Bogen, K T
2007-05-11
A relatively simple, quantitative approach is proposed to address a specific, important gap in the appr approach recommended by the USEPA Guidelines for Cancer Risk Assessment to oach address uncertainty in carcinogenic mode of action of certain chemicals when risk is extrapolated from bioassay data. These Guidelines recognize that some chemical carcinogens may have a site-specific mode of action (MOA) that is dual, involving mutation in addition to cell-killing induced hyperplasia. Although genotoxicity may contribute to increased risk at all doses, the Guidelines imply that for dual MOA (DMOA) carcinogens, judgment be used to compare and assess results obtained using separate 'linear' (genotoxic) vs. 'nonlinear' (nongenotoxic) approaches to low low-level risk extrapolation. However, the Guidelines allow the latter approach to be used only when evidence is sufficient t to parameterize a biologically based model that reliably o extrapolates risk to low levels of concern. The Guidelines thus effectively prevent MOA uncertainty from being characterized and addressed when data are insufficient to parameterize such a model, but otherwise clearly support a DMOA. A bounding factor approach - similar to that used in reference dose procedures for classic toxicity endpoints - can address MOA uncertainty in a way that avoids explicit modeling of low low-dose risk as a function of administere administered or internal dose. Even when a 'nonlinear' toxicokinetic model cannot be fully validated, implications of DMOA uncertainty on low low-dose risk may be bounded with reasonable confidence when target tumor types happen to be extremely rare. This concept was i illustrated llustrated for a likely DMOA rodent carcinogen naphthalene, specifically to the issue of risk extrapolation from bioassay data on naphthalene naphthalene-induced nasal tumors in rats. Bioassay data, supplemental toxicokinetic data, and related physiologically based p pharmacokinetic and 2 harmacokinetic 2-stage
Bogen, K T
2007-01-30
As reflected in the 2005 USEPA Guidelines for Cancer Risk Assessment, some chemical carcinogens may have a site-specific mode of action (MOA) that is dual, involving mutation in addition to cell-killing induced hyperplasia. Although genotoxicity may contribute to increased risk at all doses, the Guidelines imply that for dual MOA (DMOA) carcinogens, judgment be used to compare and assess results obtained using separate ''linear'' (genotoxic) vs. ''nonlinear'' (nongenotoxic) approaches to low-level risk extrapolation. However, the Guidelines allow the latter approach to be used only when evidence is sufficient to parameterize a biologically based model that reliably extrapolates risk to low levels of concern. The Guidelines thus effectively prevent MOA uncertainty from being characterized and addressed when data are insufficient to parameterize such a model, but otherwise clearly support a DMOA. A bounding factor approach--similar to that used in reference dose procedures for classic toxicity endpoints--can address MOA uncertainty in a way that avoids explicit modeling of low-dose risk as a function of administered or internal dose. Even when a ''nonlinear'' toxicokinetic model cannot be fully validated, implications of DMOA uncertainty on low-dose risk may be bounded with reasonable confidence when target tumor types happen to be extremely rare. This concept was illustrated for the rodent carcinogen naphthalene. Bioassay data, supplemental toxicokinetic data, and related physiologically based pharmacokinetic and 2-stage stochastic carcinogenesis modeling results all clearly indicate that naphthalene is a DMOA carcinogen. Plausibility bounds on rat-tumor-type specific DMOA-related uncertainty were obtained using a 2-stage model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Resulting bounds each provided the basis for a corresponding
Stochastic elimination of cancer cells.
Michor, Franziska; Nowak, Martin A; Frank, Steven A; Iwasa, Yoh
2003-01-01
Tissues of multicellular organisms consist of stem cells and differentiated cells. Stem cells divide to produce new stem cells or differentiated cells. Differentiated cells divide to produce new differentiated cells. We show that such a tissue design can reduce the rate of fixation of mutations that increase the net proliferation rate of cells. It has, however, no consequence for the rate of fixation of neutral mutations. We calculate the optimum relative abundance of stem cells that minimizes the rate of generating cancer cells. There is a critical fraction of stem cell divisions that is required for a stochastic elimination ('wash out') of cancer cells. PMID:14561289
A stochastic model for immunotherapy of cancer
Baar, Martina; Coquille, Loren; Mayer, Hannah; Hölzel, Michael; Rogava, Meri; Tüting, Thomas; Bovier, Anton
2016-01-01
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations. PMID:27063839
Gompertzian stochastic model with delay effect to cervical cancer growth
NASA Astrophysics Data System (ADS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Gompertzian stochastic model with delay effect to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects
NASA Technical Reports Server (NTRS)
Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip
2007-01-01
When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend
Detecting breast cancer using microwave imaging and stochastic optimization.
Jeremic, Aleksandar; Khoshrowshahli, Elham
2015-01-01
Breast cancer detection is one of the most important problems in health care as it is second most frequent cancer according to WHO. Breast cancer is among cancers which are most probably curable, only if it is diagnosed at early stages. To this purpose it has been recently proposed that microwave imaging could be used as a cheaper and safer alternative to the commonly used combination of mammography. From a physical standpoint breast cancer can be modelled as a scatterer with a significantly (tenfold) larger conductivity than a healthy tissue. In our previous work we proposed a maximum likelihood based method for detection of cancer which estimates the unknown parameters by minimizing the residual error vector assuming that the error can be modelled as a multivariate (multiple antennas) random variable. In this paper we utilize stochastic optimization technique and evaluate its applicability to the detection of cancer using numerical models. Although these models have significant limitations they are potentially useful as they provide insight in required levels of noise in order to achieve desirable detection rates.
Kerns, Sarah L.; Stock, Richard; Stone, Nelson; Buckstein, Michael; Shao, Yongzhao; Campbell, Christopher; Rath, Lynda; De Ruysscher, Dirk; Lammering, Guido; Hixson, Rosetta; Cesaretti, Jamie; Terk, Mitchell; Ostrer, Harry; Rosenstein, Barry S.
2013-01-01
Purpose: To identify single nucleotide polymorphisms (SNPs) associated with development of erectile dysfunction (ED) among prostate cancer patients treated with radiation therapy. Methods and Materials: A 2-stage genome-wide association study was performed. Patients were split randomly into a stage I discovery cohort (132 cases, 103 controls) and a stage II replication cohort (128 cases, 102 controls). The discovery cohort was genotyped using Affymetrix 6.0 genome-wide arrays. The 940 top ranking SNPs selected from the discovery cohort were genotyped in the replication cohort using Illumina iSelect custom SNP arrays. Results: Twelve SNPs identified in the discovery cohort and validated in the replication cohort were associated with development of ED following radiation therapy (Fisher combined P values 2.1 Multiplication-Sign 10{sup -5} to 6.2 Multiplication-Sign 10{sup -4}). Notably, these 12 SNPs lie in or near genes involved in erectile function or other normal cellular functions (adhesion and signaling) rather than DNA damage repair. In a multivariable model including nongenetic risk factors, the odds ratios for these SNPs ranged from 1.6 to 5.6 in the pooled cohort. There was a striking relationship between the cumulative number of SNP risk alleles an individual possessed and ED status (Sommers' D P value = 1.7 Multiplication-Sign 10{sup -29}). A 1-allele increase in cumulative SNP score increased the odds for developing ED by a factor of 2.2 (P value = 2.1 Multiplication-Sign 10{sup -19}). The cumulative SNP score model had a sensitivity of 84% and specificity of 75% for prediction of developing ED at the radiation therapy planning stage. Conclusions: This genome-wide association study identified a set of SNPs that are associated with development of ED following radiation therapy. These candidate genetic predictors warrant more definitive validation in an independent cohort.
Wang, Weikang; Quan, Yi; Fu, Qibin; Liu, Yu; Liang, Ying; Wu, Jingwen; Yang, Gen; Luo, Chunxiong; Ouyang, Qi; Wang, Yugang
2014-01-01
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy. PMID:24416258
Stochastic Effects in Computational Biology of Space Radiation Cancer Risk
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; Pluth, Janis; Harper, Jane; O'Neill, Peter
2007-01-01
Estimating risk from space radiation poses important questions on the radiobiology of protons and heavy ions. We are considering systems biology models to study radiation induced repair foci (RIRF) at low doses, in which less than one-track on average transverses the cell, and the subsequent DNA damage processing and signal transduction events. Computational approaches for describing protein regulatory networks coupled to DNA and oxidative damage sites include systems of differential equations, stochastic equations, and Monte-Carlo simulations. We review recent developments in the mathematical description of protein regulatory networks and possible approaches to radiation effects simulation. These include robustness, which states that regulatory networks maintain their functions against external and internal perturbations due to compensating properties of redundancy and molecular feedback controls, and modularity, which leads to general theorems for considering molecules that interact through a regulatory mechanism without exchange of matter leading to a block diagonal reduction of the connecting pathways. Identifying rate-limiting steps, robustness, and modularity in pathways perturbed by radiation damage are shown to be valid techniques for reducing large molecular systems to realistic computer simulations. Other techniques studied are the use of steady-state analysis, and the introduction of composite molecules or rate-constants to represent small collections of reactants. Applications of these techniques to describe spatial and temporal distributions of RIRF and cell populations following low dose irradiation are described.
Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model.
Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe
2013-10-01
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest-a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.
Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model
NASA Astrophysics Data System (ADS)
Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe
2013-10-01
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest—a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.
Little, Mark P; Vineis, Paolo; Li, Guangquan
2008-09-21
A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.
NASA Astrophysics Data System (ADS)
Warren, Patrick B.
2009-09-01
A recently proposed model for skin cell proliferation [E. Clayton , Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.
NASA Astrophysics Data System (ADS)
Zamani Dahaj, Seyed Alireza; Kumar, Niraj; Sundaram, Bala; Celli, Jonathan; Kulkarni, Rahul
The phenotypic heterogeneity of cancer cells is critical to their survival under stress. A significant contribution to heterogeneity of cancer calls derives from the epithelial-mesenchymal transition (EMT), a conserved cellular program that is crucial for embryonic development. Several studies have investigated the role of EMT in growth of early stage tumors into invasive malignancies. Also, EMT has been closely associated with the acquisition of chemoresistance properties in cancer cells. Motivated by these studies, we analyze multi-phenotype stochastic models of the evolution of cancers cell populations under stress. We derive analytical results for time-dependent probability distributions that provide insights into the competing rates underlying phenotypic switching (e.g. during EMT) and the corresponding survival of cancer cells. Experimentally, we evaluate these model-based predictions by imaging human pancreatic cancer cell lines grown with and without cytotoxic agents and measure growth kinetics, survival, morphological changes and (terminal evaluation of) biomarkers with associated epithelial and mesenchymal phenotypes. The results derived suggest approaches for distinguishing between adaptation and selection scenarios for survival in the presence of external stresses.
Figueredo, Grazziela P; Siebers, Peer-Olaf; Owen, Markus R; Reps, Jenna; Aickelin, Uwe
2014-01-01
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
Analysis of retinoblastoma age incidence data using a fully stochastic cancer model.
Little, Mark P; Kleinerman, Ruth A; Stiller, Charles A; Li, Guangquan; Kroll, Mary E; Murphy, Michael F G
2012-02-01
Retinoblastoma (RB) is an important ocular malignancy of childhood. It has been commonly accepted for some time that knockout of the two alleles of the RB1 gene is the principal molecular target associated with the occurrence of RB. In this article, we examine the validity of the two-hit theory for RB by comparing the fit of a stochastic model with two or more mutational stages. Unlike many such models, our model assumes a fully stochastic stem cell compartment, which is crucial to its behavior. Models are fitted to a population-based dataset comprising 1,553 cases of RB for the period 1962-2000 in Great Britain (England, Scotland and Wales). The population incidence of RB is best described by a fully stochastic model with two stages, although models with a deterministic stem cell compartment yield equivalent fit; models with three or more stages fit much less well. The results strongly suggest that knockout of the two alleles of the RB1 gene is necessary and may be largely sufficient for the development of RB, in support of Knudson's two-hit hypothesis.
A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer
Liu, Yifang; Lee, Chi-Guhn; Chan, Timothy C. Y.; Cho, Young-Bin; Islam, Mohammad K.
2014-02-15
Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxels on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.
Solan, Eilon; Vieille, Nicolas
2015-01-01
In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution. PMID:26556883
The National Center for Environmental Assessment (NCEA) has conducted and supported research addressing uncertainties in 2-stage clonal growth models for cancer as applied to formaldehyde. In this report, we summarized publications resulting from this research effort, discussed t...
2–stage stochastic Runge–Kutta for stochastic delay differential equations
Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah; Yeak, S. H.
2015-05-15
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.
Kossenko, M M; Hoffman, D A; Thomas, T L
2000-07-01
The Mayak Industrial Association, located in the South Ural Mountains, began operation in 1948 and was the first Russian site for the production and separation of plutonium. During the early days of operation, technological failures resulted in the release of large amounts of radioactive waste into the Techa River. Residents who lived in villages on the banks of the Techa and Iset Rivers were exposed to varying levels of radioactivity. The objective of this study is to assess stochastic (carcinogenic) effects in populations exposed to offsite releases of radioactive materials from the Mayak nuclear facility in Russia. Subjects of the present study are those individuals who lived during the period January 1950 through December 1960 in any of the exposed villages along the Techa River in Chelyabinsk Oblast. Death certificates and cancer incidence data have been routinely collected in the past from a five-rayon catchment area of Chelyabinsk Oblast. The registry of exposed residents along the Techa River assembled and maintained by the Urals Research Center for Radiation Medicine for the past 40 y is the basis for identifying study subjects for this project. Specific study objectives are to evaluate the incidence of cancer among current and former residents of Chelyabinsk Oblast who are in the exposed Techa River cohort; integrate results from the dose-reconstruction study to estimate doses for risk assessment; and develop a structure for maintaining continued follow-up of the cohort for cancer incidence. In the earlier part of our collaborative effort, the focus has been to enhance the cancer morbidity registry by updating it with cancer cases diagnosed through 1997, to conduct a series of validation procedures to ensure completeness and accuracy of the registry, and to reduce the numbers of subjects lost to follow-up. A feasibility study to determine cancer morbidity in migrants from the catchment area has been proposed. Our preliminary analyses of cancer morbidity
NASA Astrophysics Data System (ADS)
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Oroji, Amin; Omar, Mohd; Yarahmadian, Shantia
2016-10-21
In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to the cell cycle, each cell belongs to one of three subpopulations G, S, or M, representing gap, synthesis and mitosis subpopulations. Cells in the M subpopulation are highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant. Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately, the small changes in cell death rate in each subpopulation during treatment are considered. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 breast cancer cell line. Consequently, the proposed model is able to predict tumor lifespan based on the number of initial carcinoma cells. The results show the effectiveness of the radiation under the condition of stability, which describes the decreasing trend of the tumor cells population.
The 2-stage liver transplant: 3 clinical scenarios.
Gedik, Ender; Bıçakçıoğlu, Murat; Otan, Emrah; İlksen Toprak, Hüseyin; Işık, Burak; Aydın, Cemalettin; Kayaalp, Cüneyt; Yılmaz, Sezai
2015-04-01
The main goal of 2-stage liver transplant is to provide time to obtain a new liver source. We describe our experience of 3 patients with 3 different clinical conditions. A 57-year-old man was retransplanted successfully with this technique due to hepatic artery thrombosis. However, a 38-year-old woman with fulminant toxic hepatitis and a 5-year-old-boy with abdominal trauma had poor outcome. This technique could serve as a rescue therapy for liver transplant patients who have toxic liver syndrome or abdominal trauma. These patients required intensive support during long anhepatic states. The transplant team should decide early whether to use this technique before irreversible conditions develop.
NASA Astrophysics Data System (ADS)
Ross, D. K.; Moreau, William
1995-08-01
We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics ( sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h µυ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(ω), must be proportional to 1/ω 2. The proportionality constant is determined by the Planck condition that the energy density consist ofħω/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh(ω) =√16πc 2Lp/ω2. As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R iojo(Oτ-δτ/2)R kolo(O,τ+δτ/2)) of the measureable geodesic deviation tensor field,R iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order inaδτ/c provided that the temperature and acceleration satisfy the relationkT=ħa/2πc.
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
Rood, A S; McGavran, P D; Aanenson, J W; Till, J E
2001-08-01
Carbon tetrachloride is a degreasing agent that was used at the Rocky Flats Plant (RFP) in Colorado to clean product components and equipment. The chemical is considered a volatile organic compound and a probable human carcinogen. During the time the plant operated (1953-1989), most of the carbon tetrachloride was released to the atmosphere through building exhaust ducts. A smaller amount was released to the air via evaporation from open-air burn pits and ground-surface discharge points. Airborne releases from the plant were conservatively estimated to be equivalent to the amount of carbon tetrachloride consumed annually by the plant, which was estimated to be between 3.6 and 180 Mg per year. This assumption was supported by calculations that showed that most of the carbon tetrachloride discharged to the ground surface would subsequently be released to the atmosphere. Atmospheric transport of carbon tetrachloride from the plant to the surrounding community was estimated using a Gaussian Puff dispersion model (RATCHET). Time-integrated concentrations were estimated for nine hypothetical but realistic exposure scenarios that considered variation in lifestyle, location, age, and gender. Uncertainty distributions were developed for cancer slope factors and atmospheric dispersion factors. These uncertainties were propagated through to the final risk estimate using Monte Carlo techniques. The geometric mean risk estimates varied from 5.2 x 10(-6) for a hypothetical rancher or laborer working near the RFP to 3.4 x 10(-9) for an infant scenario. The distribution of incremental lifetime cancer incidence risk for the hypothetical rancher was between 1.3 x 10(-6) (5% value) and 2.1 x 10(-5) (95% value). These estimates are similar to or exceed estimated cancer risks posed by releases of radionuclides from the site.
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
Stochastic symmetries of Wick type stochastic ordinary differential equations
NASA Astrophysics Data System (ADS)
Ünal, Gazanfer
2015-04-01
We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space (S)-1N. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in (S)-1N are obtained. A stochastic version of canonical variables is also introduced.
Stochastic longshore current dynamics
NASA Astrophysics Data System (ADS)
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
Stochastic Convection Parameterizations
NASA Technical Reports Server (NTRS)
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Stochastic Pseudo-Boolean Optimization
2011-07-31
analysis of two-stage stochastic minimum s-t cut problems; (iv) exact solution algorithm for a class of stochastic bilevel knapsack problems; (v) exact...57 5 Bilevel Knapsack Problems with Stochastic Right-Hand Sides 58 6 Two-Stage Stochastic Assignment Problems 59 6.1 Introduction...programming formulations and related computational complexity issues. • Section 5 considers a specific stochastic extension of the bilevel knapsack
Research in Stochastic Processes.
1985-09-01
appear. G. Kallianpur, Finitely additive approach to nonlinear filtering, Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to...Nov. 85, in Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to appear. i. Preparation T. Hsing, Extreme value theory for...1507 Carroll, R.J., Spiegelman, C.H., Lan, K.K.G., Bailey , K.T. and Abbott, R.D., Errors in-variables for binary regression models, Aug.82. 1508
Stochastic cooling at Fermilab
Marriner, J.
1986-08-01
The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Markov stochasticity coordinates
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2017-01-01
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.
Stochastic demographic forecasting.
Lee, R D
1992-11-01
"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary.... Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented."
Analysis of bilinear stochastic systems
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Stochastic decentralized systems
NASA Astrophysics Data System (ADS)
Barfoot, Timothy David
Fundamental aspects of decentralized systems are considered from a control perspective. The stochastic framework afforded by Markov systems is presented as a formal setting in which to study decentralized systems. A stochastic algebra is introduced which allows Markov systems to be considered in matrix format but also strikes an important connection to the classic linear system originally studied by Kalman [1960]. The process of decentralization is shown to impose constraints on observability and controllability of a system. However, it is argued that communicating decentralized controllers can implement any control law possible with a centralized controller. Communication is shown to serve a dual role, both enabling sensor data to be shared and actions to be coordinated. The viabilities of these two types of communication are tested on a real network of mobile robots where they are found to be successful at a variety of tasks. Action coordination is reframed as a decentralized decision making process whereupon stochastic cellular automata (SCA) are introduced as a model. Through studies of SCA it is found that coordination in a group of arbitrarily and sparsely connected agents is possible using simple rules. The resulting stochastic mechanism may be immediately used as a practical decentralized decision making tool (it is tested on a group of mobile robots) but, it furthermore provides insight into the general features of self-organizing systems.
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Controlled Stochastic Dynamical Systems
2007-04-18
the existence of value functions of two-player zero-sum stochastic differential games Indiana Univ. Math. Journal, 38 (1989), pp 293-314. [6] George ...control problems, Adv. Appl. Prob., 15, (1983) pp 225-254. [10] Karatzas, I. Ocone, D., Wang, H. and Zervos , M., Finite fuel singular control with
Stochastic computing with biomolecular automata.
Adar, Rivka; Benenson, Yaakov; Linshiz, Gregory; Rosner, Amit; Tishby, Naftali; Shapiro, Ehud
2004-07-06
Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure.
Stochastic response surface methodology: A study in the human health area
Oliveira, Teresa A. Oliveira, Amílcar; Leal, Conceição
2015-03-10
In this paper we review Stochastic Response Surface Methodology as a tool for modeling uncertainty in the context of Risk Analysis. An application in the survival analysis in the breast cancer context is implemented with R software.
2-stage revision of 120 deep infected hip and knee prostheses using gentamicin-PMMA beads.
Janssen, Daniël M C; Geurts, Jan A P; Jütten, Liesbeth M C; Walenkamp, Geert H I M
2016-08-01
Background and purpose - A 2-stage revision is the most common treatment for late deep prosthesis-related infections and in all cases of septic loosening. However, there is no consensus about the optimal interval between the 2 stages. Patients and methods - We retrospectively studied 120 deep infections of total hip (n = 95) and knee (n = 25) prostheses that had occurred over a period of 25 years. The mean follow-up time was 5 (2-20) years. All infections had been treated with extraction, 1 or more debridements with systemic antibiotics, and implantation of gentamicin-PMMA beads. There had been different time intervals between extraction and reimplantation: median 14 (11-47) days for short-term treatment with uninterrupted hospital stay, and 7 (3-22) months for long-term treatment with temporary discharge. We analyzed the outcome regarding resolution of the infection and clinical results. Results - 88% (105/120) of the infections healed, with no difference in healing rate between short- and long-term treatment. 82 prostheses were reimplanted. In the most recent decade, we treated patients more often with a long-term treatment but reduced the length of time between the extraction and the reimplantation. More reimplantations were performed in long-term treatments than in short-term treatments, despite more having difficult-to-treat infections with worse soft-tissue condition. Interpretation - Patient, wound, and infection considerations resulted in an individualized treatment with different intervals between stages. The 2-stage revision treatment in combination with local gentamicin-PMMA beads gave good results even with difficult prosthesis infections and gentamicin-resistant bacteria.
An evaluation of a Simon 2-Stage phase II clinical trial design incorporating toxicity monitoring.
Ray, H E; Rai, S N
2011-05-01
Phase II clinical trials are usually designed to measure efficacy but patient safety is also a very important aspect. Previous authors suggested a methodology that allows one to monitor the cumulative number of toxic events after each patient is treated, which is also known as continuous toxicity monitoring. In this work we describe how to combine the continuous toxicity monitoring methodology with the Simon 2-Stage design for response. Then we investigate through simulation the combined procedure's type I and type II error rates under various combinations of design parameters. We include the underlying relationship between toxicity and response in our examination of the error rates.
Dimensional accuracy of 2-stage putty-wash impressions: influence of impression trays and viscosity.
Balkenhol, Markus; Ferger, Paul; Wöstmann, Bernd
2007-01-01
The aim of this in vitro study was to evaluate the influence of the impression tray and viscosity of the wash material on the dimensional accuracy of impressions taken using a 2-stage putty-wash technique. Identically shaped metal stock trays (MeTs) and disposable plastic stock trays (DiTs) were used for taking impressions (n = 10) of a mandibular cast (4 abutments) with 2 different impression materials. Dies were poured and the relative diameter deviation was calculated after measurement. Zero viscosity of the materials was determined. Dimensional accuracy was significantly affected when DiTs were used. Lower-viscosity wash materials led to more precise impressions.
Stochastic ice stream dynamics
NASA Astrophysics Data System (ADS)
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic ice stream dynamics
Bertagni, Matteo Bernard; Ridolfi, Luca
2016-01-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution. PMID:27457960
BLASKIEWICZ,M.BRENNAN,J.M.CAMERON,P.WEI,J.
2003-05-12
Emittance growth due to Intra-Beam Scattering significantly reduces the heavy ion luminosity lifetime in RHIC. Stochastic cooling of the stored beam could improve things considerably by counteracting IBS and preventing particles from escaping the rf bucket [1]. High frequency bunched-beam stochastic cooling is especially challenging but observations of Schottky signals in the 4-8 GHz band indicate that conditions are favorable in RHIC [2]. We report here on measurements of the longitudinal beam transfer function carried out with a pickup kicker pair on loan from FNAL TEVATRON. Results imply that for ions a coasting beam description is applicable and we outline some general features of a viable momentum cooling system for RHIC.
Methodology for Stochastic Modeling.
1985-01-01
AD-AISS 851 METHODOLOGY FOR STOCHASTIC MODELING(U) ARMY MATERIEL 11 SYSTEMS ANALYSIS ACTIYITY ABERDEEN PROVING GROUND MD H E COHEN JAN 95 RNSAA-TR-41...FORM T REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT’$ CATALOG NUMBER 4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED Methodology for...autoregression models, moving average models, ARMA, adaptive modeling, covariance methods , singular value decom- position, order determination rational
Dorogovtsev, Andrei A
2010-06-29
For sets in a Hilbert space the concept of quadratic entropy is introduced. It is shown that this entropy is finite for the range of a stochastic flow of Brownian particles on R. This implies, in particular, the fact that the total time of the free travel in the Arratia flow of all particles that started from a bounded interval is finite. Bibliography: 10 titles.
Stochastic Thermodynamics of Learning
NASA Astrophysics Data System (ADS)
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
NASA Astrophysics Data System (ADS)
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Stochastic Quantization of Instantons
NASA Astrophysics Data System (ADS)
Grandati, Y.; Bérard, A.; Grangé, P.
1996-03-01
The method of Parisi and Wu to quantize classical fields is applied to instanton solutionsϕIof euclidian non-linear theory in one dimension. The solutionϕεof the corresponding Langevin equation is built through a singular perturbative expansion inε=ℏ1/2in the frame of the center of mass of the instanton, where the differenceϕε-ϕIcarries only fluctuations of the instanton form. The relevance of the method is shown for the stochasticK dVequation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, we obtain explicit expressions for the first two orders inεof the perturbed instanton and of its Green function. Specializing to the Sine-Gordon andϕ4models, the first anharmonic correction is obtained analytically. The calculation is carried to second order for theϕ4model, showing good convergence.
Aerodynamic characteristics of the National Launch System (NLS) 1 1/2 stage launch vehicle
NASA Technical Reports Server (NTRS)
Springer, A. M.; Pokora, D. C.
1994-01-01
The National Aeronautics and Space Administration (NASA) is studying ways of assuring more reliable and cost effective means to space. One launch system studied was the NLS which included the l l/2 stage vehicle. This document encompasses the aerodynamic characteristics of the 1 l/2 stage vehicle. To support the detailed configuration definition two wind tunnel tests were conducted in the NASA Marshall Space Flight Center's 14x14-Inch Trisonic Wind Tunnel during 1992. The tests were a static stability and a pressure test, each utilizing 0.004 scale models. The static stability test resulted in the forces and moments acting on the vehicle. The aerodynamics for the reference configuration with and without feedlines and an evaluation of three proposed engine shroud configurations were also determined. The pressure test resulted in pressure distributions over the reference vehicle with and without feedlines including the reference engine shrouds. These pressure distributions were integrated and balanced to the static stability coefficients resulting in distributed aerodynamic loads on the vehicle. The wind tunnel tests covered a Mach range of 0.60 to 4.96. These ascent flight aerodynamic characteristics provide the basis for trajectory and performance analysis, loads determination, and guidance and control evaluation.
A retrodictive stochastic simulation algorithm
Vaughan, T.G. Drummond, P.D.; Drummond, A.J.
2010-05-20
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Boelter, Fred W; Xia, Yulin; Dell, Linda
2015-05-01
Sanding joint compounds is a dusty activity and exposures are not well characterized. Until the mid 1970s, asbestos-containing joint compounds were used by some people such that sanding could emit dust and asbestos fibers. We estimated the distribution of 8-h TWA concentrations and cumulative exposures to respirable dusts and chrysotile asbestos fibers for four worker groups: (1) drywall specialists, (2) generalists, (3) tradespersons who are bystanders to drywall finishing, and (4) do-it-yourselfers (DIYers). Data collected through a survey of experienced contractors, direct field observations, and literature were used to develop prototypical exposure scenarios for each worker group. To these exposure scenarios, we applied a previously developed semi-empirical mathematical model that predicts area as well as personal breathing zone respirable dust concentrations. An empirical factor was used to estimate chrysotile fiber concentrations from respirable dust concentrations. On a task basis, we found mean 8-h TWA concentrations of respirable dust and chrysotile fibers are numerically highest for specialists, followed by generalists, DIYers, and bystander tradespersons; these concentrations are estimated to be in excess of the respective current but not historical Threshold Limit Values. Due to differences in frequency of activities, annual cumulative exposures are highest for specialists, followed by generalists, bystander tradespersons, and DIYers. Cumulative exposure estimates for chrysotile fibers from drywall finishing are expected to result in few, if any, mesothelioma or excess lung cancer deaths according to recently published risk assessments. Given the dustiness of drywall finishing, we recommend diligence in the use of readily available source controls.
Stochastic Physicochemical Dynamics
NASA Astrophysics Data System (ADS)
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Stochastic thermodynamics of resetting
NASA Astrophysics Data System (ADS)
Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo
2016-03-01
Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
Stochastic ontogenetic growth model
NASA Astrophysics Data System (ADS)
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Stochastic processes in cosmology
NASA Astrophysics Data System (ADS)
Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.
1987-08-01
The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.
NASA Astrophysics Data System (ADS)
Hairer, Martin
2006-03-01
We consider a class of parabolic stochastic PDEs driven by white noise in time, and we are interested in showing ergodicity for some cases where the noise is degenerate, i.e., acts only on part of the equation. In some cases where the standard Strong Feller / Irreducibility argument fails, one can nevertheless implement a coupling construction that ensures uniqueness of the invariant measure. We focus on the example of the complex Ginzburg-Landau equation driven by real space-time white noise.
Rubinstein, Larry; Litwin, Samuel; Yothers, Greg
2012-01-01
Background Most phase II clinical trials utilize a single primary endpoint to determine the promise of a regimen for future study. However, many disorders manifest themselves in complex ways. For example, migraine headaches can cause pain, auras, photophobia, and emesis. Investigators may believe a drug is effective at reducing migraine pain and the severity of emesis during an attack. Nevertheless, they could still be interested in proceeding with development of the drug if it is effective against only one of these symptoms. Such a study would be a candidate for a clinical trial with co-primary endpoints. Purpose The purpose of the article is to provide a method for designing a 2-stage clinical trial with dichotomous co-primary endpoints of efficacy that has the ability to detect activity on either response measure with high probability when the drug is active on one or both measures, while at the same time rejecting the drug with high probability when there is little activity on both dimensions. The design enables early closure for futility and is flexible with regard to attained accrual. Methods The design is proposed in the context of cancer clinical trials where tumor response is used to assess a drug's ability to kill tumor cells and progression-free survival (PFS) status after a certain period is used to evaluate the drug's ability to stabilize tumor growth. Both endpoints are assumed to be distributed as binomial random variables, and uninteresting probabilities of success are determined from historical controls. Given the necessity of accrual flexibility, exhaustive searching algorithms to find optimum designs do not seem feasible at this time. Instead, critical values are determined for realized sample sizes using specific procedures. Then accrual windows are found to achieve a design's desired level of significance, probability of early termination (PET), and power. Results The design is illustrated with a clinical trial that examined bevacizumab in
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.
Stochastic simulation of transport phenomena
Wedgewood, L.E.; Geurts, K.R.
1995-10-01
In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
NASA Technical Reports Server (NTRS)
Whitney, W. J.; Behning, F. P.; Moffitt, T. P.; Hotz, G. M.
1980-01-01
The stage group performance of a 4 1/2 stage turbine with an average stage loading factor of 4.66 and high specific work output was determined in cold air at design equivalent speed. The four stage turbine configuration produced design equivalent work output with an efficiency of 0.856; a barely discernible difference from the 0.855 obtained for the complete 4 1/2 stage turbine in a previous investigation. The turbine was designed and the procedure embodied the following design features: (1) controlled vortex flow, (2) tailored radial work distribution, and (3) control of the location of the boundary-layer transition point on the airfoil suction surface. The efficiency forecast for the 4 1/2 stage turbine was 0.886, and the value predicted using a reference method was 0.862. The stage group performance results were used to determine the individual stage efficiencies for the condition at which design 4 1/2 stage work output was obtained. The efficiencies of stages one and four were about 0.020 lower than the predicted value, that of stage two was 0.014 lower, and that of stage three was about equal to the predicted value. Thus all the stages operated reasonably close to their expected performance levels, and the overall (4 1/2 stage) performance was not degraded by any particularly inefficient component.
Bunched beam stochastic cooling
Wei, Jie.
1992-01-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Bunched beam stochastic cooling
Wei, Jie
1992-09-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Stochastic reinforcement benefits skill acquisition.
Dayan, Eran; Averbeck, Bruno B; Richmond, Barry J; Cohen, Leonardo G
2014-02-14
Learning complex skills is driven by reinforcement, which facilitates both online within-session gains and retention of the acquired skills. Yet, in ecologically relevant situations, skills are often acquired when mapping between actions and rewarding outcomes is unknown to the learning agent, resulting in reinforcement schedules of a stochastic nature. Here we trained subjects on a visuomotor learning task, comparing reinforcement schedules with higher, lower, or no stochasticity. Training under higher levels of stochastic reinforcement benefited skill acquisition, enhancing both online gains and long-term retention. These findings indicate that the enhancing effects of reinforcement on skill acquisition depend on reinforcement schedules.
Statistical validation of stochastic models
Hunter, N.F.; Barney, P.; Paez, T.L.; Ferregut, C.; Perez, L.
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time
Stochastic Models of Polymer Systems
2016-01-01
algorithms for big data applications . (2) We studied stochastic dynamics of polymer systems in the mean field limit. (3) We studied noisy Hegselmann-Krause...DISTRIBUTION AVAILIBILITY STATEMENT 6. AUTHORS 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES 15. SUBJECT TERMS b. ABSTRACT 2. REPORT TYPE 17. LIMITATION...Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the
Stochastic roots of growth phenomena
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
Cancer begins in your cells, which are the building blocks of your body. Normally, your body forms ... be benign or malignant. Benign tumors aren't cancer while malignant ones are. Cells from malignant tumors ...
Brennan J. M.; Blaskiewicz, M.; Mernick, K.
2012-05-20
The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.
Segmentation of stochastic images with a stochastic random walker method.
Pätz, Torben; Preusser, Tobias
2012-05-01
We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.
Stacking with stochastic cooling
NASA Astrophysics Data System (ADS)
Caspers, Fritz; Möhl, Dieter
2004-10-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105 the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some considerations to the 'azimuthal' schemes.
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Stochastic simulation in systems biology
Székely, Tamás; Burrage, Kevin
2014-01-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503
Enhanced algorithms for stochastic programming
Krishna, A.S.
1993-09-01
In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean of a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Intrinsic optimization using stochastic nanomagnets
NASA Astrophysics Data System (ADS)
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-03-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Nonlinear optimization for stochastic simulations.
Johnson, Michael M.; Yoshimura, Ann S.; Hough, Patricia Diane; Ammerlahn, Heidi R.
2003-12-01
This report describes research targeting development of stochastic optimization algorithms and their application to mission-critical optimization problems in which uncertainty arises. The first section of this report covers the enhancement of the Trust Region Parallel Direct Search (TRPDS) algorithm to address stochastic responses and the incorporation of the algorithm into the OPT++ optimization library. The second section describes the Weapons of Mass Destruction Decision Analysis Center (WMD-DAC) suite of systems analysis tools and motivates the use of stochastic optimization techniques in such non-deterministic simulations. The third section details a batch programming interface designed to facilitate criteria-based or algorithm-driven execution of system-of-system simulations. The fourth section outlines the use of the enhanced OPT++ library and batch execution mechanism to perform systems analysis and technology trade-off studies in the WMD detection and response problem domain.
Stochastic excitation of stellar oscillations
NASA Astrophysics Data System (ADS)
Samadi, Reza
2001-05-01
Since more than about thirty years, solar oscillations are thought to be excited stochastically by the turbulent motions in the solar convective zone. It is currently believed that oscillations of stars lower than 2 solar masses - which possess an upper convective zone - are excited stochastically by turbulent convection in their outer layers. Providing that accurate measurements of the oscillation amplitudes and damping rates are available it is possible to evaluate the power injected into the modes and thus - by comparison with the observations - to constrain current theories. A recent theoretical work (Samadi & Goupil, 2001; Samadi et al., 2001) supplements and reinforces the theory of stochastic excitation of star vibrations. This process was generalized to a global description of the turbulent state of their convective zone. The comparison between observation and theory, thus generalized, will allow to better know the turbulent spectrum of stars, and this in particular thanks to the COROT mission.
Principal axes for stochastic dynamics
NASA Astrophysics Data System (ADS)
Vasconcelos, V. V.; Raischel, F.; Haase, M.; Peinke, J.; Wächter, M.; Lind, P. G.; Kleinhans, D.
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Stochastic determination of matrix determinants.
Dorn, Sebastian; Ensslin, Torsten A
2015-07-01
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations-matrices-acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.
NASA Technical Reports Server (NTRS)
Whitney, W. J.
1977-01-01
The stage work distribution among the three stages was very close to the design value. The specific work output-mass flow characteristics of the three stages were closely matched. The efficiency of the 3 1/2 stage turbine at design specific work output and design speed was within 0.008 of the estimated value, and this agreement was felt to demonstrate the adequacy of the prediction method in the high stage loading factor regime.
NASA Technical Reports Server (NTRS)
Lacksonen, Thomas A.
1994-01-01
Small space flight project design at NASA Langley Research Center goes through a multi-phase process from preliminary analysis to flight operations. The process insures that each system achieves its technical objectives with demonstrated quality and within planned budgets and schedules. A key technical component of early phases is decision analysis, which is a structure procedure for determining the best of a number of feasible concepts based upon project objectives. Feasible system concepts are generated by the designers and analyzed for schedule, cost, risk, and technical measures. Each performance measure value is normalized between the best and worst values and a weighted average score of all measures is calculated for each concept. The concept(s) with the highest scores are retained, while others are eliminated from further analysis. This project automated and enhanced the decision analysis process. Automation of the decision analysis process was done by creating a user-friendly, menu-driven, spreadsheet macro based decision analysis software program. The program contains data entry dialog boxes, automated data and output report generation, and automated output chart generation. The enhancements to the decision analysis process permit stochastic data entry and analysis. Rather than enter single measure values, the designers enter the range and most likely value for each measure and concept. The data can be entered at the system or subsystem level. System level data can be calculated as either sum, maximum, or product functions of the subsystem data. For each concept, the probability distributions are approximated for each measure and the total score for each concept as either constant, triangular, normal, or log-normal distributions. Based on these distributions, formulas are derived for the probability that the concept meets any given constraint, the probability that the concept meets all constraints, and the probability that the concept is within a given
Partial ASL extensions for stochastic programming.
Gay, David
2010-03-31
partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications
Stochastic Optimization of Complex Systems
Birge, John R.
2014-03-20
This project focused on methodologies for the solution of stochastic optimization problems based on relaxation and penalty methods, Monte Carlo simulation, parallel processing, and inverse optimization. The main results of the project were the development of a convergent method for the solution of models that include expectation constraints as in equilibrium models, improvement of Monte Carlo convergence through the use of a new method of sample batch optimization, the development of new parallel processing methods for stochastic unit commitment models, and the development of improved methods in combination with parallel processing for incorporating automatic differentiation methods into optimization.
Bar shapes and orbital stochasticity
Athanassoula, E. )
1990-06-01
Several independent lines of evidence suggest that the isophotes or isodensities of bars in barred galaxies are not really elliptical in shape but more rectangular. The effect this might have on the orbits in two different types of bar potentials is studied, and it is found that in both cases the percentage of stochastic orbits is much larger when the shapes are more rectangularlike or, equivalently, when the m = 4 components are more important. This can be understood with the help of the Chirikov criterion, which can predict the limit for the onset of global stochasticity. 9 refs.
QB1 - Stochastic Gene Regulation
Munsky, Brian
2012-07-23
Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.
Stochastic Kinetics of Nascent RNA
NASA Astrophysics Data System (ADS)
Xu, Heng; Skinner, Samuel O.; Sokac, Anna Marie; Golding, Ido
2016-09-01
The stochastic kinetics of transcription is typically inferred from the distribution of RNA numbers in individual cells. However, cellular RNA reflects additional processes downstream of transcription, hampering this analysis. In contrast, nascent (actively transcribed) RNA closely reflects the kinetics of transcription. We present a theoretical model for the stochastic kinetics of nascent RNA, which we solve to obtain the probability distribution of nascent RNA per gene. The model allows us to evaluate the kinetic parameters of transcription from single-cell measurements of nascent RNA. The model also predicts surprising discontinuities in the distribution of nascent RNA, a feature which we verify experimentally.
... Two kinds of lymphocytes can attack and kill cancer cells: T-cells and B-cells. Immunotherapy aims to boost the ability of the T-cell and B-cell lymphocytes to kill cancer. This kind of therapy can also be used ...
NASA Astrophysics Data System (ADS)
Michta, Mariusz
2017-02-01
In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.
Variational principles for stochastic soliton dynamics
Holm, Darryl D.; Tyranowski, Tomasz M.
2016-01-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa–Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler–Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling. PMID:27118922
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Stochastically forced zonal flows
NASA Astrophysics Data System (ADS)
Srinivasan, Kaushik
an approximate equation for the vorticity correlation function that is then solved perturbatively. The Reynolds stress of the pertubative solution can then be expressed as a function of the mean-flow and its y-derivatives. In particular, it is shown that as long as the forcing breaks mirror-symmetry, the Reynolds stress has a wave-like term, as a result of which the mean-flow is governed by a dispersive wave equation. In a separate study, Reynolds stress induced by an anisotropically forced unbounded Couette flow with uniform shear gamma, on a beta-plane, is calculated in conjunction with the eddy diffusivity of a co-evolving passive tracer. The flow is damped by linear drag on a time scale mu--1. The stochastic forcing is controlled by a parameter alpha, that characterizes whether eddies are elongated along the zonal direction (alpha < 0), the meridional direction (alpha > 0) or are isotropic (alpha = 0). The Reynolds stress varies linearly with alpha and non-linearly and non-monotonically with gamma; but the Reynolds stress is independent of beta. For positive values of alpha, the Reynolds stress displays an "anti-frictional" effect (energy is transferred from the eddies to the mean flow) and a frictional effect for negative values of alpha. With gamma = beta =0, the meridional tracer eddy diffusivity is v'2/(2mu), where v' is the meridional eddy velocity. In general, beta and gamma suppress the diffusivity below v'2/(2mu).
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Stochastic cooling: recent theoretical directions
Bisognano, J.
1983-03-01
A kinetic-equation derivation of the stochastic-cooling Fokker-Planck equation of correlation is introduced to describe both the Schottky spectrum and signal suppression. Generalizations to nonlinear gain and coupling between degrees of freedom are presented. Analysis of bunch beam cooling is included.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Brownian motors and stochastic resonance.
Mateos, José L; Alatriste, Fernando R
2011-12-01
We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.
Stochastic resonance on a circle
Wiesenfeld, K. ); Pierson, D.; Pantazelou, E.; Dames, C.; Moss, F. )
1994-04-04
We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such single-trigger'' systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.
NASA Astrophysics Data System (ADS)
Zhang, Ming
2015-10-01
A theory of 2-stage acceleration of Galactic cosmic rays in supernova remnants is proposed. The first stage is accomplished by the supernova shock front, where a power-law spectrum is established up to a certain cutoff energy. It is followed by stochastic acceleration with compressible waves/turbulence in the downstream medium. With a broad \\propto {k}-2 spectrum for the compressible plasma fluctuations, the rate of stochastic acceleration is constant over a wide range of particle momentum. In this case, the stochastic acceleration process extends the power-law spectrum cutoff energy of Galactic cosmic rays to the knee without changing the spectral slope. This situation happens as long as the rate of stochastic acceleration is faster than 1/5 of the adiabatic cooling rate. A steeper spectrum of compressible plasma fluctuations that concentrate their power in long wavelengths will accelerate cosmic rays to the knee with a small bump before its cutoff in the comic-ray energy spectrum. This theory does not require a strong amplification of the magnetic field in the upstream interstellar medium in order to accelerate cosmic rays to the knee energy.
Algorithmic advances in stochastic programming
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
... weaken. Talk with family, friends, or a support group about your feelings. Work with your health care providers throughout your treatment. Helping yourself can make you feel more in control. Support Groups The diagnosis and treatment of cancer often causes ...
Stochastic resonance in nanomechanical systems
NASA Astrophysics Data System (ADS)
Badzey, Robert L.
The phenomenon of stochastic resonance is a counter-intuitive one: adding noise to a noisy nonlinear system under the influence of a modulation results in coherent behavior. The signature of the effect is a resonance in the signal-to-noise ratio of the response over a certain range of noise power; this behavior is absent if either the modulation or the noise are absent. Stochastic resonance has attracted considerable interest over the past several decades, having been seen in a great number of physical and biological systems. Here, observation of stochastic resonance is reported for nanomechanical systems consisting of a doubly-clamped beam resonators fabricated from single-crystal silicon. Such oscillators have been found to display nonlinear and bistable behavior under the influence of large driving forces. This bistability is exploited to produce a controllable nanomechanical switch, a device that may be used as the basis for a new generation of computational memory elements. These oscillators possess large intrinsic resonance frequencies (MHz range or higher) due to their small size and relatively high stiffness; thus they have the potential to rival the current state-of-the-art of electronic and magnetic storage technologies. This small size also allows them to be packed in densities which meet or exceed the superparamagnetic limit for magnetic storage media of 100 GB/in2. Two different doubly-clamped beams were cooled to low temperatures (300 mK--4 K), and excited with a magnetomotive technique. They were driven into the nonlinear response regime, and then modulated to induce switching between their bistable states. When the modulation was reduced, the switching died out. Application of noise, either with an external broadband source or via an increase in temperature, resulted in a distinct resonance in the signal-to-noise ratio. Aside from establishing the phenomenon of stochastic resonance in yet another physical system, the observation of this effect has
Stochastic dynamics of cholera epidemics.
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Wavelet entropy of stochastic processes
NASA Astrophysics Data System (ADS)
Zunino, L.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.
2007-06-01
We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise ( -1<α< 1) and fractional Brownian motion ( 1<α< 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.
Stochastic dynamics of cholera epidemics
NASA Astrophysics Data System (ADS)
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Stochastic thermodynamics with information reservoirs
NASA Astrophysics Data System (ADS)
Barato, Andre C.; Seifert, Udo
2014-10-01
We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For a unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value of 1 /2 . For the case where energy is consumed to erase the tape, the efficiency at maximum erasure rate is found to be 1 /2 .
Stochastic background of atmospheric cascades
Wilk, G. ); Wlodarczyk, Z. )
1993-06-15
Fluctuations in the atmospheric cascades developing during the propagation of very high energy cosmic rays through the atmosphere are investigated using stochastic branching model of pure birth process with immigration. In particular, we show that the multiplicity distributions of secondaries emerging from gamma families are much narrower than those resulting from hadronic families. We argue that the strong intermittent like behaviour found recently in atmospheric families results from the fluctuations in the cascades themselves and are insensitive to the details of elementary interactions.
Stochastic Fluctuations in Gene Regulation
2005-04-01
AFRL-IF- RS -TR-2005-126 Final Technical Report April 2005 STOCHASTIC FLUCTUATIONS IN GENE REGULATION Boston University...be releasable to the general public, including foreign nations. AFRL-IF- RS -TR-2005-126 has been reviewed and is approved for publication...AGENCY REPORT NUMBER AFRL-IF- RS -TR-2005-126 11. SUPPLEMENTARY NOTES AFRL Project Engineer: Peter J. Costianes/IFED/(315) 330-4030
Stochastic resonance across bifurcation cascades
NASA Astrophysics Data System (ADS)
Nicolis, C.; Nicolis, G.
2017-03-01
The classical setting of stochastic resonance is extended to account for parameter variations leading to transitions between a unique stable state, bistability, and multistability regimes, across singularities of various kinds. Analytic expressions for the amplitude and the phase of the response in terms of key parameters are obtained. The conditions for optimal responses are derived in terms of the bifurcation parameter, the driving frequency, and the noise strength.
Optimality Functions in Stochastic Programming
2009-12-02
nonconvex. Non - convex stochastic optimization problems arise in such diverse applications as estimation of mixed logit models [2], engineering design...first- order necessary optimality conditions ; see for example Propositions 3.3.1 and 3.3.5 in [7] or Theorem 2.2.4 in [25]. If the evaluation of f j...procedures for validation analysis of a candidate point x ∈ IRn. Since P may be nonconvex, we focus on first-order necessary optimality conditions as
Stochastic cooling technology at Fermilab
NASA Astrophysics Data System (ADS)
Pasquinelli, Ralph J.
2004-10-01
The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.
Stochastic Modeling Of Biochemical Reactions
2006-11-01
chemical reactions. Often for these reactions, the dynamics of the first M-order statistical moments of the species populations do not form a closed...results a stochastic model for gene expression is investigated. We show that in gene expression mechanisms , in which a protein inhibits its own...chemical reactions [7, 8, 4, 9, 10]. Since one is often interested in only the first and second order statistical moments for the number of molecules of
Turbulence, Spontaneous Stochasticity and Climate
NASA Astrophysics Data System (ADS)
Eyink, Gregory
Turbulence is well-recognized as important in the physics of climate. Turbulent mixing plays a crucial role in the global ocean circulation. Turbulence also provides a natural source of variability, which bedevils our ability to predict climate. I shall review here a recently discovered turbulence phenomenon, called ``spontaneous stochasticity'', which makes classical dynamical systems as intrinsically random as quantum mechanics. Turbulent dissipation and mixing of scalars (passive or active) is now understood to require Lagrangian spontaneous stochasticity, which can be expressed by an exact ``fluctuation-dissipation relation'' for scalar turbulence (joint work with Theo Drivas). Path-integral methods such as developed for quantum mechanics become necessary to the description. There can also be Eulerian spontaneous stochasticity of the flow fields themselves, which is intimately related to the work of Kraichnan and Leith on unpredictability of turbulent flows. This leads to problems similar to those encountered in quantum field theory. To quantify uncertainty in forecasts (or hindcasts), we can borrow from quantum field-theory the concept of ``effective actions'', which characterize climate averages by a variational principle and variances by functional derivatives. I discuss some work with Tom Haine (JHU) and Santha Akella (NASA-Goddard) to make this a practical predictive tool. More ambitious application of the effective action is possible using Rayleigh-Ritz schemes.
Stochastic modeling of carbon oxidation
Chen, W.Y,; Kulkarni, A.; Milum, J.L.; Fan, L.T.
1999-12-01
Recent studies of carbon oxidation by scanning tunneling microscopy indicate that measured rates of carbon oxidation can be affected by randomly distributed defects in the carbon structure, which vary in size. Nevertheless, the impact of this observation on the analysis or modeling of the oxidation rate has not been critically assessed. This work focuses on the stochastic analysis of the dynamics of carbon clusters' conversions during the oxidation of a carbon sheet. According to the classic model of Nagle and Strickland-Constable (NSC), two classes of carbon clusters are involved in three types of reactions: gasification of basal-carbon clusters, gasification of edge-carbon clusters, and conversion of the edge-carbon clusters to the basal-carbon clusters due to the thermal annealing. To accommodate the dilution of basal clusters, however, the NSC model is modified for the later stage of oxidation in this work. Master equations governing the numbers of three classes of carbon clusters, basal, edge and gasified, are formulated from stochastic population balance. The stochastic pathways of three different classes of carbon during oxidation, that is, their means and the fluctuations around these means, have been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. Both algorithms have given rise to identical results.
Mechanical Autonomous Stochastic Heat Engine.
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Multiple fields in stochastic inflation
Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-06-24
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
Mechanical Autonomous Stochastic Heat Engine
NASA Astrophysics Data System (ADS)
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Yeo, Ingwon; Cha, Hoon-Suk; Yoon, Young Cheol; Park, Youn-Soo; Lim, Seung-Jae
2016-01-01
Abstract Introduction: Synovitis, acne, pustulosis, hyperostosis, and osteitis (SAPHO) syndrome is an increasingly recognized entity. The hip joint is known as a less frequently affected site in SAPHO syndrome, and there has been limited reports about hip joint diseases caused by SAPHO syndrome, and as such adequate treatment for this disease spectrum is still not fully elucidated. Case: We describe the case of a 52-year-old man admitted for SAPHO syndrome who went on to be diagnosed with advanced secondary hip arthritis associated with disabling right hip pain. The diagnosis of SAPHO syndrome was delayed; the patient was given a clinical diagnosis of osteomyelitis and treated with prolonged courses of antibiotics and open surgical debridement at previous tertiary health facility. The patient underwent 2-stage joint replacement surgery in our hospital. At 1 year after the surgery, he is well, with minimal right hip pain and the prosthesis is functioning well. Conclusion: This case shows the safety and effectiveness of the 2-stage joint replacement in treating destructive hip disease caused by SAPHO syndrome mimicking infectious arthritis. PMID:27399138
NASA Technical Reports Server (NTRS)
Springer, A.
1994-01-01
An experimental investigation of plume-induced flow separation on the National Launch System (NLS) 1 1/2-stage launch vehicle was done. This investigation resulted from concerns raised about the flow separation that was encountered on the Saturn 5. A large similarity exists between configurations and nominal trajectories. The study involved the use of solid plume simulators to simulate the base pressure encountered by the vehicle due to engine exhaust plumes at predetermined critical Mach numbers based on Saturn 5 flight plume effects. The solid plume was varied in location, resulting in a parametric study of base pressure effects on flow separation. In addition to the parametric study of arbitrary plume locations, the base pressure resulting from the nominal trajectory was tested. This analysis was accomplished through two wind tunnel tests run at NASA Marshall Space Flight Center's 14 x 14-inch Trisonic Wind Tunnel during 1992. The two tests were a static stability and a pressure test each using a 0.004-scale NLS 1 1/2-stage model. This study verified that flow separation is present at Mach 2.74 and 3.48 for predicted flight base pressures at nominal or higher levels. The flow separation at the predicted base pressure is only minor and should not be of great concern. It is not of the magnitude of the flow separation that was experienced on the Saturn 5. If the base pressure exceeds these nominal conditions, the flow separation can drastically increase, and is of concern.
Paul, Subhadip; Roy, Prasun Kumar
2016-09-01
The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition-increasing the elimination of prostate tumour cells and enhancing the relative sparing of normal tissue in fractionated radiation therapy, within a prescribed limit of total radiation dose. Our study predicts that stochastic temporal modulation in radiation dose-rate appreciably enhances prostate tumour cell elimination, without needing dose escalation in radiation therapy. However, constant higher dose-rate can also enhance the elimination of tumour cells. In this context, we have shown that the sparing of normal tissue with stochastic dose-rate is considerably more than the sparing of normal tissue with the equivalent constant higher dose-rate. Further, by contrasting the stochastic dose-rate effects under LQL and linear-quadratic (LQ) models, we have also shown that the LQ model over-estimates stochastic dose-rate effect in tumour and under-estimates the stochastic dose-rate effect in normal tissue. Our study indicates the possibility of utilizing stochastic modulation of radiation dose-rate for designing enhanced radiation therapy protocol for cancer.
Network motif identification in stochastic networks
NASA Astrophysics Data System (ADS)
Jiang, Rui; Tu, Zhidong; Chen, Ting; Sun, Fengzhu
2006-06-01
Network motifs have been identified in a wide range of networks across many scientific disciplines and are suggested to be the basic building blocks of most complex networks. Nonetheless, many networks come with intrinsic and/or experimental uncertainties and should be treated as stochastic networks. The building blocks in these networks thus may also have stochastic properties. In this article, we study stochastic network motifs derived from families of mutually similar but not necessarily identical patterns of interconnections. We establish a finite mixture model for stochastic networks and develop an expectation-maximization algorithm for identifying stochastic network motifs. We apply this approach to the transcriptional regulatory networks of Escherichia coli and Saccharomyces cerevisiae, as well as the protein-protein interaction networks of seven species, and identify several stochastic network motifs that are consistent with current biological knowledge. expectation-maximization algorithm | mixture model | transcriptional regulatory network | protein-protein interaction network
Stochastic Vorticity and Associated Filtering Theory
Amirdjanova, A.; Kallianpur, G.
2002-12-19
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki-Kallianpur-Kunita stochastic differential equation for the optimal filter is derived.
Applications of stochastic optimization, Task 4
1994-12-01
This report illustrates the power of the new stochastic optimization and stochastic programming capabilities developed around the ASPEN simulator in solving various types of design and analysis problems for advanced energy systems. A case study is presented for the Lurgi air-blown dry ash gasifier IGCC system. In addition the stochastic optimization capability can also be used for off-line quality control. The methodology is presented in the context of a simple gas turbine combustor flowsheet.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Stochastic Blockmodels with Growing Number of Classes
2011-01-01
Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS stochastic blockmodel, logit model, network confidence bounds David...simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with...assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic
Continuous Variable Teleportation Within Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
Carmichael, H. J.; Nha, Hyunchul
2004-12-01
Stochastic electrodynamics provides a local realistic interpretation of the continuous variable teleportation of coherent light. Time-domain simulations illustrate broadband features of the teleportation process.
Martin, George M.
2011-01-01
All phenotypes result from interactions between Nature, Nurture and Chance. The constitutional genome is clearly the dominant factor in explaining the striking differences in the pace and patterns of ageing among species. We are now in a position to reveal salient features underlying these differential modulations, which are likely to be dominated by regulatory domains. By contrast, I shall argue that stochastic events are the major players underlying the surprisingly large intra-specific variations in lifespan and healthspan. I shall review well established as well as more speculative categories of chance events – somatic mutations, protein synthesis error catastrophe and variegations of gene expression (epigenetic drift), with special emphasis upon the latter. I shall argue that stochastic drifts in variegated gene expression are the major contributors to intra-specific differences in the pace and patterns of ageing within members of the same species. They may be responsible for the quasi-stochastic distributions of major types of geriatric pathologies, including the “big three” of Alzheimer's disease, atherosclerosis and, via the induction of hyperplasis, cancer. They may be responsible for altered stoichiometries of heteromultimeric mitochondrial complexes, potentially leading to such disorders as sarcopenia, nonischemic cardiomyopathy and Parkinson's disease. PMID:21963385
Stochastic solution to quantum dynamics
NASA Technical Reports Server (NTRS)
John, Sarah; Wilson, John W.
1994-01-01
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
Hamilton's principle in stochastic mechanics
NASA Astrophysics Data System (ADS)
Pavon, Michele
1995-12-01
In this paper we establish three variational principles that provide new foundations for Nelson's stochastic mechanics in the case of nonrelativistic particles without spin. The resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature. We first develop two stochastic variational principles whose Hamilton-Jacobi-like equations are precisely the two coupled partial differential equations that are obtained from the Schrödinger equation (Madelung equations). The two problems are zero-sum, noncooperative, stochastic differential games that are familiar in the control theory literature. They are solved here by means of a new, absolutely elementary method based on Lagrange functionals. For both games the saddle-point equilibrium solution is given by the Nelson's process and the optimal controls for the two competing players are precisely Nelson's current velocity v and osmotic velocity u, respectively. The first variational principle includes as special cases both the Guerra-Morato variational principle [Phys. Rev. D 27, 1774 (1983)] and Schrödinger original variational derivation of the time-independent equation. It also reduces to the classical least action principle when the intensity of the underlying noise tends to zero. It appears as a saddle-point action principle. In the second variational principle the action is simply the difference between the initial and final configurational entropy. It is therefore a saddle-point entropy production principle. From the variational principles it follows, in particular, that both v(x,t) and u(x,t) are gradients of appropriate principal functions. In the variational principles, the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second. Combining the two variational
Resolution for Stochastic Boolean Satisfiability
NASA Astrophysics Data System (ADS)
Teige, Tino; Fränzle, Martin
The stochastic Boolean satisfiability (SSAT) problem was introduced by Papadimitriou in 1985 by adding a probabilistic model of uncertainty to propositional satisfiability through randomized quantification. SSAT has many applications, e.g., in probabilistic planning and, more recently by integrating arithmetic, in probabilistic model checking. In this paper, we first present a new result on the computational complexity of SSAT: SSAT remains PSPACE-complete even for its restriction to 2CNF. Second, we propose a sound and complete resolution calculus for SSAT complementing the classical backtracking search algorithms.
Stochastic Models of Human Errors
NASA Technical Reports Server (NTRS)
Elshamy, Maged; Elliott, Dawn M. (Technical Monitor)
2002-01-01
Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.
Stochastic thermodynamics of information processing
NASA Astrophysics Data System (ADS)
Cardoso Barato, Andre
2015-03-01
We consider two recent advancements on theoretical aspects of thermodynamics of information processing. First we show that the theory of stochastic thermodynamics can be generalized to include information reservoirs. These reservoirs can be seen as a sequence of bits which has its Shannon entropy changed due to the interaction with the system. Second we discuss bipartite systems, which provide a convenient description of Maxwell's demon. Analyzing a special class of bipartite systems we show that they can be used to study cellular information processing, allowing for the definition of an entropic rate that quantifies how much a cell learns about a fluctuating external environment and that is bounded by the thermodynamic entropy production.
Molecular Motors and Stochastic Models
NASA Astrophysics Data System (ADS)
Lipowsky, Reinhard
The behavior of single molecular motors such as kinesin or myosin V, which move on linear filaments, involves a nontrivial coupling between the biochemical motor cycle and the stochastic movement. This coupling can be studied in the framework of nonuniform ratchet models which are characterized by spatially localized transition rates between the different internal states of the motor. These models can be classified according to their functional relationships between the motor velocity and the concentration of the fuel molecules. The simplest such relationship applies to two subclasses of models for dimeric kinesin and agrees with experimental observations on this molecular motor.
Bifurcation and Optimal Stochastic Control.
1982-03-01
as soon as luX InW w’(0) n L nis boundeI. To sir.iplity the notations, we denote by u = 1 . Without loss of n generality we may assume that c l...Stochastic Control. F O R M I II I • Il I i ,iii i, DD I JAP7 1473 EDITION OF I NOV S IS OSOLE’TE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE i(,en bot. EntereJ) DAT FILMEI DIC
Stochastic Gain in Population Dynamics
NASA Astrophysics Data System (ADS)
Traulsen, Arne; Röhl, Torsten; Schuster, Heinz Georg
2004-07-01
We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.
Dynamically orthogonal field equations for stochastic flows and particle dynamics
2011-02-01
where uncertainty ‘lives’ as well as a system of Stochastic Di erential Equations that de nes how the uncertainty evolves in the time varying stochastic ... stochastic dynamical component that are both time and space dependent, we derive a system of field equations consisting of a Partial Differential Equation...a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new
Image-based histologic grade estimation using stochastic geometry analysis
NASA Astrophysics Data System (ADS)
Petushi, Sokol; Zhang, Jasper; Milutinovic, Aladin; Breen, David E.; Garcia, Fernando U.
2011-03-01
Background: Low reproducibility of histologic grading of breast carcinoma due to its subjectivity has traditionally diminished the prognostic value of histologic breast cancer grading. The objective of this study is to assess the effectiveness and reproducibility of grading breast carcinomas with automated computer-based image processing that utilizes stochastic geometry shape analysis. Methods: We used histology images stained with Hematoxylin & Eosin (H&E) from invasive mammary carcinoma, no special type cases as a source domain and study environment. We developed a customized hybrid semi-automated segmentation algorithm to cluster the raw image data and reduce the image domain complexity to a binary representation with the foreground representing regions of high density of malignant cells. A second algorithm was developed to apply stochastic geometry and texture analysis measurements to the segmented images and to produce shape distributions, transforming the original color images into a histogram representation that captures their distinguishing properties between various histological grades. Results: Computational results were compared against known histological grades assigned by the pathologist. The Earth Mover's Distance (EMD) similarity metric and the K-Nearest Neighbors (KNN) classification algorithm provided correlations between the high-dimensional set of shape distributions and a priori known histological grades. Conclusion: Computational pattern analysis of histology shows promise as an effective software tool in breast cancer histological grading.
From Complex to Simple: Interdisciplinary Stochastic Models
ERIC Educational Resources Information Center
Mazilu, D. A.; Zamora, G.; Mazilu, I.
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…
Stochastic Modeling of Laminar-Turbulent Transition
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Choudhari, Meelan
2002-01-01
Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.
Variational principles for stochastic fluid dynamics
Holm, Darryl D.
2015-01-01
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.
Stochastic and Coherence Resonance in Hippocampal Neurons
2007-11-02
decreases the signal to noise ratio of subthreshold synaptic inputs. Keywords - Hippocampus , neurons, stochastic resonance I. INTRODUCTION... subthreshold signals in the hippocampus ,” J. Neurophysiology , in press. [3] J. Collins C.C. Chow and T.T. Imboff, “Stochastic resonance without...nonlinear systems whereby the introduction of noise enhances the detection of subthreshold signals. Both computer simulations and experimental
RHIC stochastic cooling motion control
Gassner, D.; DeSanto, L.; Olsen, R.H.; Fu, W.; Brennan, J.M.; Liaw, CJ; Bellavia, S.; Brodowski, J.
2011-03-28
Relativistic Heavy Ion Collider (RHIC) beams are subject to Intra-Beam Scattering (IBS) that causes an emittance growth in all three-phase space planes. The only way to increase integrated luminosity is to counteract IBS with cooling during RHIC stores. A stochastic cooling system for this purpose has been developed, it includes moveable pick-ups and kickers in the collider that require precise motion control mechanics, drives and controllers. Since these moving parts can limit the beam path aperture, accuracy and reliability is important. Servo, stepper, and DC motors are used to provide actuation solutions for position control. The choice of motion stage, drive motor type, and controls are based on needs defined by the variety of mechanical specifications, the unique performance requirements, and the special needs required for remote operations in an accelerator environment. In this report we will describe the remote motion control related beam line hardware, position transducers, rack electronics, and software developed for the RHIC stochastic cooling pick-ups and kickers.
Stochastic Methods for Aircraft Design
NASA Technical Reports Server (NTRS)
Pelz, Richard B.; Ogot, Madara
1998-01-01
The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.
Stochastic thermodynamics for active matter
NASA Astrophysics Data System (ADS)
Speck, Thomas
2016-05-01
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven systems that allows to define fluctuating work and heat. We apply these definitions to active matter, assuming that dissipation can be modelled by effective non-conservative forces. We show that, through the work, conjugate extensive and intensive observables can be defined even in non-equilibrium steady states lacking a free energy. As an illustration, we derive the expressions for the pressure and interfacial tension of active Brownian particles. The latter becomes negative despite the observed stable phase separation. We discuss this apparent contradiction, highlighting the role of fluctuations, and we offer a tentative explanation.
Stochastic sensing through covalent interactions
Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen
2013-03-26
A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.
Thermodynamics of stochastic Turing machines.
Strasberg, Philipp; Cerrillo, Javier; Schaller, Gernot; Brandes, Tobias
2015-10-01
In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.
Stochastic hyperfine interactions modeling library
NASA Astrophysics Data System (ADS)
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
Heuristic-biased stochastic sampling
Bresina, J.L.
1996-12-31
This paper presents a search technique for scheduling problems, called Heuristic-Biased Stochastic Sampling (HBSS). The underlying assumption behind the HBSS approach is that strictly adhering to a search heuristic often does not yield the best solution and, therefore, exploration off the heuristic path can prove fruitful. Within the HBSS approach, the balance between heuristic adherence and exploration can be controlled according to the confidence one has in the heuristic. By varying this balance, encoded as a bias function, the HBSS approach encompasses a family of search algorithms of which greedy search and completely random search are extreme members. We present empirical results from an application of HBSS to the realworld problem of observation scheduling. These results show that with the proper bias function, it can be easy to outperform greedy search.
Multiscale Stochastic Simulation and Modeling
James Glimm; Xiaolin Li
2006-01-10
Acceleration driven instabilities of fluid mixing layers include the classical cases of Rayleigh-Taylor instability, driven by a steady acceleration and Richtmyer-Meshkov instability, driven by an impulsive acceleration. Our program starts with high resolution methods of numerical simulation of two (or more) distinct fluids, continues with analytic analysis of these solutions, and the derivation of averaged equations. A striking achievement has been the systematic agreement we obtained between simulation and experiment by using a high resolution numerical method and improved physical modeling, with surface tension. Our study is accompanies by analysis using stochastic modeling and averaged equations for the multiphase problem. We have quantified the error and uncertainty using statistical modeling methods.
Robust stochastic mine production scheduling
NASA Astrophysics Data System (ADS)
Kumral, Mustafa
2010-06-01
The production scheduling of open pit mines aims to determine the extraction sequence of blocks such that the net present value (NPV) of a mining project is maximized under capacity and access constraints. This sequencing has significant effect on the profitability of the mining venture. However, given that the values of coefficients in the optimization procedure are obtained in a medium of sparse data and unknown future events, implementations based on deterministic models may lead to destructive consequences to the company. In this article, a robust stochastic optimization (RSO) approach is used to deal with mine production scheduling in a manner such that the solution is insensitive to changes in input data. The approach seeks a trade off between optimality and feasibility. The model is demonstrated on a case study. The findings showed that the approach can be used in mine production scheduling problems efficiently.
Stochastic resonance in attention control
NASA Astrophysics Data System (ADS)
Kitajo, K.; Yamanaka, K.; Ward, L. M.; Yamamoto, Y.
2006-12-01
We investigated the beneficial role of noise in a human higher brain function, namely visual attention control. We asked subjects to detect a weak gray-level target inside a marker box either in the left or the right visual field. Signal detection performance was optimized by presenting a low level of randomly flickering gray-level noise between and outside the two possible target locations. Further, we found that an increase in eye movement (saccade) rate helped to compensate for the usual deterioration in detection performance at higher noise levels. To our knowledge, this is the first experimental evidence that noise can optimize a higher brain function which involves distinct brain regions above the level of primary sensory systems -- switching behavior between multi-stable attention states -- via the mechanism of stochastic resonance.
Multiple Stochastic Point Processes in Gene Expression
NASA Astrophysics Data System (ADS)
Murugan, Rajamanickam
2008-04-01
We generalize the idea of multiple-stochasticity in chemical reaction systems to gene expression. Using Chemical Langevin Equation approach we investigate how this multiple-stochasticity can influence the overall molecular number fluctuations. We show that the main sources of this multiple-stochasticity in gene expression could be the randomness in transcription and translation initiation times which in turn originates from the underlying bio-macromolecular recognition processes such as the site-specific DNA-protein interactions and therefore can be internally regulated by the supra-molecular structural factors such as the condensation/super-coiling of DNA. Our theory predicts that (1) in case of gene expression system, the variances ( φ) introduced by the randomness in transcription and translation initiation-times approximately scales with the degree of condensation ( s) of DNA or mRNA as φ ∝ s -6. From the theoretical analysis of the Fano factor as well as coefficient of variation associated with the protein number fluctuations we predict that (2) unlike the singly-stochastic case where the Fano factor has been shown to be a monotonous function of translation rate, in case of multiple-stochastic gene expression the Fano factor is a turn over function with a definite minimum. This in turn suggests that the multiple-stochastic processes can also be well tuned to behave like a singly-stochastic point processes by adjusting the rate parameters.
Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method
NASA Astrophysics Data System (ADS)
Voyant, Cyril; Tamas, Wani; Paoli, Christophe; Balu, Aurélia; Muselli, Marc; Nivet, Marie-Laure; Notton, Gilles
2014-03-01
A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its "black box" aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where "all" configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA.
Albuquerque, M G E; Concas, S; Bengtsson, S; Reis, M A M
2010-09-01
Polyhydroxyalkanoates (PHAs) are promising biodegradable polymers. The use of mixed microbial cultures (MMC) and low cost feedstocks have a positive impact on the cost-effectiveness of the process. It has typically been carried out in Sequencing Batch Reactors (SBR). In this study, a 2-stage CSTR system (under Feast and Famine conditions) was used to effectively select for PHA-storing organisms using fermented molasses as feedstock. The effect of influent substrate concentration (60-120 Cmmol VFA/L) and HRT ratio between the reactors (0.2-0.5h/h) on the system's selection efficiency was assessed. It was shown that Feast reactor residual substrate concentration impacted on the selective pressure for PHA storage (due to substrate-dependent kinetic limitation). Moreover, a residual substrate concentration coming from the Feast to the Famine reactor did not jeopardize the physiological adaptation required for enhanced PHA storage. The culture reached a maximum PHA content of 61%. This success opens new perspectives to the use of wastewater treatment infrastructure for PHA production, thus valorizing either excess sludge or wastewaters.
Wagstaff, Marcus James Dermot; Rooke, Michael; Caplash, Yugesh
2016-01-01
Objectives: To share our experience of an extensive calvarial reconstruction in a severely burn-injured, elderly patient in a 2-stage procedure utilizing a novel biodegradable temporizing matrix (NovoSorb BTM), followed by autograft. Materials and Methods: A 66-year-old patient with 75% full-thickness burns, including 7% total body surface area head and neck, with calvarial exposure of approximately 350 cm2, complicated by acute renal failure and smoke inhalation injury. Exposed calvarium was burred down to diploe and biodegradable temporizing matrix was applied. Over the next 29 days, the biodegradable temporizing matrix integrated by vascular and tissue ingrowth from the diploe. Delamination and grafting occurred, however, at 43 days postimplantation of biodegradable temporizing matrix due to skin graft donor-site constraints. Results: Graft take was complete, yielding a robust and aesthetically pleasing early result (26 days post–graft application). Conclusions: Biodegradable temporizing matrix offers an additional resource for reconstructive surgeons faced with fragile patients and complex wounds. PMID:27222681
Stochastic system identification in structural dynamics
Safak, Erdal
1988-01-01
Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.
Permanence of Stochastic Lotka-Volterra Systems
NASA Astrophysics Data System (ADS)
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
A stochastic subgrid model for sheared turbulence
NASA Astrophysics Data System (ADS)
Bertoglio, J. P.
A new subgrid model for homogeneous turbulence is proposed. The model is used in a method of Large Eddy Simulation coupled with an E.D.Q.N.M. prediction of the statistical properties of the small scales. The model is stochastic in order to allow a 'disaveraging' of the informations provided by the E.D.Q.N.M. closure. It is based on stochastic amplitude equations for two-point closures. It allows backflow of energy from the small scales, introduces stochasticity into L.E.S., and is well adapted to nonisotropic fields. A few results are presented here.
Connecting deterministic and stochastic metapopulation models.
Barbour, A D; McVinish, R; Pollett, P K
2015-12-01
In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.
A multilevel stochastic collocation method for SPDEs
Gunzburger, Max; Jantsch, Peter; Teckentrup, Aretha; Webster, Clayton
2015-03-10
We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.
Large Deviations for Stochastic Flows of Diffeomorphisms
2007-01-01
be the unique solution of the ordinary differential equation ∂ηs,t(x) ∂t .= b ( ηs,t(x), t ) , ηs,s(x) = x, 0 ≤ s ≤ t ≤ 1. (5.2) Then it follows that...solving finite dimensional Itô stochastic differential equations . More precisely, suppose b, fi, i = 1, . . . ,m are functions from Rd × [0, T ] to Rd...s, T ]. This stochastic process is called the solution of Itô’s stochastic differential equation based on the Brownian motion F . From [15, Theorem
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
NASA Astrophysics Data System (ADS)
Hertfelder, C.; Kümmerer, B.
2001-03-01
The mathematical model describing a light beam prepared in an arbitrary quantum optical state is a quasifree quantum stochastic process on the C* algebra of the canonical commutatation relations. For such quantum stochastic processes the concept of stochastic states is introduced. Stochastic quantum states have a classical analog in the following sense: If the light beam is prepared in a stochastic state, one can construct a generalized classical stochastic process, such that the distributions of the quantum observables and the classical random variables coincide. A sufficient algebraic condition for the stochasticity of a quantum state is formulated. The introduced formalism generalizes the Wigner representation from a single field mode to a continuum of modes. For the special case of a single field mode the stochasticity condition provides a new criterion for the positivity of the Wigner function related to the given state. As an example the quantized eletromagnetic field in empty space at temperature T=0 is discussed. It turns out that the corresponding classical stochastic process is not a white noise but a colored noise with a linearly increasing spectrum.
Liu, Meng; Wang, Ke; Wu, Qiong
2011-09-01
Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.
Modular and Stochastic Approaches to Molecular Pathway Models of ATM, TGF beta, and WNT Signaling
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; O'Neill, Peter; Ponomarev, Artem; Carra, Claudio; Whalen, Mary; Pluth, Janice M.
2009-01-01
Deterministic pathway models that describe the biochemical interactions of a group of related proteins, their complexes, activation through kinase, etc. are often the basis for many systems biology models. Low dose radiation effects present a unique set of challenges to these models including the importance of stochastic effects due to the nature of radiation tracks and small number of molecules activated, and the search for infrequent events that contribute to cancer risks. We have been studying models of the ATM, TGF -Smad and WNT signaling pathways with the goal of applying pathway models to the investigation of low dose radiation cancer risks. Modeling challenges include introduction of stochastic models of radiation tracks, their relationships to more than one substrate species that perturb pathways, and the identification of a representative set of enzymes that act on the dominant substrates. Because several pathways are activated concurrently by radiation the development of modular pathway approach is of interest.
NASA Astrophysics Data System (ADS)
Jia, Wei; Liu, Huoxing
2014-06-01
The pressing demand for future advanced gas turbine requires to identify the losses in a turbine and to understand the physical mechanisms producing them. In low pressure turbines with shrouded blades, a large portion of these losses is generated by tip shroud leakage flow and associated interaction. For this reason, shroud leakage losses are generally grouped into the losses of leakage flow itself and the losses caused by the interaction between leakage flow and mainstream. In order to evaluate the influence of shroud leakage flow and related losses on turbine performance, computational investigations for a 2-stage low pressure turbine is presented and discussed in this paper. Three dimensional steady multistage calculations using mixing plane approach were performed including detailed tip shroud geometry. Results showed that turbines with shrouded blades have an obvious advantage over unshrouded ones in terms of aerodynamic performance. A loss mechanism breakdown analysis demonstrated that the leakage loss is the main contributor in the first stage while mixing loss dominates in the second stage. Due to the blade-to-blade pressure gradient, both inlet and exit cavity present non-uniform leakage injection and extraction. The flow in the exit cavity is filled with cavity vortex, leakage jet attached to the cavity wall and recirculation zone induced by main flow ingestion. Furthermore, radial gap and exit cavity size of tip shroud have a major effect on the yaw angle near the tip region in the main flow. Therefore, a full calculation of shroud leakage flow is necessary in turbine performance analysis and the shroud geometric features need to be considered during turbine design process.
A 2-stage phase II design with direct assignment option in stage II for initial marker validation.
An, Ming-Wen; Mandrekar, Sumithra J; Sargent, Daniel J
2012-08-15
Biomarkers are critical to targeted therapies, as they may identify patients more likely to benefit from a treatment. Several prospective designs for biomarker-directed therapy have been previously proposed, differing primarily in the study population, randomization scheme, or both. Recognizing the need for randomization, yet acknowledging the possibility of promising but inconclusive results after a stage I cohort of randomized patients, we propose a 2-stage phase II design on marker-positive patients that allows for direct assignment in a stage II cohort. In stage I, marker-positive patients are equally randomized to receive experimental treatment or control. Stage II has the option to adopt "direct assignment" whereby all patients receive experimental treatment. Through simulation, we studied the power and type I error rate of our design compared with a balanced randomized two-stage design, and conducted sensitivity analyses to study the effect of timing of stage I analysis, population shift effects, and unbalanced randomization. Our proposed design has minimal loss in power (<1.8%) and increased type I error rate (<2.1%) compared with a balanced randomized design. The maximum increase in type I error rate in the presence of a population shift was between 3.1% and 5%, and the loss in power across possible timings of stage I analysis was less than 1.2%. Our proposed design has desirable statistical properties with potential appeal in practice. The direct assignment option, if adopted, provides for an "extended confirmation phase" as an alternative to stopping the trial early for evidence of efficacy in stage I.
Stochastic differential equation model to Prendiville processes
NASA Astrophysics Data System (ADS)
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Bootstrap performance profiles in stochastic algorithms assessment
Costa, Lino; Espírito Santo, Isabel A.C.P.; Oliveira, Pedro
2015-03-10
Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.
Stochastic differential equation model to Prendiville processes
Granita; Bahar, Arifah
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, Murugappan
We study the translocation of a flexible polymer in a confined geometry subjected to a time-periodic external drive to explore stochastic resonance. We describe the equilibrium translocation process in terms of a Fokker-Planck description and use a discrete two-state model to describe the effect of the external driving force on the translocation dynamics. We observe that no stochastic resonance is possible if the associated free-energy barrier is purely entropic in nature. The polymer chain experiences a stochastic resonance effect only in presence of an energy threshold in terms of polymer-pore interaction. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Extending stochastic network calculus to loss analysis.
Luo, Chao; Yu, Li; Zheng, Jun
2013-01-01
Loss is an important parameter of Quality of Service (QoS). Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Stochastic structure formation in random media
NASA Astrophysics Data System (ADS)
Klyatskin, V. I.
2016-01-01
Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.
Stochastic description of quantum Brownian dynamics
NASA Astrophysics Data System (ADS)
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Some stochastic aspects of intergranular creep cavitation
Fariborz, S.J.; Farris, J.P.; Harlow, D.G.; Delph, T.J.
1987-10-01
We present some results obtained from a simplified stochastic model of intergranular creep cavitation. The probabilistic features of the model arise from the inclusion of random cavity placement on the grain boundary and time-discrete stochastic cavity nucleation. Among the predictions of the model are Weibull-distributed creep rupture failure times and a Weibull distribution of cavity radii. Both of these predictions have qualitative experimental support. 18 refs., 7 figs.
Stochastic Semidefinite Programming: Applications and Algorithms
2012-03-03
doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming
Stochastic synchronization in finite size spiking networks.
Doiron, Brent; Rinzel, John; Reyes, Alex
2006-09-01
We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.
Complexity and synchronization in stochastic chaotic systems
NASA Astrophysics Data System (ADS)
Dang, Thai Son; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
Optimal factory scheduling using stochastic dominance A
Wurman, P.R.
1996-12-31
Generating optimal production schedules for manufacturing facilities an area of great theoretical and practical importance. During the last decade, an effort has been made to reconcile the techniques developed by the AI and OR communities. The work described here aims to continue in this vein by showing how a class of well-defined stochastic scheduling problems can be mapped into a general search procedure. This approach improves upon other methods by handling the general case of multidimensional stochastic costs.
Prediction Theory of Periodically Correlated Stochastic Processes
2015-05-12
SECURITY CLASSIFICATION OF: The research dealt with the prediction problem for periodically correlated sequences, that is the stochastic sequences...was to develop an alternative technique for analysis such sequences . In the first published paper we 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Aug-2014 Approved for Public Release; Distribution Unlimited Final Report: Prediction Theory of Periodically Correlated Stochastic Processes. The
Sequential decision analysis for nonstationary stochastic processes
NASA Technical Reports Server (NTRS)
Schaefer, B.
1974-01-01
A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.
Desynchronization of stochastically synchronized chemical oscillators
Snari, Razan; Tinsley, Mark R. E-mail: kshowalt@wvu.edu; Faramarzi, Sadegh; Showalter, Kenneth E-mail: kshowalt@wvu.edu; Wilson, Dan; Moehlis, Jeff; Netoff, Theoden Ivan
2015-12-15
Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.
Stochastic Forcing for Ocean Uncertainty Prediction
2013-09-30
shallow water waves governed by Korteweg-de Vries ( KdV ) dynamics with stochastic forcing. Uncertain Boundary Conditions and DO Equations : A...schemes to time-integrate shallow water surface waves governed by KdV equations with external stochastic forcing. We find that the DO scheme is...free- surface primitive equation model and Error Subspace Statistical Estimation (ESSE). The variability in the pdfs are illustrated and discussed
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, M.
2016-04-01
We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic learning via optimizing the variational inequalities.
Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei
2014-10-01
A wide variety of learning problems can be posed in the framework of convex optimization. Many efficient algorithms have been developed based on solving the induced optimization problems. However, there exists a gap between the theoretically unbeatable convergence rate and the practically efficient learning speed. In this paper, we use the variational inequality (VI) convergence to describe the learning speed. To this end, we avoid the hard concept of regret in online learning and directly discuss the stochastic learning algorithms. We first cast the regularized learning problem as a VI. Then, we present a stochastic version of alternating direction method of multipliers (ADMMs) to solve the induced VI. We define a new VI-criterion to measure the convergence of stochastic algorithms. While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems cannot be better than O(1/√t), the proposed stochastic ADMM (SADMM) is proved to have an O(1/t) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness. The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly. The experiments demonstrate that SADMM has almost the same performance as the state-of-the-art stochastic learning algorithms but its O(1/t) VI-convergence rate is capable of tightly characterizing the real learning speed.
Automated Flight Routing Using Stochastic Dynamic Programming
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Morando, Alex; Grabbe, Shon
2010-01-01
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Stochastic resonance during a polymer translocation process.
Mondal, Debasish; Muthukumar, M
2016-04-14
We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic modelling of animal movement
Smouse, Peter E.; Focardi, Stefano; Moorcroft, Paul R.; Kie, John G.; Forester, James D.; Morales, Juan M.
2010-01-01
Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry. PMID:20566497
Stochastic phase-change neurons
NASA Astrophysics Data System (ADS)
Tuma, Tomas; Pantazi, Angeliki; Le Gallo, Manuel; Sebastian, Abu; Eleftheriou, Evangelos
2016-08-01
Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.
Stochastic phase-change neurons.
Tuma, Tomas; Pantazi, Angeliki; Le Gallo, Manuel; Sebastian, Abu; Eleftheriou, Evangelos
2016-08-01
Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Lower hybrid wavepacket stochasticity revisited
Fuchs, V.; Krlín, L.; Pánek, R.; Preinhaelter, J.; Seidl, J.; Urban, J.
2014-02-12
Analysis is presented in support of the explanation in Ref. [1] for the observation of relativistic electrons during Lower Hybrid (LH) operation in EC pre-heated plasma at the WEGA stellarator [1,2]. LH power from the WEGA TE11 circular waveguide, 9 cm diameter, un-phased, 2.45 GHz antenna, is radiated into a B≅0.5 T, Ðœ„n{sub e}≅5×10{sup 17} 1/m{sup 3} plasma at T{sub e}≅10 eV bulk temperature with an EC generated 50 keV component [1]. The fast electrons cycle around flux or drift surfaces with few collisions, sufficient for randomizing phases but insufficient for slowing fast electrons down, and thus repeatedly interact with the rf field close to the antenna mouth, gaining energy in the process. Our antenna calculations reveal a standing electric field pattern at the antenna mouth, with which we formulate the electron dynamics via a relativistic Hamiltonian. A simple approximation of the equations of motion leads to a relativistic generalization of the area-preserving Fermi-Ulam (F-U) map [3], allowing phase-space global stochasticity analysis. At typical WEGA plasma and antenna conditions, the F-U map predicts an LH driven current of about 230 A, at about 225 W of dissipated power, in good agreement with the measurements and analysis reported in [1].
Stochastic models of intracellular transport
NASA Astrophysics Data System (ADS)
Bressloff, Paul C.; Newby, Jay M.
2013-01-01
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.
Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions.
Park, Yongseok; Taylor, Jeremy M G; Kalbfleisch, John D
2012-06-01
In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method.
Stochastic Microlensing: Mathematical Theory and Applications
NASA Astrophysics Data System (ADS)
Teguia, Alberto Mokak
Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time delay functions' random critical sets. Next we study stochastic microlensing in two distinct random microlensing scenarios: The uniform stars' distribution with constant mass spectrum and the spatial stars' distribution with general mass spectrum. For each scenario, we determine exact and asymptotic (in the large number of point masses limit) stochastic properties of the random time delay functions and associated random lensing maps and random shear tensors, including their moments and asymptotic density functions. We use these results to study certain random observables, such as random fixed lensed images, random bending angles, and random magnifications. These results are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing. Continuing our development of a mathematical theory of stochastic microlensing, we study the stochastic version of the Image Counting Problem, first considered in the non-random setting by Einstein and generalized by Petters. In particular, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images for a general random lensing scenario. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to the uniform stars' distribution random microlensing scenario, we calculate the asymptotic global
Stochastic Indicators for Waste Site Characterization
NASA Astrophysics Data System (ADS)
Christakos, George; Hristopulos, Dionissios T.
1996-08-01
Site characterization is an important prerequisite of risk assessment and remediation strategies. Evaluation of the health effects of groundwater and soil contamination depends on the adequate analysis of spatial heterogeneity, exceedance levels, and uncertainties. In this work we formulate and calculate stochastic indicators that provide a rigorous characterization of exposure levels in sites with heterogeneous contaminant distributions and offer valuable information for a cost-effective cleanup analysis. These site indicators are general and can be used for different types and distributions of groundwater and soil contaminants. Important properties of the stochastic indicators are examined which can evaluate the potential for contamination at large scales, and improve understanding of threatened and damaged ecosystems. Analytically tractable formulas are derived that allow the practical estimation of site indicators on the basis of experimental data. Scale and modeling effects on contaminant level analysis are examined in terms of the stochastic indicators. Site cleanup costs depend directly on inferred characteristics of the stochastic indicators, which thus can play an important role in waste site management. Applications are discussed that offer insight regarding certain aspects of stochastic site characterization. Analytical methods of site characterization are compared to numerical simulations. It is shown that the latter can provide a practical alternative to the former, but they could lead to inaccurate results if they are not interpreted carefully.
Robustness analysis of stochastic biochemical systems.
Ceska, Milan; Safránek, David; Dražan, Sven; Brim, Luboš
2014-01-01
We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Low-Dose Radiation and Genotoxic Chemicals Can Protect Against Stochastic Biological Effects
Scott, Bobby R.; Walker, Dale M.; Walker, Vernon E.
2004-01-01
A protective apoptosis-mediated (PAM) process that is turned on in mammalian cells by low-dose photon (X and γ) radiation and appears to also be turned on by the genotoxic chemical ethylene oxide is discussed. Because of the PAM process, exposure to low-dose photon radiation (and possibly also some genotoxic chemicals) can lead to a reduction in the risk of stochastic effects such as problematic mutations, neoplastic transformation (an early step in cancer occurrence), and cancer. These findings indicate a need to revise the current low-dose risk assessment paradigm for which risk of cancer is presumed to increase linearly with dose (without a threshold) after exposure to any amount of a genotoxic agent such as ionizing radiation. These findings support a view seldom mentioned in the past, that cancer risk can actually decrease, rather than increase, after exposure to low doses of photon radiation and possibly some other genotoxic agents. The PAM process (a form of natural protection) may contribute substantially to cancer prevention in humans and other mammals. However, new research is needed to improve our understanding of the process. The new research could unlock novel strategies for optimizing cancer prevention and novel protocols for low-dose therapy for cancer. With low-dose cancer therapy, normal tissue could be spared from severe damage while possibly eliminating the cancer. PMID:19330143
Computational stochastic model of ions implantation
Zmievskaya, Galina I. Bondareva, Anna L.; Levchenko, Tatiana V.; Maino, Giuseppe
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
Maximal stochastic transport in the Lorenz equations
NASA Astrophysics Data System (ADS)
Agarwal, Sahil; Wettlaufer, John
2015-11-01
We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering (2015), but their variation with noise amplitude exhibits surprising behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity is lost; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations. Finally, we note that these solutions demonstrate that the effect of noise is equivalent to the effect of chaos.
Stochastic Differential Equation of Earthquakes Series
NASA Astrophysics Data System (ADS)
Mariani, Maria C.; Tweneboah, Osei K.; Gonzalez-Huizar, Hector; Serpa, Laura
2016-07-01
This work is devoted to modeling earthquake time series. We propose a stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ (α, β ) process. Superposition of independent Γ (α, β ) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to the study of earthquakes by fitting the superposed Γ (α, β ) Ornstein-Uhlenbeck model to earthquake sequences in South America containing very large events (Mw ≥ 8). We obtained very good fit of the observed magnitudes of the earthquakes with the stochastic differential equations, which supports the use of this methodology for the study of earthquakes sequence.
Structural factoring approach for analyzing stochastic networks
NASA Technical Reports Server (NTRS)
Hayhurst, Kelly J.; Shier, Douglas R.
1991-01-01
The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.
Functional integral approach for multiplicative stochastic processes.
Arenas, Zochil González; Barci, Daniel G
2010-05-01
We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green's functions in the Grassman sector of the theory. We also study nonperturbative constraints imposed by Becchi, Rouet and Stora symmetry (BRS) and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory, the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.
Stochastic resonance in geomagnetic polarity reversals.
Consolini, Giuseppe; De Michelis, Paola
2003-02-07
Among noise-induced cooperative phenomena a peculiar relevance is played by stochastic resonance. In this paper we offer evidence that geomagnetic polarity reversals may be due to a stochastic resonance process. In detail, analyzing the distribution function P(tau) of polarity residence times (chrons), we found the evidence of a stochastic synchronization process, i.e., a series of peaks in the P(tau) at T(n) approximately (2n+1)T(Omega)/2 with n=0,1,...,j and T(omega) approximately 0.1 Myr. This result is discussed in connection with both the typical time scale of Earth's orbit eccentricity variation and the recent results on the typical time scale of climatic long-term variation.
Stochastic approach to equilibrium and nonequilibrium thermodynamics.
Tomé, Tânia; de Oliveira, Mário J
2015-04-01
We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.
Vaccine enhanced extinction in stochastic epidemic models
NASA Astrophysics Data System (ADS)
Billings, Lora; Mier-Y-Teran, Luis; Schwartz, Ira
2012-02-01
We address the problem of developing new and improved stochastic control methods that enhance extinction in disease models. In finite populations, extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more components or species to vanish. Using large deviation theory, we identify the location of the optimal path to extinction in epidemic models with stochastic vaccine controls. These models not only capture internal noise from random transitions, but also external fluctuations, such as stochastic vaccination scheduling. We quantify the effectiveness of the randomly applied vaccine over all possible distributions by using the location of the optimal path, and we identify the most efficient control algorithms. We also discuss how mean extinction times scale with epidemiological and social parameters.
Regeneration of stochastic processes: an inverse method
NASA Astrophysics Data System (ADS)
Ghasemi, F.; Peinke, J.; Sahimi, M.; Rahimi Tabar, M. R.
2005-10-01
We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.
Topology optimization under stochastic stiffness
NASA Astrophysics Data System (ADS)
Asadpoure, Alireza
Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations
Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system
NASA Astrophysics Data System (ADS)
Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.
2016-12-01
We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.
Vaginal cancer; Cancer - vagina; Tumor - vaginal ... Most vaginal cancers occur when another cancer, such as cervical or endometrial cancer , spreads. This is called secondary vaginal cancer. Cancer ...
Propagation of ultra-short solitons in stochastic Maxwell's equations
Kurt, Levent; Schäfer, Tobias
2014-01-15
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
On strongly GA-convex functions and stochastic processes
Bekar, Nurgül Okur; Akdemir, Hande Günay; İşcan, İmdat
2014-08-20
In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.
On strongly GA-convex functions and stochastic processes
NASA Astrophysics Data System (ADS)
Bekar, Nurgül Okur; Akdemir, Hande Günay; Işcan, Imdat
2014-08-01
In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
NASA Technical Reports Server (NTRS)
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
A Note on the Stochastic Nature of Feynman Quantum Paths
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
2016-11-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations
NASA Technical Reports Server (NTRS)
Adomian, G.; Miao, C. C.
1973-01-01
The research accomplished during this period is reported. Published abstracts and technical reports are listed. Articles presented include: boundedness of absolute values of generalized Fourier coefficients, propagation in stochastic media, and stationary conditions for stochastic differential equations.
Master-equation approach to stochastic neurodynamics
NASA Astrophysics Data System (ADS)
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
Operation of Distributed Generation Under Stochastic Prices
Siddiqui, Afzal S.; Marnay, Chris
2005-11-30
We model the operating decisions of a commercial enterprisethatneeds to satisfy its periodic electricity demand with either on-sitedistributed generation (DG) or purchases from the wholesale market. Whilethe former option involves electricity generation at relatively high andpossibly stochastic costs from a set of capacity-constrained DGtechnologies, the latter implies unlimited open-market transactions atstochastic prices. A stochastic dynamic programme (SDP) is used to solvethe resulting optimisation problem. By solving the SDP with and withoutthe availability of DG units, the implied option values of the DG unitsare obtained.
Methods for Scaling to Doubly Stochastic Form,
1981-06-26
BIRKHOFF, G.: Tres observaciones sobre le algebra lineal , Rev. univ. nec. Tucuman, ser A, . 147-151, [1948] BRUALDI, R.A., S.V. PARTER, and H. SCHNEIDER...scaling square, nonnegative matrices to dou- bly stochastic form are described. A generalized version of the convergence theorem in SINKI-ORN and KNOPP... matrices D and E for a given square nonnegative matrix, A, such that DAE is doubly stochastic--or determine that such :.p h" du:es 7’. -,.xist. A
An exact accelerated stochastic simulation algorithm.
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-14
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 23 power of the number of reaction events in a Galton-Watson process.
Fermilab recycler stochastic cooling commissioning and performance
D. Broemmelsiek; Ralph Pasquinelli
2003-06-04
The Fermilab Recycler is a fixed 8 GeV kinetic energy storage ring located in the Fermilab Main Injector tunnel near the ceiling. The Recycler has two roles in Run II. First, to store antiprotons from the Fermilab Antiproton Accumulator so that the antiproton production rate is no longer compromised by large numbers of antiprotons stored in the Accumulator. Second, to receive antiprotons from the Fermilab Tevatron at the end of luminosity periods. To perform each of these roles, stochastic cooling in the Recycler is needed to preserve and cool antiprotons in preparation for transfer to the Tevatron. The commissioning and performance of the Recycler stochastic cooling systems will be reviewed.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Stochastic processes in muon ionization cooling
NASA Astrophysics Data System (ADS)
Errede, D.; Makino, K.; Berz, M.; Johnstone, C. J.; Van Ginneken, A.
2004-02-01
A muon ionization cooling channel consists of three major components: the magnet optics, an acceleration cavity, and an energy absorber. The absorber of liquid hydrogen contained by thin aluminum windows is the only component which introduces stochastic processes into the otherwise deterministic acceleration system. The scattering dynamics of the transverse coordinates is described by Gaussian distributions. The asymmetric energy loss function is represented by the Vavilov distribution characterized by the minimum number of collisions necessary for a particle undergoing loss of the energy distribution average resulting from the Bethe-Bloch formula. Examples of the interplay between stochastic processes and deterministic beam dynamics are given.
On orthogonality preserving quadratic stochastic operators
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Canonical Bose gas simulations with stochastic gauges.
Drummond, P D; Deuar, P; Kheruntsyan, K V
2004-01-30
A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.
Stochastic 2-D Navier-Stokes Equation
Menaldi, J.L. Sritharan, S.S.
2002-10-01
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.
Stochastic model for supersymmetric particle branching process
NASA Astrophysics Data System (ADS)
Zhang, Yuanyuan; Chan, Aik Hui; Oh, Choo Hiap
2017-01-01
We develop a stochastic branching model to describe the jet evolution of supersymmetric (SUSY) particles. This model is a modified two-phase branching process, or more precisely, a two-phase simple birth process plus Poisson process. Both pure SUSY partons initiated jets and SUSY plus ordinary partons initiated jets scenarios are considered. The stochastic branching equations are established and the Multiplicity Distributions (MDs) are derived for these two scenarios. We also fit the distribution of the general case (SUSY plus ordinary partons initiated jets) with experimental data. The fitting shows the SUSY particles have not participated in branching at current collision energy yet.
Microscopic origins of stochastic crack growth
NASA Astrophysics Data System (ADS)
Pardee, W. J.; Morris, W. L.; Cox, B. N.
Physical arguments are made to obtain a mathematical model of the stochastic growth of surface fatigue cracks in a ductile metal alloy. The model is a set of coupled partial differential equations for the expected statistical density of cracks per unit area. The differential equations describe the smooth, deterministic local evolution of crack states, with the stochastic effects of abrupt local changes of material in the crack path appearing as transitions between distinct subspaces of single crack state space. Results are related to observables such as statistical distributions of crack growth rate and of time for at least one crack to reach macroscopic length.
Three-dimensional stochastic vortex flows
NASA Astrophysics Data System (ADS)
Esposito, R.; Pulvirenti, M.
1989-08-01
It is well known that the dynamics of point vortices approximate, under suitable limits, the two-dimensional Euler flow for an ideal fluid. To find particle models for three-dimensional flows is a more intricate problem. A stochastic version of the algorithm introduced by Beale amd Maida (1982) for simulating the behavior of a three-dimensional Euler flow is introduced here, and convergence to the Navier-Stokes (NS) flow in R exp 3 is shown. The result is based on a stochastic Lagrangian picture of the NS equations.
Cao Yang . E-mail: ycao@cs.ucsb.edu; Gillespie, Dan . E-mail: GillespieDT@mailaps.org; Petzold, Linda . E-mail: petzold@engineering.ucsb.edu
2005-07-01
In this paper, we introduce a multiscale stochastic simulation algorithm (MSSA) which makes use of Gillespie's stochastic simulation algorithm (SSA) together with a new stochastic formulation of the partial equilibrium assumption (PEA). This method is much more efficient than SSA alone. It works even with a very small population of fast species. Implementation details are discussed, and an application to the modeling of the heat shock response of E. Coli is presented which demonstrates the excellent efficiency and accuracy obtained with the new method.
Stochastic Dynamic Mixed-Integer Programming (SD-MIP)
2015-05-05
door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for stochastic dynamic mixed...project lays the foundation for stochastic dynamic mixed-integer and linear programming (SD-MIP). This project has produced several new ideas in...models. Recent research has opened the door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for
Stochastic model of the residual acceleration environment in microgravity
NASA Technical Reports Server (NTRS)
Vinals, Jorge
1994-01-01
We describe a theoretical investigation of the effects that stochastic residual accelerations (g-jitter) onboard spacecraft can have on experiments conducted in a microgravity environment. We first introduce a stochastic model of the residual acceleration field, and develop a numerical algorithm to solve the equations governing fluid flow that allow for a stochastic body force. We next summarize our studies of two generic situations: stochastic parametric resonance and the onset of convective flow induced by a fluctuating acceleration field.
Stochastic population growth in spatially heterogeneous environments.
Evans, Steven N; Ralph, Peter L; Schreiber, Sebastian J; Sen, Arnab
2013-02-01
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZ(t) = μZ(t)dt + σZ(t)dW(t), t ≥ 0, where the conditional law of Z(t+Δt)-Z(t) given Z(t) = z has mean and variance approximately z μΔt and z²σ²Δt when the time increment Δt is small. The long-term stochastic growth rate lim(t→∞) t⁻¹ log Z(t) for such a population equals μ − σ²/2 . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model X(t) = (X¹(t) , . . . , X(n)(t)), t ≥ 0, for the population abundances in n patches: the conditional law of X(t+Δt) given X(t) = x is such that the conditional mean of X(i)(t+Δt) − X(i)(t) is approximately [x(i)μ(i) + Σ(j) (x(j) D(ji) − x(i) D(i j) )]Δt where μ(i) is the per capita growth rate in the ith patch and D(ij) is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of X(i)(t+Δt)− X(i)(t) and X(j)(t+Δt) − X(j)(t) is approximately x(i)x(j)σ(ij)Δt for some covariance matrix Σ = (σ(ij)). We show for such a spatially extended population that if S(t) = X¹(t)+· · ·+ X(n)(t) denotes the total population abundance, then Y(t) = X(t)/S(t), the vector of patch proportions, converges in law to a random vector Y(∞) as t → ∞, and the stochastic growth rate lim(t→∞) t⁻¹ log S(t) equals the space-time average per-capita growth rate Σ(i)μ(i)E[Y(i)(∞)] experienced by the population minus half of the space-time average temporal variation E[Σ(i,j) σ(i j)Y(i)(∞) Y(j)(∞)] experienced by the population. Using this characterization of the
Stochastic population growth in spatially heterogeneous environments
Evans, Steven N.; Ralph, Peter L.; Sen, Arnab
2016-01-01
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZt = μZtdt + σ ZtdWt, t ≥ 0, where the conditional law of Zt+Δt − Zt given Zt = z has mean and variance approximately zμΔt and z2σ2Δt when the time increment Δt is small. The long-term stochastic growth rate limt→∞ t−1 log Zt for such a population equals μ−σ22. Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model Xt=(Xt1,…,Xtn), t ≥ 0, for the population abundances in n patches: the conditional law of Xt+Δt given Xt = x is such that the conditional mean of Xt+Δti−Xti is approximately [xiμi +∑j (xj Dji − xi Dij)]Δt where μi is the per capita growth rate in the ith patch and Dij is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of Xt+Δti−Xti and Xt+Δtj−Xtj is approximately xixjσijΔt for some covariance matrix Σ = (σij). We show for such a spatially extended population that if St=Xt1+⋯+Xtn denotes the total population abundance, then Yt = Xt /St, the vector of patch proportions, converges in law to a random vector Y∞ as t → ∞, and the stochastic growth rate limt→∞ t−1 log St equals the space-time average per-capita growth rate ∑iμi𝔼[Y∞j] experienced by the population minus half of the space-time average temporal variation 𝔼[∑i,jσijY∞iY∞j] experienced by the population. Using this characterization of the stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which
Teaching Tip: When a Matrix and Its Inverse Are Stochastic
ERIC Educational Resources Information Center
Ding, J.; Rhee, N. H.
2013-01-01
A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.
Influence of stochastic perturbation on prey-predator systems.
Rudnicki, Ryszard; Pichór, Katarzyna
2007-03-01
We analyse the influence of various stochastic perturbations on prey-predator systems. The prey-predator model is described by stochastic versions of a deterministic Lotka-Volterra system. We study long-time behaviour of both trajectories and distributions of the solutions. We indicate the differences between the deterministic and stochastic models.
Analysis of bilinear stochastic systems. [involving multiplicative noise processes
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Marcus, S. I.; Martin, D. N.
1974-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
NASA Technical Reports Server (NTRS)
Sadunas, J. A.; French, E. P.; Sexton, H.
1973-01-01
A 1/25 scale model S-2 stage base region thermal environment test is presented. Analytical results are included which reflect the effect of engine operating conditions, model scale, turbo-pump exhaust gas injection on base region thermal environment. Comparisons are made between full scale flight data, model test data, and analytical results. The report is prepared in two volumes. The description of analytical predictions and comparisons with flight data are presented. Tabulation of the test data is provided.
Fingering in Stochastic Growth Models
Aristotelous, Andreas C.; Durrett, Richard
2015-01-01
Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) − θ)+ and die at rate δ(θ − u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and “fingering” at a threshold θc = 0.5, while in the second case fingering always occurs, i.e., θc = 0. PMID:26430353
Stochastic light-cone CTMRG: a new DMRG approach to stochastic models
NASA Astrophysics Data System (ADS)
Kemper, A.; Gendiar, A.; Nishino, T.; Schadschneider, A.; Zittartz, J.
2003-01-01
We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 105 shows a considerable improvement on the old stochastic TMRG algorithm.
Cardaliaguet, P.; Rainer, C.
2013-08-01
We introduce a new notion of pathwise strategies for stochastic differential games. This allows us to give a correct meaning to some statement asserted in Cardaliaguet and Rainer (Appl. Math. Optim. 59: 1-36, 2009)
White Noise Path Integrals in Stochastic Neurodynamics
NASA Astrophysics Data System (ADS)
Carpio-Bernido, M. Victoria; Bernido, Christopher C.
2008-06-01
The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.
Stochastic models for turbulent reacting flows
Kerstein, A.
1993-12-01
The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.
Stochastic thermodynamics for linear kinetic equations
NASA Astrophysics Data System (ADS)
Van den Broeck, C.; Toral, R.
2015-07-01
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.
Maximal stochastic transport in the Lorenz equations
NASA Astrophysics Data System (ADS)
Agarwal, Sahil; Wettlaufer, J. S.
2016-01-01
We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.
Stochastic models for convective momentum transport.
Majda, Andrew J; Stechmann, Samuel N
2008-11-18
The improved parameterization of unresolved features of tropical convection is a central challenge in current computer models for long-range ensemble forecasting of weather and short-term climate change. Observations, theory, and detailed smaller-scale numerical simulations suggest that convective momentum transport (CMT) from the unresolved scales to the resolved scales is one of the major deficiencies in contemporary computer models. Here, a combination of mathematical and physical reasoning is utilized to build simple stochastic models that capture the significant intermittent upscale transports of CMT on the large scales due to organized unresolved convection from squall lines. Properties of the stochastic model for CMT are developed below in a test column model environment for the large-scale variables. The effects of CMT from the stochastic model on a large-scale convectively coupled wave in an idealized setting are presented below as a nontrivial test problem. Here, the upscale transports from stochastic effects are significant and even generate a large-scale mean flow which can interact with the convectively coupled wave.
Stochastic motif extraction using hidden Markov model
Fujiwara, Yukiko; Asogawa, Minoru; Konagaya, Akihiko
1994-12-31
In this paper, we study the application of an HMM (hidden Markov model) to the problem of representing protein sequences by a stochastic motif. A stochastic protein motif represents the small segments of protein sequences that have a certain function or structure. The stochastic motif, represented by an HMM, has conditional probabilities to deal with the stochastic nature of the motif. This HMM directive reflects the characteristics of the motif, such as a protein periodical structure or grouping. In order to obtain the optimal HMM, we developed the {open_quotes}iterative duplication method{close_quotes} for HMM topology learning. It starts from a small fully-connected network and iterates the network generation and parameter optimization until it achieves sufficient discrimination accuracy. Using this method, we obtained an HMM for a leucine zipper motif. Compared to the accuracy of a symbolic pattern representation with accuracy of 14.8 percent, an HMM achieved 79.3 percent in prediction. Additionally, the method can obtain an HMM for various types of zinc finger motifs, and it might separate the mixed data. We demonstrated that this approach is applicable to the validation of the protein databases; a constructed HMM b as indicated that one protein sequence annotated as {open_quotes}lencine-zipper like sequence{close_quotes} in the database is quite different from other leucine-zipper sequences in terms of likelihood, and we found this discrimination is plausible.
Elliptic Equations of Higher Stochastic Order
2009-01-01
stochastic spaces, such as Hida or Kondratiev spaces [11, 12], or even larger exponential spaces [16]. The traditional approach [17, 20, 21, etc.] has to...2, 384–408. [7] T. Hida , H-H. Kuo, J. Potthoff, and L. Sreit, White noise, Kluwer Academic Publishers, Boston, 1993. [8] H. Holden, B. Øksendal, J
Investigation of the stochastic properties of wind
NASA Astrophysics Data System (ADS)
Dimitriadis, Panayiotis; Koutsoyiannis, Demetris; Papanicolaou, Panos
2016-04-01
Understanding atmospheric motion in the form of wind is essential to many fields in hydroclimatics. The wind is considered one of the most important processes in hydrometeorology since, along with temperature, it generates and drives climate dynamics. Currently, the interest has increased due to its involvement to renewable energy resources through wind power production and forecasting. However, there seems to be a puzzle about which stochastic model best describes the wind process. In this analysis, we attempt to explain the reason around this confusion regarding the stochastic properties of the wind process using statistical as well as hydrometeorological reasoning, starting from the microscale of turbulence and extending the analysis to the macroscale of climatic processes. Particularly, some models seem to exhibit good agreement with data mostly due to instrumental errors. Moreover, we show that extending the theory of turbulence to the atmospheric motion can reveal stochastic properties that are not only accompanied with physical interference but also exhibit excellent agreement with wind measurements. Finally, we apply the theoretical analysis to multiple stations around the globe and we derive conclusions on the variation of stochastic parameters of wind regarding dominant climatic conditions.
Stochastic nonhomogeneous incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
Stochastic Cooling with Schottky Band Overlap
Lebedev, Valeri
2006-03-20
Optimal use of stochastic cooling is essential to maximize the antiproton stacking rate for Tevatron Run II. Good understanding and characterization of the cooling is important for the optimization. The paper is devoted to derivation of the Fokker-Plank equations justified in the case of near or full Schottky base overlap for both longitudinal and transverse coolings.
Stochastic Cooling with Schottky Band Overlap
NASA Astrophysics Data System (ADS)
Lebedev, Valeri
2006-03-01
Optimal use of stochastic cooling is essential to maximize the antiproton stacking rate for Tevatron Run II. Good understanding and characterization of the cooling is important for the optimization. The paper is devoted to derivation of the Fokker-Plank equations justified in the case of near or full Schottky base overlap for both longitudinal and transverse coolings.
The Stochastic Nonlinear Damped Wave Equation
Barbu, V. Da Prato, G.
2002-12-19
We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in R{sup n} of the Klein-Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied.
Comparing Several Robust Tests of Stochastic Equality.
ERIC Educational Resources Information Center
Vargha, Andras; Delaney, Harold D.
In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or…
Stochastic dominance and medical decision making.
Leshno, Moshe; Levy, Haim
2004-08-01
Stochastic Dominance (SD) criteria are decision making tools which allow us to choose among various strategies with only partial information on the decision makers' preferences. The notion of Stochastic Dominance has been extensively employed and developed in the area of economics, finance, agriculture, statistics, marketing and operation research since the late 1960s. For example, it may tell us which of two medical treatments with uncertain outcomes is preferred in the absence of full information on the patients' preferences. This paper presents a short review of the SD paradigm and demonstrates how the SD criteria may be employed in medical decision making, using the case of small abdominal aortic aneurysms as an illustration. Thus, for instance by assuming risk aversion one can employ second-degree stochastic dominance to divide the set of all possible treatments into the efficient set, from which the decision makers should always choose, and the inefficient (inferior) set. By employing Prospect Stochastic Dominance (PSD) a similar division can be conducted corresponding to all S-shaped utility functions.
Magnetohydrodynamic stability of stochastically driven accretion flows.
Nath, Sujit Kumar; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K
2013-07-01
We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.
Stochastic Resonance in Protein Folding Dynamics.
Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A
2016-05-04
Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.
Stochastic genetic networks with solvable structures
Lipan, Ovidiu
2014-12-10
We describe a set of basic stochastic biocircuits for which the Master Equation is completely solvable. Beside linear circuits, which are known to be solvable, we show that tree-like circuits with polynomial transition functions are also completely solvable. We associate a simple but unambiguous graphical representation to such circuits. The graphical representation shows the signal propagation through these simple circuits.
Stochastic processes, estimation theory and image enhancement
NASA Technical Reports Server (NTRS)
Assefi, T.
1978-01-01
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
Stochastic Differential Games with Asymmetric Information
Cardaliaguet, Pierre Rainer, Catherine
2009-02-15
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual viscosity solutions of some second order Hamilton-Jacobi equation.
Random Walk Analysis in Antagonistic Stochastic Games
2010-07-01
Journal of Mathematical Analysis and Applications , 353...and Applications, an Honorary Volume of Cambridge Scientific Publishers, Journal of Mathematical Analysis and Applications , Mathematical and Computer...J.H. and Ke, H-J., Multilayers in a Modulated Stochastic Game, Journal of Mathematical Analysis and Applications , 353 (2009), 553-565. [8
Adaptive Control of Nonlinear and Stochastic Systems
1991-01-14
Hernmndez-Lerma and S.I. Marcus, Nonparametric adaptive control of dis- crete time partially observable stochastic systems, Journal of Mathematical Analysis and Applications 137... Journal of Mathematical Analysis and Applications 137 (1989), 485-514. [19] A. Arapostathis and S.I. Marcus, Analysis of an identification algorithm
Stochastic Simulation Tool for Aerospace Structural Analysis
NASA Technical Reports Server (NTRS)
Knight, Norman F.; Moore, David F.
2006-01-01
Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.
Stochastic Prognostics for Rolling Element Bearings
NASA Astrophysics Data System (ADS)
Li, Y.; Kurfess, T. R.; Liang, S. Y.
2000-09-01
The capability to accurately predict the remaining life of a rolling element bearing is prerequisite to the optimal maintenance of rotating machinery performance in terms of cost and productivity. Due to the probabilistic nature of bearing integrity and operation condition, reliable estimation of a bearing's remaining life presents a challenging aspect in the area of maintenance optimisation and catastrophic failure avoidance. Previous study has developed an adaptive prognostic methodology to estimate the rate of bearing defect growth based on a deterministic defect-propagation model. However, deterministic models are inadequate in addressing the stochastic nature of defect-propagation. In this paper, a stochastic defect-propagation model is established by instituting a lognormal random variable in a deterministic defect-propagation rate model. The resulting stochastic model is calibrated on-line by a recursive least-squares (RLS) approach without the requirement of a priori knowledge on bearing characteristics. An augmented stochastic differential equation vector is developed with the consideration of model uncertainties, parameter estimation errors, and diagnostic model inaccuracies. It involves two ordinary differential equations for the first and second moments of its random variables. Solving the two equations gives the mean path of defect propagation and its dispersion at any instance. This approach is suitable for on-line monitoring, remaining life prediction, and decision making for optimal maintenance scheduling. The methodology has been verified by numerical simulations and the experimental testing of bearing fatigue life.
Stochastic resonance in Gaussian quantum channels
NASA Astrophysics Data System (ADS)
Lupo, Cosmo; Mancini, Stefano; Wilde, Mark M.
2013-02-01
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a ‘forbidden interval’. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the ‘forbidden interval’ may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.
A Note on Boolean Stochastic Processes
NASA Astrophysics Data System (ADS)
Fidaleo, Francesco
2015-03-01
For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.
Doubly perturbed neutral stochastic functional equations
NASA Astrophysics Data System (ADS)
Hu, Lanying; Ren, Yong
2009-09-01
In this paper, we prove the existence and uniqueness of the solution to a class of doubly perturbed neutral stochastic functional equations (DPNSFEs in short) under some non-Lipschitz conditions. The solution is constructed by successive approximation. Furthermore, we give the continuous dependence of the solution on the initial value by means of the corollary of Bihari inequality.
Perspective: Stochastic algorithms for chemical kinetics
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-01-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. PMID:23656106
Multidimensional stochastic approximation using locally contractive functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
2014-01-01
Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations. PMID:24939084
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Hosking, John Joseph Absalom
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
Stochastic variation in Cardamine hirsuta petal number
Monniaux, Marie; Pieper, Bjorn; Hay, Angela
2016-01-01
Background and Aims Floral development is remarkably robust in terms of the identity and number of floral organs in each whorl, whereas vegetative development can be quite plastic. This canalization of flower development prevents the phenotypic expression of cryptic genetic variation, even in fluctuating environments. A cruciform perianth with four petals is a hallmark of the Brassicaceae family, typified in the model species Arabidopsis thaliana. However, variable petal loss is found in Cardamine hirsuta, a genetically tractable relative of A. thaliana. Cardamine hirsuta petal number varies in response to stochastic, genetic and environmental perturbations, which makes it an interesting model to study mechanisms of decanalization and the expression of cryptic variation. Methods Multitrait quantitative trait locus (QTL) analysis in recombinant inbred lines (RILs) was used to identify whether the stochastic variation found in C. hirsuta petal number had a genetic basis. Key Results Stochastic variation (standard error of the average petal number) was found to be a heritable phenotype, and four QTL that influenced this trait were identified. The sensitivity to detect these QTL effects was increased by accounting for the effect of ageing on petal number variation. All QTL had significant effects on both average petal number and its standard error, indicating that these two traits share a common genetic basis. However, for some QTL, a degree of independence was found between the age of the flowers where allelic effects were significant for each trait. Conclusions Stochastic variation in C. hirsuta petal number has a genetic basis, and common QTL influence both average petal number and its standard error. Allelic variation at these QTL can, therefore, modify petal number in an age-specific manner via effects on the phenotypic mean and stochastic variation. These results are discussed in the context of trait evolution via a loss of robustness. PMID:26346720
Quantum stochastic calculus associated with quadratic quantum noises
NASA Astrophysics Data System (ADS)
Ji, Un Cig; Sinha, Kalyan B.
2016-02-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Quantum stochastic calculus associated with quadratic quantum noises
Ji, Un Cig; Sinha, Kalyan B.
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Zhang, Qichun; Zhou, Jinglin; Wang, Hong; Chai, Tianyou
2016-01-01
In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.
Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process.
Greenman, C D; Cooke, S L; Marshall, J; Stratton, M R; Campbell, P J
2016-01-01
Breakage-fusion-bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. Here we study the evolution space of breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are [Formula: see text] qualitatively distinct evolutions involving [Formula: see text] breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the process to show these evolutions are not equally likely, and also describe how amplicons become localized. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples.
Stochastic Models for Precipitable Water in Convection
NASA Astrophysics Data System (ADS)
Leung, Kimberly
Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test
Conditional reversibility in nonequilibrium stochastic systems
NASA Astrophysics Data System (ADS)
Bonança, Marcus V. S.; Jarzynski, Christopher
2016-02-01
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ , is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ , where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.
An exact accelerated stochastic simulation algorithm
NASA Astrophysics Data System (ADS)
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2/3 power of the number of reaction events in a Galton-Watson process.
An exact accelerated stochastic simulation algorithm
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present “ER-leap” algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2∕3 power of the number of reaction events in a Galton–Watson process. PMID:19368432
Entropy production of doubly stochastic quantum channels
NASA Astrophysics Data System (ADS)
Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.
2016-02-01
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
Double inverse stochastic resonance with dynamic synapses
NASA Astrophysics Data System (ADS)
Uzuntarla, Muhammet; Torres, Joaquin J.; So, Paul; Ozer, Mahmut; Barreto, Ernest
2017-01-01
We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
COSMIC DUST AGGREGATION WITH STOCHASTIC CHARGING
Matthews, Lorin S.; Hyde, Truell W.; Shotorban, Babak
2013-10-20
The coagulation of cosmic dust grains is a fundamental process which takes place in astrophysical environments, such as presolar nebulae and circumstellar and protoplanetary disks. Cosmic dust grains can become charged through interaction with their plasma environment or other processes, and the resultant electrostatic force between dust grains can strongly affect their coagulation rate. Since ions and electrons are collected on the surface of the dust grain at random time intervals, the electrical charge of a dust grain experiences stochastic fluctuations. In this study, a set of stochastic differential equations is developed to model these fluctuations over the surface of an irregularly shaped aggregate. Then, employing the data produced, the influence of the charge fluctuations on the coagulation process and the physical characteristics of the aggregates formed is examined. It is shown that dust with small charges (due to the small size of the dust grains or a tenuous plasma environment) is affected most strongly.
Conditional reversibility in nonequilibrium stochastic systems.
Bonança, Marcus V S; Jarzynski, Christopher
2016-02-01
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ, is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ, where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.
Stochastic robustness of linear control systems
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ryan, Laura E.
1990-01-01
A simple numerical procedure for estimating the stochastic robustness of a linear, time-invariant system is described. Monte Carlo evaluation of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This definition of robustness is an alternative to existing deterministic definitions that address both structured and unstructured parameter variations directly. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variations. Trivial extensions of the procedure admit alternate discriminants to be considered. Thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions also can be estimated. Results are particularly amenable to graphical presentation.
Stochastic resonance in a tristable optomechanical system
NASA Astrophysics Data System (ADS)
Fan, Bixuan; Xie, Min
2017-02-01
In this work we theoretically investigate the stochastic resonance (SR) effect in an optomechanical membrane system subject to two weak signals (one optical field and one mechanical force). The quadratic optomechanical coupling allows us to find a region with tristability where the noise-activated stochastic switching among three stable states occurs and SR phenomena are observed at the cooperation of input signals and noise. We show that the mechanical force and the optical field respectively serve as an additive signal and a multiplicative signal to the membrane position, and they induce completely different SR behaviors. Moreover, when two signals coexist the SR effect can be enhanced, and the beating effect appears in the SR synchronization process with unsynchronized signals.
Stochastic cooling of a high energy collider
Blaskiewicz, M.; Brennan, J.M.; Lee, R.C.; Mernick, K.
2011-09-04
Gold beams in RHIC revolve more than a billion times over the course of a data acquisition session or store. During operations with these heavy ions the event rates in the detectors decay as the beams diffuse. A primary cause for this beam diffusion is small angle Coloumb scattering of the particles within the bunches. This intra-beam scattering (IBS) is particularly problematic at high energy because the negative mass effect removes the possibility of even approximate thermal equilibrium. Stochastic cooling can combat IBS. A theory of bunched beam cooling was developed in the early eighties and stochastic cooling systems for the SPS and the Tevatron were explored. Cooling for heavy ions in RHIC was also considered.
Aquifer Structure Identification Using Stochastic Inversion
Harp, Dylan R; Dai, Zhenxue; Wolfsberg, Andrew V; Vrugt, Jasper A
2008-01-01
This study presents a stochastic inverse method for aquifer structure identification using sparse geophysical and hydraulic response data. The method is based on updating structure parameters from a transition probability model to iteratively modify the aquifer structure and parameter zonation. The method is extended to the adaptive parameterization of facies hydraulic parameters by including these parameters as optimization variables. The stochastic nature of the statistical structure parameters leads to nonconvex objective functions. A multi-method genetically adaptive evolutionary approach (AMALGAM-SO) was selected to perform the inversion given its search capabilities. Results are obtained as a probabilistic assessment of facies distribution based on indicator cokriging simulation of the optimized structural parameters. The method is illustrated by estimating the structure and facies hydraulic parameters of a synthetic example with a transient hydraulic response.
Intelligent controllers as hierarchical stochastic automata.
Lima, P U; Saridis, G N
1999-01-01
This paper introduces a design methodology for intelligent controllers, based on a hierarchical linguistic model of command translation by tasks-primitive tasks-primitive actions, and on a two-stage hierarchical learning stochastic automaton that models the translation interfaces of a three-level hierarchical intelligent controller. The methodology relies on the designer's a priori knowledge on how to implement by primitive actions the different primitive tasks which define the intelligent controller. A cost function applicable to any primitive task is introduced and used to learn on-line the optimal choices from the corresponding predesigned sets of primitive actions. The same concept applies to the optimal tasks for each command, whose choice is based on conflict sets of stochastic grammar productions. Optional designs can be compared using this performance measure. A particular design evolves towards the command translation (by tasks-primitive tasks-primitive actions) that minimizes the cost function.
Stochasticity effects in quantum radiation reaction.
Neitz, N; Di Piazza, A
2013-08-02
When an ultrarelativistic electron beam collides with a sufficiently intense laser pulse, radiation-reaction effects can strongly alter the beam dynamics. In the realm of classical electrodynamics, radiation reaction has a beneficial effect on the electron beam as it tends to reduce its energy spread. Here we show that when quantum effects become important, radiation reaction induces the opposite effect; i.e., the energy distribution of the electron beam spreads out after interacting with the laser pulse. We identify the physical origin of this opposite tendency in the intrinsic stochasticity of photon emission, which becomes substantial in the quantum regime. Our numerical simulations indicate that the predicted effects of the stochasticity can be measured already with presently available lasers and electron accelerators.
Entropy production of doubly stochastic quantum channels
Müller-Hermes, Alexander; Stilck França, Daniel Wolf, Michael M.
2016-02-15
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
Stochastic magnetization dynamics in single domain particles
NASA Astrophysics Data System (ADS)
Giordano, Stefano; Dusch, Yannick; Tiercelin, Nicolas; Pernod, Philippe; Preobrazhensky, Vladimir
2013-06-01
Magnetic particles are largely utilized in several applications ranging from magnetorheological fluids to bioscience and from nanothechnology to memories or logic devices. The behavior of each single particle at finite temperature (under thermal stochastic fluctuations) plays a central role in determining the response of the whole physical system taken into consideration. Here, the magnetization evolution is studied through the Landau-Lifshitz-Gilbert formalism and the non-equilibrium statistical mechanics is introduced with the Langevin and Fokker-Planck methodologies. As result of the combination of such techniques we analyse the stochastic magnetization dynamics and we numerically determine the convergence time, measuring the velocity of attainment of thermodynamic equilibrium, as function of the system temperature.
Stochastic dynamic models and Chebyshev splines
Fan, Ruzong; Zhu, Bin; Wang, Yuedong
2015-01-01
In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632
Dynamic range of hypercubic stochastic excitable media
NASA Astrophysics Data System (ADS)
Assis, Vladimir R. V.; Copelli, Mauro
2008-01-01
We study the response properties of d -dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modeled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h . The response function (mean density of active sites ρ versus h ) is obtained via simulations (for d=1,2,3,4 ) and mean-field approximations at the single-site and pair levels (∀d) . In any dimension, the dynamic range and sensitivity of the response function are maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d .
Relative dispersion in 2D stochastic flows
NASA Astrophysics Data System (ADS)
Piterbarg, L. I.
We investigate the relative dispersion for two types of stochastic flows—Brownian flow (Kraichnan model) and a flow with memory (inertial particles). In the first case well-known asymptotics are rigorously derived for a self-similar spectrum of the velocity field by using a half-century-old Feller's theorem. Exact limits of the asymptotics and exact values for dimensionless constants are obtained. The second part of the paper addresses a relatively new object: the first-order Markov stochastic flow modelling inertial particle motion. Both local and non-local dynamics are investigated. In the first case an exact exponential asymptotic is obtained for the relative dispersion. In turn, two regimes are considered in the case of non-smooth forcing: weak and strong turbulence. For weak turbulence the obtained asymptotic of relative dispersion is similar to that of the Brownian flow. As for strong turbulence, an upper bound is obtained for the scaling of relative dispersion.
Noise-free logical stochastic resonance.
Gupta, Animesh; Sohane, Aman; Kohar, Vivek; Murali, K; Sinha, Sudeshna
2011-11-01
The phenomena of logical stochastic resonance (LSR) was demonstrated recently [Phys. Rev. Lett. 102, 104101 (2009)]: namely, when a bistable system is driven by two inputs it consistently yields a response mirroring a logic function of the two inputs in an optimal window of moderate noise. Here we examine the intriguing possibility of obtaining dynamical behavior equivalent to LSR in a noise-free bistable system, subjected only to periodic forcing, such as sinusoidal driving or rectangular pulse trains. We find that such a system, despite having no stochastic influence, also yields phenomena analogous to LSR, in an appropriate window of frequency and amplitude of the periodic forcing. The results are corroborated by circuit experiments.
Stochastic Radiative transfer and real cloudiness
Evans, F.
1995-09-01
Plane-parallel radiative transfer modeling of clouds in GCMs is thought to be an inadequate representation of the effects of real cloudiness. A promising new approach for studying the effects of cloud horizontal inhomogeneity is stochastic radiative transfer, which computes the radiative effects of ensembles of cloud structures described by probability distributions. This approach is appropriate because cloud information is inherently statistical, and it is the mean radiative effect of complex 3D cloud structure that is desired. 2 refs., 1 fig.
Stochastic behavior of nanoscale dielectric wall buckling
Friedman, Lawrence H.; Levin, Igor; Cook, Robert F.
2016-01-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts. PMID:27330220
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
Modeling heart rate variability by stochastic feedback
NASA Technical Reports Server (NTRS)
Amaral, L. A.; Goldberger, A. L.; Stanley, H. E.
1999-01-01
We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.
STOCHASTIC COOLING STUDIES IN RHIC, II.
BLASKIEWICZ,M.BRENNAN,J.M.WEI,J.
2004-07-05
Intra-beam scattering (IBS) is unavoidable for highly charged heavy ions and causes emittance growth during the store for collision physics. A longitudinal bunched beam stochastic cooling system will confine the bunch within the RF bucket increasing the useful luminosity. We describe a series of measurements in RHIC that have been used to verify our understanding of the relevant physics and the cooling system architecture that is being prototyped.
Stochastic Orbit Prediction Using KAM Tori
2011-03-24
machine precision. The theory is extended with new mathematical techniques for determining and predicting stochastic orbits for Earth satellite...who mentored me early in the process. We will always share a special bond in our work to advance KAM theory for earth orbits. My friends and...36 2.1.4.3.1 Pseudo-Inertial J2000 Frame ...............................38 2.1.4.3.2 True of Date Rotating ( Earth -Fixed
Stochastic Games with Average Payoff Criterion
Ghosh, M. K.; Bagchi, A.
1998-11-15
We study two-person stochastic games on a Polish state and compact action spaces and with average payoff criterion under a certain ergodicity condition. For the zero-sum game we establish the existence of a value and stationary optimal strategies for both players. For the nonzero-sum case the existence of Nash equilibrium in stationary strategies is established under certain separability conditions.
Modeling stochastic noise in gene regulatory systems.
Meister, Arwen; Du, Chao; Li, Ye Henry; Wong, Wing Hung
2014-03-01
The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.
On a class of nonstationary stochastic processes
NASA Technical Reports Server (NTRS)
Miamee, A. G.; Hardin, Jay C.
1989-01-01
A new class of nonstationary stochastic processes is introduced and some of the essential properties of its members are investigated. This class is richer than the class of stationary processes and has the potential of modeling some nonstationary time series. The relation between these newly defined processes with other important classes of nonstationary processes is investigated. Several examples of linearly correlated processes which are not stationary, periodically correlated, or harmonizable are given.
Stochastic behavior of nanoscale dielectric wall buckling.
Friedman, Lawrence H; Levin, Igor; Cook, Robert F
2016-03-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties-all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.
Optimization Testbed Cometboards Extended into Stochastic Domain
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.; Patnaik, Surya N.
2010-01-01
COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials.
Planning with Continuous Resources in Stochastic Domains
NASA Technical Reports Server (NTRS)
Mausam, Mausau; Benazera, Emmanuel; Brafman, Roneu; Hansen, Eric
2005-01-01
We consider the problem of optimal planning in stochastic domains with metric resource constraints. Our goal is to generate a policy whose expected sum of rewards is maximized for a given initial state. We consider a general formulation motivated by our application domain--planetary exploration--in which the choice of an action at each step may depend on the current resource levels. We adapt the forward search algorithm AO* to handle our continuous state space efficiently.
A stochastic model for kinesin bidirectional stepping
Yao, Xiaojun; Zheng, Yujun
2014-02-28
In this paper, a hand-over-hand stochastic model for the dynamics of the conventional kinesin is constructed. In the model, both forward and backward motions are taken into consideration. First passage time distributions, average velocities, dwell times, and forward/backward step ratios are investigated based on the model. A good agreement between the results of the model and experimental data is achieved under a variety of external loads.
Stochastic histories of refractory interstellar dust
NASA Technical Reports Server (NTRS)
Liffman, Kurt; Clayton, Donald D.
1988-01-01
Histories of refractory interstellar dust particles (IDPs) are calculated. The profile of a particle population is assembled from a large number of stochastic, or Monte Carlo, histories of single particles; the probabilities for each of the events that may befall a given particle are specified, and the particle's history is unfolded by a sequence of random numbers. The assumptions that are made and the techniques of the calculation are described together with the results obtained. Several technical demonstrations are presented.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
The Foundations of Linear Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
Peña, L. De La; Cetto, A. M.
2006-03-01
An analysis is briefly presented of the possible causes of the failure of stochastic electrodynamics (SED) when applied to systems with nonlinear forces, on the basis that the main principles of the theory are correct. In light of this analysis, an alternative approach to the theory is discussed, whose postulates allow to establish contact with quantum mechanics in a natural way. The ensuing theory, linear SED, confirms the essential role of the vacuum particle interaction as the source of quantum phenomena.
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values.
Stationary conditions for stochastic differential equations
NASA Technical Reports Server (NTRS)
Adomian, G.; Walker, W. W.
1972-01-01
This is a preliminary study of possible necessary and sufficient conditions to insure stationarity in the solution process for a stochastic differential equation. It indirectly sheds some light on ergodicity properties and shows that the spectral density is generally inadequate as a statistical measure of the solution. Further work is proceeding on a more general theory which gives necessary and sufficient conditions in a form useful for applications.
Discrete Deterministic and Stochastic Petri Nets
NASA Technical Reports Server (NTRS)
Zijal, Robert; Ciardo, Gianfranco
1996-01-01
Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.
Critical Number of Fields in Stochastic Inflation.
Vennin, Vincent; Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Wands, David
2017-01-20
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e-folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δN formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation. The mean number of e-folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularized if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Stochastic self-assembly of incommensurate clusters.
D'Orsogna, M R; Lakatos, G; Chou, T
2012-02-28
Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-Döring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.
Stochastic self-assembly of incommensurate clusters
NASA Astrophysics Data System (ADS)
D'Orsogna, M. R.; Lakatos, G.; Chou, T.
2012-02-01
Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-Döring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.
Stochastic Flow Modeling for Resin Transfer Moulding
NASA Astrophysics Data System (ADS)
Desplentere, Frederik; Verpoest, Ignaas; Lomov, Stepan
2009-07-01
Liquid moulding processes suffer from inherently present scatter in the textile reinforcement properties. This variability can lead to unwanted filling patterns within the mould resulting in bad parts. If thermoplastic resins are used with the in-situ polymerisation technique, an additional difficulty appears. The time window to inject the material is small if industrial processing parameters are used (<5 minutes). To model the stochastic nature of RTM, Darcy's description of the mould filling process has been used with the permeability distribution of the preform given as a random field. The random field of the permeability is constructed as a correlated field with an exponential correlation function. Optical microscopy and X-ray micro-CT have been used to study the stochastic parameters of the geometry for 2D and 3D woven textile preforms. The parameters describing the random permeability field (average, standard deviation and correlation length) are identified based on the stochastic parameters of the geometry for the preforms, analytical estimations and CFD modelling of the permeability. In order to implement the random field for the permeability and the variability for the resin viscosity, an add-on to the mould filling simulation software PAM-RTM™ has been developed. This analysis has been validated on case studies.
Electromagnetic Propagationg of Waves in Helical Stochastic
NASA Astrophysics Data System (ADS)
Adrian, Reyes; Mendez, David
2012-02-01
We develop a model for studying the axial propagation of elliptically polarized electromagnetic waves in a spatially random helical media. We start by writing Maxwell equations for a structurally chiral medium whose helical angle contains both a stochastic contribution and a deterministic one, this latter corresponding to an uniform rotation. We write the electromagnetic equations into Marcuvitz Schwigner representation to transform them afterward by using the Oseen transformation. We exhibit that in the Oseen frame, Marcuvitz Schwigner equations turns out to be a linear vectorial stochastic system of equations with multiplicative noise. From this result and utilizing a well known formalism for treating stochastic differential equations, we find the governing equations for the first and second moments of the field amplitudes for a general correlation model for the slope angles, and calculate their corresponding band structure for a particular spectral noise density. We show that the average resulting electromagnetic fields exhibit dissipation and the appearance of a new reflection band whose chirality is the opposite of the one obtained for a simple cholesteric liquid crystals.
Recursive stochastic effects in valley hybrid inflation
NASA Astrophysics Data System (ADS)
Levasseur, Laurence Perreault; Vennin, Vincent; Brandenberger, Robert
2013-10-01
Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88, 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution.
Electron acceleration in stochastic double layers
NASA Technical Reports Server (NTRS)
Lotko, William
1987-01-01
Transversely localized double layers evolve randomly in turbulent regions of strongly magnetized plasma carrying current along the magnetic field. Results from numerical simulations and spacecraft observations in the auroral plasma indicate that the parallel electric field in such regions is microscopically intermittent or stochastic. The implications of stochastic double layer fields on electron acceleration will be discussed in terms of a statistical process involving ensemble averages over test particle motion. A Fokker-Planck equation can be derived for the electron phase space density, which depends on the mean and rms amplitudes of the double layers, the mean double layer density, and the initial electron velocity distribution. It is shown that the resulting electron acceleration is very sensitive to the ratio of the initial electron energy to the rms double layer amplitude. When this ratio is large, the acceleration process differs little from that expected in a dc electric field. When it is small, stochastic heating competes with directed acceleration. Evidence for both cases can be found in the auroral ionosphere in association with so-called inverted-V precipitation and collimated edge precipitation.
Linear stochastic degenerate Sobolev equations and applications†
NASA Astrophysics Data System (ADS)
Liaskos, Konstantinos B.; Pantelous, Athanasios A.; Stratis, Ioannis G.
2015-12-01
In this paper, a general class of linear stochastic degenerate Sobolev equations with additive noise is considered. This class of systems is the infinite-dimensional analogue of linear descriptor systems in finite dimensions. Under appropriate assumptions, the mild and strong well-posedness for the initial value problem are studied using elements of the semigroup theory and properties of the stochastic convolution. The final value problem is also examined and it is proved that this is uniquely strongly solvable and the solution is continuously dependent on the final data. Based on the results of the forward and backward problem, the conditions for the exact controllability are investigated for a special but important class of these equations. The abstract results are illustrated by applications in complex media electromagnetics, in the one-dimensional stochastic Dirac equation in the non-relativistic limit and in a potential application in input-output analysis in economics. Dedicated to Professor Grigoris Kalogeropoulos on the occasion of his seventieth birthday.
Robust stochastic optimization for reservoir operation
NASA Astrophysics Data System (ADS)
Pan, Limeng; Housh, Mashor; Liu, Pan; Cai, Ximing; Chen, Xin
2015-01-01
Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.
The Stochastic Modelling of Endemic Diseases
NASA Astrophysics Data System (ADS)
Susvitasari, Kurnia; Siswantining, Titin
2017-01-01
A study about epidemic has been conducted since a long time ago, but genuine progress was hardly forthcoming until the end of the 19th century (Bailey, 1975). Both deterministic and stochastic models were used to describe these. Then, from 1927 to 1939 Kermack and McKendrick introduced a generality of this model, including some variables to consider such as rate of infection and recovery. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, R0. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when R0 ≤ 1, minor epidemic occurs with probability one in both approaches, but when R0 > 1, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when R0 > 1 and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic’s equilibrium.
Stochastic Evolutionary Algorithms for Planning Robot Paths
NASA Technical Reports Server (NTRS)
Fink, Wolfgang; Aghazarian, Hrand; Huntsberger, Terrance; Terrile, Richard
2006-01-01
A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.
Evaluating uncertainty in stochastic simulation models
McKay, M.D.
1998-02-01
This paper discusses fundamental concepts of uncertainty analysis relevant to both stochastic simulation models and deterministic models. A stochastic simulation model, called a simulation model, is a stochastic mathematical model that incorporates random numbers in the calculation of the model prediction. Queuing models are familiar simulation models in which random numbers are used for sampling interarrival and service times. Another example of simulation models is found in probabilistic risk assessments where atmospheric dispersion submodels are used to calculate movement of material. For these models, randomness comes not from the sampling of times but from the sampling of weather conditions, which are described by a frequency distribution of atmospheric variables like wind speed and direction as a function of height above ground. A common characteristic of simulation models is that single predictions, based on one interarrival time or one weather condition, for example, are not nearly as informative as the probability distribution of possible predictions induced by sampling the simulation variables like time and weather condition. The language of model analysis is often general and vague, with terms having mostly intuitive meaning. The definition and motivations for some of the commonly used terms and phrases offered in this paper lead to an analysis procedure based on prediction variance. In the following mathematical abstraction the authors present a setting for model analysis, relate practical objectives to mathematical terms, and show how two reasonable premises lead to a viable analysis strategy.
A stochastic approach to model validation
NASA Astrophysics Data System (ADS)
Luis, Steven J.; McLaughlin, Dennis
This paper describes a stochastic approach for assessing the validity of environmental models. In order to illustrate basic concepts we focus on the problem of modeling moisture movement through an unsaturated porous medium. We assume that the modeling objective is to predict the mean distribution of moisture content over time and space. The mean moisture content describes the large-scale flow behavior of most interest in many practical applications. The model validation process attempts to determine whether the model's predictions are acceptably close to the mean. This can be accomplished by comparing small-scale measurements of moisture content to the model's predictions. Differences between these two quantities can be attributed to three distinct 'error sources': (1) measurement error, (2) spatial heterogeneity, and (3) model error. If we adopt appropriate stochastic descriptions for the first two sources of error we can view model validation as a hypothesis testing problem where the null hypothesis states that model error is negligible. We illustrate this concept by comparing the predictions of a simple two-dimensional deterministic model to measurements collected during a field experiment carried out near Las Cruces, New Mexico. Preliminary results from this field test indicate that a stochastic approach to validation can identify model deficiencies and provide objective standards for model performance.
Critical Number of Fields in Stochastic Inflation
NASA Astrophysics Data System (ADS)
Vennin, Vincent; Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Wands, David
2017-01-01
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e -folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δ N formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation. The mean number of e -folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularized if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation
NASA Astrophysics Data System (ADS)
Ma, Juan; Chen, Jian-Jun; Gao, Wei
2006-08-01
A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper.
Stochastic Models for Precipitable Water in Convection
NASA Astrophysics Data System (ADS)
Leung, Kimberly
Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test
Cancer Evolution and the Limits of Predictability in Precision Cancer Medicine
Lipinski, Kamil A.; Barber, Louise J.; Davies, Matthew N.; Ashenden, Matthew; Sottoriva, Andrea; Gerlinger, Marco
2016-01-01
The ability to predict the future behavior of an individual cancer is crucial for precision cancer medicine. The discovery of extensive intratumor heterogeneity and ongoing clonal adaptation in human tumors substantiated the notion of cancer as an evolutionary process. Random events are inherent in evolution and tumor spatial structures hinder the efficacy of selection, which is the only deterministic evolutionary force. This review outlines how the interaction of these stochastic and deterministic processes, which have been extensively studied in evolutionary biology, limits cancer predictability and develops evolutionary strategies to improve predictions. Understanding and advancing the cancer predictability horizon is crucial to improve precision medicine outcomes. PMID:26949746
Stochastic simulation of radium-223 dichloride therapy at the sub-cellular level.
Gholami, Y; Zhu, X; Fulton, R; Meikle, S; El-Fakhri, G; Kuncic, Z
2015-08-07
Radium-223 dichloride ((223)Ra) is an alpha particle emitter and a natural bone-seeking radionuclide that is currently used for treating osteoblastic bone metastases associated with prostate cancer. The stochastic nature of alpha emission, hits and energy deposition poses some challenges for estimating radiation damage. In this paper we investigate the distribution of hits to cells by multiple alpha particles corresponding to a typical clinically delivered dose using a Monte Carlo model to simulate the stochastic effects. The number of hits and dose deposition were recorded in the cytoplasm and nucleus of each cell. Alpha particle tracks were also visualized. We found that the stochastic variation in dose deposited in cell nuclei ([Formula: see text]40%) can be attributed in part to the variation in LET with pathlength. We also found that [Formula: see text]18% of cell nuclei receive less than one sigma below the average dose per cell ([Formula: see text]15.4 Gy). One possible implication of this is that the efficacy of cell kill in alpha particle therapy need not rely solely on ionization clustering on DNA but possibly also on indirect DNA damage through the production of free radicals and ensuing intracellular signaling.
Telomerase Activity Detection with Amplification-Free Single Molecule Stochastic Binding Assay.
Su, Xin; Li, Zehao; Yan, Xinzhong; Wang, Lei; Zhou, Xu; Wei, Lin; Xiao, Lehui; Yu, Changyuan
2017-03-21
Because the elongation of telomeres has been associated with tumorigenesis, it is of great interest to develop rapid and high-confidence telomerase activity detection methods for disease diagnosis. Currently, amplification-based strategies have been extensively explored for telomerase detection in vitro and in vivo. However, amplification is typically associated with poor reproducibility and high background, which hamper further applications of the strategies, particularly for real sample assays. Here, we demonstrate a new amplification-free single molecule imaging method for telomerase activity detection in vitro based on nucleic acid stochastic binding with total internal reflection fluorescence microscopy. The dynamic stochastic binding of a short fluorescent DNA probe with a genuine target yields a distinct kinetic signature from the background noise, allowing us to identify telomerase reaction products (TRPs) at the single molecule level. A limit-of-detection as low as 0.5 fM and a dynamic range of 0.5-500 fM for TRP detection were readily achieved. With this method, telomerase extracted from cancer cells was determined with sensitivity down to 10 cells. Moreover, the length distribution of TRPs was also determined by multiple stochastic probing, which could provide deep insight into the mechanistic study of telomerase catalysis.
Stochastic simulation of radium-223 dichloride therapy at the sub-cellular level
NASA Astrophysics Data System (ADS)
Gholami, Y.; Zhu, X.; Fulton, R.; Meikle, S.; El-Fakhri, G.; Kuncic, Z.
2015-08-01
Radium-223 dichloride (223Ra) is an alpha particle emitter and a natural bone-seeking radionuclide that is currently used for treating osteoblastic bone metastases associated with prostate cancer. The stochastic nature of alpha emission, hits and energy deposition poses some challenges for estimating radiation damage. In this paper we investigate the distribution of hits to cells by multiple alpha particles corresponding to a typical clinically delivered dose using a Monte Carlo model to simulate the stochastic effects. The number of hits and dose deposition were recorded in the cytoplasm and nucleus of each cell. Alpha particle tracks were also visualized. We found that the stochastic variation in dose deposited in cell nuclei (≃ 40%) can be attributed in part to the variation in LET with pathlength. We also found that ≃ 18% of cell nuclei receive less than one sigma below the average dose per cell (≃ 15.4 Gy). One possible implication of this is that the efficacy of cell kill in alpha particle therapy need not rely solely on ionization clustering on DNA but possibly also on indirect DNA damage through the production of free radicals and ensuing intracellular signaling.
Method to describe stochastic dynamics using an optimal coordinate.
Krivov, Sergei V
2013-12-01
A general method to describe the stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems: the determination of an optimal coordinate for the description of stochastic dynamics; the reconstruction of time from an ensemble of stochastic trajectories; and the decomposition of stationary stochastic dynamics into eigenmodes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated by a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multivalued function. An optimal coordinate for a random walk on a line corresponds to the conventional eigenvector of the one-dimensional Dirac equation. The equation for the optimal coordinate in a slowly varying potential reduces to the Hamilton-Jacobi equation for the action function.
Time-ordered product expansions for computational stochastic system biology.
Mjolsness, Eric
2013-06-01
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.
Problems of Mathematical Finance by Stochastic Control Methods
NASA Astrophysics Data System (ADS)
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
Stochastic effects in a seasonally forced epidemic model
NASA Astrophysics Data System (ADS)
Rozhnova, G.; Nunes, A.
2010-10-01
The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.
Second Cancers After Colorectal Cancer
... After Colorectal Cancer Colorectal Cancer After Treatment Second Cancers After Colorectal Cancer Colorectal cancer survivors can be affected by a ... many of these cancers. Follow-up after colorectal cancer treatment After completing treatment for colorectal cancer, you ...
Frank, T D
2002-07-01
Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
Płoszajczak, M.; Srokowski, T.
1997-05-01
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
Hyperbolic cross truncations for stochastic Fourier cosine series.
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions.
A stochastic method for computing hadronic matrix elements
Alexandrou, Constantia; Constantinou, Martha; Dinter, Simon; ...
2014-01-24
In this study, we present a stochastic method for the calculation of baryon 3-point functions which is an alternative to the typically used sequential method offering more versatility. We analyze the scaling of the error of the stochastically evaluated 3-point function with the lattice volume and find a favorable signal to noise ratio suggesting that the stochastic method can be extended to large volumes providing an efficient approach to compute hadronic matrix elements and form factors.
A stochastic model of AIDS and condom use
NASA Astrophysics Data System (ADS)
Dalal, Nirav; Greenhalgh, David; Mao, Xuerong
2007-01-01
In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.
Suboptimal stochastic controller for an n-body spacecraft
NASA Technical Reports Server (NTRS)
Larson, V.
1973-01-01
The problem is studied of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector, can be easily implemented, and enables system performance to be significantly improved.
Vaccination Control in a Stochastic SVIR Epidemic Model
Witbooi, Peter J.; Muller, Grant E.; Van Schalkwyk, Garth J.
2015-01-01
For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium for ℛ0 < 1, where ℛ0 denotes the basic reproduction number of the underlying deterministic model. We study an optimal control problem for the stochastic model as well as for the underlying deterministic model. In order to solve the stochastic problem numerically, we use an approximation based on the solution of the deterministic model. PMID:26089961
Sources of stochasticity in constitutive and autoregulated gene expression
NASA Astrophysics Data System (ADS)
Marathe, Rahul; Gomez, David; Klumpp, Stefan
2012-11-01
Gene expression is inherently noisy as many steps in the read-out of the genetic information are stochastic. To disentangle the effect of different sources of stochasticity in such systems, we consider various models that describe some processes as stochastic and others as deterministic. We review earlier results for unregulated (constitutive) gene expression and present new results for a gene controlled by negative autoregulation with cell growth modeled by linear volume growth.
Analysis of stochastic stem cell models with control.
Yang, Jienian; Sun, Zheng; Komarova, Natalia L
2015-08-01
Understanding the dynamics of stem cell lineages is of central importance both for healthy and cancerous tissues. We study stochastic population dynamics of stem cells and differentiated cells, where cell decisions, such as proliferation vs. differentiation decisions, or division and death decisions, are under regulation from surrounding cells. The goal is to understand how different types of control mechanisms affect the means and variances of cell numbers. We use the assumption of weak dependencies of the regulatory functions (the controls) on the cell populations near the equilibrium to formulate moment equations. We then study three different methods of closure, showing that they all lead to the same results for the highest order terms in the expressions for the moments. We derive simple explicit expressions for the means and the variances of stem cell and differentiated cell numbers. It turns out that the variance is expressed as an algebraic function of partial derivatives of the controls with respect to the population sizes at the equilibrium. We demonstrate that these findings are consistent with the results previously obtained in the context of particular systems, and also present two novel examples with negative and positive control of division and differentiation decisions. This methodology is formulated without any specific assumptions on the functional form of the controls, and thus can be used for any biological system.
Analysis of stochastically forced quasi-periodic attractors
Ryashko, Lev
2015-11-30
A problem of the analysis of stochastically forced quasi-periodic auto-oscillations of nonlinear dynamic systems is considered. A stationary distribution of random trajectories in the neighborhood of the corresponding deterministic attractor (torus) is studied. A parametric description of quadratic approximation of the quasipotential based on the stochastic sensitivity functions (SSF) technique is given. Using this technique, we analyse a dispersion of stochastic flows near the torus. For the case of two-torus in three-dimensional space, the stochastic sensitivity function is constructed.
The Sharma-Parthasarathy stochastic two-body problem
Cresson, J.
2015-03-15
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.
A heterogeneous stochastic FEM framework for elliptic PDEs
Hou, Thomas Y. Liu, Pengfei
2015-01-15
We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.
Chen, Chuchu Hong, Jialin Zhang, Liying
2016-02-01
Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.
NASA Astrophysics Data System (ADS)
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
Biologically variable respiration as a stochastic process in ventilation - a stochastic model study.
Min, Kyongyob; Hosoi, Keita; Degami, Masayuki; Kinoshita, Yoshinori
2010-01-01
Based on the fractal bronchial tree, we introduced a function of "asynchronous phasic contractions of lobular bronchiole", which would generate fluctuations in tidal volumes. Stochastic control theory was able to describe a genesis of biological variability in spontaneous respirations using a Schroedinger wave function.
ERIC Educational Resources Information Center
McMillan, Melville L.; Chan, Wing H.
2006-01-01
Efficiency scores are determined for Canadian universities using both data envelopment analysis and stochastic frontier methods for selected specifications. The outcomes are compared. There is considerable divergence in the efficiency scores and their rankings among methods and specifications. An analysis of rankings, however, reveals that the…
Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models
NASA Astrophysics Data System (ADS)
Eyink, Gregory L.
2009-08-01
We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfvén theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.
Deterministic versus stochastic trends: Detection and challenges
NASA Astrophysics Data System (ADS)
Fatichi, S.; Barbosa, S. M.; Caporali, E.; Silva, M. E.
2009-09-01
The detection of a trend in a time series and the evaluation of its magnitude and statistical significance is an important task in geophysical research. This importance is amplified in climate change contexts, since trends are often used to characterize long-term climate variability and to quantify the magnitude and the statistical significance of changes in climate time series, both at global and local scales. Recent studies have demonstrated that the stochastic behavior of a time series can change the statistical significance of a trend, especially if the time series exhibits long-range dependence. The present study examines the trends in time series of daily average temperature recorded in 26 stations in the Tuscany region (Italy). In this study a new framework for trend detection is proposed. First two parametric statistical tests, the Phillips-Perron test and the Kwiatkowski-Phillips-Schmidt-Shin test, are applied in order to test for trend stationary and difference stationary behavior in the temperature time series. Then long-range dependence is assessed using different approaches, including wavelet analysis, heuristic methods and by fitting fractionally integrated autoregressive moving average models. The trend detection results are further compared with the results obtained using nonparametric trend detection methods: Mann-Kendall, Cox-Stuart and Spearman's ρ tests. This study confirms an increase in uncertainty when pronounced stochastic behaviors are present in the data. Nevertheless, for approximately one third of the analyzed records, the stochastic behavior itself cannot explain the long-term features of the time series, and a deterministic positive trend is the most likely explanation.
Bayesian Estimation and Inference Using Stochastic Electronics
Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M.; Hamilton, Tara J.; Tapson, Jonathan; van Schaik, André
2016-01-01
In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream. PMID:27047326
Bayesian Estimation and Inference Using Stochastic Electronics.
Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André
2016-01-01
In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
Stochastic analysis of virus transport in aquifers
Campbell, Rehmann L.L.; Welty, C.; Harvey, R.W.
1999-01-01
A large-scale model of virus transport in aquifers is derived using spectral perturbation analysis. The effects of spatial variability in aquifer hydraulic conductivity and virus transport (attachment, detachment, and inactivation) parameters on large-scale virus transport are evaluated. A stochastic mean model of virus transport is developed by linking a simple system of local-scale free-virus transport and attached-virus conservation equations from the current literature with a random-field representation of aquifer and virus transport properties. The resultant mean equations for free and attached viruses are found to differ considerably from the local-scale equations on which they are based and include effects such as a free-virus effective velocity that is a function of aquifer heterogeneity as well as virus transport parameters. Stochastic mean free-virus breakthrough curves are compared with local model output in order to observe the effects of spatial variability on mean one-dimensional virus transport in three-dimensionally heterogeneous porous media. Significant findings from this theoretical analysis include the following: (1) Stochastic model breakthrough occurs earlier than local model breakthrough, and this effect is most pronounced for the least conductive aquifers studied. (2) A high degree of aquifer heterogeneity can lead to virus breakthrough actually preceding that of a conservative tracer. (3) As the mean hydraulic conductivity is increased, the mean model shows less sensitivity to the variance of the natural-logarithm hydraulic conductivity and mean virus diameter. (4) Incorporation of a heterogeneous colloid filtration term results in higher predicted concentrations than a simple first-order adsorption term for a given mean attachment rate. (5) Incorporation of aquifer heterogeneity leads to a greater range of virus diameters for which significant breakthrough occurs. (6) The mean model is more sensitive to the inactivation rate of viruses
Stochastic convex sparse principal component analysis.
Baytas, Inci M; Lin, Kaixiang; Wang, Fei; Jain, Anil K; Zhou, Jiayu
2016-12-01
Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.
Hybrid stochastic simplifications for multiscale gene networks
Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu
2009-01-01
Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach. PMID:19735554
Stochastic multiscale modeling of polycrystalline materials
NASA Astrophysics Data System (ADS)
Wen, Bin
Mechanical properties of engineering materials are sensitive to the underlying random microstructure. Quantification of mechanical property variability induced by microstructure variation is essential for the prediction of extreme properties and microstructure-sensitive design of materials. Recent advances in high throughput characterization of polycrystalline microstructures have resulted in huge data sets of microstructural descriptors and image snapshots. To utilize these large scale experimental data for computing the resulting variability of macroscopic properties, appropriate mathematical representation of microstructures is needed. By exploring the space containing all admissible microstructures that are statistically similar to the available data, one can estimate the distribution/envelope of possible properties by employing efficient stochastic simulation methodologies along with robust physics-based deterministic simulators. The focus of this thesis is on the construction of low-dimensional representations of random microstructures and the development of efficient physics-based simulators for polycrystalline materials. By adopting appropriate stochastic methods, such as Monte Carlo and Adaptive Sparse Grid Collocation methods, the variability of microstructure-sensitive properties of polycrystalline materials is investigated. The primary outcomes of this thesis include: (1) Development of data-driven reduced-order representations of microstructure variations to construct the admissible space of random polycrystalline microstructures. (2) Development of accurate and efficient physics-based simulators for the estimation of material properties based on mesoscale microstructures. (3) Investigating property variability of polycrystalline materials using efficient stochastic simulation methods in combination with the above two developments. The uncertainty quantification framework developed in this work integrates information science and materials science, and
Paul, Subhadip; Roy, Prasun Kumar
2016-02-01
Radiation therapy is one of the important treatment procedures of cancer. The day-to-day delivered dose to the tissue in radiation therapy often deviates from the planned fixed dose per fraction. This day-to-day variation of radiation dose is stochastic. Here, we have developed the mathematical formulation to represent the day-to-day stochastic dose variation effect in radiation therapy. Our analysis shows that that the fixed dose delivery approximation under-estimates the biological effective dose, even if the average delivered dose per fraction is equal to the planned dose per fraction. The magnitude of the under-estimation effect relies upon the day-to-day stochastic dose variation level, the dose fraction size and the values of the radiobiological parameters of the tissue. We have further explored the application of our mathematical formulation for adaptive dose calculation. Our analysis implies that, compared to the premise of the Linear Quadratic Linear (LQL) framework, the Linear Quadratic framework based analytical formulation under-estimates the required dose per fraction necessary to produce the same biological effective dose as originally planned. Our study provides analytical formulation to calculate iso-effect in adaptive radiation therapy considering day-to-day stochastic dose deviation from planned dose and also indicates the potential utility of LQL framework in this context.
ON NONSTATIONARY STOCHASTIC MODELS FOR EARTHQUAKES.
Safak, Erdal; Boore, David M.
1986-01-01
A seismological stochastic model for earthquake ground-motion description is presented. Seismological models are based on the physical properties of the source and the medium and have significant advantages over the widely used empirical models. The model discussed here provides a convenient form for estimating structural response by using random vibration theory. A commonly used random process for ground acceleration, filtered white-noise multiplied by an envelope function, introduces some errors in response calculations for structures whose periods are longer than the faulting duration. An alternate random process, filtered shot-noise process, eliminates these errors.
Stochastic Euler-Poincaré reduction
Arnaudon, Marc; Chen, Xin; Cruzeiro, Ana Bela
2014-08-15
We prove a Euler-Poincaré reduction theorem for stochastic processes taking values on a Lie group, which is a generalization of the reduction argument for the deterministic case [J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Texts in Applied Mathematics (Springer, 2003)]. We also show examples of its application to SO(3) and to the group of diffeomorphisms, which includes the Navier-Stokes equation on a bounded domain and the Camassa-Holm equation.
BUNCHED BEAM STOCHASTIC COOLING PROJECT FOR RHIC.
BRENNAN, J.M.; BASKIEWICZ, M.M.
2005-09-18
The main performance limitation for RHIC is emittance growth caused by IntraBeam Scattering during the store. We have developed a longitudinal bunched-beam stochastic cooling system in the 5-8 GHz band which will be used to counteract IBS longitudinal emittance growth and prevent de-bunching during the store. Solutions to the technical problems of achieving sufficient kicker voltage and overcoming the electronic saturation effects caused by coherent components within the Schottky spectrum are described. Results from tests with copper ions in RHIC during the FY05 physics run, including the observation of signal suppression, are presented.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
DNA replication in yeast is stochastic
NASA Astrophysics Data System (ADS)
Cheng-Hsin Yang, Scott; Rhind, Nicholas; Bechhoefer, John
2010-03-01
Largely on the basis of a simple --- perhaps too simple --- analysis of microarray-chip experiments, people have concluded that DNA replication in budding yeast (S. cerevisiae) is a nearly deterministic process, in which the position and activation time of each origin of replication is pre-determined. In this talk, we introduce a more quantitative approach to the analysis of microarray data. Applying our new methods to budding yeast, we show that the microarray data imply a picture of replication where the timing of origin activation is highly stochastic. We then propose a physical model (the ``multiple-initiator model") to account for the observed probability distributions of origin- activation timing.
A stochastic model of human gait dynamics
NASA Astrophysics Data System (ADS)
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
Solvable stochastic dealer models for financial markets
NASA Astrophysics Data System (ADS)
Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako
2009-05-01
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.
Nonlinear Stochastic Interaction in Aeroelastic Structures.
1988-01-29
Frangopol. D NI (1985ai Sensiti-ts of reltabiltIisbaed optimum de Boyce. W E (1966). Stochastic nonthomogeneous Sturm - Liouville problem. Strut, Dig 111. 1703...It is known that 4,2 =- qlql -q11+- q2 4j the result of any linear operator , with constant coefficients, , 1 = 3E,- - 2 q) applied to a random...Gaussian process results in a Gaussian k. - 3EIIP (2) process. However. if the operator is nonlinear, the resulting It is seen that the left-hand side of
Stochastic Gompertz model of tumour cell growth.
Lo, C F
2007-09-21
In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.
Stochastic Modelling of Gompertzian Tumor Growth
NASA Astrophysics Data System (ADS)
O'Rourke, S. F. C.; Behera, A.
2009-08-01
We study the effect of correlated noise in the Gompertzian tumor growth model for non-zero correlation time. The steady state probability distributions and average population of tumor cells are analyzed within the Fokker-Planck formalism to investigate the importance of additive and multiplicative noise. We find that the correlation strength and correlation time have opposite effects on the steady state probability distributions. It is observed that the non-bistable Gompertzian model, driven by correlated noise exhibits a stochastic resonance and phase transition. This behaviour of the Gompertz model is unaffected with the change of correlation time and occurs as a result of multiplicative noise.
Stochastic rotation dynamics for nematic liquid crystals
Lee, Kuang-Wu Mazza, Marco G.
2015-04-28
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the mesoscopic scale, while preserving microscopic thermal fluctuations.
Controlling bistability in a stochastic perception model
NASA Astrophysics Data System (ADS)
Pisarchik, A. N.; Bashkirtseva, I. A.; Ryashko, L. B.
2015-07-01
Using a simple bistable perception model, we demonstrate how coexisting states can be controlled by periodic modulation applied to a control parameter responsible for the interpretation of ambiguous images. Because of stochastic processes in the brain, any percept is statistically recognized and multistability in perception never occurs. A stable periodic orbit created by the control modulation splits in two limit cycles in an inverse gluing bifurcation, which occurs when the modulation frequency increases. The statistical analysis of transitions between the coexisting states in the presence of noise reveals conditions under which an ambiguous image can be interpreted in a desired way determined by the control.
The Traveling Salesman and Related Stochastic Problems
NASA Astrophysics Data System (ADS)
Percus, A. G.
1998-03-01
In the traveling salesman problem, one must find the length of the shortest closed tour visiting given ``cities''. We study the stochastic version of the problem, taking the locations of cities and the distances separating them to be random variables drawn from an ensemble. We consider first the ensemble where cities are placed in Euclidean space. We investigate how the optimum tour length scales with number of cities and with number of spatial dimensions. We then examine the analytical theory behind the random link ensemble, where distances between cities are independent random variables. Finally, we look at the related geometric issue of nearest neighbor distances, and find some remarkable universalities.
Stochastic model for market stocks with floors
NASA Astrophysics Data System (ADS)
Villarroel, Javier
2007-08-01
We present a model to describe the stochastic evolution of stocks that show a strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general securities that pay dividends at a continuous rate and earn a terminal payoff at maturity T is solved via the martingale probability approach.
Stochastic Euler-Poincaré reduction
NASA Astrophysics Data System (ADS)
Arnaudon, Marc; Chen, Xin; Cruzeiro, Ana Bela
2014-08-01
We prove a Euler-Poincaré reduction theorem for stochastic processes taking values on a Lie group, which is a generalization of the reduction argument for the deterministic case [J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Texts in Applied Mathematics (Springer, 2003)]. We also show examples of its application to SO(3) and to the group of diffeomorphisms, which includes the Navier-Stokes equation on a bounded domain and the Camassa-Holm equation.
Light Optics for Optical Stochastic Cooling
Andorf, Matthew; Lebedev, Valeri; Piot, Philippe; Ruan, Jinhao
2016-06-01
In Optical Stochastic Cooling (OSC) radiation generated by a particle in a "pickup" undulator is amplified and transported to a downstream "kicker" undulator where it interacts with the same particle which radiated it. Fermilab plans to carry out both passive (no optical amplifier) and active (optical amplifier) tests of OSC at the Integrable Optics Test Accelerator (IOTA) currently in construction*. The performace of the optical system is analyzed with simulations in Synchrotron Radiation Workshop (SRW) accounting for the specific temporal and spectral properties of undulator radiation and being augmented to include dispersion of lens material.
Stochastic Optimal Control and Linear Programming Approach
Buckdahn, R.; Goreac, D.; Quincampoix, M.
2011-04-15
We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.
Quantum stochastic thermodynamic on harmonic networks
NASA Astrophysics Data System (ADS)
Deffner, Sebastian
2016-01-01
Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.
A stochastic evolutionary model for survival dynamics
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2014-09-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.
Two stochastic models useful in petroleum exploration
NASA Technical Reports Server (NTRS)
Kaufman, G. M.; Bradley, P. G.
1972-01-01
A model of the petroleum exploration process that tests empirically the hypothesis that at an early stage in the exploration of a basin, the process behaves like sampling without replacement is proposed along with a model of the spatial distribution of petroleum reserviors that conforms to observed facts. In developing the model of discovery, the following topics are discussed: probabilitistic proportionality, likelihood function, and maximum likelihood estimation. In addition, the spatial model is described, which is defined as a stochastic process generating values of a sequence or random variables in a way that simulates the frequency distribution of areal extent, the geographic location, and shape of oil deposits
Spence, Sean A; Doren, Erin L; Dayicioglu, Deniz; Bernasek, Thomas
2014-06-01
We report the case of a 56-year-old patient who had posttraumatic bilateral knee arthritis and underwent sequential bilateral total knee arthroplasty (TKA). The left knee joint required 2-stage reconstruction: a free flap for enhanced soft-tissue coverage and then left knee TKA. Uniquely, at age 16 years this patient sustained a left tibia grade IIIB high-energy crush injury in a car crash and underwent reconstruction with multiple pedicle tube flaps and transfer of soft tissues. Most of that reconstruction was done between the ages of 16 and 19. At age 56 years, staged TKA was performed. To our knowledge, this is the first report of a knee reconstructed with pedicle tube flaps for a grade IIIB tibial fracture, followed years later by free-flap coverage before TKA. This report offers insights and treatment recommendations through long-term follow-up of a unique case and a historical perspective on how reconstructive options have evolved.
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... cancer is, how cancer is tracked, and the economic impact of cancer in the United States. Lifetime Risk ... Cancer? Cancer Surveillance Programs in the United States Economic Impact of Cancer Finding Cancer Information Learn how to ...
Resources - cancer ... The following organizations are good resources for information on cancer : American Cancer Society -- www.cancer.org Cancer Care -- www.cancercare.org Cancer.Net -- www.cancer.net/coping- ...
A guide to differences between stochastic point-source and stochastic finite-fault simulations
Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.
2009-01-01
Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control
Alvarado, Michelle; Ntaimo, Lewis
2016-09-16
Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.
Stochastic perturbation of the two-body problem
NASA Astrophysics Data System (ADS)
Cresson, J.; Pierret, F.; Puig, B.
2013-11-01
We study the impact of a stochastic perturbation on the classical two-body problem in particular concerning the preservation of first integrals and the Hamiltonian structure. Numerical simulations are performed which illustrate the dynamical behavior of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.
Geometric quadratic stochastic operator on countable infinite set
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
A stochastic approach to the solution of magnetohydrodynamic equations
Floriani, E.; Vilela Mendes, R.
2013-06-01
The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the magnetohydrodynamics equations. Some details are given concerning the numerical implementation of the solution which is illustrated by an example of generation of long-range magnetic fields by a velocity source.
Stochastic Schroedinger equations with general complex Gaussian noises
Bassi, Angelo
2003-06-01
Within the framework of non-Markovian stochastic Schroedinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.
Asymptotic behaviour of the stochastic Gilpin-Ayala competition models
NASA Astrophysics Data System (ADS)
Lian, Baosheng; Hu, Shigeng
2008-03-01
In this paper, we investigate a stochastic Gilpin-Ayala competition system, which is more general and more realistic than the classical Lotka-Volterra competition system.We discuss the asymptotic behaviour in detail of the stochastic Gilpin-Ayala competition system, and comparing the classical Lotka-Volterra with Gilpin-Ayala competition system, we find that the latter has better properties.
Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control
Masiero, Federica
2005-03-15
Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations.
Two Different Approaches to Nonzero-Sum Stochastic Differential Games
Rainer, Catherine
2007-06-15
We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist, the two notions of Nash equilibria coincide.
Stochastic dynamics of macromolecular-assembly networks.
NASA Astrophysics Data System (ADS)
Saiz, Leonor; Vilar, Jose
2006-03-01
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components [1]. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage λ induction switches, which rely on the formation of DNA loops by proteins [2] and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes. [1] L. Saiz and J.M.G. Vilar, submitted (2005). [2] J.M.G. Vilar and L. Saiz, Current Opinion in Genetics & Development, 15, 136-144 (2005).
Large deviations for nonlocal stochastic neural fields.
Kuehn, Christian; Riedler, Martin G
2014-04-17
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20.
Stochastic Computations in Cortical Microcircuit Models
Maass, Wolfgang
2013-01-01
Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving. PMID:24244126
Environmental stochasticity controls soil erosion variability
Kim, Jongho; Ivanov, Valeriy Y.; Fatichi, Simone
2016-01-01
Understanding soil erosion by water is essential for a range of research areas but the predictive skill of prognostic models has been repeatedly questioned because of scale limitations of empirical data and the high variability of soil loss across space and time scales. Improved understanding of the underlying processes and their interactions are needed to infer scaling properties of soil loss and better inform predictive methods. This study uses data from multiple environments to highlight temporal-scale dependency of soil loss: erosion variability decreases at larger scales but the reduction rate varies with environment. The reduction of variability of the geomorphic response is attributed to a ‘compensation effect’: temporal alternation of events that exhibit either source-limited or transport-limited regimes. The rate of reduction is related to environment stochasticity and a novel index is derived to reflect the level of variability of intra- and inter-event hydrometeorologic conditions. A higher stochasticity index implies a larger reduction of soil loss variability (enhanced predictability at the aggregated temporal scales) with respect to the mean hydrologic forcing, offering a promising indicator for estimating the degree of uncertainty of erosion assessments. PMID:26925542
Optimal Control via Self-Generated Stochasticity
NASA Technical Reports Server (NTRS)
Zak, Michail
2011-01-01
The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.
Environmental stochasticity controls soil erosion variability
NASA Astrophysics Data System (ADS)
Kim, Jongho; Ivanov, Valeriy Y.; Fatichi, Simone
2016-03-01
Understanding soil erosion by water is essential for a range of research areas but the predictive skill of prognostic models has been repeatedly questioned because of scale limitations of empirical data and the high variability of soil loss across space and time scales. Improved understanding of the underlying processes and their interactions are needed to infer scaling properties of soil loss and better inform predictive methods. This study uses data from multiple environments to highlight temporal-scale dependency of soil loss: erosion variability decreases at larger scales but the reduction rate varies with environment. The reduction of variability of the geomorphic response is attributed to a ‘compensation effect’: temporal alternation of events that exhibit either source-limited or transport-limited regimes. The rate of reduction is related to environment stochasticity and a novel index is derived to reflect the level of variability of intra- and inter-event hydrometeorologic conditions. A higher stochasticity index implies a larger reduction of soil loss variability (enhanced predictability at the aggregated temporal scales) with respect to the mean hydrologic forcing, offering a promising indicator for estimating the degree of uncertainty of erosion assessments.
Stochastic Microhertz Gravitational Radiation from Stellar Convection
NASA Astrophysics Data System (ADS)
Bennett, M. F.; Melatos, A.
2014-09-01
High Reynolds-number turbulence driven by stellar convection in main-sequence stars generates stochastic gravitational radiation. We calculate the wave-strain power spectral density as a function of the zero-age main-sequence mass for an individual star and for an isotropic, universal stellar population described by the Salpeter initial mass function and redshift-dependent Hopkins-Beacom star formation rate. The spectrum is a broken power law, which peaks near the turnover frequency of the largest turbulent eddies. The signal from the Sun dominates the universal background. For the Sun, the far-zone power spectral density peaks at S(f peak) = 5.2 × 10-52 Hz-1 at frequency f peak = 2.3 × 10-7 Hz. However, at low observing frequencies f < 3 × 10-4 Hz, the Earth lies inside the Sun's near zone and the signal is amplified to S near(f peak) = 4.1 × 10-27 Hz-1 because the wave strain scales more steeply with distance (vpropd -5) in the near zone than in the far zone (vpropd -1). Hence the Solar signal may prove relevant for pulsar timing arrays. Other individual sources and the universal background fall well below the projected sensitivities of the Laser Interferometer Space Antenna and next-generation pulsar timing arrays. Stellar convection sets a fundamental noise floor for more sensitive stochastic gravitational-wave experiments in the more distant future.
Single-particle stochastic heat engine.
Rana, Shubhashis; Pal, P S; Saha, Arnab; Jayannavar, A M
2014-10-01
We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating a Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems, we observe that the operational characteristics are model dependent. Our results clearly rule out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.
Stochastic thermodynamics of chemical reaction networks.
Schmiedl, Tim; Seifert, Udo
2007-01-28
For chemical reaction networks in a dilute solution described by a master equation, the authors define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work, and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations such as a generalized Jarzynski relation and a generalized Clausius inequality are discussed. The authors illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.
A Stochastic Model for the Ethanol Pharmacokinetics
GHADIRINEJAD, Mazyar; ATASOYLU, Emine; İZBIRAK, Gökhan; GHA-SEMI, Matina
2016-01-01
Background: The aim of this study was to propose a new stochastic model to study the time course of ethanol elimination in human bodies. Methods: The times and amount of alcohol ingested are assumed to be random in controllable intervals. Constant elimination rate follows zero order kinetics and is replaced by first order kinetics when the effects of alcohol increase due to alcohol ingestion. Simulation studies of three different models were made to compare the statistical characteristics of the ethanol effects obtained using analytical expressions. For each model, three cases were considered depending on the drinking pattern and by classifying the drinker as heavy, normal or sparse. Results: From the model formulation, we noted that as the rate of drinking increases for a given elimination rate, the expected time between overflows goes towards zero. Furthermore, as the average amount of alcohol in each drink increases, the corresponding time between overflows decreases. Conclusion: Variations in times of alcohol intakes as well as the amount of alcohol consumption can be accounted through the final created formula. The model proves that overflows occur when alcohol is ingested before the adverse effects of alcohol from the previous drink are completely eliminated. Being the first stochastic model of such a kind, we do hope that it will throw more light on interpreting experimental data of alcohol abuse. PMID:27957462
Collective stochastic coherence in recurrent neuronal networks
NASA Astrophysics Data System (ADS)
Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi
2016-09-01
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Stochastic YORP On Real Asteroid Shapes
NASA Astrophysics Data System (ADS)
McMahon, Jay W.
2015-05-01
Since its theoretical foundation and subsequent observational verification, the YORP effect has been understood to be a fundamental process that controls the evolution of small asteroids in the inner solar system. In particular, the coupling of the YORP and Yarkovsky effects are hypothesized to be largely responsible for the transport of asteroids from the main belt to the inner solar system populations. Furthermore, the YORP effect is thought to lead to rotational fission of small asteroids, which leads to the creation of multiple asteroid systems, contact binary asteroids, and asteroid pairs. However recent studies have called into question the ability of YORP to produce these results. In particular, the high sensitivity of the YORP coefficients to variations in the shape of an asteroid, combined with the possibility of a changing shape due to YORP accelerated spin rates can combine to create a stochastic YORP coefficient which can arrest or change the evolution of a small asteroid's spin state. In this talk, initial results are presented from new simulations which comprehensively model the stochastic YORP process. Shape change is governed by the surface slopes on radar based asteroid shape models, where the highest slope regions change first. The investigation of the modification of YORP coefficients and subsequent spin state evolution as a result of this dynamically influenced shape change is presented and discussed.
Stochastic simplified modelling of abrasive waterjet footprints
Torrubia, P. Lozano; Axinte, D. A.
2016-01-01
Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling. PMID:27118905
Stochastic basins of attraction for metastable states
NASA Astrophysics Data System (ADS)
Serdukova, Larissa; Zheng, Yayun; Duan, Jinqiao; Kurths, Jürgen
2016-07-01
Basin of attraction of a stable equilibrium point is an effective concept for stability analysis in deterministic systems; however, it does not contain information on the external perturbations that may affect it. Here we introduce the concept of stochastic basin of attraction (SBA) by incorporating a suitable probabilistic notion of basin. We define criteria for the size of the SBA based on the escape probability, which is one of the deterministic quantities that carry dynamical information and can be used to quantify dynamical behavior of the corresponding stochastic basin of attraction. SBA is an efficient tool to describe the metastable phenomena complementing the known exit time, escape probability, or relaxation time. Moreover, the geometric structure of SBA gives additional insight into the system's dynamical behavior, which is important for theoretical and practical reasons. This concept can be used not only in models with small noise intensity but also with noise whose amplitude is proportional or in general is a function of an order parameter. As an application of our main results, we analyze a three potential well system perturbed by two types of noise: Brownian motion and non-Gaussian α-stable Lévy motion. Our main conclusions are that the thermal fluctuations stabilize the metastable system with an asymmetric three-well potential but have the opposite effect for a symmetric one. For Lévy noise with larger jumps and lower jump frequencies ( α = 0.5 ) metastability is enhanced for both symmetric and asymmetric potentials.
A Stochastic Cratering Model for Asteroid Surfaces
NASA Technical Reports Server (NTRS)
Richardson, J. E.; Melosh, H. J.; Greenberg, R. J.
2005-01-01
The observed cratering records on asteroid surfaces (four so far: Gaspra, Ida, Mathilde, and Eros [1-4]) provide us with important clues to their past bombardment histories. Previous efforts toward interpreting these records have led to two basic modeling styles for reproducing the statistics of the observed crater populations. The first, and most direct, method is to use Monte Carlo techniques [5] to stochastically populate a matrix-model test surface with craters as a function of time [6,7]. The second method is to use a more general, parameterized approach to duplicate the statistics of the observed crater population [8,9]. In both methods, several factors must be included beyond the simple superposing of circular features: (1) crater erosion by subsequent impacts, (2) infilling of craters by impact ejecta, and (3) crater degradation and era- sure due to the seismic effects of subsequent impacts. Here we present an updated Monte Carlo (stochastic) modeling approach, designed specifically with small- to medium-sized asteroids in mind.
A hierarchical exact accelerated stochastic simulation algorithm
NASA Astrophysics Data System (ADS)
Orendorff, David; Mjolsness, Eric
2012-12-01
A new algorithm, "HiER-leap" (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled "blocks" and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms.
Recent Developments in Linear Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.
2006-01-01
A detailed analysis of stochastic electrodynamics (SED) as a foundation for quantum mechanics has shown that the reasons for its failure in the case of nonlinear forces are not to be ascribed to the founding principles of the theory but to the approximation methods introduced, particularly the use of the Fokker-Planck approximation and perturbation theory. To recover the intrinsic possibilities of SED a new, non perturbative approach has been developed, namely linear stochastic electrodynamics (LSED). We here present the basic principles on which LSED is constructed. The demand that the solutions of the SED problem comply with as few as three principles, each one of which is shown to have a clear physical meaning, leads in a natural way to the quantum mechanical description in its Heisenberg form. We briefly re-examine some of the most often discussed conceptual problems of quantum mechanics from the point of view offered by the new theory and show that it offers well defined and clear physical anwers to them, within a realist and causal perspective. To conclude we add brief comments on a couple of predictions of the theory, the test of which could eventually lead to its validation or refutation.
Single-particle stochastic heat engine
NASA Astrophysics Data System (ADS)
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2014-10-01
We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating a Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems, we observe that the operational characteristics are model dependent. Our results clearly rule out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.
The stochastic search dynamics of interneuron migration.
Britto, Joanne M; Johnston, Leigh A; Tan, Seong-Seng
2009-08-05
Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment.
Stochastic population dynamics under resource constraints
NASA Astrophysics Data System (ADS)
Gavane, Ajinkya S.; Nigam, Rahul
2016-06-01
This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations for such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.
Large Deviations for Nonlocal Stochastic Neural Fields
2014-01-01
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers’ law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations. Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20. PMID:24742297
Stochastic basins of attraction for metastable states.
Serdukova, Larissa; Zheng, Yayun; Duan, Jinqiao; Kurths, Jürgen
2016-07-01
Basin of attraction of a stable equilibrium point is an effective concept for stability analysis in deterministic systems; however, it does not contain information on the external perturbations that may affect it. Here we introduce the concept of stochastic basin of attraction (SBA) by incorporating a suitable probabilistic notion of basin. We define criteria for the size of the SBA based on the escape probability, which is one of the deterministic quantities that carry dynamical information and can be used to quantify dynamical behavior of the corresponding stochastic basin of attraction. SBA is an efficient tool to describe the metastable phenomena complementing the known exit time, escape probability, or relaxation time. Moreover, the geometric structure of SBA gives additional insight into the system's dynamical behavior, which is important for theoretical and practical reasons. This concept can be used not only in models with small noise intensity but also with noise whose amplitude is proportional or in general is a function of an order parameter. As an application of our main results, we analyze a three potential well system perturbed by two types of noise: Brownian motion and non-Gaussian α-stable Lévy motion. Our main conclusions are that the thermal fluctuations stabilize the metastable system with an asymmetric three-well potential but have the opposite effect for a symmetric one. For Lévy noise with larger jumps and lower jump frequencies ( α=0.5) metastability is enhanced for both symmetric and asymmetric potentials.
Memristor-based neural networks: Synaptic versus neuronal stochasticity
NASA Astrophysics Data System (ADS)
Naous, Rawan; AlShedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled Nabil
2016-11-01
In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.
Computational singular perturbation analysis of stochastic chemical systems with stiffness
NASA Astrophysics Data System (ADS)
Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.
2017-04-01
Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.
Stochastic mapping of the Michaelis-Menten mechanism.
Dóka, Éva; Lente, Gábor
2012-02-07
The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.
Random-order fractional bistable system and its stochastic resonance
NASA Astrophysics Data System (ADS)
Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia
2017-01-01
In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.
Empirical insights into the stochasticity of small RNA sequencing
NASA Astrophysics Data System (ADS)
Qin, Li-Xuan; Tuschl, Thomas; Singer, Samuel
2016-04-01
The choice of stochasticity distribution for modeling the noise distribution is a fundamental assumption for the analysis of sequencing data and consequently is critical for the accurate assessment of biological heterogeneity and differential expression. The stochasticity of RNA sequencing has been assumed to follow Poisson distributions. We collected microRNA sequencing data and observed that its stochasticity is better approximated by gamma distributions, likely because of the stochastic nature of exponential PCR amplification. We validated our findings with two independent datasets, one for microRNA sequencing and another for RNA sequencing. Motivated by the gamma distributed stochasticity, we provided a simple method for the analysis of RNA sequencing data and showed its superiority to three existing methods for differential expression analysis using three data examples of technical replicate data and biological replicate data.
100 years after Smoluchowski: stochastic processes in cell biology
NASA Astrophysics Data System (ADS)
Holcman, D.; Schuss, Z.
2017-03-01
100 years after Smoluchowski introduced his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from a large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here Smoluchowski’s approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation.
Terminator Detection by Support Vector Machine Utilizing aStochastic Context-Free Grammar
Francis-Lyon, Patricia; Cristianini, Nello; Holbrook, Stephen
2006-12-30
A 2-stage detector was designed to find rho-independent transcription terminators in the Escherichia coli genome. The detector includes a Stochastic Context Free Grammar (SCFG) component and a Support Vector Machine (SVM) component. To find terminators, the SCFG searches the intergenic regions of nucleotide sequence for local matches to a terminator grammar that was designed and trained utilizing examples of known terminators. The grammar selects sequences that are the best candidates for terminators and assigns them a prefix, stem-loop, suffix structure using the Cocke-Younger-Kasaami (CYK) algorithm, modified to incorporate energy affects of base pairing. The parameters from this inferred structure are passed to the SVM classifier, which distinguishes terminators from non-terminators that score high according to the terminator grammar. The SVM was trained with negative examples drawn from intergenic sequences that include both featureless and RNA gene regions (which were assigned prefix, stem-loop, suffix structure by the SCFG), so that it successfully distinguishes terminators from either of these. The classifier was found to be 96.4% successful during testing.
Chen, Bor-Sen; Tsai, Kun-Wei; Li, Cheng-Wei
2015-01-01
Molecular biologists have long recognized carcinogenesis as an evolutionary process that involves natural selection. Cancer is driven by the somatic evolution of cell lineages. In this study, the evolution of somatic cancer cell lineages during carcinogenesis was modeled as an equilibrium point (ie, phenotype of attractor) shifting, the process of a nonlinear stochastic evolutionary biological network. This process is subject to intrinsic random fluctuations because of somatic genetic and epigenetic variations, as well as extrinsic disturbances because of carcinogens and stressors. In order to maintain the normal function (ie, phenotype) of an evolutionary biological network subjected to random intrinsic fluctuations and extrinsic disturbances, a network robustness scheme that incorporates natural selection needs to be developed. This can be accomplished by selecting certain genetic and epigenetic variations to modify the network structure to attenuate intrinsic fluctuations efficiently and to resist extrinsic disturbances in order to maintain the phenotype of the evolutionary biological network at an equilibrium point (attractor). However, during carcinogenesis, the remaining (or neutral) genetic and epigenetic variations accumulate, and the extrinsic disturbances become too large to maintain the normal phenotype at the desired equilibrium point for the nonlinear evolutionary biological network. Thus, the network is shifted to a cancer phenotype at a new equilibrium point that begins a new evolutionary process. In this study, the natural selection scheme of an evolutionary biological network of carcinogenesis was derived from a robust negative feedback scheme based on the nonlinear stochastic Nash game strategy. The evolvability and phenotypic robustness criteria of the evolutionary cancer network were also estimated by solving a Hamilton–Jacobi inequality – constrained optimization problem. The simulation revealed that the phenotypic shift of the lung cancer
Heydari, M.H.; Hooshmandasl, M.R.; Cattani, C.; Maalek Ghaini, F.M.
2015-02-15
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
NASA Astrophysics Data System (ADS)
Sanchez-Vila, X.; Fernández-Garcia, D.
2016-12-01
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.
Spatiotemporal Stochastic Resonance:Theory and Experiment
NASA Astrophysics Data System (ADS)
Peter, Jung
1996-03-01
The amplification of weak periodic signals in bistable or excitable systems via stochastic resonance has been studied intensively over the last years. We are going one step further and ask: Can noise enhance spatiotemporal patterns in excitable media and can this effect be observed in nature? To this end, we are looking at large, two dimensional arrays of coupled excitable elements. Due to the coupling, excitation can propagate through the array in form of nonlinear waves. We observe target waves, rotating spiral waves and other wave forms. If the coupling between the elements is below a critical threshold, any excitational pattern will die out in the absence of noise. Below this threshold, large scale rotating spiral waves - as they are observed above threshold - can be maintained by a proper level of the noise[1]. Furthermore, their geometric features, such as the curvature can be controlled by the homogeneous noise level[2]. If the noise level is too large, break up of spiral waves and collisions with spontaneously nucleated waves yields spiral turbulence. Driving our array with a spatiotemporal pattern, e.g. a rotating spiral wave, we show that for weak coupling the excitational response of the array shows stochastic resonance - an effect we have termed spatiotemporal stochastic resonance. In the last part of the talk I'll make contact with calcium waves, observed in astrocyte cultures and hippocampus slices[3]. A. Cornell-Bell and collaborators[3] have pointed out the role of calcium waves for long-range glial signaling. We demonstrate the similarity of calcium waves with nonlinear waves in noisy excitable media. The noise level in the tissue is characterized by spontaneous activity and can be controlled by applying neuro-transmitter substances[3]. Noise effects in our model are compared with the effect of neuro-transmitters on calcium waves. [1]P. Jung and G. Mayer-Kress, CHAOS 5, 458 (1995). [2]P. Jung and G. Mayer-Kress, Phys. Rev. Lett.62, 2682 (1995). [3
The stochastic dance of early HIV infection
NASA Astrophysics Data System (ADS)
Merrill, Stephen J.
2005-12-01
The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for the immune response, the dance predicts that the immune response will be also in a variable state of readiness and capability for this task of adaptation. The description of the stochastic dance of HIV here will use the tools of stochastic models, and for the most part, simulation. The justification for this approach is that the early stages and the development of HIV diversity require that the model to be able to describe both individual sample path and patient-to-patient variability. In addition, as early viral dynamics are best described using branching processes, the explosive growth of these models both predicts high variability and rapid response of HIV to changes in system parameters.In this paper, a basic viral growth model based on a time dependent continuous-time branching process is used to describe the growth of HIV infected cells in the macrophage and lymphocyte populations. Immigration from the reservoir population is added to the basic model to describe the incubation time distribution. This distribution is deduced directly from the modeling assumptions and the model of viral growth. A system of two branching processes, one in the infected macrophage population and one in the infected lymphocyte population is used to provide a description of the relationship between the development of HIV diversity as it relates to tropism (host cell preference). The role of the immune
Lin, Guang; Tartakovsky, Alexandre M.
2010-04-01
In this study, we solve the three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation using a probabilistic collocation method (PCM) on sparse grids. Karhunen-Lo\\`{e}ve (KL) decomposition is employed to represent the three-dimensional log hydraulic conductivity $Y=\\ln K_s$. The numerical examples which demonstrate the convergence of PCM are presented. It appears that the faster convergence rate in the variance can be obtained by using the Jacobi-chaos representing the truncated Gaussian distributions than using the Hermite-chaos for the Gaussian distribution. The effect of dispersion coefficient on the mean and standard deviation of the hydraulic head and solute concentration is investigated. Additionally, we also study how the statistical properties of the hydraulic head and solute concentration vary while using different types of random distributions and different standard deviations of random hydraulic conductivity.
Coronal heating by stochastic magnetic pumping
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Uchida, Y.
1980-01-01
Recent observational data cast serious doubt on the widely held view that the Sun's corona is heated by traveling waves (acoustic or magnetohydrodynamic). It is proposed that the energy responsible for heating the corona is derived from the free energy of the coronal magnetic field derived from motion of the 'feet' of magnetic field lines in the photosphere. Stochastic motion of the feet of magnetic field lines leads, on the average, to a linear increase of magnetic free energy with time. This rate of energy input is calculated for a simple model of a single thin flux tube. The model appears to agree well with observational data if the magnetic flux originates in small regions of high magnetic field strength. On combining this energy input with estimates of energy loss by radiation and of energy redistribution by thermal conduction, we obtain scaling laws for density and temperature in terms of length and coronal magnetic field strength.
Stochastic dynamics for idiotypic immune networks
NASA Astrophysics Data System (ADS)
Barra, Adriano; Agliari, Elena
2010-12-01
In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker-Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-of-equilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.
Improving Sensorimotor Function Using Stochastic Vestibular Stimulation
NASA Technical Reports Server (NTRS)
Galvan, R. C.; Clark, T. K.; Merfeld, D. M.; Bloomberg, J. J.; Mulavara, A. P.; Oman, C. M.
2014-01-01
Astronauts experience sensorimotor changes during spaceflight, particularly during G-transition phases. Post flight sensorimotor changes may include postural and gait instability, spatial disorientation, and visual performance decrements, all of which can degrade operational capabilities of the astronauts and endanger the crew. Crewmember safety would be improved if these detrimental effects of spaceflight could be mitigated by a sensorimotor countermeasure and even further if adaptation to baseline could be facilitated. The goal of this research is to investigate the potential use of stochastic vestibular stimulation (SVS) as a technology to improve sensorimotor function. We hypothesize that low levels of SVS will improve sensorimotor performance through stochastic resonance (SR). The SR phenomenon occurs when the response of a nonlinear system to a weak input signal is optimized by the application of a particular nonzero level of noise. Two studies have been initiated to investigate the beneficial effects and potential practical usage of SVS. In both studies, electrical vestibular stimulation is applied via electrodes on the mastoid processes using a constant current stimulator. The first study aims to determine the repeatability of the effect of vestibular stimulation on sensorimotor performance and perception in order to better understand the practical use of SVS. The beneficial effect of low levels of SVS on balance performance has been shown in the past. This research uses the same balance task repeated multiple times within a day and across days to study the repeatability of the stimulation effects. The balance test consists of 50 sec trials in which the subject stands with his or her feet together, arms crossed, and eyes closed on compliant foam. Varying levels of SVS, ranging from 0-700 micro A, are applied across different trials. The subject-specific optimal SVS level is that which results in the best balance performance as measured by inertial
Non-Markovian stochastic processes: colored noise.
Łuczka, J
2005-06-01
We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.
Stochastic methods for zero energy quantum scattering
NASA Astrophysics Data System (ADS)
Koch, Justus H.; Mall, Hubertus R.; Lenz, Stefan
1998-02-01
We investigate the use of stochastic methods for zero energy quantum scattering based on a path integral approach. With the application to the scattering of a projectile from a nuclear many-body target in mind, we use the potential scattering of a particle as a test for the accuracy and efficiency of several methods. To be able to deal with complex potentials, we introduce a path sampling action and a modified scattering observable. The approaches considered are the random walk, where the points of a path are sequentially generated, and the Langevin algorithm, which updates an entire path. Several improvements are investigated. A cluster algorithm for dealing with scattering problems is finally proposed, which shows the best accuracy and stability.
Stochastic Model of Supercoiling-Dependent Transcription
NASA Astrophysics Data System (ADS)
Brackley, C. A.; Johnson, J.; Bentivoglio, A.; Corless, S.; Gilbert, N.; Gonnella, G.; Marenduzzo, D.
2016-07-01
We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix and that these enzymes bind more favorably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down regulate transcription.
Stochastic Dynamics through Hierarchically Embedded Markov Chains
NASA Astrophysics Data System (ADS)
Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.
2017-02-01
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Stochastic resonance in bistable atomic switches.
Yoshida, Kenji; Hirakawa, Kazuhiko
2017-03-24
We have investigated the conductance of bistable gold atomic switches as a function of periodic input voltages mixed with a random noise. With increasing noise amplitude, the atomic switches biased below the threshold voltage for conductance switching start exhibiting switching in conductance between two stable states. Clear synchronization between the input and output signals is observed when an optimized noise amplitude is mixed with the periodic input voltage, even when the atomic switches are driven by an input voltage as low as approximately 10% of the threshold voltage. The observed behavior can be explained in terms of the stochastic resonance. The results presented here indicate that utilization of noise can dramatically reduce the operation voltage of metal atomic switches.
Stochastic epidemic dynamics on extremely heterogeneous networks
NASA Astrophysics Data System (ADS)
Parra-Rojas, César; House, Thomas; McKane, Alan J.
2016-12-01
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
Algorithm refinement for the stochastic Burgers' equation
Bell, John B.; Foo, Jasmine; Garcia, Alejandro L. . E-mail: algarcia@algarcia.org
2007-04-10
In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations on the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency.
Stochastic damage evolution in textile laminates
NASA Technical Reports Server (NTRS)
Dzenis, Yuris A.; Bogdanovich, Alexander E.; Pastore, Christopher M.
1993-01-01
A probabilistic model utilizing random material characteristics to predict damage evolution in textile laminates is presented. Model is based on a division of each ply into two sublaminas consisting of cells. The probability of cell failure is calculated using stochastic function theory and maximal strain failure criterion. Three modes of failure, i.e. fiber breakage, matrix failure in transverse direction, as well as matrix or interface shear cracking, are taken into account. Computed failure probabilities are utilized in reducing cell stiffness based on the mesovolume concept. A numerical algorithm is developed predicting the damage evolution and deformation history of textile laminates. Effect of scatter of fiber orientation on cell properties is discussed. Weave influence on damage accumulation is illustrated with the help of an example of a Kevlar/epoxy laminate.
Conservation laws and symmetries in stochastic thermodynamics
NASA Astrophysics Data System (ADS)
Polettini, Matteo; Bulnes-Cuetara, Gregory; Esposito, Massimiliano
2016-11-01
Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.
Stochastic Stability in Internet Router Congestion Games
NASA Astrophysics Data System (ADS)
Chung, Christine; Pyrga, Evangelia
Congestion control at bottleneck routers on the internet is a long standing problem. Many policies have been proposed for effective ways to drop packets from the queues of these routers so that network endpoints will be inclined to share router capacity fairly and minimize the overflow of packets trying to enter the queues. We study just how effective some of these queuing policies are when each network endpoint is a self-interested player with no information about the other players’ actions or preferences. By employing the adaptive learning model of evolutionary game theory, we study policies such as Droptail, RED, and the greedy-flow-punishing policy proposed by Gao et al. [10] to find the stochastically stable states: the states of the system that will be reached in the long run.
Stochastic theory of log-periodic patterns
NASA Astrophysics Data System (ADS)
Canessa, Enrique
2000-12-01
We introduce an analytical model based on birth-death clustering processes to help in understanding the empirical log-periodic corrections to power law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastic theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of co-operative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t0 is derived in terms of birth-death clustering coefficients.
Hardware implementation of stochastic spiking neural networks.
Rosselló, Josep L; Canals, Vincent; Morro, Antoni; Oliver, Antoni
2012-08-01
Spiking Neural Networks, the last generation of Artificial Neural Networks, are characterized by its bio-inspired nature and by a higher computational capacity with respect to other neural models. In real biological neurons, stochastic processes represent an important mechanism of neural behavior and are responsible of its special arithmetic capabilities. In this work we present a simple hardware implementation of spiking neurons that considers this probabilistic nature. The advantage of the proposed implementation is that it is fully digital and therefore can be massively implemented in Field Programmable Gate Arrays. The high computational capabilities of the proposed model are demonstrated by the study of both feed-forward and recurrent networks that are able to implement high-speed signal filtering and to solve complex systems of linear equations.
SUCCESSFUL BUNCHED BEAM STOCHASTIC COOLING IN RHIC.
BRENNAN, J.M.; BLASKIEWICZ, M.; SEVERINO, F.
2006-06-23
We report on a successful test of bunch-beam stochastic cooling in RHIC at 100 GeV. The cooling system is designed for heavy ions but was tested in the recent RHIC run which operated only with polarized protons. To make an analog of the ion beam a special bunch was prepared with very low intensity. This bunch had {approx}1.5 x 10{sup 9} protons, while the other 100 bunches contained {approx}1.2 x 10{sup 11} protons each. With this bunch a cooling time on the order 1 hour was observed through shortening of the bunch length and increase in the peak bunch current, together with a narrowing of the spectral line width of the Scottky power at 4 GHz. The low level signal processing electronics and the isolated-frequency kicker cavities are described.
Conservation laws and symmetries in stochastic thermodynamics.
Polettini, Matteo; Bulnes-Cuetara, Gregory; Esposito, Massimiliano
2016-11-01
Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.
Supercomputer optimizations for stochastic optimal control applications
NASA Technical Reports Server (NTRS)
Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang
1991-01-01
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
Stochastic resonance in bistable atomic switches
NASA Astrophysics Data System (ADS)
Yoshida, Kenji; Hirakawa, Kazuhiko
2017-03-01
We have investigated the conductance of bistable gold atomic switches as a function of periodic input voltages mixed with a random noise. With increasing noise amplitude, the atomic switches biased below the threshold voltage for conductance switching start exhibiting switching in conductance between two stable states. Clear synchronization between the input and output signals is observed when an optimized noise amplitude is mixed with the periodic input voltage, even when the atomic switches are driven by an input voltage as low as approximately 10% of the threshold voltage. The observed behavior can be explained in terms of the stochastic resonance. The results presented here indicate that utilization of noise can dramatically reduce the operation voltage of metal atomic switches.
Stochastic fluctuations of the synaptic function.
Ventriglia, Francesco; Di Maio, Vito
2002-01-01
The peak amplitudes of the quantal Excitatory Post Synaptic Currents in single hippocampal synapses show a large variability. Here, we present the results of a mathematical, computational investigation on the main sources of this variability. A detailed description of the synaptic cleft, rigorously based on empirically-derived parameters, was used. By using a Brownian motion model of neurotransmitter molecule diffusion, quantal EPSCs were computed by a simple kinetic schema of AMPA receptor dynamics. Our results show that the lack of saturation of AMPA receptors obtained in these conditions, combined with stochastic variations in basic presynaptic elements, such as the vesicle volume, the vesicle docking position, and the vesicle neurotransmitter concentration can explain almost the entire range of EPSC variability experimentally observed.
Stochastic evolution in populations of ideas
Nicole, Robin; Sollich, Peter; Galla, Tobias
2017-01-01
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244
A stochastic model for head lice infections.
Stone, Patricia; Wilkinson-Herbots, Hilde; Isham, Valerie
2008-06-01
We investigate the dynamics of head lice infections in schools, by considering a model for endemic infection based on a stochastic SIS (susceptible-infected-susceptible) epidemic model, with the addition of an external source of infection. We deduce a range of properties of our model, including the length of a single outbreak of infection. We use the stationary distribution of the number of infected individuals, in conjunction with data from a recent study carried out in Welsh schools on the prevalence of head lice infections, and employ maximum likelihood methods to obtain estimates of the model parameters. A complication is that, for each school, only a sample of the pupils was checked for infection. Our likelihood function takes account of the missing data by incorporating a hypergeometric sampling element. We arrive at estimates of the ratios of the "within school" and "external source" transmission rates to the recovery rate and use these to obtain estimates for various quantities of interest.
Discrete-time Markovian stochastic Petri nets
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco
1995-01-01
We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
Hybrid Differential Dynamic Programming with Stochastic Search
NASA Technical Reports Server (NTRS)
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Hybrid Differential Dynamic Programming with Stochastic Search
NASA Technical Reports Server (NTRS)
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Focus on stochastic flows and climate statistics
NASA Astrophysics Data System (ADS)
Marston, JB; Williams, Paul D.
2016-09-01
The atmosphere and ocean are examples of dynamical systems that evolve in accordance with the laws of physics. Therefore, climate science is a branch of physics that is just as valid and important as the more traditional branches, which include particle physics, condensed-matter physics, and statistical mechanics. This ‘focus on’ collection of New Journal of Physics brings together original research articles from leading groups that advance our understanding of the physics of climate. Areas of climate science that can particularly benefit from input by physicists are emphasised. The collection brings together articles on stochastic models, turbulence, quasi-linear approximations, climate statistics, statistical mechanics of atmospheres and oceans, jet formation, and reduced-form climate models. The hope is that the issue will encourage more physicists to think about the climate problem.
Genetic code, hamming distance and stochastic matrices.
He, Matthew X; Petoukhov, Sergei V; Ricci, Paolo E
2004-09-01
In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are doubly stochastic and symmetric. We determine the frequency distributions of the Hamming distances, building blocks of the matrices, decomposition and iterations of matrices. We present an explicit decomposition formula for the genetic code-based matrix in terms of permutation matrices, which provides a hypercube representation of the genetic code. It is also observed that there is a Hamiltonian cycle in a genetic code-based hypercube.
Approach to Equilibrium for the Stochastic NLS
NASA Astrophysics Data System (ADS)
Lebowitz, J. L.; Mounaix, Ph.; Wang, W.-M.
2013-07-01
We study the approach to equilibrium, described by a Gibbs measure, for a system on a d-dimensional torus evolving according to a stochastic nonlinear Schrödinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is uniform in the frequency truncation N. The limit N →∞ is discussed.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Stochastic evolution in populations of ideas
NASA Astrophysics Data System (ADS)
Nicole, Robin; Sollich, Peter; Galla, Tobias
2017-01-01
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.
Wolbachia spread dynamics in stochastic environments.
Hu, Linchao; Huang, Mugen; Tang, Moxun; Yu, Jianshe; Zheng, Bo
2015-12-01
Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments.
Stochastic Electrodynamics: A Road to Quantum Gravity
NASA Astrophysics Data System (ADS)
Lavenda, B. H.
A formal analogy exists between electrodynamic and gravitational phenomena: the Coulomb potential is analogous to the Newton potential and both possess fine structure constants. There are no singularities in Nature; uncertainties in the measurement of small distances are accounted for by an extreme value probability distribution for smallest value of the radial coordinate. Quantum electrodynamic phenomena can simply be accounted for by a stochastic generalization of the Bohr model which we will then carry over to the quantum Kepler model. Both in quantum electrodynamics and gravitation all characteristic scales are related by simple powers of the fine structure constants. A new uncertainty relation between momentum and inverse separation between particles is derived. Electromagnetic and gravitational radiation phenomena are analyzed and compared.
Error Analysis of Stochastic Gradient Descent Ranking.
Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan
2012-12-31
Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.
Error analysis of stochastic gradient descent ranking.
Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan
2013-06-01
Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.
A stochastic lattice model for locust outbreak
NASA Astrophysics Data System (ADS)
Kizaki, Shinya; Katori, Makoto
The locust is a kind of grasshoppers. Gregarious locusts form swarms and can migrate over large distances and they spread and damage a large area (locust outbreak). When the density is low, each of locusts behaves as an individual insect (solitary phase). As locusts become crowded, they become to act as a part of a group (gregarious phase) as a result of interactions among them. Modeling of this phenomenon is a challenging problem of statistical physics. We introduce a stochastic cellular automaton model of locust population-dynamics on lattices. Change of environmental conditions by seasonal migration is a key factor in gregarisation of locusts and we take it into account by changing the lattice size periodically. We study this model by computer simulations and discuss the locust outbreak as a cooperative phenomena.
Stochastic annealing simulation of cascades in metals
Heinisch, H.L.
1996-04-01
The stochastic annealing simulation code ALSOME is used to investigate quantitatively the differential production of mobile vacancy and SIA defects as a function of temperature for isolated 25 KeV cascades in copper generated by MD simulations. The ALSOME code and cascade annealing simulations are described. The annealing simulations indicate that the above Stage V, where the cascade vacancy clusters are unstable,m nearly 80% of the post-quench vacancies escape the cascade volume, while about half of the post-quench SIAs remain in clusters. The results are sensitive to the relative fractions of SIAs that occur in small, highly mobile clusters and large stable clusters, respectively, which may be dependent on the cascade energy.
Stochastic competitive learning in complex networks.
Silva, Thiago Christiano; Zhao, Liang
2012-03-01
Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning..
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Delays induce novel stochastic effects in negative feedback gene circuits.
Zavala, Eder; Marquez-Lago, Tatiana T
2014-01-21
Stochastic models of reaction networks are widely used to depict gene expression dynamics. However, stochastic does not necessarily imply accurate, as subtle assumptions can yield erroneous results, masking key discrete effects. For instance, transcription and translation are not instantaneous processes-explicit delays separate their initiation from the appearance of their functional products. However, delays are often ignored in stochastic, single-gene expression models. By consequence, effects such as delay-induced stochastic oscillations at the single-cell level have remained relatively unexplored. Here, we present a systematic study of periodicity and multimodality in a simple gene circuit with negative feedback, analyzing the influence of negative feedback strength and transcriptional/translational delays on expression dynamics. We demonstrate that an oscillatory regime emerges through a Hopf bifurcation in both deterministic and stochastic frameworks. Of importance, a shift in the stochastic Hopf bifurcation evidences inaccuracies of the deterministic bifurcation analysis. Furthermore, noise fluctuations within stochastic oscillations decrease alongside increasing values of transcriptional delays and within a specific range of negative feedback strengths, whereas a strong feedback is associated with oscillations triggered by bursts. Finally, we demonstrate that explicitly accounting for delays increases the number of accessible states in the multimodal regime, and also introduces features typical of excitable systems.
a Stochastic Newmark Method for Engineering Dynamical Systems
NASA Astrophysics Data System (ADS)
ROY, D.; DASH, M. K.
2002-01-01
The purpose of this study is to develop a stochastic Newmark integration principle based on an implicit stochastic Taylor (Ito-Taylor or Stratonovich-Taylor) expansion of the vector field. As in the deterministic case, implicitness in stochastic Taylor expansions for the displacement and velocity vectors is achieved by introducing a couple of non-unique integration parameters, α and β. A rigorous error analysis is performed to put bounds on the local and global errors in computing displacements and velocities. The stochastic Newmark method is elegantly adaptable for obtaining strong sample-path solutions of linear and non-linear multi-degree-of freedom (m.d.o.f.) stochastic engineering systems with continuous and Lipschitz-bounded vector fields under (filtered) white-noise inputs. The method has presently been numerically illustrated, to a limited extent, for sample-path integration of a hardening Duffing oscillator under additive and multiplicative white-noise excitations. The results are indicative of consistency, convergence and stochastic numerical stability of the stochastic Newmark method (SNM).
Spatial Moran models, II: cancer initiation in spatially structured tissue
Foo, J; Leder, K
2016-01-01
We study the accumulation and spread of advantageous mutations in a spatial stochastic model of cancer initiation on a lattice. The parameters of this general model can be tuned to study a variety of cancer types and genetic progression pathways. This investigation contributes to an understanding of how the selective advantage of cancer cells together with the rates of mutations driving cancer, impact the process and timing of carcinogenesis. These results can be used to give insights into tumor heterogeneity and the “cancer field effect,” the observation that a malignancy is often surrounded by cells that have undergone premalignant transformation. PMID:26126947
From cusps to cores: a stochastic model
NASA Astrophysics Data System (ADS)
El-Zant, Amr A.; Freundlich, Jonathan; Combes, Françoise
2016-09-01
The cold dark matter model of structure formation faces apparent problems on galactic scales. Several threads point to excessive halo concentration, including central densities that rise too steeply with decreasing radius. Yet, random fluctuations in the gaseous component can `heat' the centres of haloes, decreasing their densities. We present a theoretical model deriving this effect from first principles: stochastic variations in the gas density are converted into potential fluctuations that act on the dark matter; the associated force correlation function is calculated and the corresponding stochastic equation solved. Assuming a power-law spectrum of fluctuations with maximal and minimal cutoff scales, we derive the velocity dispersion imparted to the halo particles and the relevant relaxation time. We further perform numerical simulations, with fluctuations realized as a Gaussian random field, which confirm the formation of a core within a time-scale comparable to that derived analytically. Non-radial collective modes enhance the energy transport process that erases the cusp, though the parametrizations of the analytical model persist. In our model, the dominant contribution to the dynamical coupling driving the cusp-core transformation comes from the largest scale fluctuations. Yet, the efficiency of the transformation is independent of the value of the largest scale and depends weakly (linearly) on the power-law exponent; it effectively depends on two parameters: the gas mass fraction and the normalization of the power spectrum. This suggests that cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrized in simple terms, the physical and numerical complexities of the various implementations notwithstanding.