, Julian

2018-03-01

Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

Identifying and correcting non-Markov states in peptide conformational dynamics

NASA Astrophysics Data System (ADS)

Nerukh, Dmitry; Jensen, Christian H.; Glen, Robert C.

2010-02-01

Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ≈50 ps and longer. However, at the time scale of 30-40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

Contemporary evolution during invasion: evidence for differentiation, natural selection, and local adaptation.

PubMed

Colautti, Robert I; Lau, Jennifer A

2015-05-01

Biological invasions are 'natural' experiments that can improve our understanding of contemporary evolution. We evaluate evidence for population differentiation, natural selection and adaptive evolution of invading plants and animals at two nested spatial scales: (i) among introduced populations (ii) between native and introduced genotypes. Evolution during invasion is frequently inferred, but rarely confirmed as adaptive. In common garden studies, quantitative trait differentiation is only marginally lower (~3.5%) among introduced relative to native populations, despite genetic bottlenecks and shorter timescales (i.e. millennia vs. decades). However, differentiation between genotypes from the native vs. introduced range is less clear and confounded by nonrandom geographic sampling; simulations suggest this causes a high false-positive discovery rate (>50%) in geographically structured populations. Selection differentials (¦s¦) are stronger in introduced than in native species, although selection gradients (¦β¦) are not, consistent with introduced species experiencing weaker genetic constraints. This could facilitate rapid adaptation, but evidence is limited. For example, rapid phenotypic evolution often manifests as geographical clines, but simulations demonstrate that nonadaptive trait clines can evolve frequently during colonization (~two-thirds of simulations). Additionally, QST-FST studies may often misrepresent the strength and form of natural selection acting during invasion. Instead, classic approaches in evolutionary ecology (e.g. selection analysis, reciprocal transplant, artificial selection) are necessary to determine the frequency of adaptive evolution during invasion and its influence on establishment, spread and impact of invasive species. These studies are rare but crucial for managing biological invasions in the context of global change. © 2015 John Wiley & Sons Ltd.

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

PAWS/STEM - PADE APPROXIMATION WITH SCALING AND SCALED TAYLOR EXPONENTIAL MATRIX (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

Traditional fault-tree techniques for analyzing the reliability of large, complex systems fail to model the dynamic reconfiguration capabilities of modern computer systems. Markov models, on the other hand, can describe fault-recovery (via system reconfiguration) as well as fault-occurrence. The Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs provide a flexible, user-friendly, language-based interface for the creation and evaluation of Markov models describing the behavior of fault-tolerant reconfigurable computer systems. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. The calculation of the probability of entering a death state of a Markov model (representing system failure) requires the solution of a set of coupled differential equations. Because of the large disparity between the rates of fault arrivals and system recoveries, Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. PAWS/STEM was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The package is written in PASCAL, ANSI compliant C-language, and FORTRAN 77. The standard distribution medium for the VMS version of PAWS/STEM (LAR-14165) is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The standard distribution medium for the Sun version of PAWS/STEM (LAR-14920) is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. PAWS/STEM was developed in 1989 and last updated in 1991. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

PAWS/STEM - PADE APPROXIMATION WITH SCALING AND SCALED TAYLOR EXPONENTIAL MATRIX (SUN VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

Traditional fault-tree techniques for analyzing the reliability of large, complex systems fail to model the dynamic reconfiguration capabilities of modern computer systems. Markov models, on the other hand, can describe fault-recovery (via system reconfiguration) as well as fault-occurrence. The Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs provide a flexible, user-friendly, language-based interface for the creation and evaluation of Markov models describing the behavior of fault-tolerant reconfigurable computer systems. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. The calculation of the probability of entering a death state of a Markov model (representing system failure) requires the solution of a set of coupled differential equations. Because of the large disparity between the rates of fault arrivals and system recoveries, Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. PAWS/STEM was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The package is written in PASCAL, ANSI compliant C-language, and FORTRAN 77. The standard distribution medium for the VMS version of PAWS/STEM (LAR-14165) is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The standard distribution medium for the Sun version of PAWS/STEM (LAR-14920) is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. PAWS/STEM was developed in 1989 and last updated in 1991. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

A tomographic test of cosmological principle using the JLA compilation of type Ia supernovae

NASA Astrophysics Data System (ADS)

Chang, Zhe; Lin, Hai-Nan; Sang, Yu; Wang, Sai

2018-05-01

We test the cosmological principle by fitting a dipolar modulation of distance modulus and searching for an evolution of this modulation with respect to cosmological redshift. Based on a redshift tomographic method, we divide the Joint Light-curve Analysis compilation of supernovae of type Ia into different redshift bins, and employ a Markov-Chain Monte-Carlo method to infer the anisotropic amplitude and direction in each redshift bin. However, we do not find any significant deviations from the cosmological principle, and the anisotropic amplitude is stringently constrained to be less than a few thousandths at 95% confidence level.

Lieb-Robinson bound and locality for general markovian quantum dynamics.

PubMed

Poulin, David

2010-05-14

The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length scale set by the Lieb-Robinson velocity and the system's relaxation time.

Computational intelligence for the Balanced Scorecard: studying performance trends of hemodialysis clinics.

PubMed

Cattinelli, Isabella; Bolzoni, Elena; Chermisi, Milena; Bellocchio, Francesco; Barbieri, Carlo; Mari, Flavio; Amato, Claudia; Menzer, Marcus; Stopper, Andrea; Gatti, Emanuele

2013-07-01

The Balanced Scorecard (BSC) is a general, widely employed instrument for enterprise performance monitoring based on the periodic assessment of strategic Key Performance Indicators that are scored against preset targets. The BSC is currently employed as an effective management support tool within Fresenius Medical Care (FME) and is routinely analyzed via standard statistical methods. More recently, the application of computational intelligence techniques (namely, self-organizing maps) to BSC data has been proposed as a way to enhance the quantity and quality of information that can be extracted from it. In this work, additional methods are presented to analyze the evolution of clinic performance over time. Performance evolution is studied at the single-clinic level by computing two complementary indexes that measure the proportion of time spent within performance clusters and improving/worsening trends. Self-organizing maps are used in conjunction with these indexes to identify the specific drivers of the observed performance. The performance evolution for groups of clinics is modeled under a probabilistic framework by resorting to Markov chain properties. These allow a study of the probability of transitioning between performance clusters as time progresses for the identification of the performance level that is expected to become dominant over time. We show the potential of the proposed methods through illustrative results derived from the analysis of BSC data of 109 FME clinics in three countries. We were able to identify the performance drivers for specific groups of clinics and to distinguish between countries whose performances are likely to improve from those where a decline in performance might be expected. According to the stationary distribution of the Markov chain, the expected trend is best in Turkey (where the highest performance cluster has the highest probability, P=0.46), followed by Portugal (where the second best performance cluster dominates, with P=0.50), and finally Italy (where the second best performance cluster has P=0.34). These results highlight the ability of the proposed methods to extract insights about performance trends that cannot be easily extrapolated using standard analyses and that are valuable in directing management strategies within a continuous quality improvement policy. Copyright © 2013 Elsevier B.V. All rights reserved.

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

A POPULATION MEMETICS APPROACH TO CULTURAL EVOLUTION IN CHAFFINCH SONG: DIFFERENTIATION AMONG POPULATIONS.

PubMed

Lynch, Alejandro; Baker, Allan J

1994-04-01

We investigated cultural evolution in populations of common chaffinches (Fringilla coelebs) in the Atlantic islands (Azores, Madeira, and Canaries) and neighboring continental regions (Morocco and Iberia) by employing a population-memetic approach. To quantify differentiation, we used the concept of a song meme, defined as a single syllable or a series of linked syllables capable of being transmitted. The levels of cultural differentiation are higher among the Canaries populations than among the Azorean ones, even though the islands are on average closer to each other geographically. This is likely the result of reduced levels of migration, lower population sizes, and bottlenecks (possibly during the colonization of these populations) in the Canaries; all these factors produce a smaller effective population size and therefore accentuate the effects of differentiation by random drift. Significant levels of among-population differentiation in the Azores, in spite of substantial levels of migration, attest to the differentiating effects of high mutation rates of memes, which allow the accumulation of new mutants in different populations before migration can disperse them throughout the entire region. © 1994 The Society for the Study of Evolution.

Reverse Engineering of Modified Genes by Bayesian Network Analysis Defines Molecular Determinants Critical to the Development of Glioblastoma

PubMed Central

Kunkle, Brian W.; Yoo, Changwon; Roy, Deodutta

2013-01-01

In this study we have identified key genes that are critical in development of astrocytic tumors. Meta-analysis of microarray studies which compared normal tissue to astrocytoma revealed a set of 646 differentially expressed genes in the majority of astrocytoma. Reverse engineering of these 646 genes using Bayesian network analysis produced a gene network for each grade of astrocytoma (Grade I–IV), and ‘key genes’ within each grade were identified. Genes found to be most influential to development of the highest grade of astrocytoma, Glioblastoma multiforme were: COL4A1, EGFR, BTF3, MPP2, RAB31, CDK4, CD99, ANXA2, TOP2A, and SERBP1. All of these genes were up-regulated, except MPP2 (down regulated). These 10 genes were able to predict tumor status with 96–100% confidence when using logistic regression, cross validation, and the support vector machine analysis. Markov genes interact with NFkβ, ERK, MAPK, VEGF, growth hormone and collagen to produce a network whose top biological functions are cancer, neurological disease, and cellular movement. Three of the 10 genes - EGFR, COL4A1, and CDK4, in particular, seemed to be potential ‘hubs of activity’. Modified expression of these 10 Markov Blanket genes increases lifetime risk of developing glioblastoma compared to the normal population. The glioblastoma risk estimates were dramatically increased with joint effects of 4 or more than 4 Markov Blanket genes. Joint interaction effects of 4, 5, 6, 7, 8, 9 or 10 Markov Blanket genes produced 9, 13, 20.9, 26.7, 52.8, 53.2, 78.1 or 85.9%, respectively, increase in lifetime risk of developing glioblastoma compared to normal population. In summary, it appears that modified expression of several ‘key genes’ may be required for the development of glioblastoma. Further studies are needed to validate these ‘key genes’ as useful tools for early detection and novel therapeutic options for these tumors. PMID:23737970

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Characterising the Dense Molecular Gas in Exceptional Local Galaxies

NASA Astrophysics Data System (ADS)

Tunnard, Richard C. A.

2016-08-01

The interferometric facilities now coming online (the Atacama Large Millimetre Array (ALMA) and the NOrthern Extended Millimeter Array (NOEMA)) and those planned for the coming decade (the Next Generation Very Large Array (ngVLA) and the Square Kilometre Array (SKA)) in the radio to sub-millimetre regimes are opening a window to the molecular gas in high-redshift galaxies. However, our understanding of similar galaxies in the local universe is still far from complete and the data analysis techniques and tools needed to interpret the observations in consistent and comparable ways are yet to be developed. I first describe the Monte Carlo Markov Chain (MCMC) script developed to empower a public radiative transfer code. I characterise both the public code and MCMC script, including an exploration of the effect of observing molecular lines at high redshift where the Cosmic Microwave Background (CMB) can provide a significant background, as well as the effect this can have on well-known local correlations. I present two studies of ultraluminous infrared galaxies (ULIRGs) in the local universe making use of literature and collaborator data. In the first of these, NGC6240, I use the wealth of available data and the geometry of the source to develop a multi-phase, multi-species model, finding evidence for a complex medium of hot diffuse and cold dense gas in pressure equilibrium. Next, I study the prototypical ULIRG Arp 220; an extraordinary galaxy rendered especially interesting by the controversy over the power source of the western of the two merger nuclei and its immense luminosity and dust obscuration. Using traditional grid based methods I explore the molecular gas conditions within the nuclei and find evidence for chemical differentiation between the two nuclei, potentially related to the obscured power source. Finally, I investigate the potential evolution of proto-clusters over cosmic time with sub-millimetre observations of 14 radio galaxies, unexpectedly finding little to no evidence for cluster evolution.

Fitting Analysis using Differential evolution Optimization (FADO):. Spectral population synthesis through genetic optimization under self-consistency boundary conditions

NASA Astrophysics Data System (ADS)

Gomes, J. M.; Papaderos, P.

2017-07-01

The goal of population spectral synthesis (pss; also referred to as inverse, semi-empirical evolutionary- or fossil record approach) is to decipher from the spectrum of a galaxy the mass, age and metallicity of its constituent stellar populations. This technique, which is the reverse of but complementary to evolutionary synthesis, has been established as fundamental tool in extragalactic research. It has been extensively applied to large spectroscopic data sets, notably the SDSS, leading to important insights into the galaxy assembly history. However, despite significant improvements over the past decade, all current pss codes suffer from two major deficiencies that inhibit us from gaining sharp insights into the star-formation history (SFH) of galaxies and potentially introduce substantial biases in studies of their physical properties (e.g., stellar mass, mass-weighted stellar age and specific star formation rate). These are I) the neglect of nebular emission in spectral fits, consequently; II) the lack of a mechanism that ensures consistency between the best-fitting SFH and the observed nebular emission characteristics of a star-forming (SF) galaxy (e.g., hydrogen Balmer-line luminosities and equivalent widths-EWs, shape of the continuum in the region around the Balmer and Paschen jump). In this article, we present fado (Fitting Analysis using Differential evolution Optimization) - a conceptually novel, publicly available pss tool with the distinctive capability of permitting identification of the SFH that reproduces the observed nebular characteristics of a SF galaxy. This so-far unique self-consistency concept allows us to significantly alleviate degeneracies in current spectral synthesis, thereby opening a new avenue to the exploration of the assembly history of galaxies. The innovative character of fado is further augmented by its mathematical foundation: fado is the first pss code employing genetic differential evolution optimization. This, in conjunction with various other currently unique elements in its mathematical concept and numerical realization (e.g., mid-analysis optimization of the spectral library using artificial intelligence, test for convergence through a procedure inspired by Markov chain Monte Carlo techniques, quasi-parallelization embedded within a modular architecture) results in key improvements with respect to computational efficiency and uniqueness of the best-fitting SFHs. Furthermore, fado incorporates within a single code the entire chain of pre-processing, modeling, post-processing, storage and graphical representation of the relevant output from pss, including emission-line measurements and estimates of uncertainties for all primary and secondary products from spectral synthesis (e.g., mass contributions of individual stellar populations, mass- and luminosity-weighted stellar ages and metallicities). This integrated concept greatly simplifies and accelerates a lengthy sequence of individual time-consuming steps that are generally involved in pss modeling, further enhancing the overall efficiency of the code and inviting to its automated application to large spectroscopic data sets. The distribution package of the FADO v.1 tool contains the binary and its auxiliary files. FADO v.1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/603/A63

Modeling of dialogue regimes of distance robot control

NASA Astrophysics Data System (ADS)

Larkin, E. V.; Privalov, A. N.

2017-02-01

Process of distance control of mobile robots is investigated. Petri-Markov net for modeling of dialogue regime is worked out. It is shown, that sequence of operations of next subjects: a human operator, a dialogue computer and an onboard computer may be simulated with use the theory of semi-Markov processes. From the semi-Markov process of the general form Markov process was obtained, which includes only states of transaction generation. It is shown, that a real transaction flow is the result of «concurrency» in states of Markov process. Iteration procedure for evaluation of transaction flow parameters, which takes into account effect of «concurrency», is proposed.

Modeling evolution of the mind and cultures: emotional Sapir-Whorf hypothesis

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2009-05-01

Evolution of cultures is ultimately determined by mechanisms of the human mind. The paper discusses the mechanisms of evolution of language from primordial undifferentiated animal cries to contemporary conceptual contents. In parallel with differentiation of conceptual contents, the conceptual contents were differentiated from emotional contents of languages. The paper suggests the neural brain mechanisms involved in these processes. Experimental evidence and theoretical arguments are discussed, including mathematical approaches to cognition and language: modeling fields theory, the knowledge instinct, and the dual model connecting language and cognition. Mathematical results are related to cognitive science, linguistics, and psychology. The paper gives an initial mathematical formulation and mean-field equations for the hierarchical dynamics of both the human mind and culture. In the mind heterarchy operation of the knowledge instinct manifests through mechanisms of differentiation and synthesis. The emotional contents of language are related to language grammar. The conclusion is an emotional version of Sapir-Whorf hypothesis. Cultural advantages of "conceptual" pragmatic cultures, in which emotionality of language is diminished and differentiation overtakes synthesis resulting in fast evolution at the price of self doubts and internal crises are compared to those of traditional cultures where differentiation lags behind synthesis, resulting in cultural stability at the price of stagnation. Multi-language, multi-ethnic society might combine the benefits of stability and fast differentiation. Unsolved problems and future theoretical and experimental directions are discussed.

Algorithms for Discovery of Multiple Markov Boundaries

PubMed Central

Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.

2013-01-01

Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

PubMed Central

Meyer, Denny; Forbes, Don; Clarke, Stephen R.

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key Points A comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition. The Markov assumption appears to be valid. However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play. Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes. PMID:24357946

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.

PubMed

Meyer, Denny; Forbes, Don; Clarke, Stephen R

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Project MINERVA's Follow-up on Wide-Field, Small Telescope Photometry to Identify Exoplanets

NASA Astrophysics Data System (ADS)

Houghton, Audrey; Henderson, Morgan; Johnson, Samson; Sergi, Anthony; Eastman, Jason D.; Beatty, Thomas G.; McCrady, Nate

2017-01-01

MINERVA is an array of four 0.7-m telescopes equipped for high precision photometry and spectroscopy dedicated to exoplanet observations. During the first 18 months of science operations, MINERVA engaged in a program of photometric follow-up of potential transiting exoplanet targets identified by the Kilodegree Extremely Little Telescope (KELT). Robotically-obtained observations are passed through our data reduction pipeline and we extract light curves via differential photometry. We seek transit signals via a Markov chain Monte Carlo fit using BATMAN. We discuss results for over 100 target stars analyzed to date.

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

NASA Astrophysics Data System (ADS)

Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

Pigment cell interactions and differential xanthophore recruitment underlying zebrafish stripe reiteration and Danio pattern evolution

PubMed Central

Patterson, Larissa B.; Bain, Emily J.; Parichy, David M.

2014-01-01

Fishes have diverse pigment patterns, yet mechanisms of pattern evolution remain poorly understood. In zebrafish, Danio rerio, pigment-cell autonomous interactions generate dark stripes of melanophores that alternate with light interstripes of xanthophores and iridophores. Here, we identify mechanisms underlying the evolution of a uniform pattern in D. albolineatus in which all three pigment cell classes are intermingled. We show that in this species xanthophores differentiate precociously over a wider area, and that cis regulatory evolution has increased expression of xanthogenic Colony Stimulating Factor-1 (Csf1). Expressing Csf1 similarly in D. rerio has cascading effects, driving the intermingling of all three pigment cell classes and resulting in the loss of stripes, as in D. albolineatus. Our results identify novel mechanisms of pattern development and illustrate how pattern diversity can be generated when a core network of pigment-cell autonomous interactions is coupled with changes in pigment cell differentiation. PMID:25374113

Dynamic Latent Trait Models with Mixed Hidden Markov Structure for Mixed Longitudinal Outcomes.

PubMed

Zhang, Yue; Berhane, Kiros

2016-01-01

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMM). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study (CHS) to jointly model questionnaire based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

Sub- and super-diffusion on Cantor sets: Beyond the paradox

NASA Astrophysics Data System (ADS)

K. Golmankhaneh, Alireza; Balankin, Alexander S.

2018-04-01

There is no way to build a nontrivial Markov process having continuous trajectories on a totally disconnected fractal embedded in the Euclidean space. Accordingly, in order to delineate the diffusion process on the totally disconnected fractal, one needs to relax the continuum requirement. Consequently, a diffusion process depends on how the continuum requirement is handled. This explains the emergence of different types of anomalous diffusion on the same totally disconnected set. In this regard, we argue that the number of effective spatial degrees of freedom of a random walker on the totally disconnected Cantor set is equal to nsp = [ D ] + 1, where [ D ] is the integer part of the Hausdorff dimension of the Cantor set. Conversely, the number of effective dynamical degrees of freedom (ds) depends on the definition of a Markov process on the totally disconnected Cantor set embedded in the Euclidean space En (n ≥nsp). This allows us to deduce the equation of diffusion by employing the local differential operators on the Fα-support. The exact solutions of this equation are obtained on the middle-ɛ Cantor sets for different kinds of the Markovian random processes. The relation of our findings to physical phenomena observed in complex systems is highlighted.

Incorporating interaction networks into the determination of functionally related hit genes in genomic experiments with Markov random fields

PubMed Central

Robinson, Sean; Nevalainen, Jaakko; Pinna, Guillaume; Campalans, Anna; Radicella, J. Pablo; Guyon, Laurent

2017-01-01

Abstract Motivation: Incorporating gene interaction data into the identification of ‘hit’ genes in genomic experiments is a well-established approach leveraging the ‘guilt by association’ assumption to obtain a network based hit list of functionally related genes. We aim to develop a method to allow for multivariate gene scores and multiple hit labels in order to extend the analysis of genomic screening data within such an approach. Results: We propose a Markov random field-based method to achieve our aim and show that the particular advantages of our method compared with those currently used lead to new insights in previously analysed data as well as for our own motivating data. Our method additionally achieves the best performance in an independent simulation experiment. The real data applications we consider comprise of a survival analysis and differential expression experiment and a cell-based RNA interference functional screen. Availability and implementation: We provide all of the data and code related to the results in the paper. Contact: sean.j.robinson@utu.fi or laurent.guyon@cea.fr Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881978

Regenerative Simulation of Harris Recurrent Markov Chains.

DTIC Science & Technology

1982-07-01

Sutijle) S. TYPE OF REPORT A PERIOD COVERED REGENERATIVE SIMULATION OF HARRIS RECURRENT Technical Report MARKOV CHAINS 14. PERFORMING ORG. REPORT NUMBER...7 AD-Ag 251 STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH /s i2/ REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS,(U) JUL 82 P W GLYNN N0001...76-C-0578 UNtLASSIFIED TR-62 NL EhhhIhEEEEEEI EEEEEIIIIIII REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS by Peter W. Glynn TECHNICAL

A dynamic multi-scale Markov model based methodology for remaining life prediction

NASA Astrophysics Data System (ADS)

Yan, Jihong; Guo, Chaozhong; Wang, Xing

2011-05-01

The ability to accurately predict the remaining life of partially degraded components is crucial in prognostics. In this paper, a performance degradation index is designed using multi-feature fusion techniques to represent deterioration severities of facilities. Based on this indicator, an improved Markov model is proposed for remaining life prediction. Fuzzy C-Means (FCM) algorithm is employed to perform state division for Markov model in order to avoid the uncertainty of state division caused by the hard division approach. Considering the influence of both historical and real time data, a dynamic prediction method is introduced into Markov model by a weighted coefficient. Multi-scale theory is employed to solve the state division problem of multi-sample prediction. Consequently, a dynamic multi-scale Markov model is constructed. An experiment is designed based on a Bently-RK4 rotor testbed to validate the dynamic multi-scale Markov model, experimental results illustrate the effectiveness of the methodology.

Preliminary testing for the Markov property of the fifteen chromatin states of the Broad Histone Track.

PubMed

Lee, Kyung-Eun; Park, Hyun-Seok

2015-01-01

Epigenetic computational analyses based on Markov chains can integrate dependencies between regions in the genome that are directly adjacent. In this paper, the BED files of fifteen chromatin states of the Broad Histone Track of the ENCODE project are parsed, and comparative nucleotide frequencies of regional chromatin blocks are thoroughly analyzed to detect the Markov property in them. We perform various tests to examine the Markov property embedded in a frequency domain by checking for the presence of the Markov property in the various chromatin states. We apply these tests to each region of the fifteen chromatin states. The results of our simulation indicate that some of the chromatin states possess a stronger Markov property than others. We discuss the significance of our findings in statistical models of nucleotide sequences that are necessary for the computational analysis of functional units in noncoding DNA.

Discrete Biogeography Based Optimization for Feature Selection in Molecular Signatures.

PubMed

Liu, Bo; Tian, Meihong; Zhang, Chunhua; Li, Xiangtao

2015-04-01

Biomarker discovery from high-dimensional data is a complex task in the development of efficient cancer diagnoses and classification. However, these data are usually redundant and noisy, and only a subset of them present distinct profiles for different classes of samples. Thus, selecting high discriminative genes from gene expression data has become increasingly interesting in the field of bioinformatics. In this paper, a discrete biogeography based optimization is proposed to select the good subset of informative gene relevant to the classification. In the proposed algorithm, firstly, the fisher-markov selector is used to choose fixed number of gene data. Secondly, to make biogeography based optimization suitable for the feature selection problem; discrete migration model and discrete mutation model are proposed to balance the exploration and exploitation ability. Then, discrete biogeography based optimization, as we called DBBO, is proposed by integrating discrete migration model and discrete mutation model. Finally, the DBBO method is used for feature selection, and three classifiers are used as the classifier with the 10 fold cross-validation method. In order to show the effective and efficiency of the algorithm, the proposed algorithm is tested on four breast cancer dataset benchmarks. Comparison with genetic algorithm, particle swarm optimization, differential evolution algorithm and hybrid biogeography based optimization, experimental results demonstrate that the proposed method is better or at least comparable with previous method from literature when considering the quality of the solutions obtained. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Parameter identifiability and regional calibration for reservoir inflow prediction

NASA Astrophysics Data System (ADS)

Kolberg, Sjur; Engeland, Kolbjørn; Tøfte, Lena S.; Bruland, Oddbjørn

2013-04-01

The large hydropower producer Statkraft is currently testing regional, distributed models for operational reservoir inflow prediction. The need for simultaneous forecasts and consistent updating in a large number of catchments supports the shift from catchment-oriented to regional models. Low-quality naturalized inflow series in the reservoir catchments further encourages the use of donor catchments and regional simulation for calibration purposes. MCMC based parameter estimation (the Dream algorithm; Vrugt et al, 2009) is adapted to regional parameter estimation, and implemented within the open source ENKI framework. The likelihood is based on the concept of effectively independent number of observations, spatially as well as in time. Marginal and conditional (around an optimum) parameter distributions for each catchment may be extracted, even though the MCMC algorithm itself is guided only by the regional likelihood surface. Early results indicate that the average performance loss associated with regional calibration (difference in Nash-Sutcliffe R2 between regionally and locally optimal parameters) is in the range of 0.06. The importance of the seasonal snow storage and melt in Norwegian mountain catchments probably contributes to the high degree of similarity among catchments. The evaluation continues for several regions, focusing on posterior parameter uncertainty and identifiability. Vrugt, J. A., C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman and D. Higdon: Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling. Int. J. of nonlinear sciences and numerical simulation 10, 3, 273-290, 2009.

Parsing parallel evolution: ecological divergence and differential gene expression in the adaptive radiations of thick-lipped Midas cichlid fishes from Nicaragua.

PubMed

Manousaki, Tereza; Hull, Pincelli M; Kusche, Henrik; Machado-Schiaffino, Gonzalo; Franchini, Paolo; Harrod, Chris; Elmer, Kathryn R; Meyer, Axel

2013-02-01

The study of parallel evolution facilitates the discovery of common rules of diversification. Here, we examine the repeated evolution of thick lips in Midas cichlid fishes (the Amphilophus citrinellus species complex)-from two Great Lakes and two crater lakes in Nicaragua-to assess whether similar changes in ecology, phenotypic trophic traits and gene expression accompany parallel trait evolution. Using next-generation sequencing technology, we characterize transcriptome-wide differential gene expression in the lips of wild-caught sympatric thick- and thin-lipped cichlids from all four instances of repeated thick-lip evolution. Six genes (apolipoprotein D, myelin-associated glycoprotein precursor, four-and-a-half LIM domain protein 2, calpain-9, GTPase IMAP family member 8-like and one hypothetical protein) are significantly underexpressed in the thick-lipped morph across all four lakes. However, other aspects of lips' gene expression in sympatric morphs differ in a lake-specific pattern, including the magnitude of differentially expressed genes (97-510). Generally, fewer genes are differentially expressed among morphs in the younger crater lakes than in those from the older Great Lakes. Body shape, lower pharyngeal jaw size and shape, and stable isotopes (δ(13)C and δ(15)N) differ between all sympatric morphs, with the greatest differentiation in the Great Lake Nicaragua. Some ecological traits evolve in parallel (those related to foraging ecology; e.g. lip size, body and head shape) but others, somewhat surprisingly, do not (those related to diet and food processing; e.g. jaw size and shape, stable isotopes). Taken together, this case of parallelism among thick- and thin-lipped cichlids shows a mosaic pattern of parallel and nonparallel evolution. © 2012 Blackwell Publishing Ltd.

Integrating prior knowledge in multiple testing under dependence with applications to detecting differential DNA methylation.

PubMed

Kuan, Pei Fen; Chiang, Derek Y

2012-09-01

DNA methylation has emerged as an important hallmark of epigenetics. Numerous platforms including tiling arrays and next generation sequencing, and experimental protocols are available for profiling DNA methylation. Similar to other tiling array data, DNA methylation data shares the characteristics of inherent correlation structure among nearby probes. However, unlike gene expression or protein DNA binding data, the varying CpG density which gives rise to CpG island, shore and shelf definition provides exogenous information in detecting differential methylation. This article aims to introduce a robust testing and probe ranking procedure based on a nonhomogeneous hidden Markov model that incorporates the above-mentioned features for detecting differential methylation. We revisit the seminal work of Sun and Cai (2009, Journal of the Royal Statistical Society: Series B (Statistical Methodology)71, 393-424) and propose modeling the nonnull using a nonparametric symmetric distribution in two-sided hypothesis testing. We show that this model improves probe ranking and is robust to model misspecification based on extensive simulation studies. We further illustrate that our proposed framework achieves good operating characteristics as compared to commonly used methods in real DNA methylation data that aims to detect differential methylation sites. © 2012, The International Biometric Society.

Calculation of prevalence estimates through differential equations: application to stroke-related disability.

PubMed

Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio

2008-01-01

Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.

Hierarchical Markov blankets and adaptive active inference. Comment on "Answering Schrödinger's question: A free-energy formulation" by Maxwell James Désormeau Ramstead et al.

NASA Astrophysics Data System (ADS)

Kirchhoff, Michael

2018-03-01

Ramstead MJD, Badcock PB, Friston KJ. Answering Schrödinger's question: A free-energy formulation. Phys Life Rev 2018. https://doi.org/10.1016/j.plrev.2017.09.001 [this issue] motivate a multiscale characterisation of living systems in terms of hierarchically structured Markov blankets - a view of living systems as comprised of Markov blankets of Markov blankets [1-4]. It is effectively a treatment of what life is and how it is realised, cast in terms of how Markov blankets of living systems self-organise via active inference - a corollary of the free energy principle [5-7].

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

NASA Technical Reports Server (NTRS)

Liu, K.; Skelton, R. E.; Sharkey, J. P.

1992-01-01

A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Application of spatial Markov chains to the analysis of the temporal-spatial evolution of soil erosion.

PubMed

Liu, Ruimin; Men, Cong; Wang, Xiujuan; Xu, Fei; Yu, Wenwen

Soil and water conservation in the Three Gorges Reservoir Area of China is important, and soil erosion is a significant issue. In the present study, spatial Markov chains were applied to explore the impacts of the regional context on soil erosion in the Xiangxi River watershed, and Thematic Mapper remote sensing data from 1999 and 2007 were employed. The results indicated that the observed changes in soil erosion were closely related to the soil erosion levels of the surrounding areas. When neighboring regions were not considered, the probability that moderate erosion transformed into slight and severe erosion was 0.8330 and 0.0049, respectively. However, when neighboring regions that displayed intensive erosion were considered, the probabilities were 0.2454 and 0.7513, respectively. Moreover, the different levels of soil erosion in neighboring regions played different roles in soil erosion. If the erosion levels in the neighboring region were lower, the probability of a high erosion class transferring to a lower level was relatively high. In contrast, if erosion levels in the neighboring region were higher, the probability was lower. The results of the present study provide important information for the planning and implementation of soil conservation measures in the study area.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullah, Ghanim; Demuro, Angelo; Parker, Ian

Amyloid beta (Aβ) oligomers associated with Alzheimer’s disease (AD) form Ca 2+-permeable plasma membrane pores, leading to a disruption of the otherwise well-controlled intracellular calcium (Ca 2+) homeostasis. The resultant up-regulation of intracellular Ca 2+ concentration has detrimental implications for memory formation and cell survival. The gating kinetics and Ca 2+ permeability of Aβ pores are not well understood. We have used computational modeling in conjunction with the ability of optical patch-clamping for massively parallel imaging of Ca 2+ flux through thousands of pores in the cell membrane of Xenopus oocytes to elucidate the kinetic properties of Aβ pores. Themore » fluorescence time-series data from individual pores were idealized and used to develop data-driven Markov chain models for the kinetics of the Aβ pore at different stages of its evolution. Our study provides the first demonstration of developing Markov chain models for ion channel gating that are driven by optical-patch clamp data with the advantage of experiments being performed under close to physiological conditions. As a result, we demonstrate the up-regulation of gating of various Ca 2+ release channels due to Aβ pores and show that the extent and spatial range of such up-regulation increases as Aβ pores with low open probability and Ca 2+ permeability transition into those with high open probability and Ca 2+ permeability.« less

Conceptual Comparison of Population Based Metaheuristics for Engineering Problems

PubMed Central

Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes. PMID:25874265

Conceptual comparison of population based metaheuristics for engineering problems.

PubMed

Adekanmbi, Oluwole; Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

An optimized digital watermarking algorithm in wavelet domain based on differential evolution for color image.

PubMed

Cui, Xinchun; Niu, Yuying; Zheng, Xiangwei; Han, Yingshuai

2018-01-01

In this paper, a new color watermarking algorithm based on differential evolution is proposed. A color host image is first converted from RGB space to YIQ space, which is more suitable for the human visual system. Then, apply three-level discrete wavelet transformation to luminance component Y and generate four different frequency sub-bands. After that, perform singular value decomposition on these sub-bands. In the watermark embedding process, apply discrete wavelet transformation to a watermark image after the scrambling encryption processing. Our new algorithm uses differential evolution algorithm with adaptive optimization to choose the right scaling factors. Experimental results show that the proposed algorithm has a better performance in terms of invisibility and robustness.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

DOE PAGES

Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; ...

2013-01-01

We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

Evolution of the human immunodeficiency virus envelope gene is dominated by purifying selection.

PubMed

Edwards, C T T; Holmes, E C; Pybus, O G; Wilson, D J; Viscidi, R P; Abrams, E J; Phillips, R E; Drummond, A J

2006-11-01

The evolution of the human immunodeficiency virus (HIV-1) during chronic infection involves the rapid, continuous turnover of genetic diversity. However, the role of natural selection, relative to random genetic drift, in governing this process is unclear. We tested a stochastic model of genetic drift using partial envelope sequences sampled longitudinally in 28 infected children. In each case the Bayesian posterior (empirical) distribution of coalescent genealogies was estimated using Markov chain Monte Carlo methods. Posterior predictive simulation was then used to generate a null distribution of genealogies assuming neutrality, with the null and empirical distributions compared using four genealogy-based summary statistics sensitive to nonneutral evolution. Because both null and empirical distributions were generated within a coalescent framework, we were able to explicitly account for the confounding influence of demography. From the distribution of corrected P-values across patients, we conclude that empirical genealogies are more asymmetric than expected if evolution is driven by mutation and genetic drift only, with an excess of low-frequency polymorphisms in the population. This indicates that although drift may still play an important role, natural selection has a strong influence on the evolution of HIV-1 envelope. A negative relationship between effective population size and substitution rate indicates that as the efficacy of selection increases, a smaller proportion of mutations approach fixation in the population. This suggests the presence of deleterious mutations. We therefore conclude that intrahost HIV-1 evolution in envelope is dominated by purifying selection against low-frequency deleterious mutations that do not reach fixation.

Discriminative motif discovery via simulated evolution and random under-sampling.

PubMed

Song, Tao; Gu, Hong

2014-01-01

Conserved motifs in biological sequences are closely related to their structure and functions. Recently, discriminative motif discovery methods have attracted more and more attention. However, little attention has been devoted to the data imbalance problem, which is one of the main reasons affecting the performance of the discriminative models. In this article, a simulated evolution method is applied to solve the multi-class imbalance problem at the stage of data preprocessing, and at the stage of Hidden Markov Models (HMMs) training, a random under-sampling method is introduced for the imbalance between the positive and negative datasets. It is shown that, in the task of discovering targeting motifs of nine subcellular compartments, the motifs found by our method are more conserved than the methods without considering data imbalance problem and recover the most known targeting motifs from Minimotif Miner and InterPro. Meanwhile, we use the found motifs to predict protein subcellular localization and achieve higher prediction precision and recall for the minority classes.

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

PubMed Central

Crawford, Forrest W.; Suchard, Marc A.

2011-01-01

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λn and a particle dies with instantaneous rate μn. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics. PMID:21984359

Evolution of olfactory receptors.

PubMed

Hoover, Kara C

2013-01-01

Olfactory receptors are a specialized set of receptor cells responsible for the detection of odors. These cells are G protein-coupled receptors and expressed in the cell membranes of olfactory sensory neurons. Once a cell is activated by a ligand, it initiates a signal transduction cascade that produces a nerve impulse to the brain where odor perception is processed. Vertebrate olfactory evolution is characterized by birth-and-death events, a special case of the stochastic continuous time Markov process. Vertebrate fish have three general types of receptor cells (two dedicated to pheromones). Terrestrial animals have different epithelial biology due to the specialized adaptation to detecting airborne odors. Two general classes of olfactory receptor gene reflect the vertebrate marine heritage (Class I) and the derived amphibian, reptile, and mammal terrestrial heritage (Class II). While we know much about olfactory receptor cells, there are still areas where our knowledge is insufficient, such as intra-individual diversity throughout the life time, epigenetic processes acting on olfactory receptors, and association of ligands to specific cells.

LECTURES ON GAME THEORY, MARKOV CHAINS, AND RELATED TOPICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thompson, G L

1958-03-01

Notes on nine lectures delivered at Sandin Corporation in August 1957 are given. Part one contains the manuscript of a paper concerning a judging problem. Part two is concerned with finite Markov-chain theory amd discusses regular Markov chains, absorbing Markov chains, the classification of states, application to the Leontief input-output model, and semimartingales. Part three contains notes on game theory and covers matrix games, the effect of psychological attitudes on the outcomes of games, extensive games, amd matrix theory applied to mathematical economics. (auth)

Markov chains: computing limit existence and approximations with DNA.

PubMed

Cardona, M; Colomer, M A; Conde, J; Miret, J M; Miró, J; Zaragoza, A

2005-09-01

We present two algorithms to perform computations over Markov chains. The first one determines whether the sequence of powers of the transition matrix of a Markov chain converges or not to a limit matrix. If it does converge, the second algorithm enables us to estimate this limit. The combination of these algorithms allows the computation of a limit using DNA computing. In this sense, we have encoded the states and the transition probabilities using strands of DNA for generating paths of the Markov chain.

The early thermal evolution of Mars

NASA Astrophysics Data System (ADS)

Bhatia, G. K.; Sahijpal, S.

2016-01-01

Hf-W isotopic systematics of Martian meteorites have provided evidence for the early accretion and rapid core formation of Mars. We present the results of numerical simulations performed to study the early thermal evolution and planetary scale differentiation of Mars. The simulations are confined to the initial 50 Myr (Ma) of the formation of solar system. The accretion energy produced during the growth of Mars and the decay energy due to the short-lived radio-nuclides 26Al, 60Fe, and the long-lived nuclides, 40K, 235U, 238U, and 232Th are incorporated as the heat sources for the thermal evolution of Mars. During the core-mantle differentiation of Mars, the molten metallic blobs were numerically moved using Stoke's law toward the center with descent velocity that depends on the local acceleration due to gravity. Apart from the accretion and the radioactive heat energies, the gravitational energy produced during the differentiation of Mars and the associated heat transfer is also parametrically incorporated in the present work to make an assessment of its contribution to the early thermal evolution of Mars. We conclude that the accretion energy alone cannot produce widespread melting and differentiation of Mars even with an efficient consumption of the accretion energy. This makes 26Al the prime source for the heating and planetary scale differentiation of Mars. We demonstrate a rapid accretion and core-mantle differentiation of Mars within the initial ~1.5 Myr. This is consistent with the chronological records of Martian meteorites.

Evolution of Life and SETI (Evo-SETI)

NASA Astrophysics Data System (ADS)

Maccone, Claudio

When SETI scientists will be able to discover a signal or just some signs of an Extra-Terrestrial (ET) Civilization, those ETs should turn out to be technologically advanced at least as much as Humans, if not more, or much more so. Comparing the technological level of two different Civilizations is then a key issue in SETI. But at the moment we only know about the development of life on Earth over the last 3.5 billion years. We thus need to mathematically model the evolution of life on Earth (RNA to Humans) and then apply our results to other extra-solar planets to find out “where they stand” along their evolution of life. In a series of recent papers and in a book (refs. [1] through [4]) this author introduced a new statistical model embracing SETI, Darwinian Evolution and Human History into a unified statistical picture and concisely called Evo-SETI (Evolution & SETI). The relevant mathematical instruments are: 1) The statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. Assuming that each input variable in the Drake equation was a random variable, rather than just a pure number, N was shown to follow the lognormal probability distribution having as mean value the sum of the input mean values, and as variance the sum of the input variances (ref. [1]). 2) Geometric Brownian Motion (GBM), the stochastic process representing Evolution as the stochastic increase of the number of Species living on Earth over the last 3.5 billion years. This GBM is well-known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing, or, more rarely (as in the Mass Extinctions of the past) a decreasing exponential of the time. 3) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (this is the so-called “Peak-Locus Theorem”). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to identify with Cladistics (refs. [2], [3], [4]). 4) The (Shannon) Entropy of such b-lognormals is then seen to represent the “degree of progress” reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, Human History may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller “chaos”), and have their peaks located on the increasing GBM exponential. This exponential is thus the “trend of progress” in Human History. 5) But our most striking new result is about the well-known “Molecular Clock of Evolution”, namely the “constant rate of Evolution at the molecular level” as shown by Kimura’s Neutral Theory of Molecular Evolution. We showed that that the Molecular Clock identifies with Entropy in our Evo-SETI model because they both grew linearly in time since the origin of life. 6) Furthermore, we applid our Evo-SETI model to lognormal stochastic processes other then the GBMs. For instance, we showed that the Markov-Korotayev (2007-2008, refs. [5], [6]) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the lognormal stochastic process is a cubic (third degree polynomial) function of the time. In conclusion: we have provided a vast mathematical model capable of embracing Molecular Evolution, SETI and Entropy into a simple set of statistical equations based upon b-lognormals pdfs and lognormal stochastic processes Keywords: Molecular Clock, Darwinian evolution, statistical Drake equation, lognormal probability densities, geometric Brownian motion, entropy. REFERENCES [1] Maccone, C. (2008), “The Statistical Drake Equation”, paper #IAC-08-A4.1.4 presented on October 1st, 2008, at the 59th International Astronautical Congress (IAC) held in Glasgow, Scotland, UK, September 29th thru October 3rd, 2008, later published in Acta Astronautica, Vol. 67 (2010), pages 1366-1383. [2] Maccone, C. (2011, b), “A Mathematical Model for Evolution and SETI”, Origins of Life and Evolutionary Biospheres (OLEB), Vol. 41, pages 609-619, available online December 3rd, 2011. [3] Maccone, C. (2012), “Mathematical SETI”, a 724-pages book published by Praxis-Springer in the fall of 2012. ISBN, ISBN-10: 3642274366 | ISBN-13: 978-3642274367 | Edition: 2012 [4] Maccone, C., (2013), “SETI, Evolution and Human History merged into a Mathematical Model”, International Journal of Astrobiology, Vol. 12, issue 3 (2013), pages 218-245. Available online since April 23, 2013. [5] Markov A., Korotayev A., “Phanerozoic marine biodiversity follows a hyperbolic trend”, Paleoworld, Volume 16, Issue 4, December 2007, Pages 311-318. [6] Markov A., Korotayev A., “Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution”, Journal of General Biology. Volume 69, 2008, N. 3, pp. 175-194.

Machine learning in sentiment reconstruction of the simulated stock market

NASA Astrophysics Data System (ADS)

Goykhman, Mikhail; Teimouri, Ali

2018-02-01

In this paper we continue the study of the simulated stock market framework defined by the driving sentiment processes. We focus on the market environment driven by the buy/sell trading sentiment process of the Markov chain type. We apply the methodology of the Hidden Markov Models and the Recurrent Neural Networks to reconstruct the transition probabilities matrix of the Markov sentiment process and recover the underlying sentiment states from the observed stock price behavior. We demonstrate that the Hidden Markov Model can successfully recover the transition probabilities matrix for the hidden sentiment process of the Markov Chain type. We also demonstrate that the Recurrent Neural Network can successfully recover the hidden sentiment states from the observed simulated stock price time series.

Markov models in dentistry: application to resin-bonded bridges and review of the literature.

PubMed

Mahl, Dominik; Marinello, Carlo P; Sendi, Pedram

2012-10-01

Markov models are mathematical models that can be used to describe disease progression and evaluate the cost-effectiveness of medical interventions. Markov models allow projecting clinical and economic outcomes into the future and are therefore frequently used to estimate long-term outcomes of medical interventions. The purpose of this paper is to demonstrate its use in dentistry, using the example of resin-bonded bridges to replace missing teeth, and to review the literature. We used literature data and a four-state Markov model to project long-term outcomes of resin-bonded bridges over a time horizon of 60 years. In addition, the literature was searched in PubMed Medline for research articles on the application of Markov models in dentistry.

Markov switching multinomial logit model: An application to accident-injury severities.

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2009-07-01

In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident-injury severities. These models assume Markov switching over time between two unobserved states of roadway safety as a means of accounting for potential unobserved heterogeneity. The states are distinct in the sense that in different states accident-severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single-state) multinomial logit models for a number of roadway classes and accident types. It is found that the more frequent state of roadway safety is correlated with better weather conditions and that the less frequent state is correlated with adverse weather conditions.

The generalization ability of SVM classification based on Markov sampling.

PubMed

Xu, Jie; Tang, Yuan Yan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang; Zhang, Baochang

2015-06-01

The previously known works studying the generalization ability of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed samples. In this paper, we go far beyond this classical framework by studying the generalization ability of SVMC based on uniformly ergodic Markov chain (u.e.M.c.) samples. We analyze the excess misclassification error of SVMC based on u.e.M.c. samples, and obtain the optimal learning rate of SVMC for u.e.M.c. We also introduce a new Markov sampling algorithm for SVMC to generate u.e.M.c. samples from given dataset, and present the numerical studies on the learning performance of SVMC based on Markov sampling for benchmark datasets. The numerical studies show that the SVMC based on Markov sampling not only has better generalization ability as the number of training samples are bigger, but also the classifiers based on Markov sampling are sparsity when the size of dataset is bigger with regard to the input dimension.

Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function

NASA Astrophysics Data System (ADS)

Ye, Jing; Dang, Yaoguo; Li, Bingjun

2018-01-01

Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

PubMed

Dixit, Purushottam D; Dill, Ken A

2018-02-13

Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C 2 M 2 ), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

Phasic Triplet Markov Chains.

PubMed

El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar

2014-11-01

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

Analysing grouping of nucleotides in DNA sequences using lumped processes constructed from Markov chains.

PubMed

Guédon, Yann; d'Aubenton-Carafa, Yves; Thermes, Claude

2006-03-01

The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is therefore addressed. In the classical approach to lumpability, this problem can be formulated as the determination of an appropriate state space (smaller than the original state space) such that the lumped chain defined on this state space retains the Markov property. We propose a different perspective on lumpability where the state space is fixed and the partitioning of this state space is represented by a one-to-many probabilistic function within a two-level stochastic process. Three nested classes of lumped processes can be defined in this way as sub-classes of first-order Markov chains. These lumped processes enable parsimonious reparameterizations of Markov chains that help to reveal relevant partitions of the state space. Characterizations of the lumped processes on the original transition probability matrix are derived. Different model selection methods relying either on hypothesis testing or on penalized log-likelihood criteria are presented as well as extensions to lumped processes constructed from high-order Markov chains. The relevance of the proposed approach to lumpability is illustrated by the analysis of DNA sequences. In particular, the use of lumped processes enables to highlight differences between intronic sequences and gene untranslated region sequences.

Multiscale modelling and analysis of collective decision making in swarm robotics.

PubMed

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

Lunar initial Nd-143/Nd-144 - Differential evolution of the lunar crust and mantle

NASA Technical Reports Server (NTRS)

Lugmair, G. W.; Marti, K.

1978-01-01

The Sm-Nd evolution of Apollo 15 green glass is discussed. The ICE age (intercept with chondritic evolution) of 3.8 + or - 0.4 eons overlaps the range of reported (Ar-39)-(Ar-40) ages and implies a distinct source region for green glass, characterized by very low and unfractionated REE abundances. Evidence is presented that LINd (lunar initial Nd) is compatible with a 'chondritic'-type Nd isotopic evolution as observed in the Juvinas meteorite. This normalization is used to study the Sm-Nd system of various lunar rock types. The results obtained from a limited number of rocks clearly indicate differential Sm-Nd evolution for the lunar crust and mantle. High-Ti basalts returned by the Apollo 11 and 17 missions were derived from distinct source regions. The Nd-143 evolution in KREEP requires a source region which is clearly distinct from any mantle reservoir.

Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI.

PubMed

Maccone, Claudio

2017-04-06

The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time . We call b -lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b -lognormal in the time . Next, our "Peak-Locus Theorem" translates cladistics : each species created by evolution is a b -lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called "Geometric Brownian Motion" (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b -lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The "molecular clock" is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) "cubic" evolution: a curve of logarithmic increase.

SARA - SURE/ASSIST RELIABILITY ANALYSIS WORKSTATION (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

SARA, the SURE/ASSIST Reliability Analysis Workstation, is a bundle of programs used to solve reliability problems. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. The Systems Validation Methods group at NASA Langley Research Center has created a set of four software packages that form the basis for a reliability analysis workstation, including three for use in analyzing reconfigurable, fault-tolerant systems and one for analyzing non-reconfigurable systems. The SARA bundle includes the three for reconfigurable, fault-tolerant systems: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), and PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920). As indicated by the program numbers in parentheses, each of these three packages is also available separately in two machine versions. The fourth package, which is only available separately, is FTC, the Fault Tree Compiler (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree which describes a non-reconfigurable system. PAWS/STEM and SURE are analysis programs which utilize different solution methods, but have a common input language, the SURE language. ASSIST is a preprocessor that generates SURE language from a more abstract definition. ASSIST, SURE, and PAWS/STEM are described briefly in the following paragraphs. For additional details about the individual packages, including pricing, please refer to their respective abstracts. ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, allows a reliability engineer to describe the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. A one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. The semi-Markov model generated by ASSIST is in the format needed for input to SURE and PAWS/STEM. The Semi-Markov Unreliability Range Evaluator, SURE, is an analysis tool for reconfigurable, fault-tolerant systems. SURE provides an efficient means for calculating accurate upper and lower bounds for the death state probabilities for a large class of semi-Markov models, not just those which can be reduced to critical-pair architectures. The calculated bounds are close enough (usually within 5 percent of each other) for use in reliability studies of ultra-reliable computer systems. The SURE bounding theorems have algebraic solutions and are consequently computationally efficient even for large and complex systems. SURE can optionally regard a specified parameter as a variable over a range of values, enabling an automatic sensitivity analysis. SURE output is tabular. The PAWS/STEM package includes two programs for the creation and evaluation of pure Markov models describing the behavior of fault-tolerant reconfigurable computer systems: the Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The programs that comprise the SARA package were originally developed for use on DEC VAX series computers running VMS and were later ported for use on Sun series computers running SunOS. They are written in C-language, Pascal, and FORTRAN 77. An ANSI compliant C compiler is required in order to compile the C portion of the Sun version source code. The Pascal and FORTRAN code can be compiled on Sun computers using Sun Pascal and Sun Fortran. For the VMS version, VAX C, VAX PASCAL, and VAX FORTRAN can be used to recompile the source code. The standard distribution medium for the VMS version of SARA (COS-10041) is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The standard distribution medium for the Sun version of SARA (COS-10039) is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the ASSIST user's manual in TeX and PostScript formats are provided on the distribution medium. DEC, VAX, VMS, and TK50 are registered trademarks of Digital Equipment Corporation. Sun, Sun3, Sun4, and SunOS are trademarks of Sun Microsystems, Inc. TeX is a trademark of the American Mathematical Society. PostScript is a registered trademark of Adobe Systems Incorporated.

SARA - SURE/ASSIST RELIABILITY ANALYSIS WORKSTATION (UNIX VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

SARA, the SURE/ASSIST Reliability Analysis Workstation, is a bundle of programs used to solve reliability problems. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. The Systems Validation Methods group at NASA Langley Research Center has created a set of four software packages that form the basis for a reliability analysis workstation, including three for use in analyzing reconfigurable, fault-tolerant systems and one for analyzing non-reconfigurable systems. The SARA bundle includes the three for reconfigurable, fault-tolerant systems: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), and PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920). As indicated by the program numbers in parentheses, each of these three packages is also available separately in two machine versions. The fourth package, which is only available separately, is FTC, the Fault Tree Compiler (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree which describes a non-reconfigurable system. PAWS/STEM and SURE are analysis programs which utilize different solution methods, but have a common input language, the SURE language. ASSIST is a preprocessor that generates SURE language from a more abstract definition. ASSIST, SURE, and PAWS/STEM are described briefly in the following paragraphs. For additional details about the individual packages, including pricing, please refer to their respective abstracts. ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, allows a reliability engineer to describe the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. A one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. The semi-Markov model generated by ASSIST is in the format needed for input to SURE and PAWS/STEM. The Semi-Markov Unreliability Range Evaluator, SURE, is an analysis tool for reconfigurable, fault-tolerant systems. SURE provides an efficient means for calculating accurate upper and lower bounds for the death state probabilities for a large class of semi-Markov models, not just those which can be reduced to critical-pair architectures. The calculated bounds are close enough (usually within 5 percent of each other) for use in reliability studies of ultra-reliable computer systems. The SURE bounding theorems have algebraic solutions and are consequently computationally efficient even for large and complex systems. SURE can optionally regard a specified parameter as a variable over a range of values, enabling an automatic sensitivity analysis. SURE output is tabular. The PAWS/STEM package includes two programs for the creation and evaluation of pure Markov models describing the behavior of fault-tolerant reconfigurable computer systems: the Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The programs that comprise the SARA package were originally developed for use on DEC VAX series computers running VMS and were later ported for use on Sun series computers running SunOS. They are written in C-language, Pascal, and FORTRAN 77. An ANSI compliant C compiler is required in order to compile the C portion of the Sun version source code. The Pascal and FORTRAN code can be compiled on Sun computers using Sun Pascal and Sun Fortran. For the VMS version, VAX C, VAX PASCAL, and VAX FORTRAN can be used to recompile the source code. The standard distribution medium for the VMS version of SARA (COS-10041) is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The standard distribution medium for the Sun version of SARA (COS-10039) is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the ASSIST user's manual in TeX and PostScript formats are provided on the distribution medium. DEC, VAX, VMS, and TK50 are registered trademarks of Digital Equipment Corporation. Sun, Sun3, Sun4, and SunOS are trademarks of Sun Microsystems, Inc. TeX is a trademark of the American Mathematical Society. PostScript is a registered trademark of Adobe Systems Incorporated.

Building Simple Hidden Markov Models. Classroom Notes

ERIC Educational Resources Information Center

Ching, Wai-Ki; Ng, Michael K.

2004-01-01

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

Using Games to Teach Markov Chains

ERIC Educational Resources Information Center

Johnson, Roger W.

2003-01-01

Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…

Sampling rare fluctuations of discrete-time Markov chains

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Sampling rare fluctuations of discrete-time Markov chains.

PubMed

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Enhancement of Markov chain model by integrating exponential smoothing: A case study on Muslims marriage and divorce

NASA Astrophysics Data System (ADS)

Jamaluddin, Fadhilah; Rahim, Rahela Abdul

2015-12-01

Markov Chain has been introduced since the 1913 for the purpose of studying the flow of data for a consecutive number of years of the data and also forecasting. The important feature in Markov Chain is obtaining the accurate Transition Probability Matrix (TPM). However to obtain the suitable TPM is hard especially in involving long-term modeling due to unavailability of data. This paper aims to enhance the classical Markov Chain by introducing Exponential Smoothing technique in developing the appropriate TPM.

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

The generalization ability of online SVM classification based on Markov sampling.

PubMed

Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

2015-03-01

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

Markovian Search Games in Heterogeneous Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

2009-01-01

We consider how to search for a mobile evader in a large heterogeneous region when sensors are used for detection. Sensors are modeled using probability of detection. Due to environmental effects, this probability will not be constant over the entire region. We map this problem to a graph search problem and, even though deterministic graph search is NP-complete, we derive a tractable, optimal, probabilistic search strategy. We do this by defining the problem as a differential game played on a Markov chain. We prove that this strategy is optimal in the sense of Nash. Simulations of an example problem illustratemore » our approach and verify our claims.« less

Effect of differential speed rolling on the texture evolution of Mg-4Zn-1Gd alloy

NASA Astrophysics Data System (ADS)

Shim, Myeong-Shik; Suh, Byeong-Chan; Kim, Jae H.; Kim, Nack J.

2015-05-01

The microstructural and texture evolution during differential speed rolling process of Mg 4Zn-1Gd (wt%) alloy have been investigated by means of electron backscatter diffraction observation and texture analysis. The angular distribution of basal poles are inclined about 10° from the normal direction towards the rolling direction and the maximum intensities of basal poles are decreased, compared to the conventional rolling process. Such an inclination of angular distribution of basal poles can be induced by the operation of shear stress along the rolling direction, as much as one quarter of tensile stress along the RD and one quarter of compressive stress along the ND. When the reduction ratios in differential speed rolling increase, there is no difference in texture evolution although there is a significant change in activated twinning systems. In addition, the engineering stresses after differential speed rolling are also similar to that after conventional rolling process, while ductility and stretch formability in the former are worse than those in the latter.

Estimation of sojourn time in chronic disease screening without data on interval cases.

PubMed

Chen, T H; Kuo, H S; Yen, M F; Lai, M S; Tabar, L; Duffy, S W

2000-03-01

Estimation of the sojourn time on the preclinical detectable period in disease screening or transition rates for the natural history of chronic disease usually rely on interval cases (diagnosed between screens). However, to ascertain such cases might be difficult in developing countries due to incomplete registration systems and difficulties in follow-up. To overcome this problem, we propose three Markov models to estimate parameters without using interval cases. A three-state Markov model, a five-state Markov model related to regional lymph node spread, and a five-state Markov model pertaining to tumor size are applied to data on breast cancer screening in female relatives of breast cancer cases in Taiwan. Results based on a three-state Markov model give mean sojourn time (MST) 1.90 (95% CI: 1.18-4.86) years for this high-risk group. Validation of these models on the basis of data on breast cancer screening in the age groups 50-59 and 60-69 years from the Swedish Two-County Trial shows the estimates from a three-state Markov model that does not use interval cases are very close to those from previous Markov models taking interval cancers into account. For the five-state Markov model, a reparameterized procedure using auxiliary information on clinically detected cancers is performed to estimate relevant parameters. A good fit of internal and external validation demonstrates the feasibility of using these models to estimate parameters that have previously required interval cancers. This method can be applied to other screening data in which there are no data on interval cases.

Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

NASA Astrophysics Data System (ADS)

Nickelsen, Daniel

2017-07-01

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

Sensory trait variation in an echolocating bat suggests roles for both selection and plasticity

PubMed Central

2014-01-01

Background Across heterogeneous environments selection and gene flow interact to influence the rate and extent of adaptive trait evolution. This complex relationship is further influenced by the rarely considered role of phenotypic plasticity in the evolution of adaptive population variation. Plasticity can be adaptive if it promotes colonization and survival in novel environments and in doing so may increase the potential for future population differentiation via selection. Gene flow between selectively divergent environments may favour the evolution of phenotypic plasticity or conversely, plasticity itself may promote gene flow, leading to a pattern of trait differentiation in the presence of gene flow. Variation in sensory traits is particularly informative in testing the role of environment in trait and population differentiation. Here we test the hypothesis of ‘adaptive differentiation with minimal gene flow’ in resting echolocation frequencies (RF) of Cape horseshoe bats (Rhinolophus capensis) across a gradient of increasingly cluttered habitats. Results Our analysis reveals a geographically structured pattern of increasing RF from open to highly cluttered habitats in R. capensis; however genetic drift appears to be a minor player in the processes influencing this pattern. Although Bayesian analysis of population structure uncovered a number of spatially defined mitochondrial groups and coalescent methods revealed regional-scale gene flow, phylogenetic analysis of mitochondrial sequences did not correlate with RF differentiation. Instead, habitat discontinuities between biomes, and not genetic and geographic distances, best explained echolocation variation in this species. We argue that both selection for increased detection distance in relatively less cluttered habitats and adaptive phenotypic plasticity may have influenced the evolution of matched echolocation frequencies and habitats across different populations. Conclusions Our study reveals significant sensory trait differentiation in the presence of historical gene flow and suggests roles for both selection and plasticity in the evolution of echolocation variation in R. capensis. These results highlight the importance of population level analyses to i) illuminate the subtle interplay between selection, plasticity and gene flow in the evolution of adaptive traits and ii) demonstrate that evolutionary processes may act simultaneously and that their relative influence may vary across different environments. PMID:24674227

Sensory trait variation in an echolocating bat suggests roles for both selection and plasticity.

PubMed

Odendaal, Lizelle J; Jacobs, David S; Bishop, Jacqueline M

2014-03-27

Across heterogeneous environments selection and gene flow interact to influence the rate and extent of adaptive trait evolution. This complex relationship is further influenced by the rarely considered role of phenotypic plasticity in the evolution of adaptive population variation. Plasticity can be adaptive if it promotes colonization and survival in novel environments and in doing so may increase the potential for future population differentiation via selection. Gene flow between selectively divergent environments may favour the evolution of phenotypic plasticity or conversely, plasticity itself may promote gene flow, leading to a pattern of trait differentiation in the presence of gene flow. Variation in sensory traits is particularly informative in testing the role of environment in trait and population differentiation. Here we test the hypothesis of 'adaptive differentiation with minimal gene flow' in resting echolocation frequencies (RF) of Cape horseshoe bats (Rhinolophus capensis) across a gradient of increasingly cluttered habitats. Our analysis reveals a geographically structured pattern of increasing RF from open to highly cluttered habitats in R. capensis; however genetic drift appears to be a minor player in the processes influencing this pattern. Although Bayesian analysis of population structure uncovered a number of spatially defined mitochondrial groups and coalescent methods revealed regional-scale gene flow, phylogenetic analysis of mitochondrial sequences did not correlate with RF differentiation. Instead, habitat discontinuities between biomes, and not genetic and geographic distances, best explained echolocation variation in this species. We argue that both selection for increased detection distance in relatively less cluttered habitats and adaptive phenotypic plasticity may have influenced the evolution of matched echolocation frequencies and habitats across different populations. Our study reveals significant sensory trait differentiation in the presence of historical gene flow and suggests roles for both selection and plasticity in the evolution of echolocation variation in R. capensis. These results highlight the importance of population level analyses to i) illuminate the subtle interplay between selection, plasticity and gene flow in the evolution of adaptive traits and ii) demonstrate that evolutionary processes may act simultaneously and that their relative influence may vary across different environments.

Observation uncertainty in reversible Markov chains.

PubMed

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

Open Markov Processes and Reaction Networks

NASA Astrophysics Data System (ADS)

Swistock Pollard, Blake Stephen

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Observability of satellite launcher navigation with INS, GPS, attitude sensors and reference trajectory

NASA Astrophysics Data System (ADS)

Beaudoin, Yanick; Desbiens, André; Gagnon, Eric; Landry, René

2018-01-01

The navigation system of a satellite launcher is of paramount importance. In order to correct the trajectory of the launcher, the position, velocity and attitude must be known with the best possible precision. In this paper, the observability of four navigation solutions is investigated. The first one is the INS/GPS couple. Then, attitude reference sensors, such as magnetometers, are added to the INS/GPS solution. The authors have already demonstrated that the reference trajectory could be used to improve the navigation performance. This approach is added to the two previously mentioned navigation systems. For each navigation solution, the observability is analyzed with different sensor error models. First, sensor biases are neglected. Then, sensor biases are modelled as random walks and as first order Markov processes. The observability is tested with the rank and condition number of the observability matrix, the time evolution of the covariance matrix and sensitivity to measurement outlier tests. The covariance matrix is exploited to evaluate the correlation between states in order to detect structural unobservability problems. Finally, when an unobservable subspace is detected, the result is verified with theoretical analysis of the navigation equations. The results show that evaluating only the observability of a model does not guarantee the ability of the aiding sensors to correct the INS estimates within the mission time. The analysis of the covariance matrix time evolution could be a powerful tool to detect this situation, however in some cases, the problem is only revealed with a sensitivity to measurement outlier test. None of the tested solutions provide GPS position bias observability. For the considered mission, the modelling of the sensor biases as random walks or Markov processes gives equivalent results. Relying on the reference trajectory can improve the precision of the roll estimates. But, in the context of a satellite launcher, the roll estimation error and gyroscope bias are only observable if attitude reference sensors are present.

A Hidden Markov Model Approach for Simultaneously Estimating Local Ancestry and Admixture Time Using Next Generation Sequence Data in Samples of Arbitrary Ploidy

PubMed Central

Nielsen, Rasmus

2017-01-01

Admixture—the mixing of genomes from divergent populations—is increasingly appreciated as a central process in evolution. To characterize and quantify patterns of admixture across the genome, a number of methods have been developed for local ancestry inference. However, existing approaches have a number of shortcomings. First, all local ancestry inference methods require some prior assumption about the expected ancestry tract lengths. Second, existing methods generally require genotypes, which is not feasible to obtain for many next-generation sequencing projects. Third, many methods assume samples are diploid, however a wide variety of sequencing applications will fail to meet this assumption. To address these issues, we introduce a novel hidden Markov model for estimating local ancestry that models the read pileup data, rather than genotypes, is generalized to arbitrary ploidy, and can estimate the time since admixture during local ancestry inference. We demonstrate that our method can simultaneously estimate the time since admixture and local ancestry with good accuracy, and that it performs well on samples of high ploidy—i.e. 100 or more chromosomes. As this method is very general, we expect it will be useful for local ancestry inference in a wider variety of populations than what previously has been possible. We then applied our method to pooled sequencing data derived from populations of Drosophila melanogaster on an ancestry cline on the east coast of North America. We find that regions of local recombination rates are negatively correlated with the proportion of African ancestry, suggesting that selection against foreign ancestry is the least efficient in low recombination regions. Finally we show that clinal outlier loci are enriched for genes associated with gene regulatory functions, consistent with a role of regulatory evolution in ecological adaptation of admixed D. melanogaster populations. Our results illustrate the potential of local ancestry inference for elucidating fundamental evolutionary processes. PMID:28045893

Markov models of genome segmentation

NASA Astrophysics Data System (ADS)

Thakur, Vivek; Azad, Rajeev K.; Ramaswamy, Ram

2007-01-01

We introduce Markov models for segmentation of symbolic sequences, extending a segmentation procedure based on the Jensen-Shannon divergence that has been introduced earlier. Higher-order Markov models are more sensitive to the details of local patterns and in application to genome analysis, this makes it possible to segment a sequence at positions that are biologically meaningful. We show the advantage of higher-order Markov-model-based segmentation procedures in detecting compositional inhomogeneity in chimeric DNA sequences constructed from genomes of diverse species, and in application to the E. coli K12 genome, boundaries of genomic islands, cryptic prophages, and horizontally acquired regions are accurately identified.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Adaptive array technique for differential-phase reflectometry in QUEST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idei, H., E-mail: idei@triam.kyushu-u.ac.jp; Hanada, K.; Zushi, H.

2014-11-15

A Phased Array Antenna (PAA) was considered as launching and receiving antennae in reflectometry to attain good directivity in its applied microwave range. A well-focused beam was obtained in a launching antenna application, and differential-phase evolution was properly measured by using a metal reflector plate in the proof-of-principle experiment at low power test facilities. Differential-phase evolution was also evaluated by using the PAA in the Q-shu University Experiment with Steady State Spherical Tokamak (QUEST). A beam-forming technique was applied in receiving phased-array antenna measurements. In the QUEST device that should be considered as a large oversized cavity, standing wave effectmore » was significantly observed with perturbed phase evolution. A new approach using derivative of measured field on propagating wavenumber was proposed to eliminate the standing wave effect.« less

Optimal choice of word length when comparing two Markov sequences using a χ 2-statistic.

PubMed

Bai, Xin; Tang, Kujin; Ren, Jie; Waterman, Michael; Sun, Fengzhu

2017-10-03

Alignment-free sequence comparison using counts of word patterns (grams, k-tuples) has become an active research topic due to the large amount of sequence data from the new sequencing technologies. Genome sequences are frequently modelled by Markov chains and the likelihood ratio test or the corresponding approximate χ 2 -statistic has been suggested to compare two sequences. However, it is not known how to best choose the word length k in such studies. We develop an optimal strategy to choose k by maximizing the statistical power of detecting differences between two sequences. Let the orders of the Markov chains for the two sequences be r 1 and r 2 , respectively. We show through both simulations and theoretical studies that the optimal k= max(r 1 ,r 2 )+1 for both long sequences and next generation sequencing (NGS) read data. The orders of the Markov chains may be unknown and several methods have been developed to estimate the orders of Markov chains based on both long sequences and NGS reads. We study the power loss of the statistics when the estimated orders are used. It is shown that the power loss is minimal for some of the estimators of the orders of Markov chains. Our studies provide guidelines on choosing the optimal word length for the comparison of Markov sequences.

Classification of Multiple Seizure-Like States in Three Different Rodent Models of Epileptogenesis.

PubMed

Guirgis, Mirna; Serletis, Demitre; Zhang, Jane; Florez, Carlos; Dian, Joshua A; Carlen, Peter L; Bardakjian, Berj L

2014-01-01

Epilepsy is a dynamical disease and its effects are evident in over fifty million people worldwide. This study focused on objective classification of the multiple states involved in the brain's epileptiform activity. Four datasets from three different rodent hippocampal preparations were explored, wherein seizure-like-events (SLE) were induced by the perfusion of a low - Mg(2+) /high-K(+) solution or 4-Aminopyridine. Local field potentials were recorded from CA3 pyramidal neurons and interneurons and modeled as Markov processes. Specifically, hidden Markov models (HMM) were used to determine the nature of the states present. Properties of the Hilbert transform were used to construct the feature spaces for HMM training. By sequentially applying the HMM training algorithm, multiple states were identified both in episodes of SLE and nonSLE activity. Specifically, preSLE and postSLE states were differentiated and multiple inner SLE states were identified. This was accomplished using features extracted from the lower frequencies (1-4 Hz, 4-8 Hz) alongside those of both the low- (40-100 Hz) and high-gamma (100-200 Hz) of the recorded electrical activity. The learning paradigm of this HMM-based system eliminates the inherent bias associated with other learning algorithms that depend on predetermined state segmentation and renders it an appropriate candidate for SLE classification.

Fast-slow asymptotics for a Markov chain model of fast sodium current

NASA Astrophysics Data System (ADS)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Evolution of plant conducting cells: perspectives from key regulators of vascular cell differentiation.

PubMed

Ohtani, Misato; Akiyoshi, Nobuhiro; Takenaka, Yuto; Sano, Ryosuke; Demura, Taku

2017-01-01

One crucial problem that plants faced during their evolution, particularly during the transition to growth on land, was how to transport water, nutrients, metabolites, and small signaling molecules within a large, multicellular body. As a solution to this problem, land plants developed specific tissues for conducting molecules, called water-conducting cells (WCCs) and food-conducting cells (FCCs). The well-developed WCCs and FCCs in extant plants are the tracheary elements and sieve elements, respectively, which are found in vascular plants. Recent molecular genetic studies revealed that transcriptional networks regulate the differentiation of tracheary and sieve elements, and that the networks governing WCC differentiation are largely conserved among land plant species. In this review, we discuss the molecular evolution of plant conducting cells. By focusing on the evolution of the key transcription factors that regulate vascular cell differentiation, the NAC transcription factor VASCULAR-RELATED NAC-DOMAIN for WCCs and the MYB-coiled-coil (CC)-type transcription factor ALTERED PHLOEM DEVELOPMENT for sieve elements, we describe how land plants evolved molecular systems to produce the specialized cells that function as WCCs and FCCs. © The Author 2016. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved. For permissions, please email: journals.permissions@oup.com.

Pulse retrieval algorithm for interferometric frequency-resolved optical gating based on differential evolution.

PubMed

Hyyti, Janne; Escoto, Esmerando; Steinmeyer, Günter

2017-10-01

A novel algorithm for the ultrashort laser pulse characterization method of interferometric frequency-resolved optical gating (iFROG) is presented. Based on a genetic method, namely, differential evolution, the algorithm can exploit all available information of an iFROG measurement to retrieve the complex electric field of a pulse. The retrieval is subjected to a series of numerical tests to prove the robustness of the algorithm against experimental artifacts and noise. These tests show that the integrated error-correction mechanisms of the iFROG method can be successfully used to remove the effect from timing errors and spectrally varying efficiency in the detection. Moreover, the accuracy and noise resilience of the new algorithm are shown to outperform retrieval based on the generalized projections algorithm, which is widely used as the standard method in FROG retrieval. The differential evolution algorithm is further validated with experimental data, measured with unamplified three-cycle pulses from a mode-locked Ti:sapphire laser. Additionally introducing group delay dispersion in the beam path, the retrieval results show excellent agreement with independent measurements with a commercial pulse measurement device based on spectral phase interferometry for direct electric-field retrieval. Further experimental tests with strongly attenuated pulses indicate resilience of differential-evolution-based retrieval against massive measurement noise.

Indexed semi-Markov process for wind speed modeling.

NASA Astrophysics Data System (ADS)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Renewable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution, Renewable Energy 28 (2003) 1787-1802.

Modelisation de l'historique d'operation de groupes turbine-alternateur

NASA Astrophysics Data System (ADS)

Szczota, Mickael

Because of their ageing fleet, the utility managers are increasingly in needs of tools that can help them to plan efficiently maintenance operations. Hydro-Quebec started a project that aim to foresee the degradation of their hydroelectric runner, and use that information to classify the generating unit. That classification will help to know which generating unit is more at risk to undergo a major failure. Cracks linked to the fatigue phenomenon are a predominant degradation mode and the loading sequences applied to the runner is a parameter impacting the crack growth. So, the aim of this memoir is to create a generator able to generate synthetic loading sequences that are statistically equivalent to the observed history. Those simulated sequences will be used as input in a life assessment model. At first, we describe how the generating units are operated by Hydro-Quebec and analyse the available data, the analysis shows that the data are non-stationnary. Then, we review modelisation and validation methods. In the following chapter a particular attention is given to a precise description of the validation and comparison procedure. Then, we present the comparison of three kind of model : Discrete Time Markov Chains, Discrete Time Semi-Markov Chains and the Moving Block Bootstrap. For the first two models, we describe how to take account for the non-stationnarity. Finally, we show that the Markov Chain is not adapted for our case, and that the Semi-Markov chains are better when they include the non-stationnarity. The final choice between Semi-Markov Chains and the Moving Block Bootstrap depends of the user. But, with a long term vision we recommend the use of Semi-Markov chains for their flexibility. Keywords: Stochastic models, Models validation, Reliability, Semi-Markov Chains, Markov Chains, Bootstrap

Saccade selection when reward probability is dynamically manipulated using Markov chains

PubMed Central

Lovejoy, Lee P.; Krauzlis, Richard J.

2012-01-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200–600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection. PMID:18330552

Saccade selection when reward probability is dynamically manipulated using Markov chains.

PubMed

Nummela, Samuel U; Lovejoy, Lee P; Krauzlis, Richard J

2008-05-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200-600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection.

Classification of customer lifetime value models using Markov chain

NASA Astrophysics Data System (ADS)

Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi

2017-10-01

A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

Metrics for Labeled Markov Systems

NASA Technical Reports Server (NTRS)

Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash

1999-01-01

Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

Comparative Sex Chromosome Genomics in Snakes: Differentiation, Evolutionary Strata, and Lack of Global Dosage Compensation

PubMed Central

Zektser, Yulia; Mahajan, Shivani; Bachtrog, Doris

2013-01-01

Snakes exhibit genetic sex determination, with female heterogametic sex chromosomes (ZZ males, ZW females). Extensive cytogenetic work has suggested that the level of sex chromosome heteromorphism varies among species, with Boidae having entirely homomorphic sex chromosomes, Viperidae having completely heteromorphic sex chromosomes, and Colubridae showing partial differentiation. Here, we take a genomic approach to compare sex chromosome differentiation in these three snake families. We identify homomorphic sex chromosomes in boas (Boidae), but completely heteromorphic sex chromosomes in both garter snakes (Colubridae) and pygmy rattlesnake (Viperidae). Detection of W-linked gametologs enables us to establish the presence of evolutionary strata on garter and pygmy rattlesnake sex chromosomes where recombination was abolished at different time points. Sequence analysis shows that all strata are shared between pygmy rattlesnake and garter snake, i.e., recombination was abolished between the sex chromosomes before the two lineages diverged. The sex-biased transmission of the Z and its hemizygosity in females can impact patterns of molecular evolution, and we show that rates of evolution for Z-linked genes are increased relative to their pseudoautosomal homologs, both at synonymous and amino acid sites (even after controlling for mutational biases). This demonstrates that mutation rates are male-biased in snakes (male-driven evolution), but also supports faster-Z evolution due to differential selective effects on the Z. Finally, we perform a transcriptome analysis in boa and pygmy rattlesnake to establish baseline levels of sex-biased expression in homomorphic sex chromosomes, and show that heteromorphic ZW chromosomes in rattlesnakes lack chromosome-wide dosage compensation. Our study provides the first full scale overview of the evolution of snake sex chromosomes at the genomic level, thus greatly expanding our knowledge of reptilian and vertebrate sex chromosomes evolution. PMID:24015111

Identifiability of tree-child phylogenetic networks under a probabilistic recombination-mutation model of evolution.

PubMed

Francis, Andrew; Moulton, Vincent

2018-06-07

Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are quite limited in terms of the complexity of the networks that are considered. In this paper, by introducing an alternative probabilistic model for evolution along a network that is based on some ground-breaking work by Thatte for pedigrees, we are able to obtain an identifiability result for a much larger class of phylogenetic networks (essentially the class of so-called tree-child networks). To prove our main theorem, we derive some new results for identifying tree-child networks combinatorially, and then adapt some techniques developed by Thatte for pedigrees to show that our combinatorial results imply identifiability in the probabilistic setting. We hope that the introduction of our new model for networks could lead to new approaches to reliably construct phylogenetic networks. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Brassica oleracea genome reveals the asymmetrical evolution of polyploid genomes

PubMed Central

Liu, Shengyi; Liu, Yumei; Yang, Xinhua; Tong, Chaobo; Edwards, David; Parkin, Isobel A. P.; Zhao, Meixia; Ma, Jianxin; Yu, Jingyin; Huang, Shunmou; Wang, Xiyin; Wang, Junyi; Lu, Kun; Fang, Zhiyuan; Bancroft, Ian; Yang, Tae-Jin; Hu, Qiong; Wang, Xinfa; Yue, Zhen; Li, Haojie; Yang, Linfeng; Wu, Jian; Zhou, Qing; Wang, Wanxin; King, Graham J; Pires, J. Chris; Lu, Changxin; Wu, Zhangyan; Sampath, Perumal; Wang, Zhuo; Guo, Hui; Pan, Shengkai; Yang, Limei; Min, Jiumeng; Zhang, Dong; Jin, Dianchuan; Li, Wanshun; Belcram, Harry; Tu, Jinxing; Guan, Mei; Qi, Cunkou; Du, Dezhi; Li, Jiana; Jiang, Liangcai; Batley, Jacqueline; Sharpe, Andrew G; Park, Beom-Seok; Ruperao, Pradeep; Cheng, Feng; Waminal, Nomar Espinosa; Huang, Yin; Dong, Caihua; Wang, Li; Li, Jingping; Hu, Zhiyong; Zhuang, Mu; Huang, Yi; Huang, Junyan; Shi, Jiaqin; Mei, Desheng; Liu, Jing; Lee, Tae-Ho; Wang, Jinpeng; Jin, Huizhe; Li, Zaiyun; Li, Xun; Zhang, Jiefu; Xiao, Lu; Zhou, Yongming; Liu, Zhongsong; Liu, Xuequn; Qin, Rui; Tang, Xu; Liu, Wenbin; Wang, Yupeng; Zhang, Yangyong; Lee, Jonghoon; Kim, Hyun Hee; Denoeud, France; Xu, Xun; Liang, Xinming; Hua, Wei; Wang, Xiaowu; Wang, Jun; Chalhoub, Boulos; Paterson, Andrew H

2014-01-01

Polyploidization has provided much genetic variation for plant adaptive evolution, but the mechanisms by which the molecular evolution of polyploid genomes establishes genetic architecture underlying species differentiation are unclear. Brassica is an ideal model to increase knowledge of polyploid evolution. Here we describe a draft genome sequence of Brassica oleracea, comparing it with that of its sister species B. rapa to reveal numerous chromosome rearrangements and asymmetrical gene loss in duplicated genomic blocks, asymmetrical amplification of transposable elements, differential gene co-retention for specific pathways and variation in gene expression, including alternative splicing, among a large number of paralogous and orthologous genes. Genes related to the production of anticancer phytochemicals and morphological variations illustrate consequences of genome duplication and gene divergence, imparting biochemical and morphological variation to B. oleracea. This study provides insights into Brassica genome evolution and will underpin research into the many important crops in this genus. PMID:24852848

Optimal Control for Stochastic Delay Evolution Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Analyzing and modeling the kinetics of amyloid beta pores associated with Alzheimer’s disease pathology

DOE PAGES

Ullah, Ghanim; Demuro, Angelo; Parker, Ian; ...

2015-09-08

Amyloid beta (Aβ) oligomers associated with Alzheimer’s disease (AD) form Ca 2+-permeable plasma membrane pores, leading to a disruption of the otherwise well-controlled intracellular calcium (Ca 2+) homeostasis. The resultant up-regulation of intracellular Ca 2+ concentration has detrimental implications for memory formation and cell survival. The gating kinetics and Ca 2+ permeability of Aβ pores are not well understood. We have used computational modeling in conjunction with the ability of optical patch-clamping for massively parallel imaging of Ca 2+ flux through thousands of pores in the cell membrane of Xenopus oocytes to elucidate the kinetic properties of Aβ pores. Themore » fluorescence time-series data from individual pores were idealized and used to develop data-driven Markov chain models for the kinetics of the Aβ pore at different stages of its evolution. Our study provides the first demonstration of developing Markov chain models for ion channel gating that are driven by optical-patch clamp data with the advantage of experiments being performed under close to physiological conditions. As a result, we demonstrate the up-regulation of gating of various Ca 2+ release channels due to Aβ pores and show that the extent and spatial range of such up-regulation increases as Aβ pores with low open probability and Ca 2+ permeability transition into those with high open probability and Ca 2+ permeability.« less

Bayesian analysis of biogeography when the number of areas is large.

PubMed

Landis, Michael J; Matzke, Nicholas J; Moore, Brian R; Huelsenbeck, John P

2013-11-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a "data-augmentation" approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

NASA Astrophysics Data System (ADS)

Han, Feng; Zheng, Yi

2018-06-01

Significant Input uncertainty is a major source of error in watershed water quality (WWQ) modeling. It remains challenging to address the input uncertainty in a rigorous Bayesian framework. This study develops the Bayesian Analysis of Input and Parametric Uncertainties (BAIPU), an approach for the joint analysis of input and parametric uncertainties through a tight coupling of Markov Chain Monte Carlo (MCMC) analysis and Bayesian Model Averaging (BMA). The formal likelihood function for this approach is derived considering a lag-1 autocorrelated, heteroscedastic, and Skew Exponential Power (SEP) distributed error model. A series of numerical experiments were performed based on a synthetic nitrate pollution case and on a real study case in the Newport Bay Watershed, California. The Soil and Water Assessment Tool (SWAT) and Differential Evolution Adaptive Metropolis (DREAM(ZS)) were used as the representative WWQ model and MCMC algorithm, respectively. The major findings include the following: (1) the BAIPU can be implemented and used to appropriately identify the uncertain parameters and characterize the predictive uncertainty; (2) the compensation effect between the input and parametric uncertainties can seriously mislead the modeling based management decisions, if the input uncertainty is not explicitly accounted for; (3) the BAIPU accounts for the interaction between the input and parametric uncertainties and therefore provides more accurate calibration and uncertainty results than a sequential analysis of the uncertainties; and (4) the BAIPU quantifies the credibility of different input assumptions on a statistical basis and can be implemented as an effective inverse modeling approach to the joint inference of parameters and inputs.

A computer program for uncertainty analysis integrating regression and Bayesian methods

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Hill, Mary C.; Poeter, Eileen P.; Curtis, Gary

2014-01-01

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity.

PubMed

Samdin, S Balqis; Ting, Chee-Ming; Ombao, Hernando; Salleh, Sh-Hussain

2017-04-01

This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions. To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages. The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods. The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality. The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

OBSERVATIONAL SIGNATURES OF CORONAL LOOP HEATING AND COOLING DRIVEN BY FOOTPOINT SHUFFLING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dahlburg, R. B.; Taylor, B. D.; Einaudi, G.

The evolution of a coronal loop is studied by means of numerical simulations of the fully compressible three-dimensional magnetohydrodynamic equations using the HYPERION code. The footpoints of the loop magnetic field are advected by random motions. As a consequence, the magnetic field in the loop is energized and develops turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets: energy is deposited at small scales where heating occurs. Dissipation is nonuniformly distributed so that only a fraction of the coronal mass and volume gets heated at any time. Temperature and density are highly structured at scalesmore » that, in the solar corona, remain observationally unresolved: the plasma of our simulated loop is multithermal, where highly dynamical hotter and cooler plasma strands are scattered throughout the loop at sub-observational scales. Numerical simulations of coronal loops of 50,000 km length and axial magnetic field intensities ranging from 0.01 to 0.04 T are presented. To connect these simulations to observations, we use the computed number densities and temperatures to synthesize the intensities expected in emission lines typically observed with the Extreme Ultraviolet Imaging Spectrometer on Hinode. These intensities are used to compute differential emission measure distributions using the Monte Carlo Markov Chain code, which are very similar to those derived from observations of solar active regions. We conclude that coronal heating is found to be strongly intermittent in space and time, with only small portions of the coronal loop being heated: in fact, at any given time, most of the corona is cooling down.« less

A Spitzer five-band analysis of the Jupiter-sized planet TrES-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cubillos, Patricio; Harrington, Joseph; Foster, Andrew S. D.

2014-12-10

With an equilibrium temperature of 1200 K, TrES-1 is one of the coolest hot Jupiters observed by Spitzer. It was also the first planet discovered by any transit survey and one of the first exoplanets from which thermal emission was directly observed. We analyzed all Spitzer eclipse and transit data for TrES-1 and obtained its eclipse depths and brightness temperatures in the 3.6 μm (0.083% ± 0.024%, 1270 ± 110 K), 4.5 μm (0.094% ± 0.024%, 1126 ± 90 K), 5.8 μm (0.162% ± 0.042%, 1205 ± 130 K), 8.0 μm (0.213% ± 0.042%, 1190 ± 130 K), and 16more » μm (0.33% ± 0.12%, 1270 ± 310 K) bands. The eclipse depths can be explained, within 1σ errors, by a standard atmospheric model with solar abundance composition in chemical equilibrium, with or without a thermal inversion. The combined analysis of the transit, eclipse, and radial-velocity ephemerides gives an eccentricity of e=0.033{sub −0.031}{sup +0.015}, consistent with a circular orbit. Since TrES-1's eclipses have low signal-to-noise ratios, we implemented optimal photometry and differential-evolution Markov Chain Monte Carlo (MCMC) algorithms in our Photometry for Orbits, Eclipses, and Transits pipeline. Benefits include higher photometric precision and ∼10 times faster MCMC convergence, with better exploration of the phase space and no manual parameter tuning.« less

Educational Aspirations: Markov and Poisson Models. Rural Industrial Development Project Working Paper Number 14, August 1971.

ERIC Educational Resources Information Center

Kayser, Brian D.

The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…

The spectral method and the central limit theorem for general Markov chains

NASA Astrophysics Data System (ADS)

Nagaev, S. V.

2017-12-01

We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

SMERFS: Stochastic Markov Evaluation of Random Fields on the Sphere

NASA Astrophysics Data System (ADS)

Creasey, Peter; Lang, Annika

2018-04-01

SMERFS (Stochastic Markov Evaluation of Random Fields on the Sphere) creates large realizations of random fields on the sphere. It uses a fast algorithm based on Markov properties and fast Fourier Transforms in 1d that generates samples on an n X n grid in O(n2 log n) and efficiently derives the necessary conditional covariance matrices.

Markov chains and semi-Markov models in time-to-event analysis.

PubMed

Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J

2013-10-25

A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.

Markov chains and semi-Markov models in time-to-event analysis

PubMed Central

Abner, Erin L.; Charnigo, Richard J.; Kryscio, Richard J.

2014-01-01

A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields. PMID:24818062

Detecting critical state before phase transition of complex systems by hidden Markov model

NASA Astrophysics Data System (ADS)

Liu, Rui; Chen, Pei; Li, Yongjun; Chen, Luonan

Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e., before-transition state, pre-transition state, and after-transition state, which can be considered as three different Markov processes. Thus, based on this dynamical feature, we present a novel computational method, i.e., hidden Markov model (HMM), to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e., the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin, and HCV-induced dysplasia and hepatocellular carcinoma.

Dynamic Routing of Aircraft in the Presence of Adverse Weather Using a POMDP Framework

NASA Technical Reports Server (NTRS)

Balaban, Edward; Roychoudhury, Indranil; Spirkovska, Lilly; Sankararaman, Shankar; Kulkarni, Chetan; Arnon, Tomer

2017-01-01

Each year weather-related airline delays result in hundreds of millions of dollars in additional fuel burn, maintenance, and lost revenue, not to mention passenger inconvenience. The current approaches for aircraft route planning in the presence of adverse weather still mainly rely on deterministic methods. In contrast, this work aims to deal with the problem using a Partially Observable Markov Decision Processes (POMDPs) framework, which allows for reasoning over uncertainty (including uncertainty in weather evolution over time) and results in solutions that are more robust to disruptions. The POMDP-based decision support system is demonstrated on several scenarios involving convective weather cells and is benchmarked against a deterministic planning system with functionality similar to those currently in use or under development.

Aspects of Complexity in Sleep Analysis

NASA Astrophysics Data System (ADS)

Leitão, José M. N.; Da Rosa, Agostinho C.

The paper presents a selection of sleep analysis problems where some aspects and concepts of complexity come about. Emphasis is given to the electroencephalogram (EEG) as the most important sleep related variable. The conception of the EEG as a message to be deciphered stresses the importance of the communication and information theories in this field. An optimal detector of K complexes and vertex sharp waves based on a stochastic model of sleep EEG is considered. Besides detecting, the algorithm is also able to follow the evolution of the basic ongoing activity. It is shown that both the ostructure and microstructure of sleep can be described in terms of symbols and interpreted as sentences of a language. Syntactic models and Markov chain representations play in this context an important role.

Distribution of chirality in the quantum walk: Markov process and entanglement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romanelli, Alejandro

The asymptotic behavior of the quantum walk on the line is investigated, focusing on the probability distribution of chirality independently of position. It is shown analytically that this distribution has a longtime limit that is stationary and depends on the initial conditions. This result is unexpected in the context of the unitary evolution of the quantum walk as it is usually linked to a Markovian process. The asymptotic value of the entanglement between the coin and the position is determined by the chirality distribution. For given asymptotic values of both the entanglement and the chirality distribution, it is possible tomore » find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions.« less

Multiscale Modelling and Analysis of Collective Decision Making in Swarm Robotics

PubMed Central

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable. PMID:25369026

Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

PubMed

Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

2010-09-01

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.

Vesta Evolution from Surface Mineralogy: Mafic and Ultramafic Mineral Distribution

NASA Technical Reports Server (NTRS)

DeSanctis, M. C.; Ammannito, E.; Palomba, E.; Longobardo, A.; Mittlefehldt, D. W.; McSween, H. Y; Marchi, S.; Capria, M. T.; Capaccioni, F.; Frigeri, A.;

Internal constitution and evolution of the moon.

NASA Technical Reports Server (NTRS)

Solomon, S. C.; Toksoz, M. N.

1973-01-01

The composition, structure and evolution of the moon's interior are narrowly constrained by a large assortment of physical and chemical data. Models of the thermal evolution of the moon that fit the chronology of igneous activity on the lunar surface, the stress history of the lunar lithosphere implied by the presence of mascons, and the surface concentrations of radioactive elements, involve extensive differentiation early in lunar history. This differentiation may be the result of rapid accretion and large-scale melting or of primary chemical layering during accretion; differences in present-day temperatures for these two possibilities are significant only in the inner 1000 km of the moon and may not be resolvable.

Population genomics of the killer whale indicates ecotype evolution in sympatry involving both selection and drift.

PubMed

Moura, Andre E; Kenny, John G; Chaudhuri, Roy; Hughes, Margaret A; J Welch, Andreanna; Reisinger, Ryan R; de Bruyn, P J Nico; Dahlheim, Marilyn E; Hall, Neil; Hoelzel, A Rus

2014-11-01

The evolution of diversity in the marine ecosystem is poorly understood, given the relatively high potential for connectivity, especially for highly mobile species such as whales and dolphins. The killer whale (Orcinus orca) has a worldwide distribution, and individual social groups travel over a wide geographic range. Even so, regional populations have been shown to be genetically differentiated, including among different foraging specialists (ecotypes) in sympatry. Given the strong matrifocal social structure of this species together with strong resource specializations, understanding the process of differentiation will require an understanding of the relative importance of both genetic drift and local adaptation. Here we provide a high-resolution analysis based on nuclear single-nucleotide polymorphic markers and inference about differentiation at both neutral loci and those potentially under selection. We find that all population comparisons, within or among foraging ecotypes, show significant differentiation, including populations in parapatry and sympatry. Loci putatively under selection show a different pattern of structure compared to neutral loci and are associated with gene ontology terms reflecting physiologically relevant functions (e.g. related to digestion). The pattern of differentiation for one ecotype in the North Pacific suggests local adaptation and shows some fixed differences among sympatric ecotypes. We suggest that differential habitat use and resource specializations have promoted sufficient isolation to allow differential evolution at neutral and functional loci, but that the process is recent and dependent on both selection and drift. © 2014 The Authors. Molecular Ecology published by John Wiley & Sons Ltd.

Population genomics of the killer whale indicates ecotype evolution in sympatry involving both selection and drift

PubMed Central

Moura, Andre E; Kenny, John G; Chaudhuri, Roy; Hughes, Margaret A; J Welch, Andreanna; Reisinger, Ryan R; de Bruyn, P J Nico; Dahlheim, Marilyn E; Hall, Neil; Hoelzel, A Rus

2014-01-01

The evolution of diversity in the marine ecosystem is poorly understood, given the relatively high potential for connectivity, especially for highly mobile species such as whales and dolphins. The killer whale (Orcinus orca) has a worldwide distribution, and individual social groups travel over a wide geographic range. Even so, regional populations have been shown to be genetically differentiated, including among different foraging specialists (ecotypes) in sympatry. Given the strong matrifocal social structure of this species together with strong resource specializations, understanding the process of differentiation will require an understanding of the relative importance of both genetic drift and local adaptation. Here we provide a high-resolution analysis based on nuclear single-nucleotide polymorphic markers and inference about differentiation at both neutral loci and those potentially under selection. We find that all population comparisons, within or among foraging ecotypes, show significant differentiation, including populations in parapatry and sympatry. Loci putatively under selection show a different pattern of structure compared to neutral loci and are associated with gene ontology terms reflecting physiologically relevant functions (e.g. related to digestion). The pattern of differentiation for one ecotype in the North Pacific suggests local adaptation and shows some fixed differences among sympatric ecotypes. We suggest that differential habitat use and resource specializations have promoted sufficient isolation to allow differential evolution at neutral and functional loci, but that the process is recent and dependent on both selection and drift. PMID:25244680

Multi-decadal evolution of ice/snow covers in the Mont-Blanc massif (France)

NASA Astrophysics Data System (ADS)

Guillet, Grégoire; Ravanel, Ludovic

2017-04-01

Dynamics and evolution of the major glaciers of the Mont-Blanc massif have been vastly studied since the XXth century. Ice/snow covers on steep rock faces as part of the cryosphere however remain poorly studied with only qualitative descriptions existing. The study of ice/snow covers is primordial to further understand permafrost degradation throughout the Mont-Blanc massif and to improve safety and prevention for mountain sports practitioners. This study focuses on quantifying the evolution of ice/snow covers surface during the past century using a specially developed monoplotting tool using Bayesian statistics and Markov Chain Monte Carlo algorithms. Combining digital elevation models and photographs covering a time-span of 110 years, we calculated the ice/snow cover surface for 3 study sites — North faces of the Tour Ronde (3792 m a.s.l.) and the Grandes Jorasses (4208 m a.s.l.) and Triangle du Tacul (3970 m a.s.l.) — and deduced the evolution of their area throughout the XXth century. First results are showing several increase/decrease periods. The first decrease in ice/snow cover surface occurs between the 1940's and the 1950's. It is followed by an increase up to the 1980's. Since then, ice/snow covers show a general decrease in surface which is faster since the 2010's. Furthermore, the gain/loss during the increase/decrease periods varies with the considered ice/snow cover, making it an interesting cryospheric entity of its own.

Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI

PubMed Central

Maccone, Claudio

2017-01-01

The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time. We call b-lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b-lognormal in the time. Next, our “Peak-Locus Theorem” translates cladistics: each species created by evolution is a b-lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called “Geometric Brownian Motion” (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b-lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The “molecular clock” is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) “cubic” evolution: a curve of logarithmic increase. PMID:28383497

Discriminative Learning with Markov Logic Networks

DTIC Science & Technology

2009-10-01

Discriminative Learning with Markov Logic Networks Tuyen N. Huynh Department of Computer Sciences University of Texas at Austin Austin, TX 78712...emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of Texas at Austin,Department of Computer

Repeated evolution of soldier sub-castes suggests parasitism drives social complexity in stingless bees.

PubMed

Grüter, Christoph; Segers, Francisca H I D; Menezes, Cristiano; Vollet-Neto, Ayrton; Falcón, Tiago; von Zuben, Lucas; Bitondi, Márcia M G; Nascimento, Fabio S; Almeida, Eduardo A B

2017-02-23

The differentiation of workers into morphological castes represents an important evolutionary innovation that is thought to improve division of labor in insect societies. Given the potential benefits of task-related worker differentiation, it is puzzling that physical worker castes, such as soldiers, are extremely rare in social bees and absent in wasps. Following the recent discovery of soldiers in a stingless bee, we studied the occurrence of worker differentiation in 28 stingless bee species from Brazil and found that several species have specialized soldiers for colony defence. Our results reveal that worker differentiation evolved repeatedly during the last ~ 25 million years and coincided with the emergence of parasitic robber bees, a major threat to many stingless bee species. Furthermore, our data suggest that these robbers are a driving force behind the evolution of worker differentiation as targets of robber bees are four times more likely to have nest guards of increased size than non-targets. These findings reveal unexpected diversity in the social organization of stingless bees.Although common in ants and termites, worker differentiation into physical castes is rare in social bees and unknown in wasps. Here, Grüter and colleagues find a guard caste in ten species of stingless bees and show that the evolution of the guard caste is associated with parasitization by robber bees.

Master of Puppets: An Animation-by-Demonstration Computer Puppetry Authoring Framework

NASA Astrophysics Data System (ADS)

Cui, Yaoyuan; Mousas, Christos

2018-03-01

This paper presents Master of Puppets (MOP), an animation-by-demonstration framework that allows users to control the motion of virtual characters (puppets) in real time. In the first step, the user is asked to perform the necessary actions that correspond to the character's motions. The user's actions are recorded, and a hidden Markov model is used to learn the temporal profile of the actions. During the runtime of the framework, the user controls the motions of the virtual character based on the specified activities. The advantage of the MOP framework is that it recognizes and follows the progress of the user's actions in real time. Based on the forward algorithm, the method predicts the evolution of the user's actions, which corresponds to the evolution of the character's motion. This method treats characters as puppets that can perform only one motion at a time. This means that combinations of motion segments (motion synthesis), as well as the interpolation of individual motion sequences, are not provided as functionalities. By implementing the framework and presenting several computer puppetry scenarios, its efficiency and flexibility in animating virtual characters is demonstrated.

Formal properties of the probability of fixation: identities, inequalities and approximations.

PubMed

McCandlish, David M; Epstein, Charles L; Plotkin, Joshua B

2015-02-01

The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent results hold for the approximate probability of fixation under the Wright-Fisher process, after an appropriate change of variables). We show that the logarithm of the fixation probability has particularly simple behavior when the selection coefficient is measured as a difference of Malthusian fitnesses, and we exploit this simplicity to derive inequalities and approximations. We also present a comprehensive comparison of both existing and new approximations for the fixation probability, highlighting those approximations that induce a reversible Markov chain when used to describe the dynamics of evolution under weak mutation. To demonstrate the power of these results, we consider the classical problem of determining the total substitution rate across an ensemble of biallelic loci and prove that, at equilibrium, a strict majority of substitutions are due to drift rather than selection. Copyright © 2014 Elsevier Inc. All rights reserved.

A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy

NASA Astrophysics Data System (ADS)

Liu, Xiangdong; Li, Qingze; Pan, Jianxin

2018-06-01

Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.

Music and Video Gaming during Breaks: Influence on Habitual versus Goal-Directed Decision Making.

PubMed

Liu, Shuyan; Schad, Daniel J; Kuschpel, Maxim S; Rapp, Michael A; Heinz, Andreas

2016-01-01

Different systems for habitual versus goal-directed control are thought to underlie human decision-making. Working memory is known to shape these decision-making systems and their interplay, and is known to support goal-directed decision making even under stress. Here, we investigated if and how decision systems are differentially influenced by breaks filled with diverse everyday life activities known to modulate working memory performance. We used a within-subject design where young adults listened to music and played a video game during breaks interleaved with trials of a sequential two-step Markov decision task, designed to assess habitual as well as goal-directed decision making. Based on a neurocomputational model of task performance, we observed that for individuals with a rather limited working memory capacity video gaming as compared to music reduced reliance on the goal-directed decision-making system, while a rather large working memory capacity prevented such a decline. Our findings suggest differential effects of everyday activities on key decision-making processes.

Music and Video Gaming during Breaks: Influence on Habitual versus Goal-Directed Decision Making

PubMed Central

Kuschpel, Maxim S.; Rapp, Michael A.; Heinz, Andreas

2016-01-01

Different systems for habitual versus goal-directed control are thought to underlie human decision-making. Working memory is known to shape these decision-making systems and their interplay, and is known to support goal-directed decision making even under stress. Here, we investigated if and how decision systems are differentially influenced by breaks filled with diverse everyday life activities known to modulate working memory performance. We used a within-subject design where young adults listened to music and played a video game during breaks interleaved with trials of a sequential two-step Markov decision task, designed to assess habitual as well as goal-directed decision making. Based on a neurocomputational model of task performance, we observed that for individuals with a rather limited working memory capacity video gaming as compared to music reduced reliance on the goal-directed decision-making system, while a rather large working memory capacity prevented such a decline. Our findings suggest differential effects of everyday activities on key decision-making processes. PMID:26982326

Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking.

PubMed

Doolittle, W Ford; Inkpen, S Andrew

2018-04-17

Many practicing biologists accept that nothing in their discipline makes sense except in the light of evolution, and that natural selection is evolution's principal sense-maker. But what natural selection actually is (a force or a statistical outcome, for example) and the levels of the biological hierarchy (genes, organisms, species, or even ecosystems) at which it operates directly are still actively disputed among philosophers and theoretical biologists. Most formulations of evolution by natural selection emphasize the differential reproduction of entities at one or the other of these levels. Some also recognize differential persistence, but in either case the focus is on lineages of material things: even species can be thought of as spatiotemporally restricted, if dispersed, physical beings. Few consider-as "units of selection" in their own right-the processes implemented by genes, cells, species, or communities. "It's the song not the singer" (ITSNTS) theory does that, also claiming that evolution by natural selection of processes is more easily understood and explained as differential persistence than as differential reproduction. ITSNTS was formulated as a response to the observation that the collective functions of microbial communities (the songs) are more stably conserved and ecologically relevant than are the taxa that implement them (the singers). It aims to serve as a useful corrective to claims that "holobionts" (microbes and their animal or plant hosts) are aggregate "units of selection," claims that often conflate meanings of that latter term. But ITSNS also seems broadly applicable, for example, to the evolution of global biogeochemical cycles and the definition of ecosystem function.

Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.

Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression

NASA Astrophysics Data System (ADS)

Bobrowski, Adam; Lipniacki, Tomasz; Pichór, Katarzyna; Rudnicki, Ryszard

2007-09-01

The paper is devoted to a stochastic process introduced in the recent paper by Lipniacki et al. [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.RE Brasier, M. Kimmel, Transcriptional stochasticity in gene expression, JE Theor. Biol. 238 (2006) 348-367] in modelling gene expression in eukaryotes. Starting from the full generator of the process we show that its distributions satisfy a (Fokker-Planck-type) system of partial differential equations. Then, we construct a c0 Markov semigroup in L1 space corresponding to this system. The main result of the paper is asymptotic stability of the involved semigroup in the set of densities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malikopoulos, Andreas; Djouadi, Seddik M; Kuruganti, Teja

We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to thosemore » studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.« less

dCLIP: a computational approach for comparative CLIP-seq analyses

PubMed Central

2014-01-01

Although comparison of RNA-protein interaction profiles across different conditions has become increasingly important to understanding the function of RNA-binding proteins (RBPs), few computational approaches have been developed for quantitative comparison of CLIP-seq datasets. Here, we present an easy-to-use command line tool, dCLIP, for quantitative CLIP-seq comparative analysis. The two-stage method implemented in dCLIP, including a modified MA normalization method and a hidden Markov model, is shown to be able to effectively identify differential binding regions of RBPs in four CLIP-seq datasets, generated by HITS-CLIP, iCLIP and PAR-CLIP protocols. dCLIP is freely available at http://qbrc.swmed.edu/software/. PMID:24398258

[Application of Markov model in post-marketing pharmacoeconomic evaluation of traditional Chinese medicine].

PubMed

Wang, Xin; Su, Xia; Sun, Wentao; Xie, Yanming; Wang, Yongyan

2011-10-01

In post-marketing study of traditional Chinese medicine (TCM), pharmacoeconomic evaluation has an important applied significance. However, the economic literatures of TCM have been unable to fully and accurately reflect the unique overall outcomes of treatment with TCM. For the special nature of TCM itself, we recommend that Markov model could be introduced into post-marketing pharmacoeconomic evaluation of TCM, and also explore the feasibility of model application. Markov model can extrapolate the study time horizon, suit with effectiveness indicators of TCM, and provide measurable comprehensive outcome. In addition, Markov model can promote the development of TCM quality of life scale and the methodology of post-marketing pharmacoeconomic evaluation.

On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains

NASA Technical Reports Server (NTRS)

Leutenegger, Scott T.; Horton, Graham

1994-01-01

Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.

Policy Transfer via Markov Logic Networks

NASA Astrophysics Data System (ADS)

Torrey, Lisa; Shavlik, Jude

We propose using a statistical-relational model, the Markov Logic Network, for knowledge transfer in reinforcement learning. Our goal is to extract relational knowledge from a source task and use it to speed up learning in a related target task. We show that Markov Logic Networks are effective models for capturing both source-task Q-functions and source-task policies. We apply them via demonstration, which involves using them for decision making in an initial stage of the target task before continuing to learn. Through experiments in the RoboCup simulated-soccer domain, we show that transfer via Markov Logic Networks can significantly improve early performance in complex tasks, and that transferring policies is more effective than transferring Q-functions.

A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms.

PubMed

Balbi, Pietro; Massobrio, Paolo; Hellgren Kotaleski, Jeanette

2017-09-01

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour.

Projected Effects of Radiation-Induced Cancers on Life Expectancy in Patients Undergoing CT Surveillance for Limited-Stage Hodgkin Lymphoma: A Markov Model.

PubMed

Lowry, Kathryn P; Turan, Ekin A; Eisenberg, Jonathan; Kong, Chung Y; Barnes, Jeffrey A; Pandharipande, Pari Vijay

2015-06-01

Patients with limited-stage Hodgkin lymphoma (HL) undergo frequent posttreatment surveillance CT examinations, raising concerns about the cumulative magnitude of radiation exposure. The purpose of this study was to project radiation-induced cancer risks relative to competing risks of HL and account for the differential timing of each. We adapted a previously developed Markov model to project lifetime mortality risks and life expectancy losses due to HL versus radiation-induced cancers in HL patients undergoing surveillance CT. In the base case, we modeled 35-year-old men and women undergoing seven CT examinations of the chest, abdomen, and pelvis over 5 years. Radiation-induced cancer risks and deaths for 17 organ systems were modeled using an organ-specific approach, accounting for specific anatomy exposed at CT. Cohorts of 20-, 50-, and 65-year-old men and women were evaluated in secondary analyses. Markov chain Monte Carlo methods were used to estimate the uncertainty of radiation risk projections. For 35-year-old adults, we projected 3324/100,000 (men) and 3345/100,000 (women) deaths from recurrent lymphoma and 245/100,000 (men, 95% uncertainty interval [UI]: 121-369) and 317/100,000 (women, 95% UI: 202-432) radiation-induced cancer deaths. Discrepancies in life expectancy losses between HL (428 days in men, 482 days in women) and radiation-induced cancers (11.6 days in men, [95% UI: 5.7-17.5], 15.6 days in women [95% UI: 9.8-21.4]) were proportionately greater because of the delayed timing of radiation-induced cancers relative to recurrent HL. Deaths and life expectancy losses from radiation-induced cancers were highest in the youngest cohorts. Given the low rate of radiation-induced cancer deaths associated with CT surveillance, modest CT benefits would justify its use in patients with limited-stage HL.

Life and Understanding: The Origins of “Understanding” in Self-Organizing Nervous Systems

PubMed Central

Yufik, Yan M.; Friston, Karl

2016-01-01

This article is motivated by a formulation of biotic self-organization in Friston (2013), where the emergence of “life” in coupled material entities (e.g., macromolecules) was predicated on bounded subsets that maintain a degree of statistical independence from the rest of the network. Boundary elements in such systems constitute a Markov blanket; separating the internal states of a system from its surrounding states. In this article, we ask whether Markov blankets operate in the nervous system and underlie the development of intelligence, enabling a progression from the ability to sense the environment to the ability to understand it. Markov blankets have been previously hypothesized to form in neuronal networks as a result of phase transitions that cause network subsets to fold into bounded assemblies, or packets (Yufik and Sheridan, 1997; Yufik, 1998a). The ensuing neuronal packets hypothesis builds on the notion of neuronal assemblies (Hebb, 1949, 1980), treating such assemblies as flexible but stable biophysical structures capable of withstanding entropic erosion. In other words, structures that maintain their integrity under changing conditions. In this treatment, neuronal packets give rise to perception of “objects”; i.e., quasi-stable (stimulus bound) feature groupings that are conserved over multiple presentations (e.g., the experience of perceiving “apple” can be interrupted and resumed many times). Monitoring the variations in such groups enables the apprehension of behavior; i.e., attributing to objects the ability to undergo changes without loss of self-identity. Ultimately, “understanding” involves self-directed composition and manipulation of the ensuing “mental models” that are constituted by neuronal packets, whose dynamics capture relationships among objects: that is, dependencies in the behavior of objects under varying conditions. For example, movement is known to involve rotation of population vectors in the motor cortex (Georgopoulos et al., 1988, 1993). The neuronal packet hypothesis associates “understanding” with the ability to detect and generate coordinated rotation of population vectors—in neuronal packets—in associative cortex and other regions in the brain. The ability to coordinate vector representations in this way is assumed to have developed in conjunction with the ability to postpone overt motor expression of implicit movement, thus creating a mechanism for prediction and behavioral optimization via mental modeling that is unique to higher species. This article advances the notion that Markov blankets—necessary for the emergence of life—have been subsequently exploited by evolution and thus ground the ways that living organisms adapt to their environment, culminating in their ability to understand it. PMID:28018185

Modeling the coupled return-spread high frequency dynamics of large tick assets

NASA Astrophysics Data System (ADS)

Curato, Gianbiagio; Lillo, Fabrizio

2015-01-01

Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We present an approach based on the hidden Markov model, also known in econometrics as the Markov switching model, for the dynamics of price changes, where the latent Markov process is described by the transitions between spreads. We then use a finite Markov mixture of logit regressions on past squared price changes to describe temporal dependencies in the dynamics of price changes. The model can thus be seen as a double chain Markov model. We show that the model describes the shape of the price change distribution at different time scales, volatility clustering, and the anomalous decrease of kurtosis. We calibrate our models based on Nasdaq stocks and we show that this model reproduces remarkably well the statistical properties of real data.

Quantum Enhanced Inference in Markov Logic Networks

NASA Astrophysics Data System (ADS)

Wittek, Peter; Gogolin, Christian

2017-04-01

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

H2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

NASA Astrophysics Data System (ADS)

Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle

2017-10-01

This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space ?. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space ? considering the infinite time horizon case.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Finding exact constants in a Markov model of Zipfs law generation

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

2017-12-01

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

Quantum Enhanced Inference in Markov Logic Networks.

PubMed

Wittek, Peter; Gogolin, Christian

2017-04-19

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Quantum Enhanced Inference in Markov Logic Networks

PubMed Central

Wittek, Peter; Gogolin, Christian

2017-01-01

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning. PMID:28422093

Stellar differential rotation and coronal time-scales

NASA Astrophysics Data System (ADS)

Gibb, G. P. S.; Jardine, M. M.; Mackay, D. H.

2014-10-01

We investigate the time-scales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion time-scale through the relation τ_Form ∝ √{τ_Lapτ_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (τLife∝τLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

Sexual and reproductive behaviour of Drosophila melanogaster from a microclimatically interslope differentiated population of "Evolution Canyon" (Mount Carmel, Israel).

PubMed

Iliadi, K; Iliadi, N; Rashkovetsky, E; Minkov, I; Nevo, E; Korol, A

2001-11-22

The strong microscale interslope environmental differences in "Evolution Canyon" provide an excellent natural model for sympatric speciation. Our previous studies revealed significant slope-specific differences for a fitness complex of Drosophila. This complex involved either adaptation traits (tolerance to high temperature, different viability and longevity pattern) or behavioural differentiation, manifested in habitat choice and non-random mating. This remarkable differentiation has evolved despite a very small interslope distance (a few hundred metres only). Our hypothesis is that strong interslope microclimatic contrast caused differential selection for fitness-related traits accompanied by behavioural differentiation and reinforced by some sexual isolation, which started incipient speciation. Here we describe the results of a systematic analysis of sexual behaviour in a non-choice situation and several reproductive parameters of D. melanogaster populations from the opposite slopes of "Evolution Canyon". The evidence indicates that: (i) mate choice derives from differences in mating propensity and discrimination; (ii) females from the milder north-facing slope discriminate strongly against males of the opposite slope; (iii) both sexes of the south-facing slope display distinct reproductive and behavioural patterns with females showing increased fecundity, shorter time before remating and relatively higher receptivity, and males showing higher mating propensity. These patterns represent adaptive life strategies contributing to higher fitness.

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

NASA Astrophysics Data System (ADS)

Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi

2017-11-01

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Assessing significance in a Markov chain without mixing.

PubMed

Chikina, Maria; Frieze, Alan; Pegden, Wesley

2017-03-14

We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a [Formula: see text] value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a [Formula: see text] outlier compared with the sampled ranks (its rank is in the bottom [Formula: see text] of sampled ranks), then this observation should correspond to a [Formula: see text] value of [Formula: see text] This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an [Formula: see text]-outlier on the walk is significant at [Formula: see text] under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at [Formula: see text] is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting.

Assessing significance in a Markov chain without mixing

PubMed Central

Chikina, Maria; Frieze, Alan; Pegden, Wesley

2017-01-01

We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a p value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a 0.1% outlier compared with the sampled ranks (its rank is in the bottom 0.1% of sampled ranks), then this observation should correspond to a p value of 0.001. This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an ε-outlier on the walk is significant at p=2ε under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at p≈ε is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting. PMID:28246331

The Impact of Modeling Assumptions in Galactic Chemical Evolution Models

NASA Astrophysics Data System (ADS)

Côté, Benoit; O'Shea, Brian W.; Ritter, Christian; Herwig, Falk; Venn, Kim A.

2017-02-01

We use the OMEGA galactic chemical evolution code to investigate how the assumptions used for the treatment of galactic inflows and outflows impact numerical predictions. The goal is to determine how our capacity to reproduce the chemical evolution trends of a galaxy is affected by the choice of implementation used to include those physical processes. In pursuit of this goal, we experiment with three different prescriptions for galactic inflows and outflows and use OMEGA within a Markov Chain Monte Carlo code to recover the set of input parameters that best reproduces the chemical evolution of nine elements in the dwarf spheroidal galaxy Sculptor. This provides a consistent framework for comparing the best-fit solutions generated by our different models. Despite their different degrees of intended physical realism, we found that all three prescriptions can reproduce in an almost identical way the stellar abundance trends observed in Sculptor. This result supports the similar conclusions originally claimed by Romano & Starkenburg for Sculptor. While the three models have the same capacity to fit the data, the best values recovered for the parameters controlling the number of SNe Ia and the strength of galactic outflows, are substantially different and in fact mutually exclusive from one model to another. For the purpose of understanding how a galaxy evolves, we conclude that only reproducing the evolution of a limited number of elements is insufficient and can lead to misleading conclusions. More elements or additional constraints such as the Galaxy’s star-formation efficiency and the gas fraction are needed in order to break the degeneracy between the different modeling assumptions. Our results show that the successes and failures of chemical evolution models are predominantly driven by the input stellar yields, rather than by the complexity of the Galaxy model itself. Simple models such as OMEGA are therefore sufficient to test and validate stellar yields. OMEGA is part of the NuGrid chemical evolution package and is publicly available online at http://nugrid.github.io/NuPyCEE.

Net Surface Flux Budget Over Tropical Oceans Estimated from the Tropical Rainfall Measuring Mission (TRMM)

NASA Astrophysics Data System (ADS)

Fan, Tai-Fang

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Magneto - Optical Imaging of Superconducting MgB2 Thin Films

NASA Astrophysics Data System (ADS)

Hummert, Stephanie Maria

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Boron Carbide Filled Neutron Shielding Textile Polymers

NASA Astrophysics Data System (ADS)

Manzlak, Derrick Anthony

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Parallel Unstructured Grid Generation for Complex Real-World Aerodynamic Simulations

NASA Astrophysics Data System (ADS)

Zagaris, George

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Polymeric Radiation Shielding for Applications in Space: Polyimide Synthesis and Modeling of Multi-Layered Polymeric Shields

NASA Astrophysics Data System (ADS)

Schiavone, Clinton Cleveland

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Processing and Conversion of Algae to Bioethanol

NASA Astrophysics Data System (ADS)

Kampfe, Sara Katherine

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

The Development of the CALIPSO LiDAR Simulator

NASA Astrophysics Data System (ADS)

Powell, Kathleen A.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Exploring a Novel Approach to Technical Nuclear Forensics Utilizing Atomic Force Microscopy

NASA Astrophysics Data System (ADS)

Peeke, Richard Scot

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Modeling of Critically-Stratified Gravity Flows: Application to the Eel River Continental Shelf, Northern California

NASA Astrophysics Data System (ADS)

Scully, Malcolm E.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Production of Cyclohexylene-Containing Diamines in Pursuit of Novel Radiation Shielding Materials

NASA Astrophysics Data System (ADS)

Bate, Norah G.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Development of Boron-Containing Polyimide Materials and Poly(arylene Ether)s for Radiation Shielding

NASA Astrophysics Data System (ADS)

Collins, Brittani May

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Magnetization Dynamics and Anisotropy in Ferromagnetic/Antiferromagnetic Ni/NiO Bilayers

NASA Astrophysics Data System (ADS)

Petersen, Andreas

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Natural selection and neutral evolution jointly drive population divergence between alpine and lowland ecotypes of the allopolyploid plant Anemone multifida (Ranunculaceae).

PubMed

McEwen, Jamie R; Vamosi, Jana C; Rogers, Sean M

2013-01-01

Population differentiation can be driven in large part by natural selection, but selectively neutral evolution can play a prominent role in shaping patters of population divergence. The decomposition of the evolutionary history of populations into the relative effects of natural selection and selectively neutral evolution enables an understanding of the causes of population divergence and adaptation. In this study, we examined heterogeneous genomic divergence between alpine and lowland ecotypes of the allopolyploid plant, Anemone multifida. Using peak height and dominant AFLP data, we quantified population differentiation at non-outlier (neutral) and outlier loci to determine the potential contribution of natural selection and selectively neutral evolution to population divergence. We found 13 candidate loci, corresponding to 2.7% of loci, with signatures of divergent natural selection between alpine and lowland populations and between alpine populations (Fst  = 0.074-0.445 at outlier loci), but neutral population differentiation was also evident between alpine populations (FST  = 0.041-0.095 at neutral loci). By examining population structure at both neutral and outlier loci, we determined that the combined effects of selection and neutral evolution are associated with the divergence of alpine populations, which may be linked to extreme abiotic conditions and isolation between alpine sites. The presence of outlier levels of genetic variation in structured populations underscores the importance of separately analyzing neutral and outlier loci to infer the relative role of divergent natural selection and neutral evolution in population divergence.

Characterization of the planetary system Kepler-101 with HARPS-N. A hot super-Neptune with an Earth-sized low-mass companion

NASA Astrophysics Data System (ADS)

Bonomo, A. S.; Sozzetti, A.; Lovis, C.; Malavolta, L.; Rice, K.; Buchhave, L. A.; Sasselov, D.; Cameron, A. C.; Latham, D. W.; Molinari, E.; Pepe, F.; Udry, S.; Affer, L.; Charbonneau, D.; Cosentino, R.; Dressing, C. D.; Dumusque, X.; Figueira, P.; Fiorenzano, A. F. M.; Gettel, S.; Harutyunyan, A.; Haywood, R. D.; Horne, K.; Lopez-Morales, M.; Mayor, M.; Micela, G.; Motalebi, F.; Nascimbeni, V.; Phillips, D. F.; Piotto, G.; Pollacco, D.; Queloz, D.; Ségransan, D.; Szentgyorgyi, A.; Watson, C.

2014-12-01

We characterize the planetary system Kepler-101 by performing a combined differential evolution Markov chain Monte Carlo analysis of Kepler data and forty radial velocities obtained with the HARPS-N spectrograph. This system was previously validated and is composed of a hot super-Neptune, Kepler-101b, and an Earth-sized planet, Kepler-101c. These two planets orbit the slightly evolved and metal-rich G-type star in 3.49 and 6.03 days, respectively. With mass Mp = 51.1-4.7+ 5.1 M⊕, radius Rp = 5.77-0.79+ 0.85 R⊕, and density ρp = 1.45-0.48+ 0.83 g cm-3, Kepler-101b is the first fully characterized super-Neptune, and its density suggests that heavy elements make up a significant fraction of its interior; more than 60% of its total mass. Kepler-101c has a radius of 1.25-0.17+ 0.19 R⊕, which implies the absence of any H/He envelope, but its mass could not be determined because of the relative faintness of the parent star for highly precise radial-velocity measurements (Kp = 13.8) and the limited number of radial velocities. The 1σ upper limit, Mp< 3.8 M⊕, excludes a pure iron composition with a probability of 68.3%. The architecture of the planetary system Kepler-101 - containing a close-in giant planet and an outer Earth-sized planet with a period ratio slightly larger than the 3:2 resonance - is certainly of interest for scenarios of planet formation and evolution. This system does not follow thepreviously reported trend that the larger planet has the longer period in the majority of Kepler systems of planet pairs with at least one Neptune-sized or larger planet. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.Table 2 is available in electronic form at http://www.aanda.org

Lie symmetries for systems of evolution equations

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goryainov, V V

2015-01-31

The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution familymore » of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles.« less

Conditioned Limit Theorems for Some Null Recurrent Markov Processes

DTIC Science & Technology

1976-08-01

Chapter 1 INTRODUCTION 1.1 Summary of Results Let (Vk, k ! 0) be a discrete time Markov process with state space EC(- , ) and let S be...explain our results in some detail. 2 We begin by stating our three basic assumptions: (1) vk s k 2 0 Is a Markov process with state space E C(-o,%); (Ii... 12 n 3. CONDITIONING ON T (, > n.................................1.9 3.1 Preliminary Results

Filtering Using Nonlinear Expectations

DTIC Science & Technology

2016-04-16

gives a solution to estimating a Markov chain observed in Gaussian noise when the variance of the noise is unkown. This paper is accepted for the IEEE...Optimization, an A* journal. A short third paper discusses how to estimate a change in the transition dynamics of a noisily observed Markov chain ...The change point time is hidden in a hidden Markov chain , so a second level of discovery is involved. This paper is accepted for Communications in

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, H.

In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications ofmore » the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability).« less

Markov and non-Markov processes in complex systems by the dynamical information entropy

NASA Astrophysics Data System (ADS)

Yulmetyev, R. M.; Gafarov, F. M.

1999-12-01

We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.

Open Quantum Systems and Classical Trajectories

NASA Astrophysics Data System (ADS)

Rebolledo, Rolando

2004-09-01

A Quantum Markov Semigroup consists of a family { T} = ({ T}t)_{t ∈ B R+} of normal ω*- continuous completely positive maps on a von Neumann algebra 𝔐 which preserve the unit and satisfy the semigroup property. This class of semigroups has been extensively used to represent open quantum systems. This article is aimed at studying the existence of a { T} -invariant abelian subalgebra 𝔄 of 𝔐. When this happens, the restriction of { T}t to 𝔄 defines a classical Markov semigroup T = (Tt)t ∈ ∝ + say, associated to a classical Markov process X = (Xt)t ∈ ∝ +. The structure (𝔄, T, X) unravels the quantum Markov semigroup { T} , providing a bridge between open quantum systems and classical stochastic processes.

Modeling haplotype block variation using Markov chains.

PubMed

Greenspan, G; Geiger, D

2006-04-01

Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity.

Markov chains for testing redundant software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1988-01-01

A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

Counting of oligomers in sequences generated by markov chains for DNA motif discovery.

PubMed

Shan, Gao; Zheng, Wei-Mou

2009-02-01

By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.

Modeling Haplotype Block Variation Using Markov Chains

PubMed Central

Greenspan, G.; Geiger, D.

2006-01-01

Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity. PMID:16361244

Validation of the SURE Program, phase 1

NASA Technical Reports Server (NTRS)

Dotson, Kelly J.

1987-01-01

Presented are the results of the first phase in the validation of the SURE (Semi-Markov Unreliability Range Evaluator) program. The SURE program gives lower and upper bounds on the death-state probabilities of a semi-Markov model. With these bounds, the reliability of a semi-Markov model of a fault-tolerant computer system can be analyzed. For the first phase in the validation, fifteen semi-Markov models were solved analytically for the exact death-state probabilities and these solutions compared to the corresponding bounds given by SURE. In every case, the SURE bounds covered the exact solution. The bounds, however, had a tendency to separate in cases where the recovery rate was slow or the fault arrival rate was fast.

Influence of credit scoring on the dynamics of Markov chain

NASA Astrophysics Data System (ADS)

Galina, Timofeeva

2015-11-01

Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.

Markov Modeling of Component Fault Growth over a Derived Domain of Feasible Output Control Effort Modifications

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

This paper introduces a novel Markov process formulation of stochastic fault growth modeling, in order to facilitate the development and analysis of prognostics-based control adaptation. A metric representing the relative deviation between the nominal output of a system and the net output that is actually enacted by an implemented prognostics-based control routine, will be used to define the action space of the formulated Markov process. The state space of the Markov process will be defined in terms of an abstracted metric representing the relative health remaining in each of the system s components. The proposed formulation of component fault dynamics will conveniently relate feasible system output performance modifications to predictions of future component health deterioration.

DM-BLD: differential methylation detection using a hierarchical Bayesian model exploiting local dependency.

PubMed

Wang, Xiao; Gu, Jinghua; Hilakivi-Clarke, Leena; Clarke, Robert; Xuan, Jianhua

2017-01-15

The advent of high-throughput DNA methylation profiling techniques has enabled the possibility of accurate identification of differentially methylated genes for cancer research. The large number of measured loci facilitates whole genome methylation study, yet posing great challenges for differential methylation detection due to the high variability in tumor samples. We have developed a novel probabilistic approach, D: ifferential M: ethylation detection using a hierarchical B: ayesian model exploiting L: ocal D: ependency (DM-BLD), to detect differentially methylated genes based on a Bayesian framework. The DM-BLD approach features a joint model to capture both the local dependency of measured loci and the dependency of methylation change in samples. Specifically, the local dependency is modeled by Leroux conditional autoregressive structure; the dependency of methylation changes is modeled by a discrete Markov random field. A hierarchical Bayesian model is developed to fully take into account the local dependency for differential analysis, in which differential states are embedded as hidden variables. Simulation studies demonstrate that DM-BLD outperforms existing methods for differential methylation detection, particularly when the methylation change is moderate and the variability of methylation in samples is high. DM-BLD has been applied to breast cancer data to identify important methylated genes (such as polycomb target genes and genes involved in transcription factor activity) associated with breast cancer recurrence. A Matlab package of DM-BLD is available at http://www.cbil.ece.vt.edu/software.htm CONTACT: Xuan@vt.eduSupplementary information: Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A Preliminary Analysis of Correlated Evolution in Mammalian Chewing Motor Patterns

PubMed Central

Williams, Susan H.; Vinyard, Christopher J.; Wall, Christine E.; Doherty, Alison H.; Crompton, Alfred W.; Hylander, William L.

2011-01-01

Descriptive and quantitative analyses of electromyograms (EMG) from the jaw adductors during feeding in mammals have demonstrated both similarities and differences among species in chewing motor patterns. These observations have led to a number of hypotheses of the evolution of motor patterns, the most comprehensive of which was proposed by Weijs in 1994. Since then, new data have been collected and additional hypotheses for the evolution of motor patterns have been proposed. Here, we take advantage of these new data and a well-resolved species-level phylogeny for mammals to test for the correlated evolution of specific components of mammalian chewing motor patterns. We focus on the evolution of the coordination of working-side (WS) and balancing-side (BS) jaw adductors (i.e., Weijs’ Triplets I and II), the evolution of WS and BS muscle recruitment levels, and the evolution of asynchrony between pairs of muscles. We converted existing chewing EMG data into binary traits to incorporate as much data as possible and facilitate robust phylogenetic analyses. We then tested hypotheses of correlated evolution of these traits across our phylogeny using a maximum likelihood method and the Bayesian Markov Chain Monte Carlo method. Both sets of analyses yielded similar results highlighting the evolutionary changes that have occurred across mammals in chewing motor patterns. We find support for the correlated evolution of (1) Triplets I and II, (2) BS deep masseter asynchrony and Triplets I and II, (3) a relative delay in the activity of the BS deep masseter and a decrease in the ratio of WS to BS muscle recruitment levels, and (4) a relative delay in the activity of the BS deep masseter and a delay in the activity of the BS posterior temporalis. In contrast, changes in relative WS and BS activity levels across mammals are not correlated with Triplets I and II. Results from this work can be integrated with dietary and morphological data to better understand how feeding and the masticatory apparatus have evolved across mammals in the context of new masticatory demands. PMID:21719433

A preliminary analysis of correlated evolution in Mammalian chewing motor patterns.

PubMed

Williams, Susan H; Vinyard, Christopher J; Wall, Christine E; Doherty, Alison H; Crompton, Alfred W; Hylander, William L

2011-08-01

Descriptive and quantitative analyses of electromyograms (EMG) from the jaw adductors during feeding in mammals have demonstrated both similarities and differences among species in chewing motor patterns. These observations have led to a number of hypotheses of the evolution of motor patterns, the most comprehensive of which was proposed by Weijs in 1994. Since then, new data have been collected and additional hypotheses for the evolution of motor patterns have been proposed. Here, we take advantage of these new data and a well-resolved species-level phylogeny for mammals to test for the correlated evolution of specific components of mammalian chewing motor patterns. We focus on the evolution of the coordination of working-side (WS) and balancing-side (BS) jaw adductors (i.e., Weijs' Triplets I and II), the evolution of WS and BS muscle recruitment levels, and the evolution of asynchrony between pairs of muscles. We converted existing chewing EMG data into binary traits to incorporate as much data as possible and facilitate robust phylogenetic analyses. We then tested hypotheses of correlated evolution of these traits across our phylogeny using a maximum likelihood method and the Bayesian Markov Chain Monte Carlo method. Both sets of analyses yielded similar results highlighting the evolutionary changes that have occurred across mammals in chewing motor patterns. We find support for the correlated evolution of (1) Triplets I and II, (2) BS deep masseter asynchrony and Triplets I and II, (3) a relative delay in the activity of the BS deep masseter and a decrease in the ratio of WS to BS muscle recruitment levels, and (4) a relative delay in the activity of the BS deep masseter and a delay in the activity of the BS posterior temporalis. In contrast, changes in relative WS and BS activity levels across mammals are not correlated with Triplets I and II. Results from this work can be integrated with dietary and morphological data to better understand how feeding and the masticatory apparatus have evolved across mammals in the context of new masticatory demands.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerrier, C.; Holcman, D., E-mail: david.holcman@ens.fr; Mathematical Institute, Oxford OX2 6GG, Newton Institute

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationallymore » greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.« less

Tropical land use land cover mapping in Pará (Brazil) using discriminative Markov random fields and multi-temporal TerraSAR-X data

NASA Astrophysics Data System (ADS)

Hagensieker, Ron; Roscher, Ribana; Rosentreter, Johannes; Jakimow, Benjamin; Waske, Björn

2017-12-01

Remote sensing satellite data offer the unique possibility to map land use land cover transformations by providing spatially explicit information. However, detection of short-term processes and land use patterns of high spatial-temporal variability is a challenging task. We present a novel framework using multi-temporal TerraSAR-X data and machine learning techniques, namely discriminative Markov random fields with spatio-temporal priors, and import vector machines, in order to advance the mapping of land cover characterized by short-term changes. Our study region covers a current deforestation frontier in the Brazilian state Pará with land cover dominated by primary forests, different types of pasture land and secondary vegetation, and land use dominated by short-term processes such as slash-and-burn activities. The data set comprises multi-temporal TerraSAR-X imagery acquired over the course of the 2014 dry season, as well as optical data (RapidEye, Landsat) for reference. Results show that land use land cover is reliably mapped, resulting in spatially adjusted overall accuracies of up to 79% in a five class setting, yet limitations for the differentiation of different pasture types remain. The proposed method is applicable on multi-temporal data sets, and constitutes a feasible approach to map land use land cover in regions that are affected by high-frequent temporal changes.

Comparative Genomics Identifies Epidermal Proteins Associated with the Evolution of the Turtle Shell.

PubMed

Holthaus, Karin Brigit; Strasser, Bettina; Sipos, Wolfgang; Schmidt, Heiko A; Mlitz, Veronika; Sukseree, Supawadee; Weissenbacher, Anton; Tschachler, Erwin; Alibardi, Lorenzo; Eckhart, Leopold

2016-03-01

The evolution of reptiles, birds, and mammals was associated with the origin of unique integumentary structures. Studies on lizards, chicken, and humans have suggested that the evolution of major structural proteins of the outermost, cornified layers of the epidermis was driven by the diversification of a gene cluster called Epidermal Differentiation Complex (EDC). Turtles have evolved unique defense mechanisms that depend on mechanically resilient modifications of the epidermis. To investigate whether the evolution of the integument in these reptiles was associated with specific adaptations of the sequences and expression patterns of EDC-related genes, we utilized newly available genome sequences to determine the epidermal differentiation gene complement of turtles. The EDC of the western painted turtle (Chrysemys picta bellii) comprises more than 100 genes, including at least 48 genes that encode proteins referred to as beta-keratins or corneous beta-proteins. Several EDC proteins have evolved cysteine/proline contents beyond 50% of total amino acid residues. Comparative genomics suggests that distinct subfamilies of EDC genes have been expanded and partly translocated to loci outside of the EDC in turtles. Gene expression analysis in the European pond turtle (Emys orbicularis) showed that EDC genes are differentially expressed in the skin of the various body sites and that a subset of beta-keratin genes within the EDC as well as those located outside of the EDC are expressed predominantly in the shell. Our findings give strong support to the hypothesis that the evolutionary innovation of the turtle shell involved specific molecular adaptations of epidermal differentiation. © The Author 2015. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

Evolution in fluctuating environments: decomposing selection into additive components of the Robertson-Price equation.

PubMed

Engen, Steinar; Saether, Bernt-Erik

2014-03-01

We analyze the stochastic components of the Robertson-Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.

Implications of monotreme and marsupial chromosome evolution on sex determination and differentiation.

PubMed

Deakin, Janine E

2017-04-01

Studies of chromosomes from monotremes and marsupials endemic to Australasia have provided important insight into the evolution of their genomes as well as uncovering fundamental differences in their sex determination/differentiation pathways. Great advances have been made this century into solving the mystery of the complicated sex chromosome system in monotremes. Monotremes possess multiple different X and Y chromosomes and a candidate sex determining gene has been identified. Even greater advancements have been made for marsupials, with reconstruction of the ancestral karyotype enabling the evolutionary history of marsupial chromosomes to be determined. Furthermore, the study of sex chromosomes in intersex marsupials has afforded insight into differences in the sexual differentiation pathway between marsupials and eutherians, together with experiments showing the insensitivity of the mammary glands, pouch and scrotum to exogenous hormones, led to the hypothesis that there is a gene (or genes) on the X chromosome responsible for the development of either pouch or scrotum. This review highlights the major advancements made towards understanding chromosome evolution and how this has impacted on our understanding of sex determination and differentiation in these interesting mammals. Copyright © 2015 Elsevier Inc. All rights reserved.

Progress toward a general species concept.

PubMed

Hausdorf, Bernhard

2011-04-01

New insights in the speciation process and the nature of "species" that accumulated in the past decade demand adjustments of the species concept. The standing of some of the most broadly accepted or most innovative species concepts in the light of the growing evidence that reproductive barriers are semipermeable to gene flow, that species can differentiate despite ongoing interbreeding, that a single species can originate polyphyletically by parallel evolution, and that uniparental organisms are organised in units that resemble species of biparental organisms is discussed. As a synthesis of ideas in existing concepts and the new insights, a generalization of the genic concept is proposed that defines species as groups of individuals that are reciprocally characterized by features that would have negative fitness effects in other groups and that cannot be regularly exchanged between groups upon contact. The benefits of this differential fitness species concept are that it classifies groups that keep differentiated and keep on differentiating despite interbreeding as species, that it is not restricted to specific mutations or mechanisms causing speciation, and that it can be applied to the whole spectrum of organisms from uni- to biparentals. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Markov modeling for the neurosurgeon: a review of the literature and an introduction to cost-effectiveness research.

PubMed

Wali, Arvin R; Brandel, Michael G; Santiago-Dieppa, David R; Rennert, Robert C; Steinberg, Jeffrey A; Hirshman, Brian R; Murphy, James D; Khalessi, Alexander A

2018-05-01

OBJECTIVE Markov modeling is a clinical research technique that allows competing medical strategies to be mathematically assessed in order to identify the optimal allocation of health care resources. The authors present a review of the recently published neurosurgical literature that employs Markov modeling and provide a conceptual framework with which to evaluate, critique, and apply the findings generated from health economics research. METHODS The PubMed online database was searched to identify neurosurgical literature published from January 2010 to December 2017 that had utilized Markov modeling for neurosurgical cost-effectiveness studies. Included articles were then assessed with regard to year of publication, subspecialty of neurosurgery, decision analytical techniques utilized, and source information for model inputs. RESULTS A total of 55 articles utilizing Markov models were identified across a broad range of neurosurgical subspecialties. Sixty-five percent of the papers were published within the past 3 years alone. The majority of models derived health transition probabilities, health utilities, and cost information from previously published studies or publicly available information. Only 62% of the studies incorporated indirect costs. Ninety-three percent of the studies performed a 1-way or 2-way sensitivity analysis, and 67% performed a probabilistic sensitivity analysis. A review of the conceptual framework of Markov modeling and an explanation of the different terminology and methodology are provided. CONCLUSIONS As neurosurgeons continue to innovate and identify novel treatment strategies for patients, Markov modeling will allow for better characterization of the impact of these interventions on a patient and societal level. The aim of this work is to equip the neurosurgical readership with the tools to better understand, critique, and apply findings produced from cost-effectiveness research.

Markovian prediction of future values for food grains in the economic survey

NASA Astrophysics Data System (ADS)

Sathish, S.; Khadar Babu, S. K.

2017-11-01

Now-a-days prediction and forecasting are plays a vital role in research. For prediction, regression is useful to predict the future value and current value on production process. In this paper, we assume food grain production exhibit Markov chain dependency and time homogeneity. The economic generative performance evaluation the balance time artificial fertilization different level in Estrusdetection using a daily Markov chain model. Finally, Markov process prediction gives better performance compare with Regression model.

Analysis of 3D OCT images for diagnosis of skin tumors

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2018-04-01

Skin cancer is one of the fastest growing type of cancer. It represents the most commonly diagnosed malignancy, surpassing lung, breast, colorectal and prostate cancer. So, diagnostics for different types of skin cancer on early stages is a very high challenge for medicine industry. New optical imaging techniques have been developed in order to improve diagnostics precision. Optical coherence tomography (OCT) is based on low-coherence interferometry to detect the intensity of backscattered infrared light from biological tissues by measuring the optical path length. OCT provides the advantage of real-time, in vivo, low-cost imaging of suspicious lesions without having to proceed directly to a tissue biopsy. The post-processing techniques can be used for improving the precision of diagnostics and providing solutions to overcome limitations for OCT. Image processing can include noise filtration and evaluation of textural, geometric, morphological, spectral, statistic and other features. The main idea of this investigation is using information received from multiple analyze on 2D- and 3D-OCT images for skin tumors differentiating. At first, we tested the computer algorithm on OCT data hypercubes and separated B- and C-scans. Combination of 2D and 3D data give us an opportunity to receive common information about tumor (geometric and morphological characteristics) and use more powerful algorithms for features evaluation (fractal and textural) on these separated scans. These groups of features provide closer connection to classical wide-used ABCDE criteria (Asymmetry, Border irregularity, Color, Diameter, Evolution). We used a set of features consisting of fractal dimension, Haralick's, Gabor's, Tamura's, Markov random fields, geometric features and many others. We could note about good results on the test sets in differentiation between BCC and Nevus, MM and Healthy Skin. We received dividing MM from Healthy Skin with sensitivity more 90% and specificity more 92% (168 B-scans from 8 species) by using three Haralick's features like Contrast, Correlation and Energy. The results are very promising to be tested for new cases and new bigger sets of OCT images.

Multiple Active Contours Guided by Differential Evolution for Medical Image Segmentation

PubMed Central

Cruz-Aceves, I.; Avina-Cervantes, J. G.; Lopez-Hernandez, J. M.; Rostro-Gonzalez, H.; Garcia-Capulin, C. H.; Torres-Cisneros, M.; Guzman-Cabrera, R.

2013-01-01

This paper presents a new image segmentation method based on multiple active contours guided by differential evolution, called MACDE. The segmentation method uses differential evolution over a polar coordinate system to increase the exploration and exploitation capabilities regarding the classical active contour model. To evaluate the performance of the proposed method, a set of synthetic images with complex objects, Gaussian noise, and deep concavities is introduced. Subsequently, MACDE is applied on datasets of sequential computed tomography and magnetic resonance images which contain the human heart and the human left ventricle, respectively. Finally, to obtain a quantitative and qualitative evaluation of the medical image segmentations compared to regions outlined by experts, a set of distance and similarity metrics has been adopted. According to the experimental results, MACDE outperforms the classical active contour model and the interactive Tseng method in terms of efficiency and robustness for obtaining the optimal control points and attains a high accuracy segmentation. PMID:23983809

Constrained multi-objective optimization of storage ring lattices

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2018-03-01

The storage ring lattice optimization is a class of constrained multi-objective optimization problem, where in addition to low beam emittance, a large dynamic aperture for good injection efficiency and improved beam lifetime are also desirable. The convergence and computation times are of great concern for the optimization algorithms, as various objectives are to be optimized and a number of accelerator parameters to be varied over a large span with several constraints. In this paper, a study of storage ring lattice optimization using differential evolution is presented. The optimization results are compared with two most widely used optimization techniques in accelerators-genetic algorithm and particle swarm optimization. It is found that the differential evolution produces a better Pareto optimal front in reasonable computation time between two conflicting objectives-beam emittance and dispersion function in the straight section. The differential evolution was used, extensively, for the optimization of linear and nonlinear lattices of Indus-2 for exploring various operational modes within the magnet power supply capabilities.

Multi Sensor Fusion Using Fitness Adaptive Differential Evolution

NASA Astrophysics Data System (ADS)

Giri, Ritwik; Ghosh, Arnob; Chowdhury, Aritra; Das, Swagatam

The rising popularity of multi-source, multi-sensor networks supports real-life applications calls for an efficient and intelligent approach to information fusion. Traditional optimization techniques often fail to meet the demands. The evolutionary approach provides a valuable alternative due to its inherent parallel nature and its ability to deal with difficult problems. We present a new evolutionary approach based on a modified version of Differential Evolution (DE), called Fitness Adaptive Differential Evolution (FiADE). FiADE treats sensors in the network as distributed intelligent agents with various degrees of autonomy. Existing approaches based on intelligent agents cannot completely answer the question of how their agents could coordinate their decisions in a complex environment. The proposed approach is formulated to produce good result for the problems that are high-dimensional, highly nonlinear, and random. The proposed approach gives better result in case of optimal allocation of sensors. The performance of the proposed approach is compared with an evolutionary algorithm coordination generalized particle model (C-GPM).

Parameter optimization of differential evolution algorithm for automatic playlist generation problem

NASA Astrophysics Data System (ADS)

Alamag, Kaye Melina Natividad B.; Addawe, Joel M.

2017-11-01

With the digitalization of music, the number of collection of music increased largely and there is a need to create lists of music that filter the collection according to user preferences, thus giving rise to the Automatic Playlist Generation Problem (APGP). Previous attempts to solve this problem include the use of search and optimization algorithms. If a music database is very large, the algorithm to be used must be able to search the lists thoroughly taking into account the quality of the playlist given a set of user constraints. In this paper we perform an evolutionary meta-heuristic optimization algorithm, Differential Evolution (DE) using different combination of parameter values and select the best performing set when used to solve four standard test functions. Performance of the proposed algorithm is then compared with normal Genetic Algorithm (GA) and a hybrid GA with Tabu Search. Numerical simulations are carried out to show better results from Differential Evolution approach with the optimized parameter values.

Enhanced differential evolution to combine optical mouse sensor with image structural patches for robust endoscopic navigation.

PubMed

Luo, Xiongbiao; Jayarathne, Uditha L; McLeod, A Jonathan; Mori, Kensaku

2014-01-01

Endoscopic navigation generally integrates different modalities of sensory information in order to continuously locate an endoscope relative to suspicious tissues in the body during interventions. Current electromagnetic tracking techniques for endoscopic navigation have limited accuracy due to tissue deformation and magnetic field distortion. To avoid these limitations and improve the endoscopic localization accuracy, this paper proposes a new endoscopic navigation framework that uses an optical mouse sensor to measure the endoscope movements along its viewing direction. We then enhance the differential evolution algorithm by modifying its mutation operation. Based on the enhanced differential evolution method, these movement measurements and image structural patches in endoscopic videos are fused to accurately determine the endoscope position. An evaluation on a dynamic phantom demonstrated that our method provides a more accurate navigation framework. Compared to state-of-the-art methods, it improved the navigation accuracy from 2.4 to 1.6 mm and reduced the processing time from 2.8 to 0.9 seconds.

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

NASA Astrophysics Data System (ADS)

Swinburne, Thomas D.; Perez, Danny

2018-05-01

A massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

NASA Astrophysics Data System (ADS)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Multiensemble Markov models of molecular thermodynamics and kinetics.

PubMed

Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank

2016-06-07

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model.

Multiensemble Markov models of molecular thermodynamics and kinetics

PubMed Central

Wu, Hao; Paul, Fabian; Noé, Frank

2016-01-01

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model. PMID:27226302

Fuzzy Markov random fields versus chains for multispectral image segmentation.

PubMed

Salzenstein, Fabien; Collet, Christophe

2006-11-01

This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.

Structure and Evolution of the Lunar Interior

NASA Technical Reports Server (NTRS)

Andrews-Hanna, J. C.; Weber, R. C.; Ishihara, Y.; Kamata, S.; Keane, J.; Kiefer, W. S.; Matsuyama, I.; Siegler, M.; Warren, P.

2017-01-01

Early in its evolution, the Moon underwent a magma ocean phase leading to its differentiation into a feldspathic crust, cumulate mantle, and iron core. However, far from the simplest view of a uniform plagioclase flotation crust, the present-day crust of the Moon varies greatly in thickness, composition, and physical properties. Recent significant improvements in both data and analysis techniques have yielded fundamental advances in our understanding of the structure and evolution of the lunar interior. The structure of the crust is revealed by gravity, topography, magnetics, seismic, radar, electromagnetic, and VNIR remote sensing data. The mantle structure of the Moon is revealed primarily by seismic and laser ranging data. Together, this data paints a picture of a Moon that is heterogeneous in all directions and across all scales, whose structure is a result of its unique formation, differentiation, and subsequent evolution. This brief review highlights a small number of recent advances in our understanding of lunar structure.

Probing the dynamics of dark energy with divergence-free parametrizations: A global fit study

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Xin

2011-09-01

The CPL parametrization is very important for investigating the property of dark energy with observational data. However, the CPL parametrization only respects the past evolution of dark energy but does not care about the future evolution of dark energy, since w ( z ) diverges in the distant future. In a recent paper [J.Z. Ma, X. Zhang, Phys. Lett. B 699 (2011) 233], a robust, novel parametrization for dark energy, w ( z ) = w + w ( l n ( 2 + z ) 1 + z - l n 2 ) , has been proposed, successfully avoiding the future divergence problem in the CPL parametrization. On the other hand, an oscillating parametrization (motivated by an oscillating quintom model) can also avoid the future divergence problem. In this Letter, we use the two divergence-free parametrizations to probe the dynamics of dark energy in the whole evolutionary history. In light of the data from 7-year WMAP temperature and polarization power spectra, matter power spectrum of SDSS DR7, and SN Ia Union2 sample, we perform a full Markov Chain Monte Carlo exploration for the two dynamical dark energy models. We find that the best-fit dark energy model is a quintom model with the EOS across -1 during the evolution. However, though the quintom model is more favored, we find that the cosmological constant still cannot be excluded.

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

NASA Astrophysics Data System (ADS)

Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.

2018-01-01

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.

Cascade heterogeneous face sketch-photo synthesis via dual-scale Markov Network

NASA Astrophysics Data System (ADS)

Yao, Saisai; Chen, Zhenxue; Jia, Yunyi; Liu, Chengyun

2018-03-01

Heterogeneous face sketch-photo synthesis is an important and challenging task in computer vision, which has widely applied in law enforcement and digital entertainment. According to the different synthesis results based on different scales, this paper proposes a cascade sketch-photo synthesis method via dual-scale Markov Network. Firstly, Markov Network with larger scale is used to synthesise the initial sketches and the local vertical and horizontal neighbour search (LVHNS) method is used to search for the neighbour patches of test patches in training set. Then, the initial sketches and test photos are jointly entered into smaller scale Markov Network. Finally, the fine sketches are obtained after cascade synthesis process. Extensive experimental results on various databases demonstrate the superiority of the proposed method compared with several state-of-the-art methods.

Hot Oxygen Transport Model for Martian Coronal Retrievals with MAVEN's IUVS Instrument

NASA Astrophysics Data System (ADS)

Deighan, Justin; Stewart, I.; Schneider, N.

2013-10-01

One of the primary goals of the upcoming Mars Atmosphere and Volatile EvolutioN (MAVEN) mission is the study of non-thermal escape of atomic oxygen to space. In support of this goal, the Imaging Ultraviolet Spectrograph (IUVS) instrument will make regular observations of the gravitationally bound O corona surrounding the planet. Interpreting these measurements requires a computationally efficient forward model to calculate collisional transport of hot O through the exosphere. To accurately treat the strong forward scattering of O at energies of a few eV, we are developing a model which applies the δ-M approximation from radiative transport theory. This method consolidates the strong forward peak of the scattering phase function into a δ-function, leaving the residual as a sum of smoothly varying Legendre polynomials. Preliminary Monte Carlo results with this approach show great promise, producing coronal O densities and escape rates with accuracies of ~5% or better. Our objective is to integrate this δ-M technique into a Markov-Chain transport model. The Markov-Chain method produces hot O particle densities and velocity distributions as a function of altitude by quantizing all possible particle states and calculating the probabilities of state transition, then solving for equilibrium using standard matrix routines. This allows for forward model run-times on the order of seconds, enabling real-time pipeline retrievals from IUVS measurements. The general method is applicable to rapidly calculating the transport of any strongly forward scattering species through a background medium.

A nonparametric test for Markovianity in the illness-death model.

PubMed

Rodríguez-Girondo, Mar; de Uña-Álvarez, Jacobo

2012-12-30

Multistate models are useful tools for modeling disease progression when survival is the main outcome, but several intermediate events of interest are observed during the follow-up time. The illness-death model is a special multistate model with important applications in the biomedical literature. It provides a suitable representation of the individual's history when a unique intermediate event can be experienced before the main event of interest. Nonparametric estimation of transition probabilities in this and other multistate models is usually performed through the Aalen-Johansen estimator under a Markov assumption. The Markov assumption claims that given the present state, the future evolution of the illness is independent of the states previously visited and the transition times among them. However, this assumption fails in some applications, leading to inconsistent estimates. In this paper, we provide a new approach for testing Markovianity in the illness-death model. The new method is based on measuring the future-past association along time. This results in a detailed inspection of the process, which often reveals a non-Markovian behavior with different trends in the association measure. A test of significance for zero future-past association at each time point is introduced, and a significance trace is proposed accordingly. Besides, we propose a global test for Markovianity based on a supremum-type test statistic. The finite sample performance of the test is investigated through simulations. We illustrate the new method through the analysis of two biomedical data analysis. Copyright © 2012 John Wiley & Sons, Ltd.

Towards robust quantification and reduction of uncertainty in hydrologic predictions: Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion

NASA Astrophysics Data System (ADS)

Wang, S.; Huang, G. H.; Baetz, B. W.; Ancell, B. C.

2017-05-01

The particle filtering techniques have been receiving increasing attention from the hydrologic community due to its ability to properly estimate model parameters and states of nonlinear and non-Gaussian systems. To facilitate a robust quantification of uncertainty in hydrologic predictions, it is necessary to explicitly examine the forward propagation and evolution of parameter uncertainties and their interactions that affect the predictive performance. This paper presents a unified probabilistic framework that merges the strengths of particle Markov chain Monte Carlo (PMCMC) and factorial polynomial chaos expansion (FPCE) algorithms to robustly quantify and reduce uncertainties in hydrologic predictions. A Gaussian anamorphosis technique is used to establish a seamless bridge between the data assimilation using the PMCMC and the uncertainty propagation using the FPCE through a straightforward transformation of posterior distributions of model parameters. The unified probabilistic framework is applied to the Xiangxi River watershed of the Three Gorges Reservoir (TGR) region in China to demonstrate its validity and applicability. Results reveal that the degree of spatial variability of soil moisture capacity is the most identifiable model parameter with the fastest convergence through the streamflow assimilation process. The potential interaction between the spatial variability in soil moisture conditions and the maximum soil moisture capacity has the most significant effect on the performance of streamflow predictions. In addition, parameter sensitivities and interactions vary in magnitude and direction over time due to temporal and spatial dynamics of hydrologic processes.

SIMULATION FROM ENDPOINT-CONDITIONED, CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE, WITH APPLICATIONS TO MOLECULAR EVOLUTION.

PubMed

Hobolth, Asger; Stone, Eric A

2009-09-01

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.

The Population Genomics of Repeated Evolution in the Blind Cavefish Astyanax mexicanus

PubMed Central

Bradic, Martina; Teotónio, Henrique; Borowsky, Richard L.

2013-01-01

Distinct populations of Astyanax mexicanus cavefish offer striking examples of repeatable convergence or parallelism in their independent evolutions from surface to cave phenotypes. However, the extent to which the repeatability of evolution occurred at the genetic level remains poorly understood. To address this, we first characterized the genetic diversity of 518 single-nucleotide polymorphisms (SNPs), obtained through RAD tag sequencing and distributed throughout the genome, in seven cave and three groups of surface populations. The cave populations represented two distinct lineages (old and new). Thirty-one SNPs were significantly differentiated between surface and old cave populations, two SNPs were differentiated between surface and new cave populations, and 44 SNPs were significantly differentiated in both old and new cave populations. In addition, we determined whether these SNPs map to the same locations of previously described quantitative trait loci (QTL) between surface and cave populations. A total of 25 differentiated SNPs co-map with several QTL, such as one containing a fibroblast growth factor gene (Fgf8) involved in eye development and lens size. Further, the identity of many SNPs that co-mapped with QTL was the same in independently derived cave populations. These conclusions were further confirmed by haplotype analyses of SNPs within QTL regions. Our findings indicate that the repeatability of evolution at the genetic level is substantial, suggesting that ancestral standing genetic variation significantly contributed to the population genetic variability used in adaptation to the cave environment. PMID:23927992

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

MicroRNAs Associated with Caste Determination and Differentiation in a Primitively Eusocial Insect

PubMed Central

Collins, David H.; Mohorianu, Irina; Beckers, Matthew; Moulton, Vincent; Dalmay, Tamas; Bourke, Andrew F. G.

2017-01-01

In eusocial Hymenoptera (ants, bees and wasps), queen and worker adult castes typically arise via environmental influences. A fundamental challenge is to understand how a single genome can thereby produce alternative phenotypes. A powerful approach is to compare the molecular basis of caste determination and differentiation along the evolutionary trajectory between primitively and advanced eusocial species, which have, respectively, relatively undifferentiated and strongly differentiated adult castes. In the advanced eusocial honeybee, Apis mellifera, studies suggest that microRNAs (miRNAs) play an important role in the molecular basis of caste determination and differentiation. To investigate how miRNAs affect caste in eusocial evolution, we used deep sequencing and Northern blots to isolate caste-associated miRNAs in the primitively eusocial bumblebee Bombus terrestris. We found that the miRNAs Bte-miR-6001-5p and -3p are more highly expressed in queen- than in worker-destined late-instar larvae. These are the first caste-associated miRNAs from outside advanced eusocial Hymenoptera, so providing evidence for caste-associated miRNAs occurring relatively early in eusocial evolution. Moreover, we found little evidence that miRNAs previously shown to be associated with caste in A. mellifera were differentially expressed across caste pathways in B. terrestris, suggesting that, in eusocial evolution, the caste-associated role of individual miRNAs is not conserved. PMID:28361900

First and second order semi-Markov chains for wind speed modeling

NASA Astrophysics Data System (ADS)

Prattico, F.; Petroni, F.; D'Amico, G.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [3] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [1], by using two models, first-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution, Renewable Energy, 28/2003 1787-1802. [2] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30/2005 693-708. [3] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Renewable Energy 29/2004, 1407-1418.

Mode identification using stochastic hybrid models with applications to conflict detection and resolution

NASA Astrophysics Data System (ADS)

Naseri Kouzehgarani, Asal

2009-12-01

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms---that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers. We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs.

Thermal evolution of the earth

NASA Technical Reports Server (NTRS)

Spohn, T.

1984-01-01

The earth's heat budget and models of the earth's thermal evolution are discussed. Sources of the planetary heat are considered and modes of heat transport are addressed, including conduction, convection, and chemical convection. Thermal and convectional models of the earth are covered, and models of thermal evolution are discussed in detail, including changes in the core, the influence of layered mantle convection on the thermal evolution, and the effect of chemical differentiation on the continents.

Natural Selection and Neutral Evolution Jointly Drive Population Divergence between Alpine and Lowland Ecotypes of the Allopolyploid Plant Anemone multifida (Ranunculaceae)

PubMed Central

McEwen, Jamie R.; Vamosi, Jana C.; Rogers, Sean M.

2013-01-01

Population differentiation can be driven in large part by natural selection, but selectively neutral evolution can play a prominent role in shaping patters of population divergence. The decomposition of the evolutionary history of populations into the relative effects of natural selection and selectively neutral evolution enables an understanding of the causes of population divergence and adaptation. In this study, we examined heterogeneous genomic divergence between alpine and lowland ecotypes of the allopolyploid plant, Anemone multifida. Using peak height and dominant AFLP data, we quantified population differentiation at non-outlier (neutral) and outlier loci to determine the potential contribution of natural selection and selectively neutral evolution to population divergence. We found 13 candidate loci, corresponding to 2.7% of loci, with signatures of divergent natural selection between alpine and lowland populations and between alpine populations (Fst  = 0.074–0.445 at outlier loci), but neutral population differentiation was also evident between alpine populations (FST  = 0.041–0.095 at neutral loci). By examining population structure at both neutral and outlier loci, we determined that the combined effects of selection and neutral evolution are associated with the divergence of alpine populations, which may be linked to extreme abiotic conditions and isolation between alpine sites. The presence of outlier levels of genetic variation in structured populations underscores the importance of separately analyzing neutral and outlier loci to infer the relative role of divergent natural selection and neutral evolution in population divergence. PMID:23874801

Diagonal couplings of quantum Markov chains

NASA Astrophysics Data System (ADS)

Kümmerer, Burkhard; Schwieger, Kay

2016-05-01

In this paper we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

Developing a Markov Model for Forecasting End Strength of Selected Marine Corps Reserve (SMCR) Officers

DTIC Science & Technology

2013-03-01

moving average ( ARIMA ) model because the data is not a times series. The best a manpower planner can do at this point is to make an educated assumption...MARKOV MODEL FOR FORECASTING END STRENGTH OF SELECTED MARINE CORPS RESERVE (SMCR) OFFICERS by Anthony D. Licari March 2013 Thesis Advisor...March 2013 3. REPORT TYPE AND DATES COVERED Master’s Thesis 4. TITLE AND SUBTITLE DEVELOPING A MARKOV MODEL FOR FORECASTING END STRENGTH OF

Transition records of stationary Markov chains.

PubMed

Naudts, Jan; Van der Straeten, Erik

2006-10-01

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains

NASA Astrophysics Data System (ADS)

Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.

2018-01-01

We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.

Markov and semi-Markov processes as a failure rate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grabski, Franciszek

2016-06-08

In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.

Evolutionary dynamics on graphs: Efficient method for weak selection

NASA Astrophysics Data System (ADS)

Fu, Feng; Wang, Long; Nowak, Martin A.; Hauert, Christoph

2009-04-01

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.

Modeling the evolution of regulatory elements by simultaneous detection and alignment with phylogenetic pair HMMs.

PubMed

Majoros, William H; Ohler, Uwe

2010-12-16

The computational detection of regulatory elements in DNA is a difficult but important problem impacting our progress in understanding the complex nature of eukaryotic gene regulation. Attempts to utilize cross-species conservation for this task have been hampered both by evolutionary changes of functional sites and poor performance of general-purpose alignment programs when applied to non-coding sequence. We describe a new and flexible framework for modeling binding site evolution in multiple related genomes, based on phylogenetic pair hidden Markov models which explicitly model the gain and loss of binding sites along a phylogeny. We demonstrate the value of this framework for both the alignment of regulatory regions and the inference of precise binding-site locations within those regions. As the underlying formalism is a stochastic, generative model, it can also be used to simulate the evolution of regulatory elements. Our implementation is scalable in terms of numbers of species and sequence lengths and can produce alignments and binding-site predictions with accuracy rivaling or exceeding current systems that specialize in only alignment or only binding-site prediction. We demonstrate the validity and power of various model components on extensive simulations of realistic sequence data and apply a specific model to study Drosophila enhancers in as many as ten related genomes and in the presence of gain and loss of binding sites. Different models and modeling assumptions can be easily specified, thus providing an invaluable tool for the exploration of biological hypotheses that can drive improvements in our understanding of the mechanisms and evolution of gene regulation.

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants.

PubMed

Sumner, Jeremy G; Taylor, Amelia; Holland, Barbara R; Jarvis, Peter D

2017-12-01

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for models with more than two states-for example DNA sequence alignments with four-state models-we find that methods which rely on phylogenetic invariants are incapable of satisfying all three of the stated statistical properties. This is because in these cases the relevant Markov invariants belong to a class of polynomials independent from the phylogenetic invariants.

High-Performance Nanocomposites Designed for Radiation Shielding in Space and an Application of GIS for Analyzing Nanopowder Dispersion in Polymer Matrixes

NASA Astrophysics Data System (ADS)

Auslander, Joseph Simcha

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Time-Resolved Magneto-Optical Imaging of Superconducting YBCO Thin Films in the High-Frequency AC Current Regime

NASA Astrophysics Data System (ADS)

Frey, Alexander

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Use of Remote Sensing to Identify Essential Habitat for Aeschynomene virginica (L.) BSP, a Threatened Tidal Freshwater Wetland Plant

NASA Astrophysics Data System (ADS)

Mountz, Elizabeth M.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Silver-Polyimide Nanocomposite Films: Single-Stage Synthesis and Analysis of Metalized Partially-Fluorinated Polyimide BTDA/4-BDAF Prepared from Silver(I) Complexes

NASA Astrophysics Data System (ADS)

Abelard, Joshua Erold Robert

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Multifunctional Polymer Synthesis and Incorporation of Gadolinium Compounds and Modified Tungsten Nanoparticles for Improvement of Radiation Shielding for use in Outer Space

NASA Astrophysics Data System (ADS)

Harbert, Emily Grace

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Particle Analysis Pitfalls

NASA Technical Reports Server (NTRS)

Hughes, David; Dazzo, Tony

2007-01-01

This viewgraph presentation reviews the use of particle analysis to assist in preparing for the 4th Hubble Space Telescope (HST) Servicing mission. During this mission the Space Telescope Imaging Spectrograph (STIS) will be repaired. The particle analysis consisted of Finite element mesh creation, Black-body viewfactors generated using I-DEAS TMG Thermal Analysis, Grey-body viewfactors calculated using Markov method, Particle distribution modeled using an iterative Monte Carlo process, (time-consuming); in house software called MASTRAM, Differential analysis performed in Excel, and Visualization provided by Tecplot and I-DEAS. Several tests were performed and are reviewed: Conformal Coat Particle Study, Card Extraction Study, Cover Fastener Removal Particle Generation Study, and E-Graf Vibration Particulate Study. The lessons learned during this analysis are also reviewed.

Conspecific Crop-Weed Introgression Influences Evolution of Weedy Rice (Oryza sativa f. spontanea) across a Geographical Range

PubMed Central

Xia, Han-Bing; Wang, Wei; Xia, Hui; Zhao, Wei; Lu, Bao-Rong

2011-01-01

Background Introgression plays an important role in evolution of plant species via its influences on genetic diversity and differentiation. Outcrossing determines the level of introgression but little is known about the relationships of outcrossing rates, genetic diversity, and differentiation particularly in a weedy taxon that coexists with its conspecific crop. Methodology/Principal Findings Eleven weedy rice (Oryza sativa f. spontanea) populations from China were analyzed using microsatellite (SSR) fingerprints to study outcrossing rate and its relationship with genetic variability and differentiation. To estimate outcrossing, six highly polymorphic SSR loci were used to analyze >5500 progeny from 216 weedy rice families, applying a mixed mating model; to estimate genetic diversity and differentiation, 22 SSR loci were analyzed based on 301 weedy individuals. Additionally, four weed-crop shared SSR loci were used to estimate the influence of introgression from rice cultivars on weedy rice differentiation. Outcrossing rates varied significantly (0.4∼11.7%) among weedy rice populations showing relatively high overall Nei's genetic diversity (0.635). The observed heterozygosity was significantly correlated with outcrossing rates among populations (r2 = 0.783; P<0.001) although no obvious correlation between outcrossing rates and genetic diversity parameters was observed. Allelic introgression from rice cultivars to their coexisting weedy rice was detected. Weedy rice populations demonstrated considerable genetic differentiation that was correlated with their spatial distribution (r2 = 0.734; P<0.001), and possibly also influenced by the introgression from rice cultivars. Conclusions/Significance Outcrossing rates can significantly affect heterozygosity of populations, which may shape the evolutionary potential of weedy rice. Introgression from the conspecific crop rice can influence the genetic differentiation and possibly evolution of its coexisting weedy rice populations. PMID:21249201

Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation

NASA Astrophysics Data System (ADS)

Laslier, Benoît; Toninelli, Fabio Lucio

2018-03-01

We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the {L× L} torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167-192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2 n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274-325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as L\\to∞ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C 2 differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007-2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model (Funaki and Spohn in Commun Math Phys 85:1-36, 1997; Nishikawa in Commun Math Phys 127:205-227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Orbital Architectures of Dynamically Complex Exoplanet Systems

NASA Astrophysics Data System (ADS)

Nelson, Benjamin E.

2015-01-01

The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. We develop a differential evolution Markov chain Monte Carlo (RUN DMC) to tackle these difficult aspects of data analysis. We apply RUN DMC to two classic multi-planet systems from radial velocity surveys, 55 Cancri and GJ 876. For 55 Cancri, we find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet's orbit to cross the stellar surface. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50±610 degrees), but they are not orbiting in a mean-motion resonance. For GJ 876, we can meaningfully constrain the three-dimensional orbital architecture of all the planets based on the radial velocity data alone. By demanding orbital stability, we find the resonant planets have low mutual inclinations (Φ) so they must be roughly coplanar (Φcb = 1.41±0.620.57 degrees and Φbe = 3.87±1.991.86 degrees). The three-dimensional Laplace argument librates with an amplitude of 50.5±7.910.0 degrees, indicating significant past disk migration and ensuring long-term stability. These empirically derived models will provide new challenges for planet formation models and motivate the need for more sophisticated algorithms to analyze exoplanet data.

A finite state projection algorithm for the stationary solution of the chemical master equation.

PubMed

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-21

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 10 6 states can be efficiently solved.

A finite state projection algorithm for the stationary solution of the chemical master equation

NASA Astrophysics Data System (ADS)

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-01

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 106 states can be efficiently solved.

A simplified parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.

Magma oceanography. I - Thermal evolution. [of lunar surface

NASA Technical Reports Server (NTRS)

Solomon, S. C.; Longhi, J.

1977-01-01

Fractional crystallization and flotation of cumulate plagioclase in a cooling 'magma ocean' provides the simplest explanation for early emplacement of a thick feldspar-rich lunar crust. The complementary mafic cumulates resulting from the differentiation of such a magma ocean have been identified as the ultimate source of mare basalt liquids on the basis or rare-earth abundance patterns and experimental petrology studies. A study is conducted concerning the thermal evolution of the early differentiation processes. A range of models of increasing sophistication are considered. The models developed contain the essence of the energetics and the time scale for magma ocean differentiation. Attention is given to constraints on a magma ocean, modeling procedures, single-component magma oceans, fractionating magma oceans, and evolving magma oceans.

Gene duplication and the evolution of phenotypic diversity in insect societies.

PubMed

Chau, Linh M; Goodisman, Michael A D

2017-12-01

Gene duplication is an important evolutionary process thought to facilitate the evolution of phenotypic diversity. We investigated if gene duplication was associated with the evolution of phenotypic differences in a highly social insect, the honeybee Apis mellifera. We hypothesized that the genetic redundancy provided by gene duplication could promote the evolution of social and sexual phenotypes associated with advanced societies. We found a positive correlation between sociality and rate of gene duplications across the Apoidea, indicating that gene duplication may be associated with sociality. We also discovered that genes showing biased expression between A. mellifera alternative phenotypes tended to be found more frequently than expected among duplicated genes than singletons. Moreover, duplicated genes had higher levels of caste-, sex-, behavior-, and tissue-biased expression compared to singletons, as expected if gene duplication facilitated phenotypic differentiation. We also found that duplicated genes were maintained in the A. mellifera genome through the processes of conservation, neofunctionalization, and specialization, but not subfunctionalization. Overall, we conclude that gene duplication may have facilitated the evolution of social and sexual phenotypes, as well as tissue differentiation. Thus this study further supports the idea that gene duplication allows species to evolve an increased range of phenotypic diversity. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

A tridiagonal parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.

Reliability Assessment of Reconfigurable Flight Control Systems Using Sure and Assist

NASA Technical Reports Server (NTRS)

Wu, N. Eva

1992-01-01

This paper presents a reliability assessment of Reconfigurable Flight Control Systems using Semi-Markov Unreliability Range Evaluator (SURE) and Abstract Semi-Markov Specification Interface to the SURE Tool (ASSIST).

The application of Markov decision process with penalty function in restaurant delivery robot

NASA Astrophysics Data System (ADS)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional Markov decision process path planning algorithm is not save, the robot is very close to the table and chairs. To solve this problem, this paper proposes the Markov Decision Process with a penalty term called MDPPT path planning algorithm according to the traditional Markov decision process (MDP). For MDP, if the restaurant delivery robot bumps into an obstacle, the reward it receives is part of the current status reward. For the MDPPT, the reward it receives not only the part of the current status but also a negative constant term. Simulation results show that the MDPPT algorithm can plan a more secure path.

Three real-time architectures - A study using reward models

NASA Technical Reports Server (NTRS)

Sjogren, J. A.; Smith, R. M.

1990-01-01

Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the evolutionary behavior of the computer system by a continuous-time Markov chain, and a reward rate is associated with each state. In reliability/availability models, upstates have reward rate 1, and down states have reward rate zero associated with them. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Steady-state expected reward rate and expected instantaneous reward rate are clearly useful measures which can be extracted from the Markov reward model. The diversity of areas where Markov reward models may be used is illustrated with a comparative study of three examples of interest to the fault tolerant computing community.

Mathematics in Physics Education: Scanning Historical Evolution of the Differential to Find a More Appropriate Model for Teaching Differential Calculus in Physics

ERIC Educational Resources Information Center

Martinez-Torregrosa, Joaquin; Lopez-Gay, Rafael; Gras-Marti, Albert

2006-01-01

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done a historic and epistemological study aimed at clarifying the role and the meaning of the differential in…

Markov reward processes

NASA Technical Reports Server (NTRS)

Smith, R. M.

1991-01-01

Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.

A reward semi-Markov process with memory for wind speed modeling

NASA Astrophysics Data System (ADS)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. The primary goal of this analysis is the study of the time history of the wind in order to assess its reliability as a source of power and to determine the associated storage levels required. In order to assess this issue we use a probabilistic model based on indexed semi-Markov process [4] to which a reward structure is attached. Our model is used to calculate the expected energy produced by a given turbine and its variability expressed by the variance of the process. Our results can be used to compare different wind farms based on their reward and also on the risk of missed production due to the intrinsic variability of the wind speed process. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and backtesting procedure is used to compare results on first and second oder moments of rewards between real and synthetic data. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic gen- eration of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Re- newable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribu- tion, Renewable Energy 28 (2003) 1787-1802. [4]F. Petroni, G. D'Amico, F. Prattico, Indexed semi-Markov process for wind speed modeling. To be submitted.

Testing the link between population genetic differentiation and clade diversification in Costa Rican orchids.

PubMed

Kisel, Yael; Moreno-Letelier, Alejandra C; Bogarín, Diego; Powell, Martyn P; Chase, Mark W; Barraclough, Timothy G

2012-10-01

Species population genetics could be an important factor explaining variation in clade species richness. Here, we use newly generated amplified fragment length polymorphism (AFLP) data to test whether five pairs of sister clades of Costa Rican orchids that differ greatly in species richness also differ in average neutral genetic differentiation within species, expecting that if the strength of processes promoting differentiation within species is phylogenetically heritable, then clades with greater genetic differentiation should diversify more. Contrary to expectation, neutral genetic differentiation does not correlate directly with total diversification in the clades studied. Neutral genetic differentiation varies greatly among species and shows no heritability within clades. Half of the variation in neutral genetic differentiation among populations can be explained by ecological variables, and species-level traits explain the most variation. Unexpectedly, we find no isolation by distance in any species, but genetic differentiation is greater between populations occupying different niches. This pattern corresponds with those observed for microscopic eukaryotes and could reflect effective widespread dispersal of tiny and numerous orchid seeds. Although not providing a definitive answer to whether population genetics processes affect clade diversification, this work highlights the potential for addressing new macroevolutionary questions using a comparative population genetic approach. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.

Merging metagenomics and geochemistry reveals environmental controls on biological diversity and evolution.

PubMed

Alsop, Eric B; Boyd, Eric S; Raymond, Jason

2014-05-28

The metabolic strategies employed by microbes inhabiting natural systems are, in large part, dictated by the physical and geochemical properties of the environment. This study sheds light onto the complex relationship between biology and environmental geochemistry using forty-three metagenomes collected from geochemically diverse and globally distributed natural systems. It is widely hypothesized that many uncommonly measured geochemical parameters affect community dynamics and this study leverages the development and application of multidimensional biogeochemical metrics to study correlations between geochemistry and microbial ecology. Analysis techniques such as a Markov cluster-based measure of the evolutionary distance between whole communities and a principal component analysis (PCA) of the geochemical gradients between environments allows for the determination of correlations between microbial community dynamics and environmental geochemistry and provides insight into which geochemical parameters most strongly influence microbial biodiversity. By progressively building from samples taken along well defined geochemical gradients to samples widely dispersed in geochemical space this study reveals strong links between the extent of taxonomic and functional diversification of resident communities and environmental geochemistry and reveals temperature and pH as the primary factors that have shaped the evolution of these communities. Moreover, the inclusion of extensive geochemical data into analyses reveals new links between geochemical parameters (e.g. oxygen and trace element availability) and the distribution and taxonomic diversification of communities at the functional level. Further, an overall geochemical gradient (from multivariate analyses) between natural systems provides one of the most complete predictions of microbial taxonomic and functional composition. Clustering based on the frequency in which orthologous proteins occur among metagenomes facilitated accurate prediction of the ordering of community functional composition along geochemical gradients, despite a lack of geochemical input. The consistency in the results obtained from the application of Markov clustering and multivariate methods to distinct natural systems underscore their utility in predicting the functional potential of microbial communities within a natural system based on system geochemistry alone, allowing geochemical measurements to be used to predict purely biological metrics such as microbial community composition and metabolism.

TH-A-BRF-02: BEST IN PHYSICS (JOINT IMAGING-THERAPY) - Modeling Tumor Evolution for Adaptive Radiation Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Y; Lee, CG; Chan, TCY

2014-06-15

Purpose: To develop mathematical models of tumor geometry changes under radiotherapy that may support future adaptive paradigms. Methods: A total of 29 cervical patients were scanned using MRI, once for planning and weekly thereafter for treatment monitoring. Using the tumor volumes contoured by a radiologist, three mathematical models were investigated based on the assumption of a stochastic process of tumor evolution. The “weekly MRI” model predicts tumor geometry for the following week from the last two consecutive MRI scans, based on the voxel transition probability. The other two models use only the first pair of consecutive MRI scans, and themore » transition probabilities were estimated via tumor type classified from the entire data set. The classification is based on either measuring the tumor volume (the “weekly volume” model), or implementing an auxiliary “Markov chain” model. These models were compared to a constant volume approach that represents the current clinical practice, using various model parameters; e.g., the threshold probability β converts the probability map into a tumor shape (larger threshold implies smaller tumor). Model performance was measured using volume conformity index (VCI), i.e., the union of the actual target and modeled target volume squared divided by product of these two volumes. Results: The “weekly MRI” model outperforms the constant volume model by 26% on average, and by 103% for the worst 10% of cases in terms of VCI under a wide range of β. The “weekly volume” and “Markov chain” models outperform the constant volume model by 20% and 16% on average, respectively. They also perform better than the “weekly MRI” model when β is large. Conclusion: It has been demonstrated that mathematical models can be developed to predict tumor geometry changes for cervical cancer undergoing radiotherapy. The models can potentially support adaptive radiotherapy paradigm by reducing normal tissue dose. This research was supported in part by the Ontario Consortium for Adaptive Interventions in Radiation Oncology (OCAIRO) funded by the Ontario Research Fund (ORF) and the MITACS Accelerate Internship Program.« less

Tracing the first step to speciation: ecological and genetic differentiation of a salamander population in a small forest.

PubMed

Steinfartz, Sebastian; Weitere, Markus; Tautz, Diethard

2007-11-01

Mechanisms and processes of ecologically driven adaptive speciation are best studied in natural situations where the splitting process is still occurring, i.e. before complete reproductive isolation is achieved. Here, we present a case of an early stage of adaptive differentiation under sympatric conditions in the fire salamander, Salamandra salamandra, that allows inferring the underlying processes for the split. Larvae of S. salamandra normally mature in small streams until metamorphosis, but in an old, continuous forest area near Bonn (the Kottenforst), we found salamander larvae not only in small streams but also in shallow ponds, which are ecologically very different from small streams. Common-environment experiments with larvae from both habitat types reveal specific adaptations to these different ecological conditions. Mitochondrial and microsatellite analyses show that the two ecologically differentiated groups also show signs of genetic differentiation. A parallel analysis of animals from a neighbouring much larger forest area (the Eifel), in which larvae mature only in streams, shows no signs of genetic differentiation, indicating that gene flow between ecologically similar types can occur over large distances. Hence, geographical factors cannot explain the differential larval habitat adaptations in the Kottenforst, in particular since adult life and mating of S. salamandra is strictly terrestrial and not associated with larval habitats. We propose therefore that the evolution of these adaptations was coupled with the evolution of cues for assortative mating which would be in line with models of sympatric speciation that suggest a co-evolution of habitat adaptations and associated mating signals.

Sex-dependent selection differentially shapes genetic variation on and off the guppy Y chromosome.

PubMed

Postma, Erik; Spyrou, Nicolle; Rollins, Lee Ann; Brooks, Robert C

2011-08-01

Because selection is often sex-dependent, alleles can have positive effects on fitness in one sex and negative effects in the other, resulting in intralocus sexual conflict. Evolutionary theory predicts that intralocus sexual conflict can drive the evolution of sex limitation, sex-linkage, and sex chromosome differentiation. However, evidence that sex-dependent selection results in sex-linkage is limited. Here, we formally partition the contribution of Y-linked and non-Y-linked quantitative genetic variation in coloration, tail, and body size of male guppies (Poecilia reticulata)-traits previously implicated as sexually antagonistic. We show that these traits are strongly genetically correlated, both on and off the Y chromosome, but that these correlations differ in sign and magnitude between both parts of the genome. As predicted, variation in attractiveness was found to be associated with the Y-linked, rather than with the non-Y-linked component of genetic variation in male ornamentation. These findings show how the evolution of Y-linkage may be able to resolve sexual conflict. More generally, they provide unique insight into how sex-specific selection has the potential to differentially shape the genetic architecture of fitness traits across different parts of the genome. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Markov chain model for demersal fish catch analysis in Indonesia

NASA Astrophysics Data System (ADS)

Firdaniza; Gusriani, N.

2018-03-01

As an archipelagic country, Indonesia has considerable potential fishery resources. One of the fish resources that has high economic value is demersal fish. Demersal fish is a fish with a habitat in the muddy seabed. Demersal fish scattered throughout the Indonesian seas. Demersal fish production in each Indonesia’s Fisheries Management Area (FMA) varies each year. In this paper we have discussed the Markov chain model for demersal fish yield analysis throughout all Indonesia’s Fisheries Management Area. Data of demersal fish catch in every FMA in 2005-2014 was obtained from Directorate of Capture Fisheries. From this data a transition probability matrix is determined by the number of transitions from the catch that lie below the median or above the median. The Markov chain model of demersal fish catch data was an ergodic Markov chain model, so that the limiting probability of the Markov chain model can be determined. The predictive value of demersal fishing yields was obtained by calculating the combination of limiting probability with average catch results below the median and above the median. The results showed that for 2018 and long-term demersal fishing results in most of FMA were below the median value.

Differential Activity-Driven Instabilities in Biphasic Active Matter

NASA Astrophysics Data System (ADS)

Weber, Christoph A.; Rycroft, Chris H.; Mahadevan, L.

2018-06-01

Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

Poorly Differentiated Thyroid Carcinoma.

PubMed

Setia, Namrata; Barletta, Justine A

2014-12-01

Poorly differentiated thyroid carcinoma (PDTC) has been recognized for the past 30 years as an entity showing intermediate differentiation and clinical behavior between well-differentiated thyroid carcinomas (ie, papillary thyroid carcinoma and follicular thyroid carcinoma) and anaplastic thyroid carcinoma; however, there has been considerable controversy around the definition of PDTC. In this review, the evolution in the definition of PDTC, current diagnostic criteria, differential diagnoses, potentially helpful immunohistochemical studies, and molecular alterations are discussed with the aim of highlighting where the diagnosis of PDTC currently stands. Published by Elsevier Inc.

Bayesian explorations of fault slip evolution over the earthquake cycle

NASA Astrophysics Data System (ADS)

Duputel, Z.; Jolivet, R.; Benoit, A.; Gombert, B.

2017-12-01

The ever-increasing amount of geophysical data continuously opens new perspectives on fundamental aspects of the seismogenic behavior of active faults. In this context, the recent fleet of SAR satellites including Sentinel-1 and COSMO-SkyMED permits the use of InSAR for time-dependent slip modeling with unprecedented resolution in time and space. However, existing time-dependent slip models rely on spatial smoothing regularization schemes, which can produce unrealistically smooth slip distributions. In addition, these models usually do not include uncertainty estimates thereby reducing the utility of such estimates. Here, we develop an entirely new approach to derive probabilistic time-dependent slip models. This Markov-Chain Monte Carlo method involves a series of transitional steps to predict and update posterior Probability Density Functions (PDFs) of slip as a function of time. We assess the viability of our approach using various slow-slip event scenarios. Using a dense set of SAR images, we also use this method to quantify the spatial distribution and temporal evolution of slip along a creeping segment of the North Anatolian Fault. This allows us to track a shallow aseismic slip transient lasting for about a month with a maximum slip of about 2 cm.

Evolutionary Divergence in Brain Size between Migratory and Resident Birds

PubMed Central

Sol, Daniel; Garcia, Núria; Iwaniuk, Andrew; Davis, Katie; Meade, Andrew; Boyle, W. Alice; Székely, Tamás

2010-01-01

Despite important recent progress in our understanding of brain evolution, controversy remains regarding the evolutionary forces that have driven its enormous diversification in size. Here, we report that in passerine birds, migratory species tend to have brains that are substantially smaller (relative to body size) than those of resident species, confirming and generalizing previous studies. Phylogenetic reconstructions based on Bayesian Markov chain methods suggest an evolutionary scenario in which some large brained tropical passerines that invaded more seasonal regions evolved migratory behavior and migration itself selected for smaller brain size. Selection for smaller brains in migratory birds may arise from the energetic and developmental costs associated with a highly mobile life cycle, a possibility that is supported by a path analysis. Nevertheless, an important fraction (over 68%) of the correlation between brain mass and migratory distance comes from a direct effect of migration on brain size, perhaps reflecting costs associated with cognitive functions that have become less necessary in migratory species. Overall, our results highlight the importance of retrospective analyses in identifying selective pressures that have shaped brain evolution, and indicate that when it comes to the brain, larger is not always better. PMID:20224776

Study of selected phenotype switching strategies in time varying environment

NASA Astrophysics Data System (ADS)

Horvath, Denis; Brutovsky, Branislav

2016-03-01

Population heterogeneity plays an important role across many research, as well as the real-world, problems. The population heterogeneity relates to the ability of a population to cope with an environment change (or uncertainty) preventing its extinction. However, this ability is not always desirable as can be exemplified by an intratumor heterogeneity which positively correlates with the development of resistance to therapy. Causation of population heterogeneity is therefore in biology and medicine an intensively studied topic. In this paper the evolution of a specific strategy of population diversification, the phenotype switching, is studied at a conceptual level. The presented simulation model studies evolution of a large population of asexual organisms in a time-varying environment represented by a stochastic Markov process. Each organism disposes with a stochastic or nonlinear deterministic switching strategy realized by discrete-time models with evolvable parameters. We demonstrate that under rapidly varying exogenous conditions organisms operate in the vicinity of the bet-hedging strategy, while the deterministic patterns become relevant as the environmental variations are less frequent. Statistical characterization of the steady state regimes of the populations is done using the Hellinger and Kullback-Leibler functional distances and the Hamming distance.

Analysis and design of a second-order digital phase-locked loop

NASA Technical Reports Server (NTRS)

Blasche, P. R.

1979-01-01

A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.

Reliability Analysis of the Electrical Control System of Subsea Blowout Preventers Using Markov Models

PubMed Central

Liu, Zengkai; Liu, Yonghong; Cai, Baoping

2014-01-01

Reliability analysis of the electrical control system of a subsea blowout preventer (BOP) stack is carried out based on Markov method. For the subsea BOP electrical control system used in the current work, the 3-2-1-0 and 3-2-0 input voting schemes are available. The effects of the voting schemes on system performance are evaluated based on Markov models. In addition, the effects of failure rates of the modules and repair time on system reliability indices are also investigated. PMID:25409010

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Path integrals and large deviations in stochastic hybrid systems.

PubMed

Bressloff, Paul C; Newby, Jay M

2014-04-01

We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

Comparative Genomics Identifies Epidermal Proteins Associated with the Evolution of the Turtle Shell

PubMed Central

Holthaus, Karin Brigit; Strasser, Bettina; Sipos, Wolfgang; Schmidt, Heiko A.; Mlitz, Veronika; Sukseree, Supawadee; Weissenbacher, Anton; Tschachler, Erwin; Alibardi, Lorenzo; Eckhart, Leopold

2016-01-01

The evolution of reptiles, birds, and mammals was associated with the origin of unique integumentary structures. Studies on lizards, chicken, and humans have suggested that the evolution of major structural proteins of the outermost, cornified layers of the epidermis was driven by the diversification of a gene cluster called Epidermal Differentiation Complex (EDC). Turtles have evolved unique defense mechanisms that depend on mechanically resilient modifications of the epidermis. To investigate whether the evolution of the integument in these reptiles was associated with specific adaptations of the sequences and expression patterns of EDC-related genes, we utilized newly available genome sequences to determine the epidermal differentiation gene complement of turtles. The EDC of the western painted turtle (Chrysemys picta bellii) comprises more than 100 genes, including at least 48 genes that encode proteins referred to as beta-keratins or corneous beta-proteins. Several EDC proteins have evolved cysteine/proline contents beyond 50% of total amino acid residues. Comparative genomics suggests that distinct subfamilies of EDC genes have been expanded and partly translocated to loci outside of the EDC in turtles. Gene expression analysis in the European pond turtle (Emys orbicularis) showed that EDC genes are differentially expressed in the skin of the various body sites and that a subset of beta-keratin genes within the EDC as well as those located outside of the EDC are expressed predominantly in the shell. Our findings give strong support to the hypothesis that the evolutionary innovation of the turtle shell involved specific molecular adaptations of epidermal differentiation. PMID:26601937

[Development of Markov models for economics evaluation of strategies on hepatitis B vaccination and population-based antiviral treatment in China].

PubMed

Yang, P C; Zhang, S X; Sun, P P; Cai, Y L; Lin, Y; Zou, Y H

2017-07-10

Objective: To construct the Markov models to reflect the reality of prevention and treatment interventions against hepatitis B virus (HBV) infection, simulate the natural history of HBV infection in different age groups and provide evidence for the economics evaluations of hepatitis B vaccination and population-based antiviral treatment in China. Methods: According to the theory and techniques of Markov chain, the Markov models of Chinese HBV epidemic were developed based on the national data and related literature both at home and abroad, including the settings of Markov model states, allowable transitions and initial and transition probabilities. The model construction, operation and verification were conducted by using software TreeAge Pro 2015. Results: Several types of Markov models were constructed to describe the disease progression of HBV infection in neonatal period, perinatal period or adulthood, the progression of chronic hepatitis B after antiviral therapy, hepatitis B prevention and control in adults, chronic hepatitis B antiviral treatment and the natural progression of chronic hepatitis B in general population. The model for the newborn was fundamental which included ten states, i.e . susceptiblity to HBV, HBsAg clearance, immune tolerance, immune clearance, low replication, HBeAg negative CHB, compensated cirrhosis, decompensated cirrhosis, hepatocellular carcinoma (HCC) and death. The susceptible state to HBV was excluded in the perinatal period model, and the immune tolerance state was excluded in the adulthood model. The model for general population only included two states, survive and death. Among the 5 types of models, there were 9 initial states assigned with initial probabilities, and 27 states for transition probabilities. The results of model verifications showed that the probability curves were basically consistent with the situation of HBV epidemic in China. Conclusion: The Markov models developed can be used in economics evaluation of hepatitis B vaccination and treatment for the elimination of HBV infection in China though the structures and parameters in the model have uncertainty with dynamic natures.

Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms

PubMed Central

Rechner, Steffen; Berger, Annabell

2016-01-01

We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442

A Langevin equation for the rates of currency exchange based on the Markov analysis

NASA Astrophysics Data System (ADS)

Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G. R.; Ghasemi, F.; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2007-11-01

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D and D, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.

Decomposition of conditional probability for high-order symbolic Markov chains.

PubMed

Melnik, S S; Usatenko, O V

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Monte Carlo estimation of total variation distance of Markov chains on large spaces, with application to phylogenetics.

PubMed

Herbei, Radu; Kubatko, Laura

2013-03-26

Markov chains are widely used for modeling in many areas of molecular biology and genetics. As the complexity of such models advances, it becomes increasingly important to assess the rate at which a Markov chain converges to its stationary distribution in order to carry out accurate inference. A common measure of convergence to the stationary distribution is the total variation distance, but this measure can be difficult to compute when the state space of the chain is large. We propose a Monte Carlo method to estimate the total variation distance that can be applied in this situation, and we demonstrate how the method can be efficiently implemented by taking advantage of GPU computing techniques. We apply the method to two Markov chains on the space of phylogenetic trees, and discuss the implications of our findings for the development of algorithms for phylogenetic inference.

A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

NASA Astrophysics Data System (ADS)

Hersvik, K.; Endrerud, O.-E. V.

2017-12-01

A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

Decomposition of conditional probability for high-order symbolic Markov chains

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China☆

PubMed Central

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-01-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China.

PubMed

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-05-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology.

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

NASA Astrophysics Data System (ADS)

Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes

2018-03-01

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

VAMPnets for deep learning of molecular kinetics.

PubMed

Mardt, Andreas; Pasquali, Luca; Wu, Hao; Noé, Frank

2018-01-02

There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Potential for the evolution of heavy metal tolerance in Bryum argenteum, a moss. II. Generalized tolerances among diverse populations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shaw, A.J.; Albright, D.L.

Tolerance of copper, zinc, lead, and nickel were measured in two individuals from each of seven populations of Bryum argenteum. The populations represented a range of habitats including industrial sites subject to atmospheric metal deposition, metal-contaminated mine tailings, serpentine barrens, and urban areas. Nevertheless, there was no evidence of adaptive differentiation in tolerance to any of the metals. Populations did differ significantly in general growth vigor across all experimental treatments. These observations contrast with results from studies of angiosperms, in which the evolution of heavy-metal tolerance almost always involves ecotypic differentiation among populations, but fit an emerging picture of B.more » argenteum as a plastic, broadly tolerant species with surprisingly little genetic differentiation among populations.« less

The magma ocean concept and lunar evolution

NASA Technical Reports Server (NTRS)

Warren, P. H.

1985-01-01

The model of lunar evolution in which the anorthositic plagioclase-rich oldest crust of the moon is formed over a period of 300 Myr or less by crystallization as it floats on a global ocean of magma tens or hundreds of km thick is examined in a review of petrological and theoretical studies. Consideration is given to the classification of lunar rocks, the evidence for primordial deep global differentiation, constraints on the depth of the molten zone, the effects of pressure on mineral stability relationships, mainly-liquid vs mainly-magmifer ocean models, and the evidence for multiple ancient differentiation episodes. A synthesis of the model of primordial differentiation and its aftereffects is presented, and the generalization of the model to the earth and to Mars, Mercury, Venus, and the asteroids is discussed.

QoS Differential Scheduling in Cognitive-Radio-Based Smart Grid Networks: An Adaptive Dynamic Programming Approach.

PubMed

Yu, Rong; Zhong, Weifeng; Xie, Shengli; Zhang, Yan; Zhang, Yun

2016-02-01

As the next-generation power grid, smart grid will be integrated with a variety of novel communication technologies to support the explosive data traffic and the diverse requirements of quality of service (QoS). Cognitive radio (CR), which has the favorable ability to improve the spectrum utilization, provides an efficient and reliable solution for smart grid communications networks. In this paper, we study the QoS differential scheduling problem in the CR-based smart grid communications networks. The scheduler is responsible for managing the spectrum resources and arranging the data transmissions of smart grid users (SGUs). To guarantee the differential QoS, the SGUs are assigned to have different priorities according to their roles and their current situations in the smart grid. Based on the QoS-aware priority policy, the scheduler adjusts the channels allocation to minimize the transmission delay of SGUs. The entire transmission scheduling problem is formulated as a semi-Markov decision process and solved by the methodology of adaptive dynamic programming. A heuristic dynamic programming (HDP) architecture is established for the scheduling problem. By the online network training, the HDP can learn from the activities of primary users and SGUs, and adjust the scheduling decision to achieve the purpose of transmission delay minimization. Simulation results illustrate that the proposed priority policy ensures the low transmission delay of high priority SGUs. In addition, the emergency data transmission delay is also reduced to a significantly low level, guaranteeing the differential QoS in smart grid.