Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Adame, J.; Warzel, S.

2015-11-01

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

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

Adame, J.; Warzel, S., E-mail: warzel@ma.tum.de

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Theory for Transitions Between Exponential and Stationary Phases: Universal Laws for Lag Time

NASA Astrophysics Data System (ADS)

Himeoka, Yusuke; Kaneko, Kunihiko

2017-04-01

The quantitative characterization of bacterial growth has attracted substantial attention since Monod's pioneering study. Theoretical and experimental works have uncovered several laws for describing the exponential growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in which cell growth is highly suppressed, for which quantitative laws or theories are markedly underdeveloped. In fact, the models commonly adopted for the exponential phase that consist of autocatalytic chemical components, including ribosomes, can only show exponential growth or decay in a population; thus, phases that halt growth are not realized. Here, we propose a simple, coarse-grained cell model that includes an extra class of macromolecular components in addition to the autocatalytic active components that facilitate cellular growth. These extra components form a complex with the active components to inhibit the catalytic process. Depending on the nutrient condition, the model exhibits typical transitions among the lag, exponential, stationary, and death phases. Furthermore, the lag time needed for growth recovery after starvation follows the square root of the starvation time and is inversely related to the maximal growth rate. This is in agreement with experimental observations, in which the length of time of cell starvation is memorized in the slow accumulation of molecules. Moreover, the lag time distributed among cells is skewed with a long time tail. If the starvation time is longer, an exponential tail appears, which is also consistent with experimental data. Our theory further predicts a strong dependence of lag time on the speed of substrate depletion, which can be tested experimentally. The present model and theoretical analysis provide universal growth laws beyond the exponential phase, offering insight into how cells halt growth without entering the death phase.

Understanding Exponential Growth: As Simple as a Drop in a Bucket.

ERIC Educational Resources Information Center

Goldberg, Fred; Shuman, James

1984-01-01

Provides procedures for a simple laboratory activity on exponential growth and its characteristic doubling time. The equipment needed consists of a large plastic bucket, an eyedropper, a stopwatch, an assortment of containers and graduated cylinders, and a supply of water. (JN)

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry.

PubMed

Ouyang, Wenjun; Subotnik, Joseph E

2017-05-07

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.

Simple approximation of total emissivity of CO2-H2O mixture used in the zonal method of calculation of heat transfer by radiation

NASA Astrophysics Data System (ADS)

Lisienko, V. G.; Malikov, G. K.; Titaev, A. A.

2014-12-01

The paper presents a new simple-to-use expression to calculate the total emissivity of a mixture of gases CO2 and H2O used for modeling heat transfer by radiation in industrial furnaces. The accuracy of this expression is evaluated using the exponential wide band model. It is found that the time taken to calculate the total emissivity in this expression is 1.5 times less than in other approximation methods.

Exploiting fast detectors to enter a new dimension in room-temperature crystallography

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

Owen, Robin L., E-mail: robin.owen@diamond.ac.uk; Paterson, Neil; Axford, Danny

2014-05-01

A departure from a linear or an exponential decay in the diffracting power of macromolecular crystals is observed and accounted for through consideration of a multi-state sequential model. A departure from a linear or an exponential intensity decay in the diffracting power of protein crystals as a function of absorbed dose is reported. The observation of a lag phase raises the possibility of collecting significantly more data from crystals held at room temperature before an intolerable intensity decay is reached. A simple model accounting for the form of the intensity decay is reintroduced and is applied for the first timemore » to high frame-rate room-temperature data collection.« less

PLEMT: A NOVEL PSEUDOLIKELIHOOD BASED EM TEST FOR HOMOGENEITY IN GENERALIZED EXPONENTIAL TILT MIXTURE MODELS.

PubMed

Hong, Chuan; Chen, Yong; Ning, Yang; Wang, Shuang; Wu, Hao; Carroll, Raymond J

2017-01-01

Motivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and non-differentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g. mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and non-identifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood based expectation-maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects.

Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Conceptualizing the seasonal and hydrological dynamics of riparian zone control on DOC in boreal headwater streams

NASA Astrophysics Data System (ADS)

Winterdahl, M.; Laudon, H.; Köhler, S.; Seibert, J.; Bishop, K.

2009-04-01

Dissolved organic material (DOM) plays a key role in many natural surface waters. Despite the importance of DOC for the hydrochemistry in boreal headwaters there are few models that conceptualize the controls on short-term variability in stream DOC. A relatively simple model has been proposed where the vertical profile of DOC in the riparian soil solution, serves as an instantaneous "chemostat" setting the DOC of laterally flowing groundwater just before it enters the stream. This paper considers whether the addition of seasonality (in the form of soil temperature) and antecedent flows can improve the predictions of daily DOC concentrations. The model was developed and tested using field data from the Krycklan catchment on the Svartberget Research Station in northern Sweden where a transect of soil solution sampling sites equipped with suction lysimeters and wells for monitoring groundwater level have been installed and monitored for over a decade. The field data showed an exponential correlation between depth and DOC concentration in the soil solution. There was also an exponential correlation between stream discharge and groundwater table position. The expressions for these two correlations (exponential functions) have been combined into a simple riparian DOC model. To simulate effects of seasonality and/or antecedent flow, modules for soil temperature evolution and/or groundwater flow were added and tested. The model was calibrated and tested against 8 years of data from the Västrabäcken headwater catchment in the Krycklan area. To estimate the uncertainty in the model and the observed data a Hornberger-Spear-Young sensitivity analysis together with a GLUE uncertainty analysis was performed.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Gas production in the Barnett Shale obeys a simple scaling theory

PubMed Central

Patzek, Tad W.; Male, Frank; Marder, Michael

2013-01-01

Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States’ oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet. PMID:24248376

Gas production in the Barnett Shale obeys a simple scaling theory.

PubMed

Patzek, Tad W; Male, Frank; Marder, Michael

2013-12-03

Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States' oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

PubMed

Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

2014-12-01

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.

PubMed

Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T

2010-03-10

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

Wen, J. T.; Bayard, D. S.

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Stability of the thermodynamic equilibrium - A test of the validity of dynamic models as applied to gyroviscous perpendicular magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Faghihi, Mustafa; Scheffel, Jan; Spies, Guenther O.

1988-05-01

Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfven waves in a spatially homogeneous static equilibrium with scalar pressure.

On the Matrix Exponential Function

ERIC Educational Resources Information Center

Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai

2006-01-01

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

Role of community tolerance level (CTL) in predicting the prevalence of the annoyance of road and rail noise.

PubMed

Schomer, Paul; Mestre, Vincent; Fidell, Sanford; Berry, Bernard; Gjestland, Truls; Vallet, Michel; Reid, Timothy

2012-04-01

Fidell et al. [(2011), J. Acoust. Soc. Am. 130(2), 791-806] have shown (1) that the rate of growth of annoyance with noise exposure reported in attitudinal surveys of the annoyance of aircraft noise closely resembles the exponential rate of change of loudness with sound level, and (2) that the proportion of a community highly annoyed and the variability in annoyance prevalence rates in communities are well accounted for by a simple model with a single free parameter: a community tolerance level (abbreviated CTL, and represented symbolically in mathematical expressions as L(ct)), expressed in units of DNL. The current study applies the same modeling approach to predicting the prevalence of annoyance of road traffic and rail noise. The prevalence of noise-induced annoyance of all forms of transportation noise is well accounted for by a simple, loudness-like exponential function with community-specific offsets. The model fits all of the road traffic findings well, but the prevalence of annoyance due to rail noise is more accurately predicted separately for interviewing sites with and without high levels of vibration and/or rattle.

Improving deep convolutional neural networks with mixed maxout units.

PubMed

Zhao, Hui-Zhen; Liu, Fu-Xian; Li, Long-Yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that "non-maximal features are unable to deliver" and "feature mapping subspace pooling is insufficient," we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth's carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth s carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth s carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O'Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Predictability of monthly temperature and precipitation using automatic time series forecasting methods

NASA Astrophysics Data System (ADS)

Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

2018-02-01

We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.

Characterization of x-ray framing cameras for the National Ignition Facility using single photon pulse height analysis.

PubMed

Holder, J P; Benedetti, L R; Bradley, D K

2016-11-01

Single hit pulse height analysis is applied to National Ignition Facility x-ray framing cameras to quantify gain and gain variation in a single micro-channel plate-based instrument. This method allows the separation of gain from detectability in these photon-detecting devices. While pulse heights measured by standard-DC calibration methods follow the expected exponential distribution at the limit of a compound-Poisson process, gain-gated pulse heights follow a more complex distribution that may be approximated as a weighted sum of a few exponentials. We can reproduce this behavior with a simple statistical-sampling model.

Configurational coupled cluster approach with applications to magnetic model systems

NASA Astrophysics Data System (ADS)

Wu, Siyuan; Nooijen, Marcel

2018-05-01

A general exponential, coupled cluster like, approach is discussed to extract an effective Hamiltonian in configurational space, as a sum of 1-body, 2-body up to n-body operators. The simplest two-body approach is illustrated by calculations on simple magnetic model systems. A key feature of the approach is that equations up to a certain rank do not depend on higher body cluster operators.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

A simple theoretical model for ⁶³Ni betavoltaic battery.

PubMed

Zuo, Guoping; Zhou, Jianliang; Ke, Guotu

2013-12-01

A numerical simulation of the energy deposition distribution in semiconductors is performed for ⁶³Ni beta particles. Results show that the energy deposition distribution exhibits an approximate exponential decay law. A simple theoretical model is developed for ⁶³Ni betavoltaic battery based on the distribution characteristics. The correctness of the model is validated by two literature experiments. Results show that the theoretical short-circuit current agrees well with the experimental results, and the open-circuit voltage deviates from the experimental results in terms of the influence of the PN junction defects and the simplification of the source. The theoretical model can be applied to ⁶³Ni and ¹⁴⁷Pm betavoltaic batteries. Copyright © 2013 Elsevier Ltd. All rights reserved.

Multi-step rhodopsin inactivation schemes can account for the size variability of single photon responses in Limulus ventral photoreceptors

PubMed Central

1994-01-01

Limulus ventral photoreceptors generate highly variable responses to the absorption of single photons. We have obtained data on the size distribution of these responses, derived the distribution predicted from simple transduction cascade models and compared the theory and data. In the simplest of models, the active state of the visual pigment (defined by its ability to activate G protein) is turned off in a single reaction. The output of such a cascade is predicted to be highly variable, largely because of stochastic variation in the number of G proteins activated. The exact distribution predicted is exponential, but we find that an exponential does not adequately account for the data. The data agree much better with the predictions of a cascade model in which the active state of the visual pigment is turned off by a multi-step process. PMID:8057085

Proportional Feedback Control of Energy Intake During Obesity Pharmacotherapy.

PubMed

Hall, Kevin D; Sanghvi, Arjun; Göbel, Britta

2017-12-01

Obesity pharmacotherapies result in an exponential time course for energy intake whereby large early decreases dissipate over time. This pattern of declining drug efficacy to decrease energy intake results in a weight loss plateau within approximately 1 year. This study aimed to elucidate the physiology underlying the exponential decay of drug effects on energy intake. Placebo-subtracted energy intake time courses were examined during long-term obesity pharmacotherapy trials for 14 different drugs or drug combinations within the theoretical framework of a proportional feedback control system regulating human body weight. Assuming each obesity drug had a relatively constant effect on average energy intake and did not affect other model parameters, our model correctly predicted that long-term placebo-subtracted energy intake was linearly related to early reductions in energy intake according to a prespecified equation with no free parameters. The simple model explained about 70% of the variance between drug studies with respect to the long-term effects on energy intake, although a significant proportional bias was evident. The exponential decay over time of obesity pharmacotherapies to suppress energy intake can be interpreted as a relatively constant effect of each drug superimposed on a physiological feedback control system regulating body weight. © 2017 The Obesity Society.

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

Extended q -Gaussian and q -exponential distributions from gamma random variables

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

Exponential growth kinetics for Polyporus versicolor and Pleurotus ostreatus in submerged culture

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

Carroad, P.A.; Wilke, C.R.

1977-04-01

Simple mathematical models for a batch culture of pellet-forming fungi in submerged culture were tested on growth data for Polyporus versicolor (ATCC 12679) and Pleurotus ostreatus (ATCC 9415). A kinetic model based on a growth rate proportional to the two-thirds power of the cell mass was shown to be satisfactory. A model based on a growth rate directly proportional to the cell mass fitted the data equally well, however, and may be preferable because of mathematical simplicity.

Queueing Network Models for Parallel Processing of Task Systems: an Operational Approach

NASA Technical Reports Server (NTRS)

Mak, Victor W. K.

1986-01-01

Computer performance modeling of possibly complex computations running on highly concurrent systems is considered. Earlier works in this area either dealt with a very simple program structure or resulted in methods with exponential complexity. An efficient procedure is developed to compute the performance measures for series-parallel-reducible task systems using queueing network models. The procedure is based on the concept of hierarchical decomposition and a new operational approach. Numerical results for three test cases are presented and compared to those of simulations.

A model of canopy photosynthesis incorporating protein distribution through the canopy and its acclimation to light, temperature and CO2

PubMed Central

Johnson, Ian R.; Thornley, John H. M.; Frantz, Jonathan M.; Bugbee, Bruce

2010-01-01

Background and Aims The distribution of photosynthetic enzymes, or nitrogen, through the canopy affects canopy photosynthesis, as well as plant quality and nitrogen demand. Most canopy photosynthesis models assume an exponential distribution of nitrogen, or protein, through the canopy, although this is rarely consistent with experimental observation. Previous optimization schemes to derive the nitrogen distribution through the canopy generally focus on the distribution of a fixed amount of total nitrogen, which fails to account for the variation in both the actual quantity of nitrogen in response to environmental conditions and the interaction of photosynthesis and respiration at similar levels of complexity. Model A model of canopy photosynthesis is presented for C3 and C4 canopies that considers a balanced approach between photosynthesis and respiration as well as plant carbon partitioning. Protein distribution is related to irradiance in the canopy by a flexible equation for which the exponential distribution is a special case. The model is designed to be simple to parameterize for crop, pasture and ecosystem studies. The amount and distribution of protein that maximizes canopy net photosynthesis is calculated. Key Results The optimum protein distribution is not exponential, but is quite linear near the top of the canopy, which is consistent with experimental observations. The overall concentration within the canopy is dependent on environmental conditions, including the distribution of direct and diffuse components of irradiance. Conclusions The widely used exponential distribution of nitrogen or protein through the canopy is generally inappropriate. The model derives the optimum distribution with characteristics that are consistent with observation, so overcoming limitations of using the exponential distribution. Although canopies may not always operate at an optimum, optimization analysis provides valuable insight into plant acclimation to environmental conditions. Protein distribution has implications for the prediction of carbon assimilation, plant quality and nitrogen demand. PMID:20861273

Experimental characterization of post rigor mortis human muscle subjected to small tensile strains and application of a simple hyper-viscoelastic model.

PubMed

Gras, Laure-Lise; Laporte, Sébastien; Viot, Philippe; Mitton, David

2014-10-01

In models developed for impact biomechanics, muscles are usually represented with one-dimensional elements having active and passive properties. The passive properties of muscles are most often obtained from experiments performed on animal muscles, because limited data on human muscle are available. The aim of this study is thus to characterize the passive response of a human muscle in tension. Tensile tests at different strain rates (0.0045, 0.045, and 0.45 s⁻¹) were performed on 10 extensor carpi ulnaris muscles. A model composed of a nonlinear element defined with an exponential law in parallel with one or two Maxwell elements and considering basic geometrical features was proposed. The experimental results were used to identify the parameters of the model. The results for the first- and second-order model were similar. For the first-order model, the mean parameters of the exponential law are as follows: Young's modulus E (6.8 MPa) and curvature parameter α (31.6). The Maxwell element mean values are as follows: viscosity parameter η (1.2 MPa s) and relaxation time τ (0.25 s). Our results provide new data on a human muscle tested in vitro and a simple model with basic geometrical features that represent its behavior in tension under three different strain rates. This approach could be used to assess the behavior of other human muscles. © IMechE 2014.

Galileon bounce after ekpyrotic contraction

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

Osipov, M.; Rubakov, V., E-mail: osipov@ms2.inr.ac.ru, E-mail: rubakov@ms2.inr.ac.ru

We consider a simple cosmological model that includes a long ekpyrotic contraction stage and smooth bounce after it. Ekpyrotic behavior is due to a scalar field with a negative exponential potential, whereas the Galileon field produces bounce. We give an analytical picture of how the bounce occurs within the weak gravity regime, and then perform numerical analysis to extend our results to a non-perturbative regime.

An Approximation to the Adaptive Exponential Integrate-and-Fire Neuron Model Allows Fast and Predictive Fitting to Physiological Data.

PubMed

Hertäg, Loreen; Hass, Joachim; Golovko, Tatiana; Durstewitz, Daniel

2012-01-01

For large-scale network simulations, it is often desirable to have computationally tractable, yet in a defined sense still physiologically valid neuron models. In particular, these models should be able to reproduce physiological measurements, ideally in a predictive sense, and under different input regimes in which neurons may operate in vivo. Here we present an approach to parameter estimation for a simple spiking neuron model mainly based on standard f-I curves obtained from in vitro recordings. Such recordings are routinely obtained in standard protocols and assess a neuron's response under a wide range of mean-input currents. Our fitting procedure makes use of closed-form expressions for the firing rate derived from an approximation to the adaptive exponential integrate-and-fire (AdEx) model. The resulting fitting process is simple and about two orders of magnitude faster compared to methods based on numerical integration of the differential equations. We probe this method on different cell types recorded from rodent prefrontal cortex. After fitting to the f-I current-clamp data, the model cells are tested on completely different sets of recordings obtained by fluctuating ("in vivo-like") input currents. For a wide range of different input regimes, cell types, and cortical layers, the model could predict spike times on these test traces quite accurately within the bounds of physiological reliability, although no information from these distinct test sets was used for model fitting. Further analyses delineated some of the empirical factors constraining model fitting and the model's generalization performance. An even simpler adaptive LIF neuron was also examined in this context. Hence, we have developed a "high-throughput" model fitting procedure which is simple and fast, with good prediction performance, and which relies only on firing rate information and standard physiological data widely and easily available.

Preparation of an exponentially rising optical pulse for efficient excitation of single atoms in free space.

PubMed

Dao, Hoang Lan; Aljunid, Syed Abdullah; Maslennikov, Gleb; Kurtsiefer, Christian

2012-08-01

We report on a simple method to prepare optical pulses with exponentially rising envelope on the time scale of a few ns. The scheme is based on the exponential transfer function of a fast transistor, which generates an exponentially rising envelope that is transferred first on a radio frequency carrier, and then on a coherent cw laser beam with an electro-optical phase modulator. The temporally shaped sideband is then extracted with an optical resonator and can be used to efficiently excite a single (87)Rb atom.

Human population and atmospheric carbon dioxide growth dynamics: Diagnostics for the future

NASA Astrophysics Data System (ADS)

Hüsler, A. D.; Sornette, D.

2014-10-01

We analyze the growth rates of human population and of atmospheric carbon dioxide by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive feedbacks, either direct or mediated by other dynamical variables, as shown in our presentation of a simple endogenous macroeconomic dynamical growth model describing the growth dynamics of coupled processes involving human population (labor in economic terms), capital and technology (proxies by CO2 emissions). Human population in the context of our energy intensive economies constitutes arguably the most important underlying driving variable of the content of carbon dioxide in the atmosphere. Using some of the best databases available, we perform empirical analyses confirming that the human population on Earth has been growing super-exponentially until the mid-1960s, followed by a decelerated sub-exponential growth, with a tendency to plateau at just an exponential growth in the last decade with an average growth rate of 1.0% per year. In contrast, we find that the content of carbon dioxide in the atmosphere has continued to accelerate super-exponentially until 1990, with a transition to a progressive deceleration since then, with an average growth rate of approximately 2% per year in the last decade. To go back to CO2 atmosphere contents equal to or smaller than the level of 1990 as has been the broadly advertised goals of international treaties since 1990 requires herculean changes: from a dynamical point of view, the approximately exponential growth must not only turn to negative acceleration but also negative velocity to reverse the trend.

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

PubMed Central

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, L. F.

2013-01-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. PMID:24204236

Model for the accumulation of strontium and calcium by recently molted crayfish (Cambarus longulus longerostris Ort.)

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

SCHURR, J. M.; STAMPER, M. N.

1962-10-01

After molting, crayfish absorbed Sr 85 rapidly; rates of uptake decreased exponentially as an upper limit was approached (T 1/2 = 1 to 2 days). A simple mathematical model attributes this limit to the number of sites available for deposition in the exoskeleton. Deposited ions are relatively immobile until 2 to 4 days prior to the next molt, when some are redistributed to the calcareous gastroliths prior to reuse.

Improving deep convolutional neural networks with mixed maxout units

PubMed Central

Liu, Fu-xian; Li, Long-yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that “non-maximal features are unable to deliver” and “feature mapping subspace pooling is insufficient,” we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance. PMID:28727737

Model-based analysis of multi-shell diffusion MR data for tractography: How to get over fitting problems

PubMed Central

Jbabdi, Saad; Sotiropoulos, Stamatios N; Savio, Alexander M; Graña, Manuel; Behrens, Timothy EJ

2012-01-01

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-mono-exponential decay, commonly observed in experimental data, is shown to induce over-fitting in the distribution of fibre orientations when not considered in the model. Extra fibre orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous Gamma distribution of diffusivities, which significantly improves the fitting and reduces the over-fitting. Using in-vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-mono-exponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fibre orientations in white matter and near the cortex. PMID:22334356

Poverty trap formed by the ecology of infectious diseases

PubMed Central

Bonds, Matthew H.; Keenan, Donald C.; Rohani, Pejman; Sachs, Jeffrey D.

2010-01-01

While most of the world has enjoyed exponential economic growth, more than one-sixth of the world is today roughly as poor as their ancestors were many generations ago. Widely accepted general explanations for the persistence of such poverty have been elusive and are needed by the international development community. Building on a well-established model of human infectious diseases, we show how formally integrating simple economic and disease ecology models can naturally give rise to poverty traps, where initial economic and epidemiological conditions determine the long-term trajectory of the health and economic development of a society. This poverty trap may therefore be broken by improving health conditions of the population. More generally, we demonstrate that simple human ecological models can help explain broad patterns of modern economic organization. PMID:20007179

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Money Earlier or Later? Simple Heuristics Explain Intertemporal Choices Better than Delay Discounting1

PubMed Central

Marzilli Ericson, Keith M.; White, John Myles; Laibson, David; Cohen, Jonathan D.

2015-01-01

Heuristic models have been proposed for many domains of choice. We compare heuristic models of intertemporal choice, which can account for many of the known intertemporal choice anomalies, to discounting models. We conduct an out-of-sample, cross-validated comparison of intertemporal choice models. Heuristic models outperform traditional utility discounting models, including models of exponential and hyperbolic discounting. The best performing models predict choices by using a weighted average of absolute differences and relative (percentage) differences of the attributes of the goods in a choice set. We conclude that heuristic models explain time-money tradeoff choices in experiments better than utility discounting models. PMID:25911124

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Determination of bulk and interface density of states in metal oxide semiconductor thin-film transistors by using capacitance-voltage characteristics

NASA Astrophysics Data System (ADS)

Wei, Xixiong; Deng, Wanling; Fang, Jielin; Ma, Xiaoyu; Huang, Junkai

2017-10-01

A physical-based straightforward extraction technique for interface and bulk density of states in metal oxide semiconductor thin film transistors (TFTs) is proposed by using the capacitance-voltage (C-V) characteristics. The interface trap density distribution with energy has been extracted from the analysis of capacitance-voltage characteristics. Using the obtained interface state distribution, the bulk trap density has been determined. With this method, for the interface trap density, it is found that deep state density nearing the mid-gap is approximately constant and tail states density increases exponentially with energy; for the bulk trap density, it is a superposition of exponential deep states and exponential tail states. The validity of the extraction is verified by comparisons with the measured current-voltage (I-V) characteristics and the simulation results by the technology computer-aided design (TCAD) model. This extraction method uses non-numerical iteration which is simple, fast and accurate. Therefore, it is very useful for TFT device characterization.

A study of hyperelastic models for predicting the mechanical behavior of extensor apparatus.

PubMed

Elyasi, Nahid; Taheri, Kimia Karimi; Narooei, Keivan; Taheri, Ali Karimi

2017-06-01

In this research, the nonlinear elastic behavior of human extensor apparatus was investigated. To this goal, firstly the best material parameters of hyperelastic strain energy density functions consisting of the Mooney-Rivlin, Ogden, invariants, and general exponential models were derived for the simple tension experimental data. Due to the significance of stress response in other deformation modes of nonlinear models, the calculated parameters were used to study the pure shear and balance biaxial tension behavior of the extensor apparatus. The results indicated that the Mooney-Rivlin model predicts an unstable behavior in the balance biaxial deformation of the extensor apparatus, while the Ogden order 1 represents a stable behavior, although the fitting of experimental data and theoretical model was not satisfactory. However, the Ogden order 6 model was unstable in the simple tension mode and the Ogden order 5 and general exponential models presented accurate and stable results. In order to reduce the material parameters, the invariants model with four material parameters was investigated and this model presented the minimum error and stable behavior in all deformation modes. The ABAQUS Explicit solver was coupled with the VUMAT subroutine code of the invariants model to simulate the mechanical behavior of the central and terminal slips of the extensor apparatus during the passive finger flexion, which is important in the prediction of boutonniere deformity and chronic mallet finger injuries, respectively. Also, to evaluate the adequacy of constitutive models in simulations, the results of the Ogden order 5 were presented. The difference between the predictions was attributed to the better fittings of the invariants model compared with the Ogden model.

Simplifying the Mathematical Treatment of Radioactive Decay

ERIC Educational Resources Information Center

Auty, Geoff

2011-01-01

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Comparing Exponential and Exponentiated Models of Drug Demand in Cocaine Users

PubMed Central

Strickland, Justin C.; Lile, Joshua A.; Rush, Craig R.; Stoops, William W.

2016-01-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model, but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use), whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values impact demand parameters and their association with drug-use outcomes when using the exponential model, but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency, in addition to demonstrating construct validity and generalizability. PMID:27929347

Comparing exponential and exponentiated models of drug demand in cocaine users.

PubMed

Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W

2016-12-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function.

PubMed

Aggarwal, Ankush

2017-08-01

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

Nonholonomic stability aspects of piecewise holonomic systems

NASA Astrophysics Data System (ADS)

Ruina, Andy

1998-10-01

We consider mechanical systems with intermittent contact that are smooth and holonomic except at the instants of transition. Overall such systems can be nonholonomic in that the accessible configuration space can have larger dimension than the instantaneous motions allowed by the constraints. The known examples of such mechanical systems are also dissipative. By virtue of their nonholonomy and of their dissipation such systems are not Hamiltonian. Thus there is no reason to expect them to adhere to the Hamiltonian property that exponential stability of steady motions is impossible. Since nonholonomy and energy dissipation are simultaneously present in these systems, it is usually not clear whether their sometimes-observed exponential stability should be attributed solely to dissipation, to nonholonomy, or to both. However, it is shown here on the basis of one simple example, that the observed exponential stability of such systems can follow solely from the nonholonomic nature of intermittent contact and not from dissipation. In particular, it is shown that a discrete sister model of the Chaplygin sleigh, a rigid body on the plane constrained by one skate, inherits the stability eigenvalues of the smooth system even as the dissipation tends to zero. Thus it seems that discrete nonholonomy can contribute to exponential stability of mechanical systems.

Money earlier or later? Simple heuristics explain intertemporal choices better than delay discounting does.

PubMed

Ericson, Keith M Marzilli; White, John Myles; Laibson, David; Cohen, Jonathan D

2015-06-01

Heuristic models have been proposed for many domains involving choice. We conducted an out-of-sample, cross-validated comparison of heuristic models of intertemporal choice (which can account for many of the known intertemporal choice anomalies) and discounting models. Heuristic models outperformed traditional utility-discounting models, including models of exponential and hyperbolic discounting. The best-performing models predicted choices by using a weighted average of absolute differences and relative percentage differences of the attributes of the goods in a choice set. We concluded that heuristic models explain time-money trade-off choices in experiments better than do utility-discounting models. © The Author(s) 2015.

Implications of Biospheric Energization

NASA Astrophysics Data System (ADS)

Budding, Edd; Demircan, Osman; Gündüz, Güngör; Emin Özel, Mehmet

2016-07-01

Our physical model relating to the origin and development of lifelike processes from very simple beginnings is reviewed. This molecular ('ABC') process is compared with the chemoton model, noting the role of the autocatalytic tuning to the time-dependent source of energy. This substantiates a Darwinian character to evolution. The system evolves from very simple beginnings to a progressively more highly tuned, energized and complex responding biosphere, that grows exponentially; albeit with a very low net growth factor. Rates of growth and complexity in the evolution raise disturbing issues of inherent stability. Autocatalytic processes can include a fractal character to their development allowing recapitulative effects to be observed. This property, in allowing similarities of pattern to be recognized, can be useful in interpreting complex (lifelike) systems.

Calculation of Rate Spectra from Noisy Time Series Data

PubMed Central

Voelz, Vincent A.; Pande, Vijay S.

2011-01-01

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Towards this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discrete inverse Laplace transform is an ill-conditioned inverse problem, so a regularization procedure must be used to perform the calculation. Here, we show the results of different regularization procedures applied to noisy multi-exponential and stretched exponential time series, as well as data from time-resolved folding kinetics experiments. In each case, the rate spectrum method recapitulates the relevant distribution of timescales present in the data, with different priors on the rate amplitudes naturally corresponding to common biases toward simple phenomenological models. These results suggest an attractive alternative to the “Occam’s razor” philosophy of simply choosing models with the fewest number of relaxation rates. PMID:22095854

Detecting biodiversity hotspots by species-area relationships: a case study of Mediterranean beetles.

PubMed

Fattorini, Simone

2006-08-01

Any method of identifying hotspots should take into account the effect of area on species richness. I examined the importance of the species-area relationship in determining tenebrionid (Coleoptera: Tenebrionidae) hotspots on the Aegean Islands (Greece). Thirty-two islands and 170 taxa (species and subspecies) were included in this study. I tested several species-area relationship models with linear and nonlinear regressions, including power exponential, negative exponential, logistic, Gompertz, Weibull, Lomolino, and He-Legendre functions. Islands with positive residuals were identified as hotspots. I also analyzed the values of the C parameter of the power function and the simple species-area ratios. Species richness was significantly correlated with island area for all models. The power function model was the most convenient one. Most functions, however identified certain islands as hotspots. The importance of endemics in insular biotas should be evaluated carefully because they are of high conservation concern. The simple use of the species-area relationship can be problematic when areas with no endemics are included. Therefore the importance of endemics should be evaluated according to different methods, such as percentages, to take into account different levels of endemism and different kinds of "endemics" (e.g., endemic to single islands vs. endemic to the archipelago). Because the species-area relationship is a key pattern in ecology, my findings can be applied at broader scales.

Complex Autocatalysis in Simple Chemistries.

PubMed

Virgo, Nathaniel; Ikegami, Takashi; McGregor, Simon

2016-01-01

Life on Earth must originally have arisen from abiotic chemistry. Since the details of this chemistry are unknown, we wish to understand, in general, which types of chemistry can lead to complex, lifelike behavior. Here we show that even very simple chemistries in the thermodynamically reversible regime can self-organize to form complex autocatalytic cycles, with the catalytic effects emerging from the network structure. We demonstrate this with a very simple but thermodynamically reasonable artificial chemistry model. By suppressing the direct reaction from reactants to products, we obtain the simplest kind of autocatalytic cycle, resulting in exponential growth. When these simple first-order cycles are prevented from forming, the system achieves superexponential growth through more complex, higher-order autocatalytic cycles. This leads to nonlinear phenomena such as oscillations and bistability, the latter of which is of particular interest regarding the origins of life.

Check the Lambert-Beer-Bouguer law: a simple trick to boost the confidence of students toward both exponential laws and the discrete approach to experimental physics

NASA Astrophysics Data System (ADS)

Di Capua, R.; Offi, F.; Fontana, F.

2014-07-01

Exponential decay is a prototypical functional behaviour for many physical phenomena, and therefore it deserves great attention in physics courses at an academic level. The absorption of the electromagnetic radiation that propagates in a dissipative medium provides an example of the decay of light intensity, as stated by the law of Lambert-Beer-Bourguer. We devised a very simple experiment to check this law. The experimental setup, its realization, and the data analysis of the experiment are definitely simple. Our main goal was to create an experiment that is accessible to all students, including those in their first year of academic courses and those with poorly equipped laboratories. As illustrated in this paper, our proposal allowed us to develop a deep discussion about some general mathematical and numerical features of exponential decay. Furthermore, the special setup of the absorbing medium (sliced in finite thickness slabs) and the experimental outcomes allow students to understand the transition from the discrete to the continuum approach in experimental physics.

The Mass-dependent Star Formation Histories of Disk Galaxies: Infall Model Versus Observations

NASA Astrophysics Data System (ADS)

Chang, R. X.; Hou, J. L.; Shen, S. Y.; Shu, C. G.

2010-10-01

We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk originate and grows by continuous gas infall. The gas infall rate is parameterized by the Gaussian formula with one free parameter: the infall-peak time tp . The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at a given galactic stellar mass M *, the model adopting a late infall-peak time tp results in blue colors, low-metallicity, high specific star formation rate (SFR), and high gas fraction, while the gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we "construct" a mass-dependent model by assuming that the low-mass galaxy has a later infall-peak time tp and a larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also with the observed correlations between specific SFR and galactic stellar mass SFR/M * ~ M * at intermediate redshifts z < 1. Comparison between the Gaussian-infall model and the exponential-infall model is also presented. It shows that the exponential-infall model predicts a higher SFR at early stage and a lower SFR later than that of Gaussian infall. Our results suggest that the Gaussian infall rate may be more reasonable in describing the gas cooling process than the exponential infall rate, especially for low-mass systems.

Modelling the interactions between Pseudomonas putida and Escherichia coli O157:H7 in fish-burgers: use of the lag-exponential model and of a combined interaction index.

PubMed

Speranza, B; Bevilacqua, A; Mastromatteo, M; Sinigaglia, M; Corbo, M R

2010-08-01

The objective of the current study was to examine the interactions between Pseudomonas putida and Escherichia coli O157:H7 in coculture studies on fish-burgers packed in air and under different modified atmospheres (30 : 40 : 30 O(2) : CO(2) : N(2), 5 : 95 O(2) : CO(2) and 50 : 50 O(2) : CO(2)), throughout the storage at 8 degrees C. The lag-exponential model was applied to describe the microbial growth. To give a quantitative measure of the occurring microbial interactions, two simple parameters were developed: the combined interaction index (CII) and the partial interaction index (PII). Under air, the interaction was significant (P < 0.05) only within the exponential growth phase (CII, 1.72), whereas under the modified atmospheres, the interactions were highly significant (P < 0.001) and occurred both in the exponential and in the stationary phase (CII ranged from 0.33 to 1.18). PII values for E. coli O157:H7 were lower than those calculated for Ps. putida. The interactions occurring into the system affected both E. coli O157:H7 and pseudomonads subpopulations. The packaging atmosphere resulted in a key element. The article provides some useful information on the interactions occurring between E. coli O157:H7 and Ps. putida on fish-burgers. The proposed index describes successfully the competitive growth of both micro-organisms, giving also a quantitative measure of a qualitative phenomenon.

A Simple Mechanical Experiment on Exponential Growth

ERIC Educational Resources Information Center

McGrew, Ralph

2015-01-01

With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…

Studies in Dialogue and Discourse: An Exponential Law of Successive Questioning

ERIC Educational Resources Information Center

Mishler, Elliot G.

1975-01-01

The structure of natural conversations in first-grade classrooms is the focus of this inquiry. Analyses of a particular type of discourse, namely, connected conversations initiated and sustained by questioning, suggest that the probability that a conversation will be continued may be expressed as a simple exponential function. (Author/RM)

Spontaneous emergence of catalytic cycles with colloidal spheres

NASA Astrophysics Data System (ADS)

Zeravcic, Zorana; Brenner, Michael P.

2017-04-01

Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson’s notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.

Using phenomenological models for forecasting the 2015 Ebola challenge.

PubMed

Pell, Bruce; Kuang, Yang; Viboud, Cecile; Chowell, Gerardo

2018-03-01

The rising number of novel pathogens threatening the human population has motivated the application of mathematical modeling for forecasting the trajectory and size of epidemics. We summarize the real-time forecasting results of the logistic equation during the 2015 Ebola challenge focused on predicting synthetic data derived from a detailed individual-based model of Ebola transmission dynamics and control. We also carry out a post-challenge comparison of two simple phenomenological models. In particular, we systematically compare the logistic growth model and a recently introduced generalized Richards model (GRM) that captures a range of early epidemic growth profiles ranging from sub-exponential to exponential growth. Specifically, we assess the performance of each model for estimating the reproduction number, generate short-term forecasts of the epidemic trajectory, and predict the final epidemic size. During the challenge the logistic equation consistently underestimated the final epidemic size, peak timing and the number of cases at peak timing with an average mean absolute percentage error (MAPE) of 0.49, 0.36 and 0.40, respectively. Post-challenge, the GRM which has the flexibility to reproduce a range of epidemic growth profiles ranging from early sub-exponential to exponential growth dynamics outperformed the logistic growth model in ascertaining the final epidemic size as more incidence data was made available, while the logistic model underestimated the final epidemic even with an increasing amount of data of the evolving epidemic. Incidence forecasts provided by the generalized Richards model performed better across all scenarios and time points than the logistic growth model with mean RMS decreasing from 78.00 (logistic) to 60.80 (GRM). Both models provided reasonable predictions of the effective reproduction number, but the GRM slightly outperformed the logistic growth model with a MAPE of 0.08 compared to 0.10, averaged across all scenarios and time points. Our findings further support the consideration of transmission models that incorporate flexible early epidemic growth profiles in the forecasting toolkit. Such models are particularly useful for quickly evaluating a developing infectious disease outbreak using only case incidence time series of the early phase of an infectious disease outbreak. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

A thorough investigation of the progressive reset dynamics in HfO{sub 2}-based resistive switching structures

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

Lorenzi, P., E-mail: lorenzi@die.uniroma1.it; Rao, R.; Irrera, F.

2015-09-14

According to previous reports, filamentary electron transport in resistive switching HfO{sub 2}-based metal-insulator-metal structures can be modeled using a diode-like conduction mechanism with a series resistance. Taking the appropriate limits, the model allows simulating the high (HRS) and low (LRS) resistance states of the devices in terms of exponential and linear current-voltage relationships, respectively. In this letter, we show that this simple equivalent circuit approach can be extended to represent the progressive reset transition between the LRS and HRS if a generalized logistic growth model for the pre-exponential diode current factor is considered. In this regard, it is demonstrated heremore » that a Verhulst logistic model does not provide accurate results. The reset dynamics is interpreted as the sequential deactivation of multiple conduction channels spanning the dielectric film. Fitting results for the current-voltage characteristics indicate that the voltage sweep rate only affects the deactivation rate of the filaments without altering the main features of the switching dynamics.« less

The Development of a High Speed Exponential Function Generator for Linearization of Microwave Voltage Controlled Oscillators.

DTIC Science & Technology

1985-10-01

characteristic of a p-n junction to provide exponential linearization in a simple, thermally-stable, wide band circuit. RESME Les oscillateurs A...exponentielle (fr6quence/tension) que V’on 1 retrouve chez plusieurs oscillateurs . Ce circuit, d’une grande largeur de bande, utilise la caractfiristique

Conditional optimal spacing in exponential distribution.

PubMed

Park, Sangun

2006-12-01

In this paper, we propose the conditional optimal spacing defined as the optimal spacing after specifying a predetermined order statistic. If we specify a censoring time, then the optimal inspection times for grouped inspection can be determined from this conditional optimal spacing. We take an example of exponential distribution, and provide a simple method of finding the conditional optimal spacing.

Size-Frequency Distributions of Rocks on Mars and Earth Analog Sites: Implications for Future Landed Missions

NASA Technical Reports Server (NTRS)

Golombeck, M.; Rapp, D.

1996-01-01

The size-frequency distribution of rocks and the Vicking landing sites and a variety of rocky locations on the Earth that formed from a number of geologic processes all have the general shape of simple exponential curves, which have been combined with remote sensing data and models on rock abundance to predict the frequency of boulders potentially hazardous to future Mars landers and rovers.

Accumulated distribution of material gain at dislocation crystal growth

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

Rakin, V. I., E-mail: rakin@geo.komisc.ru

2016-05-15

A model for slowing down the tangential growth rate of an elementary step at dislocation crystal growth is proposed based on the exponential law of impurity particle distribution over adsorption energy. It is established that the statistical distribution of material gain on structurally equivalent faces obeys the Erlang law. The Erlang distribution is proposed to be used to calculate the occurrence rates of morphological combinatorial types of polyhedra, presenting real simple crystallographic forms.

Concepts in solid tumor evolution.

PubMed

Sidow, Arend; Spies, Noah

2015-04-01

Evolutionary mechanisms in cancer progression give tumors their individuality. Cancer evolution is different from organismal evolution, however, and we discuss where concepts from evolutionary genetics are useful or limited in facilitating an understanding of cancer. Based on these concepts we construct and apply the simplest plausible model of tumor growth and progression. Simulations using this simple model illustrate the importance of stochastic events early in tumorigenesis, highlight the dominance of exponential growth over linear growth and differentiation, and explain the clonal substructure of tumors. Copyright © 2015 Elsevier Ltd. All rights reserved.

Performance of wind turbines in a turbulent atmosphere

NASA Technical Reports Server (NTRS)

Sundar, R. M.; Sullivan, J. P.

1981-01-01

The effect of atmospheric turbulence on the power fluctuations of large wind turbines was studied. The significance of spatial non-uniformities of the wind is emphasized. The turbulent wind with correlation in time and space is simulated on the computer by Shinozukas method. The wind turbulence is modelled according to the Davenport spectrum with an exponential spatial correlation function. The rotor aerodynamics is modelled by simple blade element theory. Comparison of the spectrum of power output signal between 1-D and 3-D turbulence, shows the significant power fluctuations centered around the blade passage frequency.

A search for refraction in the Kepler gas giant data set

NASA Astrophysics Data System (ADS)

Sheets, Holly A.; Jacob, Laurent; Cowan, Nicolas; Deming, Drake

2018-06-01

I present the results of our systematic search for refraction in the atmospheres of giant planets in the Kepler data set. We chose our candidates using the approximations of Sidis and Sari (ApJ, 2010, 720, 904S), selecting those that had an expected signal greater than 10 parts per million. We model the refraction shoulders as simple exponentials outside of transit and fit a transit+shoulder model to individual candidates. We find that the effect is not present to the extent predicted from the approximations.

When growth models are not universal: evidence from marine invertebrates

PubMed Central

Hirst, Andrew G.; Forster, Jack

2013-01-01

The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691

Why fast magnetic reconnection is so prevalent

NASA Astrophysics Data System (ADS)

Boozer, Allen H.

2018-02-01

Evolving magnetic fields are shown to generically reach a state of fast magnetic reconnection in which magnetic field line connections change and magnetic energy is released at an Alfvénic rate. This occurs even in plasmas with zero resistivity; only the finiteness of the mass of the lightest charged particle, an electron, is required. The speed and prevalence of Alfvénic or fast magnetic reconnection imply that its cause must be contained within the ideal evolution equation for magnetic fields, , where is the velocity of the magnetic field lines. For a generic , neighbouring magnetic field lines develop a separation that increases exponentially, as \\unicode[STIX]{x1D70E(\\ell ,t)}$ with the distance along a line. This exponentially enhances the sensitivity of the evolution to non-ideal effects. An analogous effect, the importance of stirring to produce a large-scale flow and enhance mixing, has been recognized by cooks through many millennia, but the importance of the large-scale flow to reconnection is customarily ignored. In part this is due to the sixty-year focus of recognition theory on two-coordinate models, which eliminate the exponential enhancement that is generic with three coordinates. A simple three-coordinate model is developed, which could be used to address many unanswered questions.

Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.

Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition

NASA Astrophysics Data System (ADS)

Penati, Tiziano; Flach, Sergej

2007-06-01

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincaré-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

NASA Astrophysics Data System (ADS)

Dalkilic, Turkan Erbay; Apaydin, Aysen

2009-11-01

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+[epsilon]. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the [`]switching regression model' and it is expressed with . Here li indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665-685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363-399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306-310]. In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.

Application of a linked stress release model in Corinth Gulf and Central Ionian Islands (Greece)

NASA Astrophysics Data System (ADS)

Mangira, Ourania; Vasiliadis, Georgios; Papadimitriou, Eleftheria

2017-06-01

Spatio-temporal stress changes and interactions between adjacent fault segments consist of the most important component in seismic hazard assessment, as they can alter the occurrence probability of strong earthquake onto these segments. The investigation of the interactions between adjacent areas by means of the linked stress release model is attempted for moderate earthquakes ( M ≥ 5.2) in the Corinth Gulf and the Central Ionian Islands (Greece). The study areas were divided in two subareas, based on seismotectonic criteria. The seismicity of each subarea is investigated by means of a stochastic point process and its behavior is determined by the conditional intensity function, which usually gets an exponential form. A conditional intensity function of Weibull form is used for identifying the most appropriate among the models (simple, independent and linked stress release model) for the interpretation of the earthquake generation process. The appropriateness of the models was decided after evaluation via the Akaike information criterion. Despite the fact that the curves of the conditional intensity functions exhibit similar behavior, the use of the exponential-type conditional intensity function seems to fit better the data.

Fermion masses and mixing in general warped extra dimensional models

NASA Astrophysics Data System (ADS)

Frank, Mariana; Hamzaoui, Cherif; Pourtolami, Nima; Toharia, Manuel

2015-06-01

We analyze fermion masses and mixing in a general warped extra dimensional model, where all the Standard Model (SM) fields, including the Higgs, are allowed to propagate in the bulk. In this context, a slightly broken flavor symmetry imposed universally on all fermion fields, without distinction, can generate the full flavor structure of the SM, including quarks, charged leptons and neutrinos. For quarks and charged leptons, the exponential sensitivity of their wave functions to small flavor breaking effects yield hierarchical masses and mixing as it is usual in warped models with fermions in the bulk. In the neutrino sector, the exponential wave-function factors can be flavor blind and thus insensitive to the small flavor symmetry breaking effects, directly linking their masses and mixing angles to the flavor symmetric structure of the five-dimensional neutrino Yukawa couplings. The Higgs must be localized in the bulk and the model is more successful in generalized warped scenarios where the metric background solution is different than five-dimensional anti-de Sitter (AdS5 ). We study these features in two simple frameworks, flavor complimentarity and flavor democracy, which provide specific predictions and correlations between quarks and leptons, testable as more precise data in the neutrino sector becomes available.

Snowmelt runoff modeling in simulation and forecasting modes with the Martinec-Mango model

NASA Technical Reports Server (NTRS)

Shafer, B.; Jones, E. B.; Frick, D. M. (Principal Investigator)

1982-01-01

The Martinec-Rango snowmelt runoff model was applied to two watersheds in the Rio Grande basin, Colorado-the South Fork Rio Grande, a drainage encompassing 216 sq mi without reservoirs or diversions and the Rio Grande above Del Norte, a drainage encompassing 1,320 sq mi without major reservoirs. The model was successfully applied to both watersheds when run in a simulation mode for the period 1973-79. This period included both high and low runoff seasons. Central to the adaptation of the model to run in a forecast mode was the need to develop a technique to forecast the shape of the snow cover depletion curves between satellite data points. Four separate approaches were investigated-simple linear estimation, multiple regression, parabolic exponential, and type curve. Only the parabolic exponential and type curve methods were run on the South Fork and Rio Grande watersheds for the 1980 runoff season using satellite snow cover updates when available. Although reasonable forecasts were obtained in certain situations, neither method seemed ready for truly operational forecasts, possibly due to a large amount of estimated climatic data for one or two primary base stations during the 1980 season.

Landscape movements of Anopheles gambiae malaria vector mosquitoes in rural Gambia.

PubMed

Thomas, Christopher J; Cross, Dónall E; Bøgh, Claus

2013-01-01

For malaria control in Africa it is crucial to characterise the dispersal of its most efficient vector, Anopheles gambiae, in order to target interventions and assess their impact spatially. Our study is, we believe, the first to present a statistical model of dispersal probability against distance from breeding habitat to human settlements for this important disease vector. We undertook post-hoc analyses of mosquito catches made in The Gambia to derive statistical dispersal functions for An. gambiae sensu lato collected in 48 villages at varying distances to alluvial larval habitat along the River Gambia. The proportion dispersing declined exponentially with distance, and we estimated that 90% of movements were within 1.7 km. Although a 'heavy-tailed' distribution is considered biologically more plausible due to active dispersal by mosquitoes seeking blood meals, there was no statistical basis for choosing it over a negative exponential distribution. Using a simple random walk model with daily survival and movements previously recorded in Burkina Faso, we were able to reproduce the dispersal probabilities observed in The Gambia. Our results provide an important quantification of the probability of An. gambiae s.l. dispersal in a rural African setting typical of many parts of the continent. However, dispersal will be landscape specific and in order to generalise to other spatial configurations of habitat and hosts it will be necessary to produce tractable models of mosquito movements for operational use. We show that simple random walk models have potential. Consequently, there is a pressing need for new empirical studies of An. gambiae survival and movements in different settings to drive this development.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Foreign exchange market as a lattice gauge theory

NASA Astrophysics Data System (ADS)

Young, K.

1999-10-01

A simple model of the foreign exchange market is exactly a lattice gauge theory. Exchange rates are the exponentials of gauge potentials defined on spatial links while interest rates are related to gauge potentials on temporal links. Arbitrage opportunities are given by nonzero values of the gauge-invariant field tensor or curvature defined on closed loops. Arbitrage opportunities involving cross-rates at one time are "magnetic fields," while arbitrage opportunities involving future contracts are "electric fields."

Numerical simulations in stochastic mechanics

NASA Astrophysics Data System (ADS)

McClendon, Marvin; Rabitz, Herschel

1988-05-01

The stochastic differential equation of Nelson's stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside's method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker's momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of H2. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.

Electrodiffusion kinetics of ionic transport in a simple membrane channel.

PubMed

Valent, Ivan; Petrovič, Pavol; Neogrády, Pavel; Schreiber, Igor; Marek, Miloš

2013-11-21

We employ numerical techniques for solving time-dependent full Poisson-Nernst-Planck (PNP) equations in 2D to analyze transient behavior of a simple ion channel subject to a sudden electric potential jump across the membrane (voltage clamp). Calculated spatiotemporal profiles of the ionic concentrations and electric potential show that two principal exponential processes can be distinguished in the electrodiffusion kinetics, in agreement with original Planck's predictions. The initial fast process corresponds to the dielectric relaxation, while the steady state is approached in a second slower exponential process attributed to the nonlinear ionic redistribution. Effects of the model parameters such as the channel length, height of the potential step, boundary concentrations, permittivity of the channel interior, and ionic mobilities on electrodiffusion kinetics are studied. Numerical solutions are used to determine spatiotemporal profiles of the electric field, ionic fluxes, and both the conductive and displacement currents. We demonstrate that the displacement current is a significant transient component of the total electric current through the channel. The presented results provide additional information about the classical voltage-clamp problem and offer further physical insights into the mechanism of electrodiffusion. The used numerical approach can be readily extended to multi-ionic models with a more structured domain geometry in 2D or 3D, and it is directly applicable to other systems, such as synthetic nanopores, nanofluidic channels, and nanopipettes.

Modeling transitions in body composition: the approach to steady state for anthropometric measures and physiological functions in the Minnesota human starvation study

PubMed Central

Hargrove, James L; Heinz, Grete; Heinz, Otto

2008-01-01

Background This study evaluated whether the changes in several anthropometric and functional measures during caloric restriction combined with walking and treadmill exercise would fit a simple model of approach to steady state (a plateau) that can be solved using spreadsheet software (Microsoft Excel®). We hypothesized that transitions in waist girth and several body compartments would fit a simple exponential model that approaches a stable steady-state. Methods The model (an equation) was applied to outcomes reported in the Minnesota starvation experiment using Microsoft Excel's Solver® function to derive rate parameters (k) and projected steady state values. However, data for most end-points were available only at t = 0, 12 and 24 weeks of caloric restriction. Therefore, we derived 2 new equations that enable model solutions to be calculated from 3 equally spaced data points. Results For the group of male subjects in the Minnesota study, body mass declined with a first order rate constant of about 0.079 wk-1. The fractional rate of loss of fat free mass, which includes components that remained almost constant during starvation, was 0.064 wk-1, compared to a rate of loss of fat mass of 0.103 wk-1. The rate of loss of abdominal fat, as exemplified by the change in the waist girth, was 0.213 wk-1. On average, 0.77 kg was lost per cm of waist girth. Other girths showed rates of loss between 0.085 and 0.131 wk-1. Resting energy expenditure (REE) declined at 0.131 wk-1. Changes in heart volume, hand strength, work capacity and N excretion showed rates of loss in the same range. The group of 32 subjects was close to steady state or had already reached steady state for the variables under consideration at the end of semi-starvation. Conclusion When energy intake is changed to new, relatively constant levels, while physical activity is maintained, changes in several anthropometric and physiological measures can be modeled as an exponential approach to steady state using software that is widely available. The 3 point method for parameter estimation provides a criterion for testing whether change in a variable can be usefully modelled with exponential kinetics within the time range for which data are available. PMID:18840293

Valuation of exotic options in the framework of Levy processes

NASA Astrophysics Data System (ADS)

Milev, Mariyan; Georgieva, Svetla; Markovska, Veneta

2013-12-01

In this paper we explore a straightforward procedure to price derivatives by using the Monte Carlo approach when the underlying process is a jump-diffusion. We have compared the Black-Scholes model with one of its extensions that is the Merton model. The latter model is better in capturing the market's phenomena and is comparative to stochastic volatility models in terms of pricing accuracy. We have presented simulations of asset paths and pricing of barrier options for both Geometric Brownian motion and exponential Levy processes as it is the concrete case of the Merton model. A desired level of accuracy is obtained with simple computer operations in MATLAB for efficient computational time.

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

PubMed

Zhao, Shouwei

2011-06-01

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

Using simple environmental variables to estimate below-ground productivity in grasslands

USGS Publications Warehouse

Gill, R.A.; Kelly, R.H.; Parton, W.J.; Day, K.A.; Jackson, R.B.; Morgan, J.A.; Scurlock, J.M.O.; Tieszen, L.L.; Castle, J.V.; Ojima, D.S.; Zhang, X.S.

2002-01-01

In many temperate and annual grasslands, above-ground net primary productivity (NPP) can be estimated by measuring peak above-ground biomass. Estimates of below-ground net primary productivity and, consequently, total net primary productivity, are more difficult. We addressed one of the three main objectives of the Global Primary Productivity Data Initiative for grassland systems to develop simple models or algorithms to estimate missing components of total system NPP. Any estimate of below-ground NPP (BNPP) requires an accounting of total root biomass, the percentage of living biomass and annual turnover of live roots. We derived a relationship using above-ground peak biomass and mean annual temperature as predictors of below-ground biomass (r2 = 0.54; P = 0.01). The percentage of live material was 0.6, based on published values. We used three different functions to describe root turnover: constant, a direct function of above-ground biomass, or as a positive exponential relationship with mean annual temperature. We tested the various models against a large database of global grassland NPP and the constant turnover and direct function models were approximately equally descriptive (r2 = 0.31 and 0.37), while the exponential function had a stronger correlation with the measured values (r2 = 0.40) and had a better fit than the other two models at the productive end of the BNPP gradient. When applied to extensive data we assembled from two grassland sites with reliable estimates of total NPP, the direct function was most effective, especially at lower productivity sites. We provide some caveats for its use in systems that lie at the extremes of the grassland gradient and stress that there are large uncertainties associated with measured and modelled estimates of BNPP.

A Physically Based Coupled Chemical and Physical Weathering Model for Simulating Soilscape Evolution

NASA Astrophysics Data System (ADS)

Willgoose, G. R.; Welivitiya, D.; Hancock, G. R.

2015-12-01

A critical missing link in existing landscape evolution models is a dynamic soil evolution models where soils co-evolve with the landform. Work by the authors over the last decade has demonstrated a computationally manageable model for soil profile evolution (soilscape evolution) based on physical weathering. For chemical weathering it is clear that full geochemistry models such as CrunchFlow and PHREEQC are too computationally intensive to be couplable to existing soilscape and landscape evolution models. This paper presents a simplification of CrunchFlow chemistry and physics that makes the task feasible, and generalises it for hillslope geomorphology applications. Results from this simplified model will be compared with field data for soil pedogenesis. Other researchers have previously proposed a number of very simple weathering functions (e.g. exponential, humped, reverse exponential) as conceptual models of the in-profile weathering process. The paper will show that all of these functions are possible for specific combinations of in-soil environmental, geochemical and geologic conditions, and the presentation will outline the key variables controlling which of these conceptual models can be realistic models of in-profile processes and under what conditions. The presentation will finish by discussing the coupling of this model with a physical weathering model, and will show sample results from our SSSPAM soilscape evolution model to illustrate the implications of including chemical weathering in the soilscape evolution model.

Statistics of Optical Coherence Tomography Data From Human Retina

PubMed Central

de Juan, Joaquín; Ferrone, Claudia; Giannini, Daniela; Huang, David; Koch, Giorgio; Russo, Valentina; Tan, Ou; Bruni, Carlo

2010-01-01

Optical coherence tomography (OCT) has recently become one of the primary methods for noninvasive probing of the human retina. The pseudoimage formed by OCT (the so-called B-scan) varies probabilistically across pixels due to complexities in the measurement technique. Hence, sensitive automatic procedures of diagnosis using OCT may exploit statistical analysis of the spatial distribution of reflectance. In this paper, we perform a statistical study of retinal OCT data. We find that the stretched exponential probability density function can model well the distribution of intensities in OCT pseudoimages. Moreover, we show a small, but significant correlation between neighbor pixels when measuring OCT intensities with pixels of about 5 µm. We then develop a simple joint probability model for the OCT data consistent with known retinal features. This model fits well the stretched exponential distribution of intensities and their spatial correlation. In normal retinas, fit parameters of this model are relatively constant along retinal layers, but varies across layers. However, in retinas with diabetic retinopathy, large spikes of parameter modulation interrupt the constancy within layers, exactly where pathologies are visible. We argue that these results give hope for improvement in statistical pathology-detection methods even when the disease is in its early stages. PMID:20304733

Granular convection observed by magnetic resonance imaging.

PubMed

Ehrichs, E E; Jaeger, H M; Karczmar, G S; Knight, J B; Kuperman, V Y; Nagel, S R

1995-03-17

Vibrations in a granular material can spontaneously produce convection rolls reminiscent of those seen in fluids. Magnetic resonance imaging provides a sensitive and noninvasive probe for the detection of these convection currents, which have otherwise been difficult to observe. A magnetic resonance imaging study of convection in a column of poppy seeds yielded data about the detailed shape of the convection rolls and the depth dependence of the convection velocity. The velocity was found to decrease exponentially with depth; a simple model for this behavior is presented here.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

A measurement-based performability model for a multiprocessor system

NASA Technical Reports Server (NTRS)

Ilsueh, M. C.; Iyer, Ravi K.; Trivedi, K. S.

1987-01-01

A measurement-based performability model based on real error-data collected on a multiprocessor system is described. Model development from the raw errror-data to the estimation of cumulative reward is described. Both normal and failure behavior of the system are characterized. The measured data show that the holding times in key operational and failure states are not simple exponential and that semi-Markov process is necessary to model the system behavior. A reward function, based on the service rate and the error rate in each state, is then defined in order to estimate the performability of the system and to depict the cost of different failure types and recovery procedures.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

The use of models to predict potential contamination aboard orbital vehicles

NASA Technical Reports Server (NTRS)

Boraas, Martin E.; Seale, Dianne B.

1989-01-01

A model of fungal growth on air-exposed, nonnutritive solid surfaces, developed for utilization aboard orbital vehicles is presented. A unique feature of this testable model is that the development of a fungal mycelium can facilitate its own growth by condensation of water vapor from its environment directly onto fungal hyphae. The fungal growth rate is limited by the rate of supply of volatile nutrients and fungal biomass is limited by either the supply of nonvolatile nutrients or by metabolic loss processes. The model discussed is structurally simple, but its dynamics can be quite complex. Biofilm accumulation can vary from a simple linear increase to sustained exponential growth, depending on the values of the environmental variable and model parameters. The results of the model are consistent with data from aquatic biofilm studies, insofar as the two types of systems are comparable. It is shown that the model presented is experimentally testable and provides a platform for the interpretation of observational data that may be directly relevant to the question of growth of organisms aboard the proposed Space Station.

Escape time, relaxation, and sticky states of a softened Henon-Heiles model: Low-frequency vibrational mode effects and glass relaxation

NASA Astrophysics Data System (ADS)

Toledo-Marín, J. Quetzalcóatl; Naumis, Gerardo G.

2018-04-01

Here we study the relaxation of a chain consisting of three masses joined by nonlinear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles system. By reducing the stiffness of one low-frequency vibrational mode, a faster relaxation is enabled. This is due to a reduction of the energy barrier heights along the softened normal mode as well as for a widening of the opening channels of the energy landscape in configurational space. The relaxation is for the most part exponential, and can be explained by a simple flux equation. Yet, for some initial conditions the relaxation follows as a power law, and in many cases there is a regime change from exponential to power-law decay. We pinpoint the initial conditions for the power-law decay, finding two regions of sticky states. For such states, quasiperiodic orbits are found since almost for all components of the initial momentum orientation, the system is trapped inside two pockets of configurational space. The softened Henon-Heiles model presented here is intended as the simplest model in order to understand the interplay of rigidity, nonlinear interactions and relaxation for nonequilibrium systems such as glass-forming melts or soft matter. Our softened system can be applied to model β relaxation in glasses and suggest that local reorientational jumps can have an exponential and a nonexponential contribution for relaxation, the latter due to asymmetric molecules sticking in cages for certain orientations.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

Science and Facebook: The same popularity law!

PubMed

Néda, Zoltán; Varga, Levente; Biró, Tamás S

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

Science and Facebook: The same popularity law!

PubMed Central

Varga, Levente; Biró, Tamás S.

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of “shares” for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4. PMID:28678796

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels

PubMed Central

Afshar, Saeed; George, Libin; Tapson, Jonathan; van Schaik, André; Hamilton, Tara J.

2014-01-01

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively “hiding” its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research. PMID:25505378

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels.

PubMed

Afshar, Saeed; George, Libin; Tapson, Jonathan; van Schaik, André; Hamilton, Tara J

2014-01-01

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively "hiding" its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research.

libprofit: Image creation from luminosity profiles

NASA Astrophysics Data System (ADS)

Robotham, A. S. G.; Taranu, D.; Tobar, R.

2016-12-01

libprofit is a C++ library for image creation based on different luminosity profiles. It offers fast and accurate two-dimensional integration for a useful number of profiles, including Sersic, Core-Sersic, broken-exponential, Ferrer, Moffat, empirical King, point-source and sky, with a simple mechanism for adding new profiles. libprofit provides a utility to read the model and profile parameters from the command-line and generate the corresponding image. It can output the resulting image as text values, a binary stream, or as a simple FITS file. It also provides a shared library exposing an API that can be used by any third-party application. R and Python interfaces are available: ProFit (ascl:1612.004) and PyProfit (ascl:1612.005).

Stretched exponential dynamics of coupled logistic maps on a small-world network

NASA Astrophysics Data System (ADS)

Mahajan, Ashwini V.; Gade, Prashant M.

2018-02-01

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in a coarse grained sense acts as an excellent order parameter to study this transition. We investigate the phase diagram by varying coupling strength and small-world rewiring probability p of nonlocal connections. The persistent region is a compact region bounded by two critical lines where band-merging crisis occurs. On one critical line, the persistent sites shows a nonexponential (stretched exponential) decay for all p while for another one, it shows crossover from nonexponential to exponential behavior as p → 1 . With an effectively antiferromagnetic coupling, coupling to two neighbors on either side leads to exchange frustration. Apart from exchange frustration, non-bipartite topology and nonlocal couplings in a small-world network could be a reason for anomalous relaxation. The distribution of trap times in asymptotic regime has a long tail as well. The dependence of temporal evolution of persistence on initial conditions is studied and a scaling form for persistence after waiting time is proposed. We present a simple possible model for this behavior.

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

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

Sharma, Sanjeev, E-mail: sanjeevsharma145@gmail.com; Kumar, Rajendra, E-mail: khundrakpam-ss@yahoo.com; Singh, Kh. S., E-mail: khundrakpam-ss@yahoo.com

A simple design of broadband one dimensional dielectric/semiconductor multilayer structure having refractive index profile of exponentially graded material has been proposed. The theoretical analysis shows that the proposed structure works as a perfect mirror within a certain wavelength range (1550 nm). In order to calculate the reflection properties a transfer matrix method (TMM) has been used. This property shows that binary graded photonic crystal structures have widened omnidirectional reflector (ODR) bandgap. Hence a exponentially graded photonic crystal structure can be used as a broadband optical reflector and the range of reflection can be tuned to any wavelength region by varying themore » refractive index profile of exponentially graded photonic crystal structure.« less

How exponential are FREDs?

NASA Astrophysics Data System (ADS)

Schaefer, Bradley E.; Dyson, Samuel E.

1996-08-01

A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.

Repairable-conditionally repairable damage model based on dual Poisson processes.

PubMed

Lind, B K; Persson, L M; Edgren, M R; Hedlöf, I; Brahme, A

2003-09-01

The advent of intensity-modulated radiation therapy makes it increasingly important to model the response accurately when large volumes of normal tissues are irradiated by controlled graded dose distributions aimed at maximizing tumor cure and minimizing normal tissue toxicity. The cell survival model proposed here is very useful and flexible for accurate description of the response of healthy tissues as well as tumors in classical and truly radiobiologically optimized radiation therapy. The repairable-conditionally repairable (RCR) model distinguishes between two different types of damage, namely the potentially repairable, which may also be lethal, i.e. if unrepaired or misrepaired, and the conditionally repairable, which may be repaired or may lead to apoptosis if it has not been repaired correctly. When potentially repairable damage is being repaired, for example by nonhomologous end joining, conditionally repairable damage may require in addition a high-fidelity correction by homologous repair. The induction of both types of damage is assumed to be described by Poisson statistics. The resultant cell survival expression has the unique ability to fit most experimental data well at low doses (the initial hypersensitive range), intermediate doses (on the shoulder of the survival curve), and high doses (on the quasi-exponential region of the survival curve). The complete Poisson expression can be approximated well by a simple bi-exponential cell survival expression, S(D) = e(-aD) + bDe(-cD), where the first term describes the survival of undamaged cells and the last term represents survival after complete repair of sublethal damage. The bi-exponential expression makes it easy to derive D(0), D(q), n and alpha, beta values to facilitate comparison with classical cell survival models.

Quantum decay model with exact explicit analytical solution

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Self-diffusion and microscopic dynamics in a gold-silicon liquid investigated with quasielastic neutron scattering

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

Evenson, Zach, E-mail: Zachary.Evenson@frm2.tum.de; Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt; Yang, Fan

2016-03-21

We use incoherent quasielastic neutron scattering to study the atomic dynamics of gold in a eutectic Au{sub 81}Si{sub 19} melt. Despite the glass-forming nature of this system, the gold self-diffusivity displays an Arrhenius behavior with a low activation energy characteristic of simple liquids. At high temperatures, long-range transport of gold atoms is well described by hydrodynamic theory with a simple exponential decay of the self-correlation function. On cooling towards the melting temperature, structural relaxation crosses over to a highly stretched exponential behavior. This suggests the onset of a heterogeneous dynamics, even in the equilibrium melt, and is indicative of amore » very fragile liquid.« less

Essays on the statistical mechanics of the labor market and implications for the distribution of earned income

NASA Astrophysics Data System (ADS)

Schneider, Markus P. A.

This dissertation contributes to two areas in economics: the understanding of the distribution of earned income and to Bayesian analysis of distributional data. Recently, physicists claimed that the distribution of earned income is exponential (see Yakovenko, 2009). The first chapter explores the perspective that the economy is a statistical mechanical system and the implication for labor market outcomes is considered critically. The robustness of the empirical results that lead to the physicists' claims, the significance of the exponential distribution in statistical mechanics, and the case for a conservation law in economics are discussed. The conclusion reached is that physicists' conception of the economy is too narrow even within their chosen framework, but that their overall approach is insightful. The dual labor market theory of segmented labor markets is invoked to understand why the observed distribution may be a mixture of distributional components, corresponding to different generating mechanisms described in Reich et al. (1973). The application of informational entropy in chapter II connects this work to Bayesian analysis and maximum entropy econometrics. The analysis follows E. T. Jaynes's treatment of Wolf's dice data, but is applied to the distribution of earned income based on CPS data. The results are calibrated to account for rounded survey responses using a simple simulation, and answer the graphical analyses by physicists. The results indicate that neither the income distribution of all respondents nor of the subpopulation used by physicists appears to be exponential. The empirics do support the claim that a mixture with exponential and log-normal distributional components ts the data. In the final chapter, a log-linear model is used to fit the exponential to the earned income distribution. Separating the CPS data by gender and marital status reveals that the exponential is only an appropriate model for a limited number of subpopulations, namely the never married and women. The estimated parameter for never-married men's incomes is significantly different from the parameter estimated for never-married women, implying that either the combined distribution is not exponential or that the individual distributions are not exponential. However, it substantiates the existence of a persistent gender income gap among the never-married. References: Reich, M., D. M. Gordon, and R. C. Edwards (1973). A Theory of Labor Market Segmentation. Quarterly Journal of Economics 63, 359-365. Yakovenko, V. M. (2009). Econophysics, Statistical Mechanics Approach to. In R. A. Meyers (Ed.), Encyclopedia of Complexity and System Science. Springer.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

Tensile properties of craniofacial tendons in the mature and aged zebrafish

PubMed Central

Shah, Rishita R.; Nerurkar, Nandan L.; Wang, Calvin; Galloway, Jenna L.

2015-01-01

The zebrafish Danio rerio is a powerful model for the study of development, regenerative biology, and human disease. However, the analysis of load-bearing tissues such as tendons and ligaments has been limited in this system. This is largely due to technical limitations that preclude accurate measurement of their mechanical properties. Here, we present a custom tensile testing system that applies nano-Newton scale forces to zebrafish tendons as small as 1 mm in length. Tendon properties were remarkably similar to mammalian tendons, including stress-strain nonlinearity and a linear modulus (515±152 MPa) that aligned closely with mammalian data. Additionally, a simple exponential constitutive law used to describe tendon mechanics was successfully fit to zebrafish tendons; the associated material constants agreed with literature values for mammalian tendons. Finally, mature and aged zebrafish comparisons revealed a significant decline in mechanical function with age. Based on the exponential constitutive model, age related changes were primarily caused by a reduction in nonlinearity (e.g. changes in collagen crimp or fiber recruitment). These findings demonstrate the utility of zebrafish as a model to study tendon biomechanics in health and disease. Moreover, these findings suggest that tendon mechanical behavior is highly conserved across vertebrates. PMID:25665155

Exponential rise of dynamical complexity in quantum computing through projections.

PubMed

Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

2014-10-10

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

The many faces of the quantum Liouville exponentials

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup; Schnittger, Jens

1994-01-01

First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.

Liver fibrosis: stretched exponential model outperforms mono-exponential and bi-exponential models of diffusion-weighted MRI.

PubMed

Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin

2018-07-01

To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p < 0.001), D t (0.575 ± 0.05, p < 0.001) and f (0.669 ± 0.04, p = 0.035). The parameters from stretched exponential DWI and D p showed higher areas under the ROC curve (AUCs) for determining significant fibrosis (≥F2) and cirrhosis (F = 4) than other parameters. However, D p showed significantly higher measurement variability (CoV, 74.6%) than DDC # (16.1%, p < 0.001) and α # (15.1%, p < 0.001). Stretched exponential DWI is a promising method for HF staging with good diagnostic performance and fewer b-value acquisitions, allowing shorter acquisition time. • Stretched exponential DWI provides a precise and accurate model for HF staging. • Stretched exponential DWI parameters are more reliable than D p from bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.

Performability modeling based on real data: A case study

NASA Technical Reports Server (NTRS)

Hsueh, M. C.; Iyer, R. K.; Trivedi, K. S.

1988-01-01

Described is a measurement-based performability model based on error and resource usage data collected on a multiprocessor system. A method for identifying the model structure is introduced and the resulting model is validated against real data. Model development from the collection of raw data to the estimation of the expected reward is described. Both normal and error behavior of the system are characterized. The measured data show that the holding times in key operational and error states are not simple exponentials and that a semi-Markov process is necessary to model system behavior. A reward function, based on the service rate and the error rate in each state, is then defined in order to estimate the performability of the system and to depict the cost of apparent types of errors.

Performability modeling based on real data: A casestudy

NASA Technical Reports Server (NTRS)

Hsueh, M. C.; Iyer, R. K.; Trivedi, K. S.

1987-01-01

Described is a measurement-based performability model based on error and resource usage data collected on a multiprocessor system. A method for identifying the model structure is introduced and the resulting model is validated against real data. Model development from the collection of raw data to the estimation of the expected reward is described. Both normal and error behavior of the system are characterized. The measured data show that the holding times in key operational and error states are not simple exponentials and that a semi-Markov process is necessary to model the system behavior. A reward function, based on the service rate and the error rate in each state, is then defined in order to estimate the performability of the system and to depict the cost of different types of errors.

Modeling the Pre-Industrial Roots of Modern Super-Exponential Population Growth

PubMed Central

Stutz, Aaron Jonas

2014-01-01

To Malthus, rapid human population growth—so evident in 18th Century Europe—was obviously unsustainable. In his Essay on the Principle of Population, Malthus cogently argued that environmental and socioeconomic constraints on population rise were inevitable. Yet, he penned his essay on the eve of the global census size reaching one billion, as nearly two centuries of super-exponential increase were taking off. Introducing a novel extension of J. E. Cohen's hallmark coupled difference equation model of human population dynamics and carrying capacity, this article examines just how elastic population growth limits may be in response to demographic change. The revised model involves a simple formalization of how consumption costs influence carrying capacity elasticity over time. Recognizing that complex social resource-extraction networks support ongoing consumption-based investment in family formation and intergenerational resource transfers, it is important to consider how consumption has impacted the human environment and demography—especially as global population has become very large. Sensitivity analysis of the consumption-cost model's fit to historical population estimates, modern census data, and 21st Century demographic projections supports a critical conclusion. The recent population explosion was systemically determined by long-term, distinctly pre-industrial cultural evolution. It is suggested that modern globalizing transitions in technology, susceptibility to infectious disease, information flows and accumulation, and economic complexity were endogenous products of much earlier biocultural evolution of family formation's embeddedness in larger, hierarchically self-organizing cultural systems, which could potentially support high population elasticity of carrying capacity. Modern super-exponential population growth cannot be considered separately from long-term change in the multi-scalar political economy that connects family formation and intergenerational resource transfers to wider institutions and social networks. PMID:25141019

The Analysis of Fluorescence Decay by a Method of Moments

PubMed Central

Isenberg, Irvin; Dyson, Robert D.

1969-01-01

The fluorescence decay of the excited state of most biopolymers, and biopolymer conjugates and complexes, is not, in general, a simple exponential. The method of moments is used to establish a means of analyzing such multi-exponential decays. The method is tested by the use of computer simulated data, assuming that the limiting error is determined by noise generated by a pseudorandom number generator. Multi-exponential systems with relatively closely spaced decay constants may be successfully analyzed. The analyses show the requirements, in terms of precision, that data must meet. The results may be used both as an aid in the design of equipment and in the analysis of data subsequently obtained. PMID:5353139

Andreev bound states. Some quasiclassical reflections

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

Lin, Y., E-mail: yiriolin@illinois.edu; Leggett, A. J.

2014-12-15

We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for “normal” reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.

Self-excited electrostatic pendulum showing electrohydrodynamic-force-induced oscillation

NASA Astrophysics Data System (ADS)

Stephan, Karl D.; Hernandez Guerrero, José M.

2017-12-01

The electrohydrodynamic (EHD) effect ("ion wind") associated with corona discharges in air has been extensively investigated and modeled. We present a simple experiment that shows how both the magnitude and direction of EHD forces can change in such a way as to impart energy continuously to an oscillating electrostatic pendulum. The amplitude of oscillations of an electrostatic pendulum subject to EHD forces can grow approximately exponentially over a period of minutes, and we describe a qualitative theory to account for this effect, along with implications of these experiments for theories of ball lightning.

Andreev bound states. Some quasiclassical reflections

NASA Astrophysics Data System (ADS)

Lin, Y.; Leggett, A. J.

2014-12-01

We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for "normal" reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.

Water quality trend analysis for the Karoon River in Iran.

PubMed

Naddafi, K; Honari, H; Ahmadi, M

2007-11-01

The Karoon River basin, with a basin area of 67,000 km(2), is located in the southern part of Iran. Monthly measurements of the discharge and the water quality variables have been monitored at the Gatvand and Khorramshahr stations of the Karoon River on a monthly basis for the period 1967-2005 and 1969-2005 for Gatvand and Khorramshahr stations, respectively. In this paper the time series of monthly values of water quality parameters and the discharge were analyzed using statistical methods and the existence of trends and the evaluation of the best fitted models were performed. The Kolmogorov-Smirnov test was used to select the theoretical distribution which best fitted the data. Simple regression was used to examine the concentration-time relationships. The concentration-time relationships showed better correlation in Khorramshahr station than that of Gatvand station. The exponential model expresses better concentration - time relationships in Khorramshahr station, but in Gatvand station the logarithmic model is more fitted. The correlation coefficients are positive for all of the variables in Khorramshahr station also in Gatvand station all of the variables are positive except magnesium (Mg2+), bicarbonates (HCO3-) and temporary hardness which shows a decreasing relationship. The logarithmic and the exponential models describe better the concentration-time relationships for two stations.

Does the Australian desert ant Melophorus bagoti approximate a Lévy search by an intrinsic bi-modal walk?

PubMed

Reynolds, Andy M; Schultheiss, Patrick; Cheng, Ken

2014-01-07

We suggest that the Australian desert ant Melophorus bagoti approximates a Lévy search pattern by using an intrinsic bi-exponential walk and does so when a Lévy search pattern is advantageous. When attempting to locate its nest, M. bagoti adopt a stereotypical search pattern. These searches begin at the location where the ant expects to find the nest, and comprise loops that start and end at this location, and are directed in different azimuthal directions. Loop lengths are exponentially distributed when searches are in visually familiar surroundings and are well described by a mixture of two exponentials when searches are in unfamiliar landscapes. The latter approximates a power-law distribution, the hallmark of a Lévy search. With the aid of a simple analytically tractable theory, we show that an exponential loop-length distribution is advantageous when the distance to the nest can be estimated with some certainty and that a bi-exponential distribution is advantageous when there is considerable uncertainty regarding the nest location. The best bi-exponential search patterns are shown to be those that come closest to approximating advantageous Lévy looping searches. The bi-exponential search patterns of M. bagoti are found to approximate advantageous Lévy search patterns. Copyright © 2013. Published by Elsevier Ltd.

A Simple Model of Cirrus Horizontal Inhomogeneity and Cloud Fraction

NASA Technical Reports Server (NTRS)

Smith, Samantha A.; DelGenio, Anthony D.

1998-01-01

A simple model of horizontal inhomogeneity and cloud fraction in cirrus clouds has been formulated on the basis that all internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of the ice water mixing ratio (and extinction) and the normalized variability of cloud depth. Using radar cloud depth data as input, the model reproduced well the in-cloud ice water mixing ratio histograms obtained from horizontal runs during the FIRE2 cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud fraction decreased to exponential distributions which peaked at the lowest nonzero ice value for cloud fractions below 90%. Cloud fractions predicted by the model were always within 28% of the observed value. The predicted average ice water mixing ratios were within 34% of the observed values. This model could be used in a GCM to produce the ice mixing ratio probability distribution function and to estimate cloud fraction. It only requires basic meteorological parameters, the depth of the saturated layer and the standard deviation of cloud depth as input.

Simple model for multiple-choice collective decision making

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Lucas, Andrew

2014-11-01

We describe a simple model of heterogeneous, interacting agents making decisions between n ≥2 discrete choices. For a special class of interactions, our model is the mean field description of random field Potts-like models and is effectively solved by finding the extrema of the average energy E per agent. In these cases, by studying the propagation of decision changes via avalanches, we argue that macroscopic dynamics is well captured by a gradient flow along E . We focus on the permutation symmetric case, where all n choices are (on average) the same, and spontaneous symmetry breaking (SSB) arises purely from cooperative social interactions. As examples, we show that bimodal heterogeneity naturally provides a mechanism for the spontaneous formation of hierarchies between decisions and that SSB is a preferred instability to discontinuous phase transitions between two symmetric points. Beyond the mean field limit, exponentially many stable equilibria emerge when we place this model on a graph of finite mean degree. We conclude with speculation on decision making with persistent collective oscillations. Throughout the paper, we emphasize analogies between methods of solution to our model and common intuition from diverse areas of physics, including statistical physics and electromagnetism.

A model for complex flows of soft glassy materials with application to flows through fixed fiber beds

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

Sarkar, Arijit; Koch, Donald L., E-mail: dlk15@cornell.edu

2015-11-15

The soft glassy rheology (SGR) model has successfully described the time dependent simple shear rheology of a broad class of complex fluids including foams, concentrated emulsions, colloidal glasses, and solvent-free nanoparticle-organic hybrid materials (NOHMs). The model considers a distribution of mesoscopic fluid elements that hop from trap to trap at a rate which is enhanced by the work done to strain the fluid element. While an SGR fluid has a broad exponential distribution of trap energies, the rheology of NOHMs is better described by a narrower energy distribution and we consider both types of trap energy distributions in this study.more » We introduce a tensorial version of these models with a hopping rate that depends on the orientation of the element relative to the mean stress field, allowing a range of relative strengths of the extensional and simple shear responses of the fluid. As an application of these models we consider the flow of a soft glassy material through a dilute fixed bed of fibers. The dilute fixed bed exhibits a range of local linear flows which alternate in a chaotic manner with time in a Lagrangian reference frame. It is amenable to an analytical treatment and has been used to characterize the strong flow response of many complex fluids including fiber suspensions, dilute polymer solutions and emulsions. We show that the accumulated strain in the fluid elements has an abrupt nonlinear growth at a Deborah number of order one in a manner similar to that observed for polymer solutions. The exponential dependence of the hopping rate on strain leads to a fluid element deformation that grows logarithmically with Deborah number at high Deborah numbers. SGR fluids having a broad range of trap energies flowing through fixed beds can exhibit a range of rheological behaviors at small Deborah numbers ranging from a yield stress, to a power law response and finally to Newtonian behavior.« less

Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Network structures sustained by internal links and distributed lifetime of old nodes in stationary state of number of nodes

NASA Astrophysics Data System (ADS)

Ikeda, Nobutoshi

2017-12-01

In network models that take into account growth properties, deletion of old nodes has a serious impact on degree distributions, because old nodes tend to become hub nodes. In this study, we aim to provide a simple explanation for why hubs can exist even in conditions where the number of nodes is stationary due to the deletion of old nodes. We show that an exponential increase in the degree of nodes is a natural consequence of the balance between the deletion and addition of nodes as long as a preferential attachment mechanism holds. As a result, the largest degree is determined by the magnitude relationship between the time scale of the exponential growth of degrees and lifetime of old nodes. The degree distribution exhibits a power-law form ˜ k -γ with exponent γ = 1 when the lifetime of nodes is constant. However, various values of γ can be realized by introducing distributed lifetime of nodes.

The topology of large Open Connectome networks for the human brain.

PubMed

Gastner, Michael T; Ódor, Géza

2016-06-07

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to nodes and edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension D and the small-world coefficient σ of these networks. While σ suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

The topology of large Open Connectome networks for the human brain

NASA Astrophysics Data System (ADS)

Gastner, Michael T.; Ódor, Géza

2016-06-01

The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to nodes and edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension D and the small-world coefficient σ of these networks. While σ suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

Turbulent particle transport in streams: can exponential settling be reconciled with fluid mechanics?

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances. Copyright © 2012 Elsevier Ltd. All rights reserved.

Value of the distant future: Model-independent results

NASA Astrophysics Data System (ADS)

Katz, Yuri A.

2017-01-01

This paper shows that the model-independent account of correlations in an interest rate process or a log-consumption growth process leads to declining long-term tails of discount curves. Under the assumption of an exponentially decaying memory in fluctuations of risk-free real interest rates, I derive the analytical expression for an apt value of the long run discount factor and provide a detailed comparison of the obtained result with the outcome of the benchmark risk-free interest rate models. Utilizing the standard consumption-based model with an isoelastic power utility of the representative economic agent, I derive the non-Markovian generalization of the Ramsey discounting formula. Obtained analytical results allowing simple calibration, may augment the rigorous cost-benefit and regulatory impact analysis of long-term environmental and infrastructure projects.

Robust master-slave synchronization for general uncertain delayed dynamical model based on adaptive control scheme.

PubMed

Wang, Tianbo; Zhou, Wuneng; Zhao, Shouwei; Yu, Weiqin

2014-03-01

In this paper, the robust exponential synchronization problem for a class of uncertain delayed master-slave dynamical system is investigated by using the adaptive control method. Different from some existing master-slave models, the considered master-slave system includes bounded unmodeled dynamics. In order to compensate the effect of unmodeled dynamics and effectively achieve synchronization, a novel adaptive controller with simple updated laws is proposed. Moreover, the results are given in terms of LMIs, which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the method. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Coagulation-Fragmentation Model for Animal Group-Size Statistics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.

2017-04-01

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent -2/3 for small size to -3/2 for large size, with an exponential cutoff.

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

NASA Astrophysics Data System (ADS)

Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

2012-08-01

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining significant differences between the three approaches. All together, a full MRS forward response is calculated in about 20 s and scales so that on 10 processors the calculation time is reduced to about 3-4 s. The proposed approach is examined through synthetic data and through a field example, which demonstrate the capability of the scheme. The results of the field example agree well the information from an in-site borehole.

Responses of single cells in cat visual cortex to prolonged stimulus movement: neural correlates of visual aftereffects.

PubMed

Vautin, R G; Berkley, M A

1977-09-01

1. The activity of single cortical cells in area 17 of anesthetized and unanesthetized cats was recorded in response to prolonged stimulation with moving stimuli. 2. Under the appropriate conditions, all cells observed showed a progressive response decrement during the stimulation period, regardless of cell classification, i.e., simple, complex, or hypercomplex. 3. The observed response decrement was shown to be largely cortical in origin and could be adequately described with an exponential function of the form R = Rf +(R1-Rf)e-t/T. Time constants derived from such calculations yielded values ranging from 1.92 to 12.45 s under conditions of optimal-stimulation. 4. Most cells showed poststimulation effects, usually a brief period of reduced responsiveness that recovered exponentially. Recovery was essentially complete in about 5-35 s. 5. The degree to which stimuli were effective at inducing response was shown to have significant effects on the magnitude of the response decrement. 6. Several cells showed neural patterns of response and recovery that suggested the operation of intracortical inhibitory mechanisms. 7. A simple two-process model that adequately describes the behavior of all the studied cells is presented. 8. Because the properties of the cells studied correlate well with human psychophysical measures of contour and movement adaptation and recovery, a causal relationship to similar neural mechanisms in humans is suggested.

Cluster-cluster aggregation with particle replication and chemotaxy: a simple model for the growth of animal cells in culture

NASA Astrophysics Data System (ADS)

Alves, S. G.; Martins, M. L.

2010-09-01

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and in vitro drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture.

λ-Repressor Oligomerization Kinetics at High Concentrations Using Fluorescence Correlation Spectroscopy in Zero-Mode Waveguides

PubMed Central

Samiee, K. T.; Foquet, M.; Guo, L.; Cox, E. C.; Craighead, H. G.

2005-01-01

Fluorescence correlation spectroscopy (FCS) has demonstrated its utility for measuring transport properties and kinetics at low fluorophore concentrations. In this article, we demonstrate that simple optical nanostructures, known as zero-mode waveguides, can be used to significantly reduce the FCS observation volume. This, in turn, allows FCS to be applied to solutions with significantly higher fluorophore concentrations. We derive an empirical FCS model accounting for one-dimensional diffusion in a finite tube with a simple exponential observation profile. This technique is used to measure the oligomerization of the bacteriophage λ repressor protein at micromolar concentrations. The results agree with previous studies utilizing conventional techniques. Additionally, we demonstrate that the zero-mode waveguides can be used to assay biological activity by measuring changes in diffusion constant as a result of ligand binding. PMID:15613638

[Litter decomposition and nutrient release in Acacia mangium plantations established on degraded soils of Colombia].

PubMed

Castellanos-Barliza, Jeiner; León Peláez, Juan Diego

2011-03-01

Several factors control the decomposition in terrestrial ecosystems such as humidity, temperature, quality of litter and microbial activity. We investigated the effects of rainfall and soil plowing prior to the establishment of Acacia mangium plantations, using the litterbag technique, during a six month period, in forests plantations in Bajo Cauca region, Colombia. The annual decomposition constants (k) of simple exponential model, oscillated between 1.24 and 1.80, meanwhile k1 y k2 decomposition constants of double exponential model were 0.88-1.81 and 0.58-7.01. At the end of the study, the mean residual dry matter (RDM) was 47% of the initial value for the three sites. We found a slow N, Ca and Mg release pattern from the A. mangium leaf litter, meanwhile, phosphorus (P) showed a dominant immobilization phase, suggesting its low availability in soils. Chemical leaf litter quality parameters (e.g. N and P concentrations, C/N, N/P ratios and phenols content) showed an important influence on decomposition rates. The results of this study indicated that rainfall plays an important role on the decomposition process, but not soil plowing.

Multi-Mode Analysis of Dual Ridged Waveguide Systems for Material Characterization

DTIC Science & Technology

2015-09-17

characterization is the process of determining the dielectric, magnetic, and magnetoelectric properties of a material. For simple (i.e., linear ...field expressions in terms of elementary functions (sines, cosines, exponentials and Bessel functions) and corresponding propagation constants of the...with material parameters 0 and µ0. • The MUT is simple ( linear , isotropic, homogeneous), and the sample has a uniform thickness. • The waveguide

Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies

PubMed Central

Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.

2016-01-01

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373

Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria

PubMed Central

Hui, Sheng; Silverman, Josh M; Chen, Stephen S; Erickson, David W; Basan, Markus; Wang, Jilong; Hwa, Terence; Williamson, James R

2015-01-01

A central aim of cell biology was to understand the strategy of gene expression in response to the environment. Here, we study gene expression response to metabolic challenges in exponentially growing Escherichia coli using mass spectrometry. Despite enormous complexity in the details of the underlying regulatory network, we find that the proteome partitions into several coarse-grained sectors, with each sector's total mass abundance exhibiting positive or negative linear relations with the growth rate. The growth rate-dependent components of the proteome fractions comprise about half of the proteome by mass, and their mutual dependencies can be characterized by a simple flux model involving only two effective parameters. The success and apparent generality of this model arises from tight coordination between proteome partition and metabolism, suggesting a principle for resource allocation in proteome economy of the cell. This strategy of global gene regulation should serve as a basis for future studies on gene expression and constructing synthetic biological circuits. Coarse graining may be an effective approach to derive predictive phenomenological models for other ‘omics’ studies. PMID:25678603

Predator prey oscillations in a simple cascade model of drift wave turbulence

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

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

DBI-essence

NASA Astrophysics Data System (ADS)

Martin, Jérôme; Yamaguchi, Masahide

2008-06-01

Models where the dark energy is a scalar field with a nonstandard Dirac-Born-Infeld (DBI) kinetic term are investigated. Scaling solutions are studied and proven to be attractors. The corresponding shape of the brane tension and of the potential is also determined and found to be, as in the standard case, either exponentials or power law of the DBI field. In these scenarios, in contrast to the standard situation, the vacuum expectation value of the field at small redshifts can be small in comparison to the Planck mass which could be an advantage from the model building point of view. This situation arises when the present-day value of the Lorentz factor is large, this property being per se interesting. Serious shortcomings are also present such as the fact that, for simple potentials, the equation of state appears to be too far from the observational favored value -1. Another problem is that, although simple stringy-inspired models precisely lead to the power-law shape that has been shown to possess a tracking behavior, the power index turns out to have the wrong sign. Possible solutions to these issues are discussed.

Seeing How Money Grows.

ERIC Educational Resources Information Center

Metz, James

2001-01-01

Describes an activity designed to help students connect the ideas of linear growth and exponential growth through graphs of the future value of accounts that earn simple interest and accounts that earn compound interest. Includes worksheets and solutions. (KHR)

Evo-SETI SCALE to measure Life on Exoplanets

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2016-04-01

Darwinian Evolution over the last 3.5 billion years was an increase in the number of living species from 1 (RNA?) to the current 50 million. This increasing trend in time looks like being exponential, but one may not assume an exactly exponential curve since many species went extinct in the past, even in mass extinctions. Thus, the simple exponential curve must be replaced by a stochastic process having an exponential mean value. Borrowing from financial mathematics (;Black-Scholes models;), this ;exponential; stochastic process is called Geometric Brownian Motion (GBM), and its probability density function (pdf) is a lognormal (not a Gaussian) (Proof: see ref. Maccone [3], Chapter 30, and ref. Maccone [4]). Lognormal also is the pdf of the statistical number of communicating ExtraTerrestrial (ET) civilizations in the Galaxy at a certain fixed time, like a snapshot: this result was found in 2008 by this author as his solution to the Statistical Drake Equation of SETI (Proof: see ref. Maccone [1]). Thus, the GBM of Darwinian Evolution may also be regarded as the extension in time of the Statistical Drake equation (Proof: see ref. Maccone [4]). But the key step ahead made by this author in his Evo-SETI (Evolution and SETI) mathematical model was to realize that LIFE also is just a b-lognormal in time: every living organism (a cell, a human, a civilization, even an ET civilization) is born at a certain time b (;birth;), grows up to a peak p (with an ascending inflexion point in between, a for adolescence), then declines from p to s (senility, i.e. descending inflexion point) and finally declines linearly and dies at a final instant d (death). In other words, the infinite tail of the b-lognormal was cut away and replaced by just a straight line between s and d, leading to simple mathematical formulae (;History Formulae;) allowing one to find this ;finite b-lognormal; when the three instants b, s, and d are assigned. Next the crucial Peak-Locus Theorem comes. It means that the GBM exponential may be regarded as the geometric locus of all the peaks of a one-parameter (i.e. the peak time p) family of b-lognormals. Since b-lognormals are pdf-s, the area under each of them always equals 1 (normalization condition) and so, going from left to right on the time axis, the b-lognormals become more and more ;peaky;, and so they last less and less in time. This is precisely what happened in human history: civilizations that lasted millennia (like Ancient Greece and Rome) lasted just centuries (like the Italian Renaissance and Portuguese, Spanish, French, British and USA Empires) but they were more and more advanced in the ;level of civilization;. This ;level of civilization; is what physicists call ENTROPY. Also, in refs. Maccone [3] and [4], this author proved that, for all GBMs, the (Shannon) Entropy of the b-lognormals in his Peak-Locus Theorem grows LINEARLY in time. The Molecular Clock, well known to geneticists since 50 years, shows that the DNA base-substitutions occur LINEARLY in time since they are neutral with respect to Darwinian selection. In simple words: DNA evolved by obeying the laws of quantum physics only (microscopic laws) and not by obeying assumed ;Darwinian selection laws; (macroscopic laws). This is Kimura's neutral theory of molecular evolution. The conclusion is that the Molecular Clock and the b-lognormal Entropy are the same thing. At last, we reach the new, original result justifying the publication of this paper. On exoplanets, molecular evolution is proceeding at about the same rate as it did proceed on Earth: rather independently of the physical conditions of the exoplanet, if the DNA had the possibility to evolve in water initially. Thus, Evo-Entropy, i.e. the (Shannon) Entropy of the generic b-lognormal of the Peak-Locus Theorem, provides the Evo-SETI SCALE to measure the evolution of life on exoplanets.

Singularities in loop quantum cosmology.

PubMed

Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

2008-12-19

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

Photoconductivity response time in amorphous semiconductors

NASA Astrophysics Data System (ADS)

Adriaenssens, G. J.; Baranovskii, S. D.; Fuhs, W.; Jansen, J.; Öktü, Ö.

1995-04-01

The photoconductivity response time of amorphous semiconductors is examined theoretically on the basis of standard definitions for free- and trapped-carrier lifetimes, and experimentally for a series of a-Si1-xCx:H alloys with x<0.1. Particular attention is paid to its dependence on carrier generation rate and temperature. As no satisfactory agreement between models and experiments emerges, a simple theory is developed that can account for the experimental observations on the basis of the usual multiple-trappping ideas, provided a small probability of direct free-carrier recombination is included. The theory leads to a stretched-exponential photocurrent decay.

A Modified Tri-Exponential Model for Multi-b-value Diffusion-Weighted Imaging: A Method to Detect the Strictly Diffusion-Limited Compartment in Brain

PubMed Central

Zeng, Qiang; Shi, Feina; Zhang, Jianmin; Ling, Chenhan; Dong, Fei; Jiang, Biao

2018-01-01

Purpose: To present a new modified tri-exponential model for diffusion-weighted imaging (DWI) to detect the strictly diffusion-limited compartment, and to compare it with the conventional bi- and tri-exponential models. Methods: Multi-b-value diffusion-weighted imaging (DWI) with 17 b-values up to 8,000 s/mm2 were performed on six volunteers. The corrected Akaike information criterions (AICc) and squared predicted errors (SPE) were calculated to compare these three models. Results: The mean f0 values were ranging 11.9–18.7% in white matter ROIs and 1.2–2.7% in gray matter ROIs. In all white matter ROIs: the AICcs of the modified tri-exponential model were the lowest (p < 0.05 for five ROIs), indicating the new model has the best fit among these models; the SPEs of the bi-exponential model were the highest (p < 0.05), suggesting the bi-exponential model is unable to predict the signal intensity at ultra-high b-value. The mean ADCvery−slow values were extremely low in white matter (1–7 × 10−6 mm2/s), but not in gray matter (251–445 × 10−6 mm2/s), indicating that the conventional tri-exponential model fails to represent a special compartment. Conclusions: The strictly diffusion-limited compartment may be an important component in white matter. The new model fits better than the other two models, and may provide additional information. PMID:29535599

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

Model of Yield Response of Corn to Plant Population and Absorption of Solar Energy

PubMed Central

Overman, Allen R.; Scholtz, Richard V.

2011-01-01

Biomass yield of agronomic crops is influenced by a number of factors, including crop species, soil type, applied nutrients, water availability, and plant population. This article is focused on dependence of biomass yield (Mg ha−1 and g plant−1) on plant population (plants m−2). Analysis includes data from the literature for three independent studies with the warm-season annual corn (Zea mays L.) grown in the United States. Data are analyzed with a simple exponential mathematical model which contains two parameters, viz. Ym (Mg ha−1) for maximum yield at high plant population and c (m2 plant−1) for the population response coefficient. This analysis leads to a new parameter called characteristic plant population, xc = 1/c (plants m−2). The model is shown to describe the data rather well for the three field studies. In one study measurements were made of solar radiation at different positions in the plant canopy. The coefficient of absorption of solar energy was assumed to be the same as c and provided a physical basis for the exponential model. The three studies showed no definitive peak in yield with plant population, but generally exhibited asymptotic approach to maximum yield with increased plant population. Values of xc were very similar for the three field studies with the same crop species. PMID:21297960

Using soil properties to predict in vivo bioavailability of lead in soils.

PubMed

Wijayawardena, M A Ayanka; Naidu, Ravi; Megharaj, Mallavarapu; Lamb, Dane; Thavamani, Palanisami; Kuchel, Tim

2015-11-01

Soil plays a significant role in controlling the potential bioavailability of contaminants in the environment. In this study, eleven soils were used to investigate the relationship between soil properties and relative bioavailability (RB) of lead (Pb). To minimise the effect of source of Pb on in vivo bioavailability, uncontaminated study soils were spiked with 1500 mg Pb/kg soil and aged for 10-12 months prior to investigating the relationships between soil properties and in vivo RB of Pb using swine model. The biological responses to oral administration of Pb in aqueous phase or as spiked soils were compared by applying a two-compartment pharmacokinetic model to blood Pb concentration. The study revealed that RB of Pb from aged soils ranged from 30±9% to 83±7%. The very different RB of Pb in these soils was attributed to variations in the soils' physico-chemical properties. This was established using sorption studies showing: firstly, Freundlich partition coefficients that ranged from 21 to 234; and secondly, a strongly significant (R(2)=0.94, P<0.001) exponential relationship between RB and Freundlich partition coefficient (Kd). This simple exponential model can be used to predict relative bioavailability of Pb in contaminated soils. To the best of our knowledge, this is the first such model derived using sorption partition coefficient to predict the relative bioavailability of Pb. Copyright © 2015 Elsevier Ltd. All rights reserved.

A stochastic step model of replicative senescence explains ROS production rate in ageing cell populations.

PubMed

Lawless, Conor; Jurk, Diana; Gillespie, Colin S; Shanley, Daryl; Saretzki, Gabriele; von Zglinicki, Thomas; Passos, João F

2012-01-01

Increases in cellular Reactive Oxygen Species (ROS) concentration with age have been observed repeatedly in mammalian tissues. Concomitant increases in the proportion of replicatively senescent cells in ageing mammalian tissues have also been observed. Populations of mitotic human fibroblasts cultured in vitro, undergoing transition from proliferation competence to replicative senescence are useful models of ageing human tissues. Similar exponential increases in ROS with age have been observed in this model system. Tracking individual cells in dividing populations is difficult, and so the vast majority of observations have been cross-sectional, at the population level, rather than longitudinal observations of individual cells.One possible explanation for these observations is an exponential increase in ROS in individual fibroblasts with time (e.g. resulting from a vicious cycle between cellular ROS and damage). However, we demonstrate an alternative, simple hypothesis, equally consistent with these observations which does not depend on any gradual increase in ROS concentration: the Stochastic Step Model of Replicative Senescence (SSMRS). We also demonstrate that, consistent with the SSMRS, neither proliferation-competent human fibroblasts of any age, nor populations of hTERT overexpressing human fibroblasts passaged beyond the Hayflick limit, display high ROS concentrations. We conclude that longitudinal studies of single cells and their lineages are now required for testing hypotheses about roles and mechanisms of ROS increase during replicative senescence.

A Stochastic Step Model of Replicative Senescence Explains ROS Production Rate in Ageing Cell Populations

PubMed Central

Lawless, Conor; Jurk, Diana; Gillespie, Colin S.; Shanley, Daryl; Saretzki, Gabriele; von Zglinicki, Thomas; Passos, João F.

2012-01-01

Increases in cellular Reactive Oxygen Species (ROS) concentration with age have been observed repeatedly in mammalian tissues. Concomitant increases in the proportion of replicatively senescent cells in ageing mammalian tissues have also been observed. Populations of mitotic human fibroblasts cultured in vitro, undergoing transition from proliferation competence to replicative senescence are useful models of ageing human tissues. Similar exponential increases in ROS with age have been observed in this model system. Tracking individual cells in dividing populations is difficult, and so the vast majority of observations have been cross-sectional, at the population level, rather than longitudinal observations of individual cells. One possible explanation for these observations is an exponential increase in ROS in individual fibroblasts with time (e.g. resulting from a vicious cycle between cellular ROS and damage). However, we demonstrate an alternative, simple hypothesis, equally consistent with these observations which does not depend on any gradual increase in ROS concentration: the Stochastic Step Model of Replicative Senescence (SSMRS). We also demonstrate that, consistent with the SSMRS, neither proliferation-competent human fibroblasts of any age, nor populations of hTERT overexpressing human fibroblasts passaged beyond the Hayflick limit, display high ROS concentrations. We conclude that longitudinal studies of single cells and their lineages are now required for testing hypotheses about roles and mechanisms of ROS increase during replicative senescence. PMID:22359661

Investigation of hyperelastic models for nonlinear elastic behavior of demineralized and deproteinized bovine cortical femur bone.

PubMed

Hosseinzadeh, M; Ghoreishi, M; Narooei, K

2016-06-01

In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Measurement-based reliability/performability models

NASA Technical Reports Server (NTRS)

Hsueh, Mei-Chen

1987-01-01

Measurement-based models based on real error-data collected on a multiprocessor system are described. Model development from the raw error-data to the estimation of cumulative reward is also described. A workload/reliability model is developed based on low-level error and resource usage data collected on an IBM 3081 system during its normal operation in order to evaluate the resource usage/error/recovery process in a large mainframe system. Thus, both normal and erroneous behavior of the system are modeled. The results provide an understanding of the different types of errors and recovery processes. The measured data show that the holding times in key operational and error states are not simple exponentials and that a semi-Markov process is necessary to model the system behavior. A sensitivity analysis is performed to investigate the significance of using a semi-Markov process, as opposed to a Markov process, to model the measured system.

A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

NASA Technical Reports Server (NTRS)

Klein, Vladislav; Noderer, Keith D.

1994-01-01

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.

Interpretable Deep Models for ICU Outcome Prediction

PubMed Central

Che, Zhengping; Purushotham, Sanjay; Khemani, Robinder; Liu, Yan

2016-01-01

Exponential surge in health care data, such as longitudinal data from electronic health records (EHR), sensor data from intensive care unit (ICU), etc., is providing new opportunities to discover meaningful data-driven characteristics and patterns ofdiseases. Recently, deep learning models have been employedfor many computational phenotyping and healthcare prediction tasks to achieve state-of-the-art performance. However, deep models lack interpretability which is crucial for wide adoption in medical research and clinical decision-making. In this paper, we introduce a simple yet powerful knowledge-distillation approach called interpretable mimic learning, which uses gradient boosting trees to learn interpretable models and at the same time achieves strong prediction performance as deep learning models. Experiment results on Pediatric ICU dataset for acute lung injury (ALI) show that our proposed method not only outperforms state-of-the-art approaches for morality and ventilator free days prediction tasks but can also provide interpretable models to clinicians. PMID:28269832

Recursive solution of number of reachable states of a simple subclass of FMS

NASA Astrophysics Data System (ADS)

Chao, Daniel Yuh

2014-03-01

This paper aims to compute the number of reachable (forbidden, live and deadlock) states for flexible manufacturing systems (FMS) without the construction of reachability graph. The problem is nontrivial and takes, in general, an exponential amount of time to solve. Hence, this paper focusses on a simple version of Systems of Simple Sequential Processes with Resources (S3PR), called kth-order system, where each resource place holds one token to be shared between two processes. The exact number of reachable (forbidden, live and deadlock) states can be computed recursively.

Understanding the persistence of measles: reconciling theory, simulation and observation.

PubMed Central

Keeling, Matt J; Grenfell, Bryan T

2002-01-01

Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'. PMID:11886620

A comparative assessment of preclinical chemotherapeutic response of tumors using quantitative non-Gaussian diffusion MRI

PubMed Central

Xu, Junzhong; Li, Ke; Smith, R. Adam; Waterton, John C.; Zhao, Ping; Ding, Zhaohua; Does, Mark D.; Manning, H. Charles; Gore, John C.

2016-01-01

Background Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear. Methods Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models. Results All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred. Conclusion Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work. PMID:27919785

Apparent power-law distributions in animal movements can arise from intraspecific interactions

PubMed Central

Breed, Greg A.; Severns, Paul M.; Edwards, Andrew M.

2015-01-01

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight. PMID:25519992

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Magnetic confinement, Alfven wave reflection, and the origins of X-ray and mass-loss 'dividing lines' for late-type giants and supergiants

NASA Technical Reports Server (NTRS)

Rosner, R.; An, C.-H.; Musielak, Z. E.; Moore, R. L.; Suess, S. T.

1991-01-01

A simple qualitative model for the origin of the coronal and mass-loss dividing lines separating late-type giants and supergiants with and without hot, X-ray-emitting corona, and with and without significant mass loss is discussed. The basic physical effects considered are the necessity of magnetic confinement for hot coronal material on the surface of such stars and the large reflection efficiency for Alfven waves in cool exponential atmospheres. The model assumes that the magnetic field geometry of these stars changes across the observed 'dividing lines' from being mostly closed on the high effective temperature side to being mostly open on the low effective temperature side.

Slow dynamics in glasses: A comparison between theory and experiment

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

Phillips, J. C.

Minimalist theories of complex systems are broadly of two kinds: mean field and axiomatic. So far, all theories of complex properties absent from simple systems and intrinsic to glasses are axiomatic. Stretched Exponential Relaxation (SER) is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex nonequilibrium materials, including luminescent electronic Coulomb glasses. A critical comparison of alternative axiomatic theories with both numerical simulations and experiments strongly favors channeled dynamical trap models over static percolative or energy landscape models. The topics discussed cover those reported since the author'smore » review article in 1996, with an emphasis on parallels between channel bifurcation in electronic and molecular relaxation.« less

μ SR studies of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1)

NASA Astrophysics Data System (ADS)

Lee, Suheon; Lee, Wonjun; Mitchell, John; Choi, Kwang-Yong

We present a μSR study of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1), which are made up of an alternating stacking of triangular and kagome layers. The parent material YBaCo4O7.0 undergoes a structural phase transition at 310 K, releasing geometrical frustration and thereby stabilizing an antiferromagnetically ordered state below TN = 106 K. The μSR spectra of YBaCo4O7.0 exhibit the loss of initial asymmetry and the development of a fast relaxation component below TN = 111 K. This indicates that the Co spins in the kagome planes remain in an inhomogeneous and dynamically fluctuating state down to 4 K, while the triangular spins order antiferromagnetically below TN. The nonstoichiometric YBaCo4O7.1 compound with no magnetic ordering exhibits a disparate spin dynamics between the fast cooling (10 K/min) and slow cooling (1 K/min) procedures. While the fast-cooled μSR spectra show a simple exponential decay, the slow-cooled spectra are described with a sum of a simple exponential function and a stretched exponential function. These are in agreements with the occurrence of the phase separation between interstitial oxygen-rich and poor regions in the slow-cooling measurements.

Proceedings of the Third International Workshop on Multistrategy Learning, May 23-25 Harpers Ferry, WV.

DTIC Science & Technology

1996-09-16

approaches are: • Adaptive filtering • Single exponential smoothing (Brown, 1963) * The Box-Jenkins methodology ( ARIMA modeling ) - Linear exponential... ARIMA • Linear exponential smoothing: Holt’s two parameter modeling (Box and Jenkins, 1976). However, there are two approach (Holt et al., 1960) very...crucial disadvantages: The most important point in - Winters’ three parameter method (Winters, 1960) ARIMA modeling is model identification. As shown in

Universality classes of fluctuation dynamics in hierarchical complex systems

NASA Astrophysics Data System (ADS)

Macêdo, A. M. S.; González, Iván R. Roa; Salazar, D. S. P.; Vasconcelos, G. L.

2017-03-01

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

Exponential model for option prices: Application to the Brazilian market

NASA Astrophysics Data System (ADS)

Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.

2016-03-01

In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.

Possible stretched exponential parametrization for humidity absorption in polymers.

PubMed

Hacinliyan, A; Skarlatos, Y; Sahin, G; Atak, K; Aybar, O O

2009-04-01

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.

Forecasting in foodservice: model development, testing, and evaluation.

PubMed

Miller, J L; Thompson, P A; Orabella, M M

1991-05-01

This study was designed to develop, test, and evaluate mathematical models appropriate for forecasting menu-item production demand in foodservice. Data were collected from residence and dining hall foodservices at Ohio State University. Objectives of the study were to collect, code, and analyze the data; develop and test models using actual operation data; and compare forecasting results with current methods in use. Customer count was forecast using deseasonalized simple exponential smoothing. Menu-item demand was forecast by multiplying the count forecast by a predicted preference statistic. Forecasting models were evaluated using mean squared error, mean absolute deviation, and mean absolute percentage error techniques. All models were more accurate than current methods. A broad spectrum of forecasting techniques could be used by foodservice managers with access to a personal computer and spread-sheet and database-management software. The findings indicate that mathematical forecasting techniques may be effective in foodservice operations to control costs, increase productivity, and maximize profits.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Increased intra-individual reaction time variability in attention-deficit/hyperactivity disorder across response inhibition tasks with different cognitive demands.

PubMed

Vaurio, Rebecca G; Simmonds, Daniel J; Mostofsky, Stewart H

2009-10-01

One of the most consistent findings in children with ADHD is increased moment-to-moment variability in reaction time (RT). The source of increased RT variability can be examined using ex-Gaussian analyses that divide variability into normal and exponential components and Fast Fourier transform (FFT) that allow for detailed examination of the frequency of responses in the exponential distribution. Prior studies of ADHD using these methods have produced variable results, potentially related to differences in task demand. The present study sought to examine the profile of RT variability in ADHD using two Go/No-go tasks with differing levels of cognitive demand. A total of 140 children (57 with ADHD and 83 typically developing controls), ages 8-13 years, completed both a "simple" Go/No-go task and a more "complex" Go/No-go task with increased working memory load. Repeated measures ANOVA of ex-Gaussian functions revealed for both tasks children with ADHD demonstrated increased variability in both the normal/Gaussian (significantly elevated sigma) and the exponential (significantly elevated tau) components. In contrast, FFT analysis of the exponential component revealed a significant task x diagnosis interaction, such that infrequent slow responses in ADHD differed depending on task demand (i.e., for the simple task, increased power in the 0.027-0.074 Hz frequency band; for the complex task, decreased power in the 0.074-0.202 Hz band). The ex-Gaussian findings revealing increased variability in both the normal (sigma) and exponential (tau) components for the ADHD group, suggest that both impaired response preparation and infrequent "lapses in attention" contribute to increased variability in ADHD. FFT analyses reveal that the periodicity of intermittent lapses of attention in ADHD varies with task demand. The findings provide further support for intra-individual variability as a candidate intermediate endophenotype of ADHD.

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

NASA Technical Reports Server (NTRS)

Rodriguez, Pedro I.

1986-01-01

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Universality in stochastic exponential growth.

PubMed

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.

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.

Seasonal Influenza Forecasting in Real Time Using the Incidence Decay With Exponential Adjustment Model.

PubMed

Nasserie, Tahmina; Tuite, Ashleigh R; Whitmore, Lindsay; Hatchette, Todd; Drews, Steven J; Peci, Adriana; Kwong, Jeffrey C; Friedman, Dara; Garber, Gary; Gubbay, Jonathan; Fisman, David N

2017-01-01

Seasonal influenza epidemics occur frequently. Rapid characterization of seasonal dynamics and forecasting of epidemic peaks and final sizes could help support real-time decision-making related to vaccination and other control measures. Real-time forecasting remains challenging. We used the previously described "incidence decay with exponential adjustment" (IDEA) model, a 2-parameter phenomenological model, to evaluate the characteristics of the 2015-2016 influenza season in 4 Canadian jurisdictions: the Provinces of Alberta, Nova Scotia and Ontario, and the City of Ottawa. Model fits were updated weekly with receipt of incident virologically confirmed case counts. Best-fit models were used to project seasonal influenza peaks and epidemic final sizes. The 2015-2016 influenza season was mild and late-peaking. Parameter estimates generated through fitting were consistent in the 2 largest jurisdictions (Ontario and Alberta) and with pooled data including Nova Scotia counts (R 0 approximately 1.4 for all fits). Lower R 0 estimates were generated in Nova Scotia and Ottawa. Final size projections that made use of complete time series were accurate to within 6% of true final sizes, but final size was using pre-peak data. Projections of epidemic peaks stabilized before the true epidemic peak, but these were persistently early (~2 weeks) relative to the true peak. A simple, 2-parameter influenza model provided reasonably accurate real-time projections of influenza seasonal dynamics in an atypically late, mild influenza season. Challenges are similar to those seen with more complex forecasting methodologies. Future work includes identification of seasonal characteristics associated with variability in model performance.

Exponential Formulae and Effective Operations

NASA Technical Reports Server (NTRS)

Mielnik, Bogdan; Fernandez, David J. C.

1996-01-01

One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).

Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Splines and control theory

NASA Technical Reports Server (NTRS)

Zhang, Zhimin; Tomlinson, John; Martin, Clyde

1994-01-01

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

Peculiar spectral statistics of ensembles of trees and star-like graphs

NASA Astrophysics Data System (ADS)

Kovaleva, V.; Maximov, Yu; Nechaev, S.; Valba, O.

2017-07-01

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the ‘Lifshitz singularity’ emerging in the one-dimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, reflecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of an ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

Peculiar spectral statistics of ensembles of trees and star-like graphs

DOE PAGES

Kovaleva, V.; Maximov, Yu; Nechaev, S.; ...

2017-07-11

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

Peculiar spectral statistics of ensembles of trees and star-like graphs

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

Kovaleva, V.; Maximov, Yu; Nechaev, S.

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

High activity and Levy searches: jellyfish can search the water column like fish.

PubMed

Hays, Graeme C; Bastian, Thomas; Doyle, Thomas K; Fossette, Sabrina; Gleiss, Adrian C; Gravenor, Michael B; Hobson, Victoria J; Humphries, Nicolas E; Lilley, Martin K S; Pade, Nicolas G; Sims, David W

2012-02-07

Over-fishing may lead to a decrease in fish abundance and a proliferation of jellyfish. Active movements and prey search might be thought to provide a competitive advantage for fish, but here we use data-loggers to show that the frequently occurring coastal jellyfish (Rhizostoma octopus) does not simply passively drift to encounter prey. Jellyfish (327 days of data from 25 jellyfish with depth collected every 1 min) showed very dynamic vertical movements, with their integrated vertical movement averaging 619.2 m d(-1), more than 60 times the water depth where they were tagged. The majority of movement patterns were best approximated by exponential models describing normal random walks. However, jellyfish also showed switching behaviour from exponential patterns to patterns best fitted by a truncated Lévy distribution with exponents (mean μ=1.96, range 1.2-2.9) close to the theoretical optimum for searching for sparse prey (μopt≈2.0). Complex movements in these 'simple' animals may help jellyfish to compete effectively with fish for plankton prey, which may enhance their ability to increase in dominance in perturbed ocean systems.

Understanding mobility degeneration mechanism in organic thin-film transistors (OTFT)

NASA Astrophysics Data System (ADS)

Wang, Wei; Wang, Long; Xu, Guangwei; Gao, Nan; Wang, Lingfei; Ji, Zhuoyu; Lu, Congyan; Lu, Nianduan; Li, Ling; Liu, Miwng

2017-08-01

Mobility degradation at high gate bias is often observed in organic thin film transistors. We propose a mechanism for this confusing phenomenon, based on the percolation theory with the presence of disordered energy landscape with an exponential density of states. Within a simple model we show how the surface states at insulator/organic interface trap a portion of channel carriers, and result in decrease of mobility as well as source/drain current with gate voltage. Depending on the competition between the carrier accumulation and surface trapping effect, two different carrier density dependences of mobility are obtained, in excellent agreement with experiment data.

Codecaying Dark Matter.

PubMed

Dror, Jeff Asaf; Kuflik, Eric; Ng, Wee Hao

2016-11-18

We propose a new mechanism for thermal dark matter freeze-out, called codecaying dark matter. Multicomponent dark sectors with degenerate particles and out-of-equilibrium decays can codecay to obtain the observed relic density. The dark matter density is exponentially depleted through the decay of nearly degenerate particles rather than from Boltzmann suppression. The relic abundance is set by the dark matter annihilation cross section, which is predicted to be boosted, and the decay rate of the dark sector particles. The mechanism is viable in a broad range of dark matter parameter space, with a robust prediction of an enhanced indirect detection signal. Finally, we present a simple model that realizes codecaying dark matter.

A modified impulse-response representation of the global near-surface air temperature and atmospheric concentration response to carbon dioxide emissions

NASA Astrophysics Data System (ADS)

Millar, Richard J.; Nicholls, Zebedee R.; Friedlingstein, Pierre; Allen, Myles R.

2017-06-01

Projections of the response to anthropogenic emission scenarios, evaluation of some greenhouse gas metrics, and estimates of the social cost of carbon often require a simple model that links emissions of carbon dioxide (CO2) to atmospheric concentrations and global temperature changes. An essential requirement of such a model is to reproduce typical global surface temperature and atmospheric CO2 responses displayed by more complex Earth system models (ESMs) under a range of emission scenarios, as well as an ability to sample the range of ESM response in a transparent, accessible and reproducible form. Here we adapt the simple model of the Intergovernmental Panel on Climate Change 5th Assessment Report (IPCC AR5) to explicitly represent the state dependence of the CO2 airborne fraction. Our adapted model (FAIR) reproduces the range of behaviour shown in full and intermediate complexity ESMs under several idealised carbon pulse and exponential concentration increase experiments. We find that the inclusion of a linear increase in 100-year integrated airborne fraction with cumulative carbon uptake and global temperature change substantially improves the representation of the response of the climate system to CO2 on a range of timescales and under a range of experimental designs.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Parameter estimation and order selection for an empirical model of VO2 on-kinetics.

PubMed

Alata, O; Bernard, O

2007-04-27

In humans, VO2 on-kinetics are noisy numerical signals that reflect the pulmonary oxygen exchange kinetics at the onset of exercise. They are empirically modelled as a sum of an offset and delayed exponentials. The number of delayed exponentials; i.e. the order of the model, is commonly supposed to be 1 for low-intensity exercises and 2 for high-intensity exercises. As no ground truth has ever been provided to validate these postulates, physiologists still need statistical methods to verify their hypothesis about the number of exponentials of the VO2 on-kinetics especially in the case of high-intensity exercises. Our objectives are first to develop accurate methods for estimating the parameters of the model at a fixed order, and then, to propose statistical tests for selecting the appropriate order. In this paper, we provide, on simulated Data, performances of Simulated Annealing for estimating model parameters and performances of Information Criteria for selecting the order. These simulated Data are generated with both single-exponential and double-exponential models, and noised by white and Gaussian noise. The performances are given at various Signal to Noise Ratio (SNR). Considering parameter estimation, results show that the confidences of estimated parameters are improved by increasing the SNR of the response to be fitted. Considering model selection, results show that Information Criteria are adapted statistical criteria to select the number of exponentials.

Is it growing exponentially fast? -- Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics.

PubMed

Chowell, Gerardo; Viboud, Cécile

2016-10-01

The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.

Comparison of remote sensing algorithms for retrieval of suspended particulate matter concentration from reflectance in coastal waters

NASA Astrophysics Data System (ADS)

Freeman, Lauren A.; Ackleson, Steven G.; Rhea, William Joseph

2017-10-01

Suspended particulate matter (SPM) is a key environmental indicator for rivers, estuaries, and coastal waters, which can be calculated from remote sensing reflectance obtained by an airborne or satellite imager. Here, algorithms from prior studies are applied to a dataset of in-situ at surface hyperspectral remote sensing reflectance, collected in three geographic regions representing different water types. These data show the optically inherent exponential nature of the relationship between reflectance and sediment concentration. However, linear models are also shown to provide a reasonable estimate of sediment concentration when utilized with care in similar conditions to those under which the algorithms were developed, particularly at lower SPM values (0 to 20 mg/L). Fifteen published SPM algorithms are tested, returning strong correlations of R2>0.7, and in most cases, R2>0.8. Very low SPM values show weaker correlation with algorithm calculated SPM that is not wavelength dependent. None of the tested algorithms performs well for high SPM values (>30 mg/L), with most algorithms underestimating SPM. A shift toward a smaller number of simple exponential or linear models relating satellite remote sensing reflectance to suspended sediment concentration with regional consideration will greatly aid larger spatiotemporal studies of suspended sediment trends.

A simple approach to measure transmissibility and forecast incidence.

PubMed

Nouvellet, Pierre; Cori, Anne; Garske, Tini; Blake, Isobel M; Dorigatti, Ilaria; Hinsley, Wes; Jombart, Thibaut; Mills, Harriet L; Nedjati-Gilani, Gemma; Van Kerkhove, Maria D; Fraser, Christophe; Donnelly, Christl A; Ferguson, Neil M; Riley, Steven

2018-03-01

Outbreaks of novel pathogens such as SARS, pandemic influenza and Ebola require substantial investments in reactive interventions, with consequent implementation plans sometimes revised on a weekly basis. Therefore, short-term forecasts of incidence are often of high priority. In light of the recent Ebola epidemic in West Africa, a forecasting exercise was convened by a network of infectious disease modellers. The challenge was to forecast unseen "future" simulated data for four different scenarios at five different time points. In a similar method to that used during the recent Ebola epidemic, we estimated current levels of transmissibility, over variable time-windows chosen in an ad hoc way. Current estimated transmissibility was then used to forecast near-future incidence. We performed well within the challenge and often produced accurate forecasts. A retrospective analysis showed that our subjective method for deciding on the window of time with which to estimate transmissibility often resulted in the optimal choice. However, when near-future trends deviated substantially from exponential patterns, the accuracy of our forecasts was reduced. This exercise highlights the urgent need for infectious disease modellers to develop more robust descriptions of processes - other than the widespread depletion of susceptible individuals - that produce non-exponential patterns of incidence. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

A gamma variate model that includes stretched exponential is a better fit for gastric emptying data from mice

PubMed Central

Bajzer, Željko; Gibbons, Simon J.; Coleman, Heidi D.; Linden, David R.

2015-01-01

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to better fit mouse gastric emptying data including when two peaks are present in the gastric emptying curve. We fitted 175 gastric emptying data sets with two standard models (gamma variate and power exponential), with a gamma variate model that includes stretched exponential and with a proposed two-component model. The appropriateness of the fit was assessed by the Akaike Information Criterion. We found that extension of the gamma variate model to include a stretched exponential improves the fit, which allows for a better estimation of T1/2 and Tlag. When two distinct peaks in gastric emptying are present, a two-component model is required for the most appropriate fit. We conclude that use of a stretched exponential gamma variate model and when appropriate a two-component model will result in a better estimate of physiologically relevant parameters when analyzing mouse gastric emptying data. PMID:26045615

Constraining f(T) teleparallel gravity by big bang nucleosynthesis: f(T) cosmology and BBN.

PubMed

Capozziello, S; Lambiase, G; Saridakis, E N

2017-01-01

We use Big Bang Nucleosynthesis (BBN) observational data on the primordial abundance of light elements to constrain f ( T ) gravity. The three most studied viable f ( T ) models, namely the power law, the exponential and the square-root exponential are considered, and the BBN bounds are adopted in order to extract constraints on their free parameters. For the power-law model, we find that the constraints are in agreement with those obtained using late-time cosmological data. For the exponential and the square-root exponential models, we show that for reliable regions of parameters space they always satisfy the BBN bounds. We conclude that viable f ( T ) models can successfully satisfy the BBN constraints.

Rotation of a spheroid in a Couette flow at moderate Reynolds numbers.

PubMed

Yu, Zhaosheng; Phan-Thien, Nhan; Tanner, Roger I

2007-08-01

The rotation of a single spheroid in a planar Couette flow as a model for simple shear flow is numerically simulated with the distributed Lagrangian multiplier based fictitious domain method. The study is focused on the effects of inertia on the orbital behavior of prolate and oblate spheroids. The numerical orbits are found to be well described by a simple empirical model, which states that the rate of the spheroid rotation about the vorticity axis is a sinusoidal function of the corresponding projection angle in the flow-gradient plane, and that the exponential growth rate of the orbit function is a constant. The following transitions in the steady state with increasing Reynolds number are identified: Jeffery orbit, tumbling, quasi-Jeffery orbit, log rolling, and inclined rolling for a prolate spheroid; and Jeffery orbit, log rolling, inclined rolling, and motionless state for an oblate spheroid. In addition, it is shown that the orbit behavior is sensitive to the initial orientation in the case of strong inertia and there exist different steady states for certain shear Reynolds number regimes.

Convergent chaos

NASA Astrophysics Data System (ADS)

Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael

2017-07-01

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

Tl+-induced micros gating of current indicates instability of the MaxiK selectivity filter as caused by ion/pore interaction.

PubMed

Schroeder, Indra; Hansen, Ulf-Peter

2008-04-01

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed at high temporal resolution (50-kHz filter) in asymmetrical solutions containing 0, 25, 50, or 150 mM Tl+ on the luminal or cytosolic side with [K+] + [Tl+] = 150 mM and 150 mM K+ on the other side. Outward current in the presence of cytosolic Tl+ did not show fast gating behavior that was significantly different from that in the absence of Tl+. With luminal Tl+ and at membrane potentials more negative than -40 mV, the single-channel current showed a negative slope resistance concomitantly with a flickery block, resulting in an artificially reduced apparent single-channel current I(app). The analysis of the amplitude histograms by beta distributions enabled the estimation of the true single-channel current and the determination of the rate constants of a simple two-state O-C Markov model for the gating in the bursts. The voltage dependence of the gating ratio R = I(true)/I(app) = (k(CO) + k(OC))/k(CO) could be described by exponential functions with different characteristic voltages above or below 50 mM Tl(+). The true single-channel current I(true) decreased with Tl+ concentrations up to 50 mM and stayed constant thereafter. Different models were considered. The most likely ones related the exponential increase of the gating ratio to ion depletion at the luminal side of the selectivity filter, whereas the influence of [Tl+] on the characteristic voltage of these exponential functions and of the value of I(true) were determined by [Tl+] at the inner side of the selectivity filter or in the cavity.

Circularly Polarized Luminescence from Simple Organic Molecules

PubMed Central

Sánchez-Carnerero, Esther M.; Agarrabeitia, Antonia R.; Moreno, Florencio; Maroto, Beatriz L.; Muller, Gilles; Ortiz, María J.

2015-01-01

This article aims to show the identity of “CPL-active simple organic molecules” as a new concept in Organic Chemistry due to the potential interest of these molecules, as availed by the exponentially growing number of research articles related to them. In particular, it describes and highlights the interest and difficulty in developing chiral simple (small and nonaggregated) organic molecules able to emit left- or right-circularly polarized light efficiently, the efforts realized up to now to reach this challenging objective, and the most significant milestones achieved to date. General guidelines for the preparation of these interesting molecules are also presented. PMID:26136234

Updated radiometric calibration for the Landsat-5 thematic mapper reflective bands

USGS Publications Warehouse

Helder, D.L.; Markham, B.L.; Thome, K.J.; Barsi, J.A.; Chander, G.; Malla, R.

2008-01-01

The Landsat-5 Thematic Mapper (TM) has been the workhorse of the Landsat system. Launched in 1984, it continues collecting data through the time frame of this paper. Thus, it provides an invaluable link to the past history of the land features of the Earth's surface, and it becomes imperative to provide an accurate radiometric calibration of the reflective bands to the user community. Previous calibration has been based on information obtained from prelaunch, the onboard calibrator, vicarious calibration attempts, and cross-calibration with Landsat-7. Currently, additional data sources are available to improve this calibration. Specifically, improvements in vicarious calibration methods and development of the use of pseudoinvariant sites for trending provide two additional independent calibration sources. The use of these additional estimates has resulted in a consistent calibration approach that ties together all of the available calibration data sources. Results from this analysis indicate a simple exponential, or a constant model may be used for all bands throughout the lifetime of Landsat-5 TM. Where previously time constants for the exponential models were approximately one year, the updated model has significantly longer time constants in bands 1-3. In contrast, bands 4, 5, and 7 are shown to be best modeled by a constant. The models proposed in this paper indicate calibration knowledge of 5% or better early in life, decreasing to nearly 2% later in life. These models have been implemented at the U.S. Geological Survey Earth Resources Observation and Science (EROS) and are the default calibration used for all Landsat TM data now distributed through EROS. ?? 2008 IEEE.

Milky Way Mass Models and MOND

NASA Astrophysics Data System (ADS)

McGaugh, Stacy S.

2008-08-01

Using the Tuorla-Heidelberg model for the mass distribution of the Milky Way, I determine the rotation curve predicted by MOND (modified Newtonian dynamics). The result is in good agreement with the observed terminal velocities interior to the solar radius and with estimates of the Galaxy's rotation curve exterior thereto. There are no fit parameters: given the mass distribution, MOND provides a good match to the rotation curve. The Tuorla-Heidelberg model does allow for a variety of exponential scale lengths; MOND prefers short scale lengths in the range 2.0 kpc lesssim Rdlesssim 2.5 kpc. The favored value of Rd depends somewhat on the choice of interpolation function. There is some preference for the "simple" interpolation function as found by Famaey & Binney. I introduce an interpolation function that shares the advantages of the simple function on galaxy scales while having a much smaller impact in the solar system. I also solve the inverse problem, inferring the surface mass density distribution of the Milky Way from the terminal velocities. The result is a Galaxy with "bumps and wiggles" in both its luminosity profile and rotation curve that are reminiscent of those frequently observed in external galaxies.

An approach to multivariable control of manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.

General mechanism of two-state protein folding kinetics.

PubMed

Rollins, Geoffrey C; Dill, Ken A

2014-08-13

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.

Non-perturbative reheating and Nnaturalness

NASA Astrophysics Data System (ADS)

Hardy, Edward

2017-11-01

We study models in which reheating happens only through non-perturbative processes. The energy transferred can be exponentially suppressed unless the inflaton is coupled to a particle with a parametrically small mass. Additionally, in some models a light scalar with a negative mass squared parameter leads to much more efficient reheating than one with a positive mass squared of the same magnitude. If a theory contains many sectors similar to the Standard Model coupled to the inflaton via their Higgses, such dynamics can realise the Nnaturalness solution to the hierarchy problem. A sector containing a light Higgs with a non-zero vacuum expectation value is dominantly reheated and there is little energy transferred to the other sectors, consistent with cosmological constraints. The inflaton must decouple from other particles and have a flat potential at large field values, in which case the visible sector UV cutoff can be raised to 10 TeV in a simple model.

The matrix exponential in transient structural analysis

NASA Technical Reports Server (NTRS)

Minnetyan, Levon

1987-01-01

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Enviromental influences on the {sup 137}Cs kinetics of the yellow-bellied turtle (Trachemys Scripta)

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

Peters, E.L.; Brisbin, L.I. Jr.

1996-02-01

Assessments of ecological risk require accurate predictions of contaminant dynamics in natural populations. However, simple deterministic models that assume constant uptake rates and elimination fractions may compromise both their ecological realism and their general application to animals with variable metabolism or diets. In particular, the temperature-dependent model of metabolic rates characteristic of ectotherms may lead to significant differences between observed and predicted contaminant kinetics. We examined the influence of a seasonally variable thermal environment on predicting the uptake and annual cycling of contaminants by ectotherms, using a temperature-dependent model of {sup 137}Cs kinetics in free-living yellow-bellied turtles, Trachemys scripta. Wemore » compared predictions from this model with those of deterministics negative exponential and flexibly shaped Richards sigmoidal models. Concentrations of {sup 137}Cs in a population if this species in Pond B, a radionuclide-contaminated nuclear reactor cooling reservoir, and {sup 137}Cs uptake by the uncontaminated turtles held captive in Pond B for 4 yr confirmed both the pattern of uptake and the equilibrium concentrations predicted by the temperature-dependent model. Almost 90% of the variance on the predicted time-integrated {sup 137}Cs concentration was explainable by linear relationships with model paramaters. The model was also relatively insensitive to uncertainties in the estimates of ambient temperature, suggesting that adequate estimates of temperature-dependent ingestion and elimination may require relatively few measurements of ambient conditions at sites of interest. Analyses of Richards sigmoidal models of {sup 137}Cs uptake indicated significant differences from a negative exponential trajectory in the 1st yr after the turtles` release into Pond B. 76 refs., 7 figs., 5 tabs.« less

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

Bourdon, J.C.; Peltier, B.; Cooper, G.A.

In this paper, field drill-off test results are compared with data from laboratory simulations. A simple theory for analyzing drill-off tests is developed. The weight-on bit (WOB) decay with time is close to exponential, but large threshold WOB's, resulting from poor weight transmission downhole, are sometimes observed in field tests.

Boiling Temperature vs. Composition. An Almost-Exact Explicit Equation for a Binary Mixture Following Raoult's Law.

ERIC Educational Resources Information Center

Cardinali, Mario Emilio; Giomini, Claudio

1989-01-01

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Signal transmissibility in marginal granular materials

NASA Astrophysics Data System (ADS)

Pinson, Matthew B.; Witten, Thomas A.

2016-12-01

We examine the ‘transmissibility’ of a simulated two-dimensional pack of frictionless disks formed by confining dilute disks in a shrinking, periodic box to the point of mechanical stability. Two opposite boundaries are then removed, thus allowing a set of free motions. Small free displacements on one boundary then induce proportional displacements on the opposite boundary. Transmissibility is the ability to distinguish different perturbations by their distant responses. We assess transmissibility by successively identifying free orthonormal modes of motion that have the smallest distant responses. The last modes to be identified in this ‘pessimistic’ basis are the most transmissive. The transmitted amplitudes of these most transmissive modes fall off exponentially with mode number. Similar exponential falloff is seen in a simple elastic medium, though the responsible modes differ greatly in structure in the two systems. Thus the marginal pack’s transmissibility is qualitatively similar to that of a simple elastic medium. We compare our results with recent findings based on the projection of the space of free motion onto interior sites.

Hierarchical modeling for reliability analysis using Markov models. B.S./M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Fagundo, Arturo

1994-01-01

Markov models represent an extremely attractive tool for the reliability analysis of many systems. However, Markov model state space grows exponentially with the number of components in a given system. Thus, for very large systems Markov modeling techniques alone become intractable in both memory and CPU time. Often a particular subsystem can be found within some larger system where the dependence of the larger system on the subsystem is of a particularly simple form. This simple dependence can be used to decompose such a system into one or more subsystems. A hierarchical technique is presented which can be used to evaluate these subsystems in such a way that their reliabilities can be combined to obtain the reliability for the full system. This hierarchical approach is unique in that it allows the subsystem model to pass multiple aggregate state information to the higher level model, allowing more general systems to be evaluated. Guidelines are developed to assist in the system decomposition. An appropriate method for determining subsystem reliability is also developed. This method gives rise to some interesting numerical issues. Numerical error due to roundoff and integration are discussed at length. Once a decomposition is chosen, the remaining analysis is straightforward but tedious. However, an approach is developed for simplifying the recombination of subsystem reliabilities. Finally, a real world system is used to illustrate the use of this technique in a more practical context.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Bothner, Thomas

2018-02-01

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297-311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697-721, 1998) using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058-1092, 1977).

Bimodal star formation - Constraints from the solar neighborhood

NASA Technical Reports Server (NTRS)

Wyse, Rosemary F. G.; Silk, J.

1987-01-01

The chemical evolution resulting from a simple model of bimodal star formulation is investigated, using constraints from the solar neighborhood to set the parameters of the initial mass function and star formation rate. The two modes are an exclusively massive star mode, which forms stars at an exponentially declining rate, and a mode which contains stars of all masses and has a constant star formation rate. Satisfactory agreement with the age-metallicity relation for the thin disk and with the metallicity structure of the thin-disk and spheroid stars is possible only for a small range of parameter values. The preferred model offers a resolution to several of the long-standing problems of galactic chemical evolution, including explanations of the age-metallicity relation, the gas consumption time scale, and the stellar cumulative metallicity distributions.

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

PubMed Central

Sozanski, Krzysztof; Wisniewska, Agnieszka; Kalwarczyk, Tomasz; Sznajder, Anna; Holyst, Robert

2016-01-01

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales—from diffusion of molecular probes to macroscopic viscous flow—we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid. PMID:27536866

Superionic state in double-layer capacitors with nanoporous electrodes.

PubMed

Kondrat, S; Kornyshev, A

2011-01-19

In recent experiments (Chmiola et al 2006 Science 313 1760; Largeot et al 2008 J. Am. Chem. Soc. 130 2730) an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer capacitor has been observed. We explain this effect by image forces which exponentially screen out the electrostatic interactions of ions in the interior of a pore. Packing of ions of the same sign becomes easier and is mainly limited by steric interactions. We call this state 'superionic' and suggest a simple model to describe it. The model reveals the possibility of a voltage-induced first order transition between a cation(anion)-deficient phase and a cation(anion)-rich phase which manifests itself in a jump of capacitance as a function of voltage.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Convective Detrainment and Control of the Tropical Water Vapor Distribution

NASA Astrophysics Data System (ADS)

Kursinski, E. R.; Rind, D.

2006-12-01

Sherwood et al. (2006) developed a simple power law model describing the relative humidity distribution in the tropical free troposphere where the power law exponent is the ratio of a drying time scale (tied to subsidence rates) and a moistening time which is the average time between convective moistening events whose temporal distribution is described as a Poisson distribution. Sherwood et al. showed that the relative humidity distribution observed by GPS occultations and MLS is indeed close to a power law, approximately consistent with the simple model's prediction. Here we modify this simple model to be in terms of vertical length scales rather than time scales in a manner that we think more correctly matches the model predictions to the observations. The subsidence is now in terms of the vertical distance the air mass has descended since it last detrained from a convective plume. The moisture source term becomes a profile of convective detrainment flux versus altitude. The vertical profile of the convective detrainment flux is deduced from the observed distribution of the specific humidity at each altitude combined with sinking rates estimated from radiative cooling. The resulting free tropospheric detrainment profile increases with altitude above 3 km somewhat like an exponential profile which explains the approximate power law behavior observed by Sherwood et al. The observations also reveal a seasonal variation in the detrainment profile reflecting changes in the convective behavior expected by some based on observed seasonal changes in the vertical structure of convective regions. The simple model results will be compared with the moisture control mechanisms in a GCM with many additional mechanisms, the GISS climate model, as described in Rind (2006). References Rind. D., 2006: Water-vapor feedback. In Frontiers of Climate Modeling, J. T. Kiehl and V. Ramanathan (eds), Cambridge University Press [ISBN-13 978-0-521- 79132-8], 251-284. Sherwood, S., E. R. Kursinski and W. Read, A distribution law for free-tropospheric relative humidity, J. Clim. In press. 2006

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Ray-theory approach to electrical-double-layer interactions.

PubMed

Schnitzer, Ory

2015-02-01

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress-associated with the ray contributions interacting nonlinearly-decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

Non-London electrodynamics in a multiband London model: Anisotropy-induced nonlocalities and multiple magnetic field penetration lengths

NASA Astrophysics Data System (ADS)

Silaev, Mihail; Winyard, Thomas; Babaev, Egor

2018-05-01

The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multiband extensions, where the presence of multiple bands merely renormalizes the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multiband London models are not this simple, and the anisotropy leads to the interband phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems having N +1 penetration lengths, where N is the number of field components or bands. That is, in a given direction, the magnetic field decay is described by N +1 modes with different amplitudes and different decay length scales. For certain anisotropies we obtain magnetic modes with complex masses. That means that magnetic field decay is not described by a monotonic exponential increment set by a real penetration length but instead is oscillating. Some of the penetration lengths are shown to diverge away from the superconducting phase transition when the mass of the phase-difference mode vanishes. Finally the anisotropy-driven hybridization of the London mode with the Leggett modes can provide an effectively nonlocal magnetic response in the nominally local London model. Focusing on the two-component model, we discuss the magnetic field inversion that results from the effective nonlocality, both near the surface of the superconductor and around vortices. In the regime where the magnetic field decay becomes nonmonotonic, the multiband London superconductor is shown to form weakly-bound states of vortices.

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Coupled large eddy simulation and discrete element model of bedload motion

NASA Astrophysics Data System (ADS)

Furbish, D.; Schmeeckle, M. W.

2011-12-01

We combine a three-dimensional large eddy simulation of turbulence to a three-dimensional discrete element model of turbulence. The large eddy simulation of the turbulent fluid is extended into the bed composed of non-moving particles by adding resistance terms to the Navier-Stokes equations in accordance with the Darcy-Forchheimer law. This allows the turbulent velocity and pressure fluctuations to penetrate the bed of discrete particles, and this addition of a porous zone results in turbulence structures above the bed that are similar to previous experimental and numerical results for hydraulically-rough beds. For example, we reproduce low-speed streaks that are less coherent than those over smooth-beds due to the episodic outflow of fluid from the bed. Local resistance terms are also added to the Navier-Stokes equations to account for the drag of individual moving particles. The interaction of the spherical particles utilizes a standard DEM soft-sphere Hertz model. We use only a simple drag model to calculate the fluid forces on the particles. The model reproduces an exponential distribution of bedload particle velocities that we have found experimentally using high-speed video of a flat bed of moving sand in a recirculating water flume. The exponential distribution of velocity results from the motion of many particles that are nearly constantly in contact with other bed particles and come to rest after short distances, in combination with a relatively few particles that are entrained further above the bed and have velocities approaching that of the fluid. Entrainment and motion "hot spots" are evident that are not perfectly correlated with the local, instantaneous fluid velocity. Zones of the bed that have recently experienced motion are more susceptible to motion because of the local configuration of particle contacts. The paradigm of a characteristic saltation hop length in riverine bedload transport has infused many aspects of geomorphic thought, including even bedrock erosion. In light of our theoretical, experimental, and numerical findings supporting the exponential distribution of bedload particle motion, the idea of a characteristic saltation hop should be scrapped or substantially modified.

A Fluid-driven Earthquake Cycle, Omori's Law, and Fluid-driven Aftershocks

NASA Astrophysics Data System (ADS)

Miller, S. A.

2015-12-01

Few models exist that predict the Omori's Law of aftershock rate decay, with rate-state friction the only physically-based model. ETAS is a probabilistic model of cascading failures, and is sometimes used to infer rate-state frictional properties. However, the (perhaps dominant) role of fluids in the earthquake process is being increasingly realised, so a fluid-based physical model for Omori's Law should be available. In this talk, I present an hypothesis for a fluid-driven earthquake cycle where dehydration and decarbonization at depth provides continuous sources of buoyant high pressure fluids that must eventually make their way back to the surface. The natural pathway for fluid escape is along plate boundaries, where in the ductile regime high pressure fluids likely play an integral role in episodic tremor and slow slip earthquakes. At shallower levels, high pressure fluids pool at the base of seismogenic zones, with the reservoir expanding in scale through the earthquake cycle. Late in the cycle, these fluids can invade and degrade the strength of the brittle crust and contribute to earthquake nucleation. The mainshock opens permeable networks that provide escape pathways for high pressure fluids and generate aftershocks along these flow paths, while creating new pathways by the aftershocks themselves. Thermally activated precipitation then seals up these pathways, returning the system to a low-permeability environment and effective seal during the subsequent tectonic stress buildup. I find that the multiplicative effect of an exponential dependence of permeability on the effective normal stress coupled with an Arrhenius-type, thermally activated exponential reduction in permeability results in Omori's Law. I simulate this scenario using a very simple model that combines non-linear diffusion and a step-wise increase in permeability when a Mohr Coulomb failure condition is met, and allow permeability to decrease as an exponential function in time. I show very strong spatial correlations of the simulated evolved permeability and fluid pressure field with aftershock hypocenters from this 1992 Landers and 1994 Northridge aftershock sequences, and reproduce the observed aftershock decay rates. Controls on the decay rates (p-value) will also be discussed.

Exceptional point in a simple textbook example

NASA Astrophysics Data System (ADS)

Fernández, Francisco M.

2018-07-01

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

Power law incidence rate in epidemic models. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Allen, Linda J. S.

2016-09-01

Dr. Chowell and colleagues emphasize the importance of considering a variety of modeling approaches to characterize the growth of an epidemic during the early stages [1]. A fit of data from the 2009 H1N1 influenza pandemic and the 2014-2015 Ebola outbreak to models indicates sub-exponential growth, in contrast to the classic, homogeneous-mixing SIR model with exponential growth. With incidence rate βSI / N and S approximately equal to the total population size N, the number of new infections in an SIR epidemic model grows exponentially as in the differential equation,

A Simulation To Model Exponential Growth.

ERIC Educational Resources Information Center

Appelbaum, Elizabeth Berman

2000-01-01

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

Seasonal Influenza Forecasting in Real Time Using the Incidence Decay With Exponential Adjustment Model

PubMed Central

Nasserie, Tahmina; Tuite, Ashleigh R; Whitmore, Lindsay; Hatchette, Todd; Drews, Steven J; Peci, Adriana; Kwong, Jeffrey C; Friedman, Dara; Garber, Gary; Gubbay, Jonathan

2017-01-01

Abstract Background Seasonal influenza epidemics occur frequently. Rapid characterization of seasonal dynamics and forecasting of epidemic peaks and final sizes could help support real-time decision-making related to vaccination and other control measures. Real-time forecasting remains challenging. Methods We used the previously described “incidence decay with exponential adjustment” (IDEA) model, a 2-parameter phenomenological model, to evaluate the characteristics of the 2015–2016 influenza season in 4 Canadian jurisdictions: the Provinces of Alberta, Nova Scotia and Ontario, and the City of Ottawa. Model fits were updated weekly with receipt of incident virologically confirmed case counts. Best-fit models were used to project seasonal influenza peaks and epidemic final sizes. Results The 2015–2016 influenza season was mild and late-peaking. Parameter estimates generated through fitting were consistent in the 2 largest jurisdictions (Ontario and Alberta) and with pooled data including Nova Scotia counts (R0 approximately 1.4 for all fits). Lower R0 estimates were generated in Nova Scotia and Ottawa. Final size projections that made use of complete time series were accurate to within 6% of true final sizes, but final size was using pre-peak data. Projections of epidemic peaks stabilized before the true epidemic peak, but these were persistently early (~2 weeks) relative to the true peak. Conclusions A simple, 2-parameter influenza model provided reasonably accurate real-time projections of influenza seasonal dynamics in an atypically late, mild influenza season. Challenges are similar to those seen with more complex forecasting methodologies. Future work includes identification of seasonal characteristics associated with variability in model performance. PMID:29497629

Two-stage unified stretched-exponential model for time-dependence of threshold voltage shift under positive-bias-stresses in amorphous indium-gallium-zinc oxide thin-film transistors

NASA Astrophysics Data System (ADS)

Jeong, Chan-Yong; Kim, Hee-Joong; Hong, Sae-Young; Song, Sang-Hun; Kwon, Hyuck-In

2017-08-01

In this study, we show that the two-stage unified stretched-exponential model can more exactly describe the time-dependence of threshold voltage shift (ΔV TH) under long-term positive-bias-stresses compared to the traditional stretched-exponential model in amorphous indium-gallium-zinc oxide (a-IGZO) thin-film transistors (TFTs). ΔV TH is mainly dominated by electron trapping at short stress times, and the contribution of trap state generation becomes significant with an increase in the stress time. The two-stage unified stretched-exponential model can provide useful information not only for evaluating the long-term electrical stability and lifetime of the a-IGZO TFT but also for understanding the stress-induced degradation mechanism in a-IGZO TFTs.

A simple method for evaluating the wavefront compensation error of diffractive liquid-crystal wavefront correctors.

PubMed

Cao, Zhaoliang; Mu, Quanquan; Hu, Lifa; Lu, Xinghai; Xuan, Li

2009-09-28

A simple method for evaluating the wavefront compensation error of diffractive liquid-crystal wavefront correctors (DLCWFCs) for atmospheric turbulence correction is reported. A simple formula which describes the relationship between pixel number, DLCWFC aperture, quantization level, and atmospheric coherence length was derived based on the calculated atmospheric turbulence wavefronts using Kolmogorov atmospheric turbulence theory. It was found that the pixel number across the DLCWFC aperture is a linear function of the telescope aperture and the quantization level, and it is an exponential function of the atmosphere coherence length. These results are useful for people using DLCWFCs in atmospheric turbulence correction for large-aperture telescopes.

A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.

Hyperopic photorefractive keratectomy and central islands

NASA Astrophysics Data System (ADS)

Gobbi, Pier Giorgio; Carones, Francesco; Morico, Alessandro; Vigo, Luca; Brancato, Rosario

1998-06-01

We have evaluated the refractive evolution in patients treated with yhyperopic PRK to assess the extent of the initial overcorrection and the time constant of regression. To this end, the time history of the refractive error (i.e. the difference between achieved and intended refractive correction) has been fitted by means of an exponential statistical model, giving information characterizing the surgical procedure with a direct clinical meaning. Both hyperopic and myopic PRk procedures have been analyzed by this method. The analysis of the fitting model parameters shows that hyperopic PRK patients exhibit a definitely higher initial overcorrection than myopic ones, and a regression time constant which is much longer. A common mechanism is proposed to be responsible for the refractive outcomes in hyperopic treatments and in myopic patients exhibiting significant central islands. The interpretation is in terms of superhydration of the central cornea, and is based on a simple physical model evaluating the amount of centripetal compression in the apical cornea.

Energy Dissipation-Based Method for Fatigue Life Prediction of Rock Salt

NASA Astrophysics Data System (ADS)

He, Mingming; Huang, Bingqian; Zhu, Caihui; Chen, Yunsheng; Li, Ning

2018-05-01

The fatigue test for rock salt is conducted under different stress amplitudes, loading frequencies, confining pressures and loading rates, from which the evaluation rule of the dissipated energy is revealed and analysed. The evolution of energy dissipation under fatigue loading is divided into three stages: the initial stage, the second stage and the acceleration stage. In the second stage, the energy dissipation per cycle remains stable and shows an exponential relation with the stress amplitude; the failure dissipated energy only depends on the mechanical behaviour of the rock salt and confining pressure, but it is immune to the loading conditions. The energy dissipation of fatigued rock salt is discussed, and a novel model for fatigue life prediction is proposed on the basis of energy dissipation. A simple model for evolution of the accumulative dissipated energy is established. Its prediction results are compared with the test results, and the proposed model is validated.

Homeopathic potentization based on nanoscale domains.

PubMed

Czerlinski, George; Ypma, Tjalling

2011-12-01

The objectives of this study were to present a simple descriptive and quantitative model of how high potencies in homeopathy arise. The model begins with the mechanochemical production of hydrogen and hydroxyl radicals from water and the electronic stabilization of the resulting nanodomains of water molecules. The life of these domains is initially limited to a few days, but may extend to years when the electromagnetic characteristic of a homeopathic agent is copied onto the domains. This information is transferred between the original agent and the nanodomains, and also between previously imprinted nanodomains and new ones. The differential equations previously used to describe these processes are replaced here by exponential expressions, corresponding to simplified model mechanisms. Magnetic stabilization is also involved, since these long-lived domains apparently require the presence of the geomagnetic field. Our model incorporates this factor in the formation of the long-lived compound. Numerical simulation and graphs show that the potentization mechanism can be described quantitatively by a very simplified mechanism. The omitted factors affect only the fine structure of the kinetics. Measurements of pH changes upon absorption of different electromagnetic frequencies indicate that about 400 nanodomains polymerize to form one cooperating unit. Singlet excited states of some compounds lead to dramatic changes in their hydrogen ion dissociation constant, explaining this pH effect and suggesting that homeopathic information is imprinted as higher singlet excited states. A simple description is provided of the process of potentization in homeopathic dilutions. With the exception of minor details, this simple model replicates the results previously obtained from a more complex model. While excited states are short lived in isolated molecules, they become long lived in nanodomains that form coherent cooperative aggregates controlled by the geomagnetic field. These domains either slowly emit biophotons or perform specific biochemical work at their target.

Some new exact solitary wave solutions of the van der Waals model arising in nature

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

Universal bursty behavior in the air transportation system.

PubMed

Ito, Hidetaka; Nishinari, Katsuhiro

2015-12-01

Social activities display bursty behavior characterized by heavy-tailed interevent time distributions. We examine the bursty behavior of airplanes' arrivals in hub airports. The analysis indicates that the air transportation system universally follows a power-law interarrival time distribution with an exponent α=2.5 and an exponential cutoff. Moreover, we investigate the mechanism of this bursty behavior by introducing a simple model to describe it. In addition, we compare the extent of the hub-and-spoke structure and the burstiness of various airline networks in the system. Remarkably, the results suggest that the hub-and-spoke network of the system and the carriers' strategy to facilitate transit are the origins of this universality.

A Pedagogical Approach to the Magnus Expansion

ERIC Educational Resources Information Center

Blanes, S.; Casas, F.; Oteo, J. A.; Ros, J.

2010-01-01

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the "Magnus expansion" (also known as "exponential perturbation theory") provides such unitary approximate solutions. The purpose is to illustrate the importance and…

The Beer Lambert Law Measurement Made Easy

ERIC Educational Resources Information Center

Onorato, Pasquale; Gratton, Luigi M.; Polesell, Marta; Salmoiraghi, Alessandro; Oss, Stefano

2018-01-01

We propose the use of a smartphone based apparatus as a valuable tool for investigating the optical absorption of a material and to verify the exponential decay predicted by Beer's law. The very simple experimental activities presented here, suitable for undergraduate students, allows one to measure the material transmittance including its…

Self-charging of identical grains in the absence of an external field.

PubMed

Yoshimatsu, R; Araújo, N A M; Wurm, G; Herrmann, H J; Shinbrot, T

2017-01-06

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Self-charging of identical grains in the absence of an external field

NASA Astrophysics Data System (ADS)

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Something from nothing: self-charging of identical grains

NASA Astrophysics Data System (ADS)

Shinbrot, Troy; Yoshimatsu, Ryuta; Nuno Araujo, Nuno; Wurm, Gerhard; Herrmann, Hans

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. I acknowledge support from NSF/DMR, award 1404792.

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

State of charge modeling of lithium-ion batteries using dual exponential functions

NASA Astrophysics Data System (ADS)

Kuo, Ting-Jung; Lee, Kung-Yen; Huang, Chien-Kang; Chen, Jau-Horng; Chiu, Wei-Li; Huang, Chih-Fang; Wu, Shuen-De

2016-05-01

A mathematical model is developed by fitting the discharging curve of LiFePO4 batteries and used to investigate the relationship between the state of charge and the closed-circuit voltage. The proposed mathematical model consists of dual exponential terms and a constant term which can fit the characteristics of dual equivalent RC circuits closely, representing a LiFePO4 battery. One exponential term presents the stable discharging behavior and the other one presents the unstable discharging behavior and the constant term presents the cut-off voltage.

Self-charging of identical grains in the absence of an external field

PubMed Central

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. PMID:28059124

Stretched exponential distributions in nature and economy: ``fat tails'' with characteristic scales

NASA Astrophysics Data System (ADS)

Laherrère, J.; Sornette, D.

1998-04-01

To account quantitatively for many reported "natural" fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.

Freezing of simple systems using density functional theory

NASA Astrophysics Data System (ADS)

de Kuijper, A.; Vos, W. L.; Barrat, J.-L.; Hansen, J.-P.; Schouten, J. A.

1990-10-01

Density functional theory (DFT) has been applied to the study of the fluid-solid transition in systems with realistic potentials (soft cores and attractive forces): the purely repulsive WCA Lennard-Jones reference potential (LJT), the full Lennard-Jones potential (LJ) and the exponential-6 potential appropriate for helium and hydrogen. Three different DFT formalisms were used: the formulation of Haymet and Oxtoby (HO) and the new theories of Denton and Ashcroft (MWDA) and of Baus (MELA). The results for the melting pressure are compared with recent simulation and experimental data. The results of the HO version are always too high, the deviation increasing when going from the repulsive Lennard-Jones to the exponential-6 potential of H2. The MWDA gives too low results for the repulsive Lennard-Jones potential. At low temperatures, it fails for the full LJ potential while at high temperatures it is in good agreement. Including the attraction as a mean-field correction gives good results also for low temperatures. The MWDA results are too high for the exponential-6 potentials. The MELA fails completely for the LJT potential and the hydrogen exponential-6 potential, since it does not give a stable solid phase.

Scaling behavior of ground-state energy cluster expansion for linear polyenes

NASA Astrophysics Data System (ADS)

Griffin, L. L.; Wu, Jian; Klein, D. J.; Schmalz, T. G.; Bytautas, L.

Ground-state energies for linear-chain polyenes are additively expanded in a sequence of terms for chemically relevant conjugated substructures of increasing size. The asymptotic behavior of the large-substructure limit (i.e., high-polymer limit) is investigated as a means of characterizing the rapidity of convergence and consequent utility of this energy cluster expansion. Consideration is directed to computations via: simple Hückel theory, a refined Hückel scheme with geometry optimization, restricted Hartree-Fock self-consistent field (RHF-SCF) solutions of fixed bond-length Parisier-Parr-Pople (PPP)/Hubbard models, and ab initio SCF approaches with and without geometry optimization. The cluster expansion in what might be described as the more "refined" approaches appears to lead to qualitatively more rapid convergence: exponentially fast as opposed to an inverse power at the simple Hückel or SCF-Hubbard levels. The substructural energy cluster expansion then seems to merit special attention. Its possible utility in making accurate extrapolations from finite systems to extended polymers is noted.

Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure.

PubMed

Abdelnour, Farras; Dayan, Michael; Devinsky, Orrin; Thesen, Thomas; Raj, Ashish

2018-05-15

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses. Copyright © 2018. Published by Elsevier Inc.

Fast and Accurate Circuit Design Automation through Hierarchical Model Switching.

PubMed

Huynh, Linh; Tagkopoulos, Ilias

2015-08-21

In computer-aided biological design, the trifecta of characterized part libraries, accurate models and optimal design parameters is crucial for producing reliable designs. As the number of parts and model complexity increase, however, it becomes exponentially more difficult for any optimization method to search the solution space, hence creating a trade-off that hampers efficient design. To address this issue, we present a hierarchical computer-aided design architecture that uses a two-step approach for biological design. First, a simple model of low computational complexity is used to predict circuit behavior and assess candidate circuit branches through branch-and-bound methods. Then, a complex, nonlinear circuit model is used for a fine-grained search of the reduced solution space, thus achieving more accurate results. Evaluation with a benchmark of 11 circuits and a library of 102 experimental designs with known characterization parameters demonstrates a speed-up of 3 orders of magnitude when compared to other design methods that provide optimality guarantees.

Piecewise exponential models to assess the influence of job-specific experience on the hazard of acute injury for hourly factory workers

PubMed Central

2013-01-01

Background An inverse relationship between experience and risk of injury has been observed in many occupations. Due to statistical challenges, however, it has been difficult to characterize the role of experience on the hazard of injury. In particular, because the time observed up to injury is equivalent to the amount of experience accumulated, the baseline hazard of injury becomes the main parameter of interest, excluding Cox proportional hazards models as applicable methods for consideration. Methods Using a data set of 81,301 hourly production workers of a global aluminum company at 207 US facilities, we compared competing parametric models for the baseline hazard to assess whether experience affected the hazard of injury at hire and after later job changes. Specific models considered included the exponential, Weibull, and two (a hypothesis-driven and a data-driven) two-piece exponential models to formally test the null hypothesis that experience does not impact the hazard of injury. Results We highlighted the advantages of our comparative approach and the interpretability of our selected model: a two-piece exponential model that allowed the baseline hazard of injury to change with experience. Our findings suggested a 30% increase in the hazard in the first year after job initiation and/or change. Conclusions Piecewise exponential models may be particularly useful in modeling risk of injury as a function of experience and have the additional benefit of interpretability over other similarly flexible models. PMID:23841648

Modeling the dynamics of a phreatic eruption based on a tilt observation: Barrier breakage leading to the 2014 eruption of Mount Ontake, Japan

NASA Astrophysics Data System (ADS)

Maeda, Yuta; Kato, Aitaro; Yamanaka, Yoshiko

2017-02-01

Although phreatic eruptions are common volcanic phenomena that sometimes result in significant disasters, their dynamics are poorly understood. In this study, we address the dynamics of the phreatic eruption of Mount Ontake, Japan, in 2014 based on analyses of a tilt change observed immediately (450 s) before the eruption onset. We conducted two sets of analysis: a waveform inversion and a modified phase-space analysis. Our waveform inversion of the tilt signal points to a vertical tensile crack at a depth of 1100 m. Our modified phase-space analysis suggests that the tilt change was at first a linear function in time that then switched to exponential growth. We constructed simple analytical models to explain these temporal functions. The linear function was explained by the boiling of underground water controlled by a constant heat supply from a greater depth. The exponential function was explained by the decompression-induced boiling of water and the upward Darcy flow of the water vapor through a permeable region of small cracks that were newly created in response to ongoing boiling. We interpret that this region was intact prior to the start of the tilt change, and thus, it has acted as a permeability barrier for the upward migration of fluids; it was a breakage of this barrier that led to the eruption.

Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

PubMed

Shukla, Rahul; Dragotti, Pier Luigi; Do, Minh N; Vetterli, Martin

2005-03-01

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.

Probing solvation decay length in order to characterize hydrophobicity-induced bead-bead attractive interactions in polymer chains.

PubMed

Das, Siddhartha; Chakraborty, Suman

2011-08-01

In this paper, we quantitatively demonstrate that exponentially decaying attractive potentials can effectively mimic strong hydrophobic interactions between monomer units of a polymer chain dissolved in aqueous solvent. Classical approaches to modeling hydrophobic solvation interactions are based on invariant attractive length scales. However, we demonstrate here that the solvation interaction decay length may need to be posed as a function of the relative separation distances and the sizes of the interacting species (or beads or monomers) to replicate the necessary physical interactions. As an illustrative example, we derive a universal scaling relationship for a given solute-solvent combination between the solvation decay length, the bead radius, and the distance between the interacting beads. With our formalism, the hydrophobic component of the net attractive interaction between monomer units can be synergistically accounted for within the unified framework of a simple exponentially decaying potential law, where the characteristic decay length incorporates the distinctive and critical physical features of the underlying interaction. The present formalism, even in a mesoscopic computational framework, is capable of incorporating the essential physics of the appropriate solute-size dependence and solvent-interaction dependence in the hydrophobic force estimation, without explicitly resolving the underlying molecular level details.

A Novel Method for Age Estimation in Solar-Type Stars Through GALEX FUV Magnitudes

NASA Astrophysics Data System (ADS)

Ho, Kelly; Subramonian, Arjun; Smith, Graeme; Shouru Shieh

2018-01-01

Utilizing an inverse association known to exist between Galaxy Evolution Explorer (GALEX) far ultraviolet (FUV) magnitudes and the chromospheric activity of F, G, and K dwarfs, we explored a method of age estimation in solar-type stars through GALEX FUV magnitudes. Sample solar-type star data were collected from refereed publications and filtered by B-V and absolute visual magnitude to ensure similarities in temperature and luminosity to the Sun. We determined FUV-B and calculated a residual index Q for all the stars, using the temperature-induced upper bound on FUV-B as the fiducial. Plotting current age estimates for the stars against Q, we discovered a strong and significant association between the variables. By applying a log-linear transformation to the data to produce a strong correlation between Q and loge Age, we confirmed the association between Q and age to be exponential. Thus, least-squares regression was used to generate an exponential model relating Q to age in solar-type stars, which can be used by astronomers. The Q-method of stellar age estimation is simple and more efficient than existing spectroscopic methods and has applications to galactic archaeology and stellar chemical composition analysis.

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

A Simulation of the ECSS Help Desk with the Erlang a Model

DTIC Science & Technology

2011-03-01

a popular distribution is the exponential distribution as shown in Figure 3. Figure 3: Exponential Distribution ( Bourke , 2001) Exponential...System Sciences, Vol 8, 235B. Bourke , P. (2001, January). Miscellaneous Functions. Retrieved January 22, 2011, from http://local.wasp.uwa.edu.au

Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

Emergence of power-law in a market with mixed models

NASA Astrophysics Data System (ADS)

Ali Saif, M.; Gade, Prashant M.

2007-10-01

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.

On E-discretization of tori of compact simple Lie groups. II

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Comparison of Two Methods for Calculating the Frictional Properties of Articular Cartilage Using a Simple Pendulum and Intact Mouse Knee Joints

PubMed Central

Drewniak, Elizabeth I.; Jay, Gregory D.; Fleming, Braden C.; Crisco, Joseph J.

2009-01-01

In attempts to better understand the etiology of osteoarthritis, a debilitating joint disease that results in the degeneration of articular cartilage in synovial joints, researchers have focused on joint tribology, the study of joint friction, lubrication, and wear. Several different approaches have been used to investigate the frictional properties of articular cartilage. In this study, we examined two analysis methods for calculating the coefficient of friction (μ) using a simple pendulum system and BL6 murine knee joints (n=10) as the fulcrum. A Stanton linear decay model (Lin μ) and an exponential model that accounts for viscous damping (Exp μ) were fit to the decaying pendulum oscillations. Root mean square error (RMSE), asymptotic standard error (ASE), and coefficient of variation (CV) were calculated to evaluate the fit and measurement precision of each model. This investigation demonstrated that while Lin μ was more repeatable, based on CV (5.0% for Lin μ; 18% for Exp μ), Exp μ provided a better fitting model, based on RMSE (0.165° for Exp μ; 0.391° for Lin μ) and ASE (0.033 for Exp μ; 0.185 for Lin μ), and had a significantly lower coefficient of friction value (0.022±0.007 for Exp μ; 0.042±0.016 for Lin μ) (p=0.001). This study details the use of a simple pendulum for examining cartilage properties in situ that will have applications investigating cartilage mechanics in a variety of species. The Exp μ model provided a more accurate fit to the experimental data for predicting the frictional properties of intact joints in pendulum systems. PMID:19632680

The Common Patterns of Nature

PubMed Central

Frank, Steven A.

2010-01-01

We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased or random stochastic fluctuations: random connections of network nodes; amino acid substitutions with no effect on fitness; species that arise or disappear from communities randomly. These neutral generative models often match common patterns of nature. In this paper, I present the theoretical background by which we can understand why these neutral generative models are so successful. I show where the classic patterns come from, such as the Poisson pattern, the normal or Gaussian pattern, and many others. Each classic pattern was often discovered by a simple neutral generative model. The neutral patterns share a special characteristic: they describe the patterns of nature that follow from simple constraints on information. For example, any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves information only about the geometric mean attracts to the power law pattern. I present a simple and consistent informational framework of the common patterns of nature based on the method of maximum entropy. This framework shows that each neutral generative model is a special case that helps to discover a particular set of informational constraints; those informational constraints define a much wider domain of non-neutral generative processes that attract to the same neutral pattern. PMID:19538344

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Forecasting Chikungunya spread in the Americas via data-driven empirical approaches.

PubMed

Escobar, Luis E; Qiao, Huijie; Peterson, A Townsend

2016-02-29

Chikungunya virus (CHIKV) is endemic to Africa and Asia, but the Asian genotype invaded the Americas in 2013. The fast increase of human infections in the American epidemic emphasized the urgency of developing detailed predictions of case numbers and the potential geographic spread of this disease. We developed a simple model incorporating cases generated locally and cases imported from other countries, and forecasted transmission hotspots at the level of countries and at finer scales, in terms of ecological features. By late January 2015, >1.2 M CHIKV cases were reported from the Americas, with country-level prevalences between nil and more than 20 %. In the early stages of the epidemic, exponential growth in case numbers was common; later, however, poor and uneven reporting became more common, in a phenomenon we term "surveillance fatigue." Economic activity of countries was not associated with prevalence, but diverse social factors may be linked to surveillance effort and reporting. Our model predictions were initially quite inaccurate, but improved markedly as more data accumulated within the Americas. The data-driven methodology explored in this study provides an opportunity to generate descriptive and predictive information on spread of emerging diseases in the short-term under simple models based on open-access tools and data that can inform early-warning systems and public health intelligence.

Evolution and mass extinctions as lognormal stochastic processes

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics). (5) But the most striking new result is that the well-known `Molecular Clock of Evolution', namely the `constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms. (7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time. In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are the particular case of exponential growth.

Analytical study of index-coupled herd behavior in financial markets

NASA Astrophysics Data System (ADS)

Berman, Yonatan; Shapira, Yoash; Schwartz, Moshe

2016-12-01

Herd behavior in financial markets had been investigated extensively in the past few decades. Scholars have argued that the behavioral tendency of traders and investors to follow the market trend, notably reflected in indices both on short and long time scales, is substantially affecting the overall market behavior. Research has also been devoted to revealing these behaviors and characterizing the market herd behavior. In this paper we present a simple herd behavior model for the dynamics of financial variables by introducing a simple coupling mechanism of stock returns to the index return, deriving analytic expressions for statistical properties of the returns. We found that several important phenomena in the stock market, namely the correlations between stock market returns and the exponential decay of short-term autocorrelations, are derived from our model. These phenomena have been given various explanations and theories, with herd market behavior being one of the leading. We conclude that the coupling mechanism, which essentially encapsulates the herd behavior, indeed creates correlation and autocorrelation. We also show that this introduces a time scale to the system, which is the characteristic time lag between a change in the index and its effect on the return of a stock.

Magnetic pattern at supergranulation scale: the void size distribution

NASA Astrophysics Data System (ADS)

Berrilli, F.; Scardigli, S.; Del Moro, D.

2014-08-01

The large-scale magnetic pattern observed in the photosphere of the quiet Sun is dominated by the magnetic network. This network, created by photospheric magnetic fields swept into convective downflows, delineates the boundaries of large-scale cells of overturning plasma and exhibits "voids" in magnetic organization. These voids include internetwork fields, which are mixed-polarity sparse magnetic fields that populate the inner part of network cells. To single out voids and to quantify their intrinsic pattern we applied a fast circle-packing-based algorithm to 511 SOHO/MDI high-resolution magnetograms acquired during the unusually long solar activity minimum between cycles 23 and 24. The computed void distribution function shows a quasi-exponential decay behavior in the range 10-60 Mm. The lack of distinct flow scales in this range corroborates the hypothesis of multi-scale motion flows at the solar surface. In addition to the quasi-exponential decay, we have found that the voids depart from a simple exponential decay at about 35 Mm.

Exponential decline of aftershocks of the M7.9 1868 great Kau earthquake, Hawaii, through the 20th century

USGS Publications Warehouse

Klein, F.W.; Wright, Tim

2008-01-01

The remarkable catalog of Hawaiian earthquakes going back to the 1820s is based on missionary diaries, newspaper accounts, and instrumental records and spans the great M7.9 Kau earthquake of April 1868 and its aftershock sequence. The earthquake record since 1868 defines a smooth curve complete to M5.2 of the declining rate into the 21st century, after five short volcanic swarms are removed. A single aftershock curve fits the earthquake record, even with numerous M6 and 7 main shocks and eruptions. The timing of some moderate earthquakes may be controlled by magmatic stresses, but their overall long-term rate reflects one of aftershocks of the Kau earthquake. The 1868 earthquake is, therefore, the largest and most controlling stress event in the 19th and 20th centuries. We fit both the modified Omori (power law) and stretched exponential (SE) functions to the earthquakes. We found that the modified Omori law is a good fit to the M ??? 5.2 earthquake rate for the first 10 years or so and the more rapidly declining SE function fits better thereafter, as supported by three statistical tests. The switch to exponential decay suggests that a possible change in aftershock physics may occur from rate and state fault friction, with no change in the stress rate, to viscoelastic stress relaxation. The 61-year exponential decay constant is at the upper end of the range of geodetic relaxation times seen after other global earthquakes. Modeling deformation in Hawaii is beyond the scope of this paper, but a simple interpretation of the decay suggests an effective viscosity of 1019 to 1020 Pa s pertains in the volcanic spreading of Hawaii's flanks. The rapid decline in earthquake rate poses questions for seismic hazard estimates in an area that is cited as one of the most hazardous in the United States.

Software and Critical Technology Protection Against Side-Channel Analysis Through Dynamic Hardware Obfuscation

DTIC Science & Technology

2011-03-01

resampling a second time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 70 Plot of RSA bitgroup exponentiation with DAILMOM after a...14 DVFS Dynamic Voltage and Frequency Switching . . . . . . . . . . . . . . . . . . . 14 MDPL Masked Dual-Rail...algorithms to prevent whole-sale discovery of PINs and other simple methods to prevent employee tampering [5]. In time , cryptographic systems have

DESCARTES' RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA.

PubMed

Bhaskar, Anand; Song, Yun S

2014-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.

DESCARTES’ RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA1

PubMed Central

Bhaskar, Anand; Song, Yun S.

2016-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the “folded” SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes’ rule of signs for polynomials to the Laplace transform of piecewise continuous functions. PMID:28018011

Anatomy-based transmission factors for technique optimization in portable chest x-ray

NASA Astrophysics Data System (ADS)

Liptak, Christopher L.; Tovey, Deborah; Segars, William P.; Dong, Frank D.; Li, Xiang

2015-03-01

Portable x-ray examinations often account for a large percentage of all radiographic examinations. Currently, portable examinations do not employ automatic exposure control (AEC). To aid in the design of a size-specific technique chart, acrylic slabs of various thicknesses are often used to estimate x-ray transmission for patients of various body thicknesses. This approach, while simple, does not account for patient anatomy, tissue heterogeneity, and the attenuation properties of the human body. To better account for these factors, in this work, we determined x-ray transmission factors using computational patient models that are anatomically realistic. A Monte Carlo program was developed to model a portable x-ray system. Detailed modeling was done of the x-ray spectrum, detector positioning, collimation, and source-to-detector distance. Simulations were performed using 18 computational patient models from the extended cardiac-torso (XCAT) family (9 males, 9 females; age range: 2-58 years; weight range: 12-117 kg). The ratio of air kerma at the detector with and without a patient model was calculated as the transmission factor. Our study showed that the transmission factor decreased exponentially with increasing patient thickness. For the range of patient thicknesses examined (12-28 cm), the transmission factor ranged from approximately 21% to 1.9% when the air kerma used in the calculation represented an average over the entire imaging field of view. The transmission factor ranged from approximately 21% to 3.6% when the air kerma used in the calculation represented the average signals from two discrete AEC cells behind the lung fields. These exponential relationships may be used to optimize imaging techniques for patients of various body thicknesses to aid in the design of clinical technique charts.

Circularly Polarized Luminescence from Simple Organic Molecules.

PubMed

Sánchez-Carnerero, Esther M; Agarrabeitia, Antonia R; Moreno, Florencio; Maroto, Beatriz L; Muller, Gilles; Ortiz, María J; de la Moya, Santiago

2015-09-21

This article aims to show the identity of "circularly polarized luminescent active simple organic molecules" as a new concept in organic chemistry due to the potential interest of these molecules, as availed by the exponentially growing number of research articles related to them. In particular, it describes and highlights the interest and difficulty in developing chiral simple (small and non-aggregated) organic molecules able to emit left- or right-circularly polarized light efficiently, the efforts realized up to now to reach this challenging objective, and the most significant milestones achieved to date. General guidelines for the preparation of these interesting molecules are also presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mathematical Modeling of Extinction of Inhomogeneous Populations

PubMed Central

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

The Decompression Sickness and Venous Gas Emboli Consequences of Air Breaks During 100% Oxygen Prebreathe

NASA Technical Reports Server (NTRS)

Conkin, J.; Gernhardt, M. L.; Powell, M. R.

2004-01-01

Not enough is known about the increased risk of hypobaric decompression sickness (DCS) and production of venous (VGE) and arterial (AGE) gas emboli following an air break in an otherwise normal 100% resting oxygen (O2) prebreathe (PB), and certainly a break in PB when exercise is used to accelerate nitrogen (N2) elimination from the tissues. Current Aeromedical Flight Rules at the Johnson Space Center about additional PB payback times are untested, possibly too conservative, and therefore not optimized for operational use. A 10 min air break at 90 min into a 120 min PB that includes initial dual-cycle ergometry for 10 min will show a measurable increase in the risk of DCS and VGE after ascent to 4.3 psia compared to a 10 min break at 15 min into the PB, or when there is no break in PB. Data collection with humans begins in 2005, but here we first evaluate the hypothesis using three models of tissue N2 kinetics: Model I is a simple single half-time compartment exponential model, Model II is a three compartment half-time exponential model, and Model III is a variable half-time compartment model where the percentage of maximum O2 consumption for the subject during dual-cycle ergometry exercise defines the half-time compartment. Model I with large rate constants to simulate an exercise effect always showed a late break in PB had the greatest consequence. Model II showed an early break had the greatest consequence. Model III showed there was no difference between early or late break in exercise PB. Only one of these outcomes will be observed when humans are tested. Our results will favor one of these models, and so advance our understanding of tissue N2 kinetics, and of altitude DCS after an air break in PB.

General Mechanism of Two-State Protein Folding Kinetics

PubMed Central

Rollins, Geoffrey C.; Dill, Ken A.

2016-01-01

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s. PMID:25056406

A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation

PubMed Central

Eddy, Sean R.

2008-01-01

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ = log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments. PMID:18516236

Using Exponential Smoothing to Specify Intervention Models for Interrupted Time Series.

ERIC Educational Resources Information Center

Mandell, Marvin B.; Bretschneider, Stuart I.

1984-01-01

The authors demonstrate how exponential smoothing can play a role in the identification of the intervention component of an interrupted time-series design model that is analogous to the role that the sample autocorrelation and partial autocorrelation functions serve in the identification of the noise portion of such a model. (Author/BW)

A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new Belehdradek-type model for evaluating the effect of temperature on growth rate

USDA-ARS?s Scientific Manuscript database

A new mechanistic growth model was developed to describe microbial growth under isothermal conditions. The new mathematical model was derived from the basic observation of bacterial growth that may include lag, exponential, and stationary phases. With this model, the lag phase duration and exponen...

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth

ERIC Educational Resources Information Center

Castillo-Garsow, Carlos

2010-01-01

Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…

Review of "Going Exponential: Growing the Charter School Sector's Best"

ERIC Educational Resources Information Center

Garcia, David

2011-01-01

This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…

Correlation between the change in the kinetics of the ribosomal RNA rrnB P2 promoter and the transition from lag to exponential phase with Pseudomonas fluorescens.

PubMed

McKellar, Robin C

2008-01-15

Developing accurate mathematical models to describe the pre-exponential lag phase in food-borne pathogens presents a considerable challenge to food microbiologists. While the growth rate is influenced by current environmental conditions, the lag phase is affected in addition by the history of the inoculum. A deeper understanding of physiological changes taking place during the lag phase would improve accuracy of models, and in earlier studies a strain of Pseudomonas fluorescens containing the Tn7-luxCDABE gene cassette regulated by the rRNA promoter rrnB P2 was used to measure the influence of starvation, growth temperature and sub-lethal heating on promoter expression and subsequent growth. The present study expands the models developed earlier to include a model which describes the change from exponential to linear increase in promoter expression with time when the exponential phase of growth commences. A two-phase linear model with Poisson weighting was used to estimate the lag (LPDLin) and the rate (RLin) for this linear increase in bioluminescence. The Spearman rank correlation coefficient (r=0.830) between the LPDLin and the growth lag phase (LPDOD) was extremely significant (P

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

PubMed Central

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

2006-01-01

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

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

PubMed

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

2006-01-01

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

Measurement of the relaxation rate of the magnetization in Mn12O12-acetate using proton NMR echo

PubMed

Jang; Lascialfari; Borsa; Gatteschi

2000-03-27

We present a novel method to measure the relaxation rate W of the magnetization of Mn 12O (12)-acetate (Mn12) magnetic molecular cluster in its S = 10 ground state at low T. It is based on the observation of an exponential growth in time of the proton NMR signal during the thermal equilibration of the magnetization of the molecules. We can explain the novel effect with a simple model which relates the intensity of the proton echo signal to the microscopic reversal of the magnetization of each individual Mn12 molecule during the equilibration process. The method should find wide application in the study of magnetic molecular clusters in off-equilibrium conditions.

Coherent spin transport through a 350 micron thick silicon wafer.

PubMed

Huang, Biqin; Monsma, Douwe J; Appelbaum, Ian

2007-10-26

We use all-electrical methods to inject, transport, and detect spin-polarized electrons vertically through a 350-micron-thick undoped single-crystal silicon wafer. Spin precession measurements in a perpendicular magnetic field at different accelerating electric fields reveal high spin coherence with at least 13pi precession angles. The magnetic-field spacing of precession extrema are used to determine the injector-to-detector electron transit time. These transit time values are associated with output magnetocurrent changes (from in-plane spin-valve measurements), which are proportional to final spin polarization. Fitting the results to a simple exponential spin-decay model yields a conduction electron spin lifetime (T1) lower bound in silicon of over 500 ns at 60 K.

Giant adsorption of microswimmers: Duality of shape asymmetry and wall curvature

NASA Astrophysics Data System (ADS)

Wysocki, Adam; Elgeti, Jens; Gompper, Gerhard

2015-05-01

The effect of shape asymmetry of microswimmers on their adsorption capacity at confining channel walls is studied by a simple dumbbell model. For a shape polarity of a forward-swimming cone, like the stroke-averaged shape of a sperm, extremely long wall retention times are found, caused by a nonvanishing component of the propulsion force pointing steadily into the wall, which grows exponentially with the self-propulsion velocity and the shape asymmetry. A direct duality relation between shape asymmetry and wall curvature is proposed and verified. Our results are relevant for the design microswimmer with controlled wall-adhesion properties. In addition, we confirm that pressure in active systems is strongly sensitive to the details of the particle-wall interactions.

The impacts of precipitation amount simulation on hydrological modeling in Nordic watersheds

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

Stochastic modeling of daily precipitation is very important for hydrological modeling, especially when no observed data are available. Precipitation is usually modeled by two component model: occurrence generation and amount simulation. For occurrence simulation, the most common method is the first-order two-state Markov chain due to its simplification and good performance. However, various probability distributions have been reported to simulate precipitation amount, and spatiotemporal differences exist in the applicability of different distribution models. Therefore, assessing the applicability of different distribution models is necessary in order to provide more accurate precipitation information. Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential, and hybrid exponential/Pareto distributions) are directly and indirectly evaluated on their ability to reproduce the original observed time series of precipitation amount. Data from 24 weather stations and two watersheds (Chute-du-Diable and Yamaska watersheds) in the province of Quebec (Canada) are used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three-parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear-cut when the simulated time series are used to drive a hydrological model. While the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modeling. The implications of choosing a distribution function with respect to hydrological modeling and climate change impact studies are also discussed.

Integrated Multiscale Modeling of Molecular Computing Devices

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

Gregory Beylkin

2012-03-23

Significant advances were made on all objectives of the research program. We have developed fast multiresolution methods for performing electronic structure calculations with emphasis on constructing efficient representations of functions and operators. We extended our approach to problems of scattering in solids, i.e. constructing fast algorithms for computing above the Fermi energy level. Part of the work was done in collaboration with Robert Harrison and George Fann at ORNL. Specific results (in part supported by this grant) are listed here and are described in greater detail. (1) We have implemented a fast algorithm to apply the Green's function for themore » free space (oscillatory) Helmholtz kernel. The algorithm maintains its speed and accuracy when the kernel is applied to functions with singularities. (2) We have developed a fast algorithm for applying periodic and quasi-periodic, oscillatory Green's functions and those with boundary conditions on simple domains. Importantly, the algorithm maintains its speed and accuracy when applied to functions with singularities. (3) We have developed a fast algorithm for obtaining and applying multiresolution representations of periodic and quasi-periodic Green's functions and Green's functions with boundary conditions on simple domains. (4) We have implemented modifications to improve the speed of adaptive multiresolution algorithms for applying operators which are represented via a Gaussian expansion. (5) We have constructed new nearly optimal quadratures for the sphere that are invariant under the icosahedral rotation group. (6) We obtained new results on approximation of functions by exponential sums and/or rational functions, one of the key methods that allows us to construct separated representations for Green's functions. (7) We developed a new fast and accurate reduction algorithm for obtaining optimal approximation of functions by exponential sums and/or their rational representations.« less

Exponential Acceleration of VT Seismicity in the Years Prior to Major Eruptions of Basaltic Volcanoes

NASA Astrophysics Data System (ADS)

Lengline, O.; Marsan, D.; Got, J.; Pinel, V.

2007-12-01

The evolution of the seismicity at three basaltic volcanoes (Kilauea, Mauna-Loa and Piton de la Fournaise) is analysed during phases of magma accumulation. We show that the VT seismicity during these time-periods is characterized by an exponential increase at long-time scale (years). Such an exponential acceleration can be explained by a model of seismicity forced by the replenishment of a magmatic reservoir. The increase in stress in the edifice caused by this replenishment is modeled. This stress history leads to a cumulative number of damage, ie VT earthquakes, following the same exponential increase as found for seismicity. A long-term seismicity precursor is thus detected at basaltic volcanoes. Although this precursory signal is not able to predict the onset times of futures eruptions (as no diverging point is present in the model), it may help mitigating volcanic hazards.

Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.

Changes in speed distribution: Applying aggregated safety effect models to individual vehicle speeds.

PubMed

Vadeby, Anna; Forsman, Åsa

2017-06-01

This study investigated the effect of applying two aggregated models (the Power model and the Exponential model) to individual vehicle speeds instead of mean speeds. This is of particular interest when the measure introduced affects different parts of the speed distribution differently. The aim was to examine how the estimated overall risk was affected when assuming the models are valid on an individual vehicle level. Speed data from two applications of speed measurements were used in the study: an evaluation of movable speed cameras and a national evaluation of new speed limits in Sweden. The results showed that when applied on individual vehicle speed level compared with aggregated level, there was essentially no difference between these for the Power model in the case of injury accidents. However, for fatalities the difference was greater, especially for roads with new cameras where those driving fastest reduced their speed the most. For the case with new speed limits, the individual approach estimated a somewhat smaller effect, reflecting that changes in the 15th percentile (P15) were somewhat larger than changes in P85 in this case. For the Exponential model there was also a clear, although small, difference between applying the model to mean speed changes and individual vehicle speed changes when speed cameras were used. This applied both for injury accidents and fatalities. There were also larger effects for the Exponential model than for the Power model, especially for injury accidents. In conclusion, applying the Power or Exponential model to individual vehicle speeds is an alternative that provides reasonable results in relation to the original Power and Exponential models, but more research is needed to clarify the shape of the individual risk curve. It is not surprising that the impact on severe traffic crashes was larger in situations where those driving fastest reduced their speed the most. Further investigations on use of the Power and/or the Exponential model at individual vehicle level would require more data on the individual level from a range of international studies. Copyright © 2017 Elsevier Ltd. All rights reserved.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States.

PubMed

Steimer, Andreas; Schindler, Kaspar

2015-01-01

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon's implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike's preceding ISI. As we show, the EIF's exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron's ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Spectrum and Morphology of the Two Brightest Milagro Sources in the Cygnus Region: MGRO J2019+37 and MGRO J2031+41

NASA Astrophysics Data System (ADS)

Abdo, A. A.; Abeysekara, U.; Allen, B. T.; Aune, T.; Berley, D.; Bonamente, E.; Christopher, G. E.; DeYoung, T.; Dingus, B. L.; Ellsworth, R. W.; Galbraith-Frew, J. G.; Gonzalez, M. M.; Goodman, J. A.; Hoffman, C. M.; Hüntemeyer, P. H.; Hui, C. M.; Kolterman, B. E.; Linnemann, J. T.; McEnery, J. E.; Mincer, A. I.; Morgan, T.; Nemethy, P.; Pretz, J.; Ryan, J. M.; Saz Parkinson, P. M.; Shoup, A.; Sinnis, G.; Smith, A. J.; Vasileiou, V.; Walker, G. P.; Williams, D. A.; Yodh, G. B.

2012-07-01

The Cygnus region is a very bright and complex portion of the TeV sky, host to unidentified sources and a diffuse excess with respect to conventional cosmic-ray propagation models. Two of the brightest TeV sources, MGRO J2019+37 and MGRO J2031+41, are analyzed using Milagro data with a new technique, and their emission is tested under two different spectral assumptions: a power law and a power law with an exponential cutoff. The new analysis technique is based on an energy estimator that uses the fraction of photomultiplier tubes in the observatory that detect the extensive air shower. The photon spectrum is measured in the range 1-100 TeV using the last three years of Milagro data (2005-2008), with the detector in its final configuration. An F-test indicates that MGRO J2019+37 is better fit by a power law with an exponential cutoff than by a simple power law. The best-fitting parameters for the power law with exponential cutoff model are a normalization at 10 TeV of 7+5 -2 × 10-10 s-1 m-2 TeV-1, a spectral index of 2.0+0.5 -1.0, and a cutoff energy of 29+50 -16 TeV. MGRO J2031+41 shows no evidence of a cutoff. The best-fitting parameters for a power law are a normalization of 2.1+0.6 -0.6 × 10-10 s-1 m-2 TeV-1 and a spectral index of 3.22+0.23 -0.18. The overall flux is subject to a ~30% systematic uncertainty. The systematic uncertainty on the power-law indices is ~0.1. Both uncertainties have been verified with cosmic-ray data. A comparison with previous results from TeV J2032+4130, MGRO J2031+41, and MGRO J2019+37 is also presented.

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Automatic selection of arterial input function using tri-exponential models

NASA Astrophysics Data System (ADS)

Yao, Jianhua; Chen, Jeremy; Castro, Marcelo; Thomasson, David

2009-02-01

Dynamic Contrast Enhanced MRI (DCE-MRI) is one method for drug and tumor assessment. Selecting a consistent arterial input function (AIF) is necessary to calculate tissue and tumor pharmacokinetic parameters in DCE-MRI. This paper presents an automatic and robust method to select the AIF. The first stage is artery detection and segmentation, where knowledge about artery structure and dynamic signal intensity temporal properties of DCE-MRI is employed. The second stage is AIF model fitting and selection. A tri-exponential model is fitted for every candidate AIF using the Levenberg-Marquardt method, and the best fitted AIF is selected. Our method has been applied in DCE-MRIs of four different body parts: breast, brain, liver and prostate. The success rates in artery segmentation for 19 cases are 89.6%+/-15.9%. The pharmacokinetic parameters computed from the automatically selected AIFs are highly correlated with those from manually determined AIFs (R2=0.946, P(T<=t)=0.09). Our imaging-based tri-exponential AIF model demonstrated significant improvement over a previously proposed bi-exponential model.

Comparison of kinetic model for biogas production from corn cob

NASA Astrophysics Data System (ADS)

Shitophyta, L. M.; Maryudi

2018-04-01

Energy demand increases every day, while the energy source especially fossil energy depletes increasingly. One of the solutions to overcome the energy depletion is to provide renewable energies such as biogas. Biogas can be generated by corn cob and food waste. In this study, biogas production was carried out by solid-state anaerobic digestion. The steps of biogas production were the preparation of feedstock, the solid-state anaerobic digestion, and the measurement of biogas volume. This study was conducted on TS content of 20%, 22%, and 24%. The aim of this research was to compare kinetic models of biogas production from corn cob and food waste as a co-digestion using the linear, exponential equation, and first-kinetic models. The result showed that the exponential equation had a better correlation than the linear equation on the ascending graph of biogas production. On the contrary, the linear equation had a better correlation than the exponential equation on the descending graph of biogas production. The correlation values on the first-kinetic model had the smallest value compared to the linear and exponential models.

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

NASA Astrophysics Data System (ADS)

Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye

2016-10-01

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).

[Application of exponential smoothing method in prediction and warning of epidemic mumps].

PubMed

Shi, Yun-ping; Ma, Jia-qi

2010-06-01

To analyze the daily data of epidemic Mumps in a province from 2004 to 2008 and set up exponential smoothing model for the prediction. To predict and warn the epidemic mumps in 2008 through calculating 7-day moving summation and removing the effect of weekends to the data of daily reported mumps cases during 2005-2008 and exponential summation to the data from 2005 to 2007. The performance of Holt-Winters exponential smoothing is good. The result of warning sensitivity was 76.92%, specificity was 83.33%, and timely rate was 80%. It is practicable to use exponential smoothing method to warn against epidemic Mumps.

The Spectrum and Morphology of the Fermi Bubbles

NASA Technical Reports Server (NTRS)

Ackermann, M.; Albert, A.; Atwood, W. B.; Baldini, L.; Ballet, J.; Barbiellini, G.; Bastieri, D.; Bellazini, R.; Bissaldi, E.; Brandt, T. J.;

The release of alginate lyase from growing Pseudomonas syringae pathovar phaseolicola

NASA Technical Reports Server (NTRS)

Ott, C. M.; Day, D. F.; Koenig, D. W.; Pierson, D. L.

2001-01-01

Pseudomonas syringae pathovar phaseolicola, which produces alginate during stationary growth phase, displayed elevated extracellular alginate lyase activity during both mid-exponential and late-stationary growth phases of batch growth. Intracellular activity remained below 22% of the total activity during exponential growth, suggesting that alginate lyase has an extracellular function for this organism. Extracellular enzyme activity in continuous cultures, grown in either nutrient broth or glucose-simple salts medium, peaked at 60% of the washout rate, although nutrient broth-grown cultures displayed more than twice the activity per gram of cell mass. These results imply that growth rate, nutritional composition, or both initiate a release of alginate lyase from viable P. syringae pv. phaseolicola, which could modify its entrapping biofilm.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

The Beer Lambert law measurement made easy

NASA Astrophysics Data System (ADS)

Onorato, Pasquale; Gratton, Luigi M.; Polesello, Marta; Salmoiraghi, Alessandro; Oss, Stefano

2018-05-01

We propose the use of a smartphone based apparatus as a valuable tool for investigating the optical absorption of a material and to verify the exponential decay predicted by Beer’s law. The very simple experimental activities presented here, suitable for undergraduate students, allows one to measure the material transmittance including its dependence on the incident radiation wavelength.

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Nanoscale swimmers: hydrodynamic interactions and propulsion of molecular machines

NASA Astrophysics Data System (ADS)

Sakaue, T.; Kapral, R.; Mikhailov, A. S.

2010-06-01

Molecular machines execute nearly regular cyclic conformational changes as a result of ligand binding and product release. This cyclic conformational dynamics is generally non-reciprocal so that under time reversal a different sequence of machine conformations is visited. Since such changes occur in a solvent, coupling to solvent hydrodynamic modes will generally result in self-propulsion of the molecular machine. These effects are investigated for a class of coarse grained models of protein machines consisting of a set of beads interacting through pair-wise additive potentials. Hydrodynamic effects are incorporated through a configuration-dependent mobility tensor, and expressions for the propulsion linear and angular velocities, as well as the stall force, are obtained. In the limit where conformational changes are small so that linear response theory is applicable, it is shown that propulsion is exponentially small; thus, propulsion is nonlinear phenomenon. The results are illustrated by computations on a simple model molecular machine.

Black holes from large N singlet models

NASA Astrophysics Data System (ADS)

Amado, Irene; Sundborg, Bo; Thorlacius, Larus; Wintergerst, Nico

2018-03-01

The emergent nature of spacetime geometry and black holes can be directly probed in simple holographic duals of higher spin gravity and tensionless string theory. To this end, we study time dependent thermal correlation functions of gauge invariant observables in suitably chosen free large N gauge theories. At low temperature and on short time scales the correlation functions encode propagation through an approximate AdS spacetime while interesting departures emerge at high temperature and on longer time scales. This includes the existence of evanescent modes and the exponential decay of time dependent boundary correlations, both of which are well known indicators of bulk black holes in AdS/CFT. In addition, a new time scale emerges after which the correlation functions return to a bulk thermal AdS form up to an overall temperature dependent normalization. A corresponding length scale was seen in equal time correlation functions in the same models in our earlier work.

A consensus-based dynamics for market volumes

NASA Astrophysics Data System (ADS)

Sabatelli, Lorenzo; Richmond, Peter

2004-12-01

We develop a model of trading orders based on opinion dynamics. The agents may be thought as the share holders of a major mutual fund rather than as direct traders. The balance between their buy and sell orders determines the size of the fund order (volume) and has an impact on prices and indexes. We assume agents interact simultaneously to each other through a Sznajd-like interaction. Their degree of connection is determined by the probability of changing opinion independently of what their neighbours are doing. We assume that such a probability may change randomly, after each transaction, of an amount proportional to the relative difference between the volatility then measured and a benchmark that we assume to be an exponential moving average of the past volume values. We show how this simple model is compatible with some of the main statistical features observed for the asset volumes in financial markets.

Rockfall travel distances theoretical distributions

NASA Astrophysics Data System (ADS)

Jaboyedoff, Michel; Derron, Marc-Henri; Pedrazzini, Andrea

2017-04-01

The probability of propagation of rockfalls is a key part of hazard assessment, because it permits to extrapolate the probability of propagation of rockfall either based on partial data or simply theoretically. The propagation can be assumed frictional which permits to describe on average the propagation by a line of kinetic energy which corresponds to the loss of energy along the path. But loss of energy can also be assumed as a multiplicative process or a purely random process. The distributions of the rockfall block stop points can be deduced from such simple models, they lead to Gaussian, Inverse-Gaussian, Log-normal or exponential negative distributions. The theoretical background is presented, and the comparisons of some of these models with existing data indicate that these assumptions are relevant. The results are either based on theoretical considerations or by fitting results. They are potentially very useful for rockfall hazard zoning and risk assessment. This approach will need further investigations.

Long-Range Interaction Forces between Polymer-Supported Lipid Bilayer Membranes

PubMed Central

Seitz, Markus; Park, Chad K.; Wong, Joyce Y.

2009-01-01

Much of the short-range forces and structures of softly supported DMPC bilayers has been described previously. However, one interesting feature of the measured force–distance profile that remained unexplained is the presence of a long-range exponentially decaying repulsive force that is not observed between rigidly supported bilayers on solid mica substrate surfaces. This observation is discussed in detail here based on recent static and dynamic surface force experiments. The repulsive forces in the intermediate distance regime (mica–mica separations from 15 to 40 nm) are shown to be due not to an electrostatic force between the bilayers but to compression (deswelling) of the underlying soft polyelectrolyte layer, which may be thought of as a model cytoskeleton. The experimental data can be fit by simple theoretical models of polymer interactions from which the elastic properties of the polymer layer can be deduced. PMID:21359166

Galacti chemical evolution: Hygrogen through zinc

NASA Technical Reports Server (NTRS)

Timmes, F. X.; Woosley, S. E.; Weaver, Thomas A.

1995-01-01

Using the output from a grid of 60 Type II supernova models (Woosley & Weaver 1995) of varying mass (11 approx. less than (M/solar mass) approx. less than 40) and metallicity (0, 10(exp -4), 0.01, and 1 solar metallicity), the chemical evolution of 76 stable isotopes, from hydrogen to zinc, is calculated. The chemical evolution calculation employs a simple dynamical model for the Galaxy (infall with a 4 Gyr e-folding timescale onto a exponential dsk and 1/r(exp 2) bulge), and standard evolution parameters, such as a Salpeter initial mass function and a quadratic Schmidt star formation rate. The theoretical results are compared in detail with observed stellar abundances in stars with metallicities in the range -3.0 approx. less than (Fe/H) approx. less than 0.0 dex. While our discussion focuses on the solar neighborhood where there are the most observations, the supernova rates, an intrinsically Galactic quality, are also discussed.

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

PubMed Central

Gustman, Alan L.; Steinmeier, Thomas L.

2012-01-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. PMID:22711946

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.

PubMed

Gustman, Alan L; Steinmeier, Thomas L

2012-06-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.

On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

NASA Astrophysics Data System (ADS)

Ernazarov, K. K.

2017-12-01

We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Seamount statistics in the Pacific Ocean

NASA Astrophysics Data System (ADS)

Smith, Deborah K.; Jordan, Thomas H.

1988-04-01

We apply the wide-beam sampling technique of Jordan et al. (1983) to approximately 157,000 km of wide-beam profiles to obtain seamount population statistics for eight regions in the eastern and southern Pacific Ocean. Population statistics derived from wide-beam echograms are compared with seamount counts from Sea Beam swaths and with counts from bathymetric maps. We find that the average number of seamounts with summit heights h ≥ H is well-approximated by the exponential frequency-size distribution: ν(H)=νoe-βH. The exponential model for seamount sizes, characterized by the single scale parameter β-1, is found to be superior to a power-law (self-similar) model, which has no intrinsic scale, in describing the average distribution of Pacific seamounts, and it appears to be valid over a size spectrum spanning 5 orders of magnitude in abundance. Large-scale regional variations in seamount populations are documented. We observe significant differences in seamount densities across the Murray fracture zone in the North Pacific and the Eltanin fracture zone system in the South Pacific. The Eltanin discontinuity is equally evident on both sides of the Pacific-Antarctic ridge. In the South Pacific, regions symmetrically disposed about the ridge axis have very similar seamount densities, despite the large difference between Pacific plate and Antarctic plate absolute velocities; evidently, any differences in the shear flows at the base of the Pacific and Antarctic plates do not affect seamount emplacement. Systematic variations in νo and β are observed as a function of lithospheric age, with the number of large seamounts increasing more rapidly than small seamounts. These observations have been used to develop a simple model for seamount production under the assumptions that (1) an exponential size-frequency distribution is maintained, (2) production is steady state, and (3) most small seamounts are formed on or near the ridge axis. The limited data available from this study appear to be consistent with the model, but they are insufficient to provide a rigorous test of the assumptions or determine accurately the model parameters. However, the data from the South Pacific indicate that the off-axis production of large seamounts probably accounts for the majority of seamounts with summit heights greater than 1000 m.

Dynamic modeling of sludge compaction and consolidation processes in wastewater secondary settling tanks.

PubMed

Abusam, A; Keesman, K J

2009-01-01

The double exponential settling model is the widely accepted model for wastewater secondary settling tanks. However, this model does not estimate accurately solids concentrations in the settler underflow stream, mainly because sludge compression and consolidation processes are not considered. In activated sludge systems, accurate estimation of the solids in the underflow stream will facilitate the calibration process and can lead to correct estimates of particularly kinetic parameters related to biomass growth. Using principles of compaction and consolidation, as in soil mechanics, a dynamic model of the sludge consolidation processes taking place in the secondary settling tanks is developed and incorporated to the commonly used double exponential settling model. The modified double exponential model is calibrated and validated using data obtained from a full-scale wastewater treatment plant. Good agreement between predicted and measured data confirmed the validity of the modified model.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Rich client data exploration and research prototyping for NOAA

NASA Astrophysics Data System (ADS)

Grossberg, Michael; Gladkova, Irina; Guch, Ingrid; Alabi, Paul; Shahriar, Fazlul; Bonev, George; Aizenman, Hannah

2009-08-01

Data from satellites and model simulations is increasing exponentially as observations and model computing power improve rapidly. Not only is technology producing more data, but it often comes from sources all over the world. Researchers and scientists who must collaborate are also located globally. This work presents a software design and technologies which will make it possible for groups of researchers to explore large data sets visually together without the need to download these data sets locally. The design will also make it possible to exploit high performance computing remotely and transparently to analyze and explore large data sets. Computer power, high quality sensing, and data storage capacity have improved at a rate that outstrips our ability to develop software applications that exploit these resources. It is impractical for NOAA scientists to download all of the satellite and model data that may be relevant to a given problem and the computing environments available to a given researcher range from supercomputers to only a web browser. The size and volume of satellite and model data are increasing exponentially. There are at least 50 multisensor satellite platforms collecting Earth science data. On the ground and in the sea there are sensor networks, as well as networks of ground based radar stations, producing a rich real-time stream of data. This new wealth of data would have limited use were it not for the arrival of large-scale high-performance computation provided by parallel computers, clusters, grids, and clouds. With these computational resources and vast archives available, it is now possible to analyze subtle relationships which are global, multi-modal and cut across many data sources. Researchers, educators, and even the general public, need tools to access, discover, and use vast data center archives and high performance computing through a simple yet flexible interface.

A decades-long fast-rise-exponential-decay flare in low-luminosity AGN NGC 7213

NASA Astrophysics Data System (ADS)

Yan, Zhen; Xie, Fu-Guo

2018-03-01

We analysed the four-decades-long X-ray light curve of the low-luminosity active galactic nucleus (LLAGN) NGC 7213 and discovered a fast-rise-exponential-decay (FRED) pattern, i.e. the X-ray luminosity increased by a factor of ≈4 within 200 d, and then decreased exponentially with an e-folding time ≈8116 d (≈22.2 yr). For the theoretical understanding of the observations, we examined three variability models proposed in the literature: the thermal-viscous disc instability model, the radiation pressure instability model, and the TDE model. We find that a delayed tidal disruption of a main-sequence star is most favourable; either the thermal-viscous disc instability model or radiation pressure instability model fails to explain some key properties observed, thus we argue them unlikely.

Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise.

PubMed

Hertäg, Loreen; Durstewitz, Daniel; Brunel, Nicolas

2014-01-01

Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise.

Simple inflationary quintessential model. II. Power law potentials

NASA Astrophysics Data System (ADS)

de Haro, Jaume; Amorós, Jaume; Pan, Supriya

2016-09-01

The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive improvement of the observational data.

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

New pharmacokinetic methods. III. Two simple test for deep pool effect

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

Browne, T.R.; Greenblatt, D.J.; Schumacher, G.E.

1990-08-01

If a portion of administered drug is distributed into a deep peripheral compartment, the drug's actual elimination half-life during the terminal exponential phase of elimination may be longer than determined by a single dose study or a tracer dose study (deep pool effect). Two simple methods of testing for deep pool effect applicable to drugs with either linear or nonlinear pharmacokinetic properties are described. The methods are illustrated with stable isotope labeled (13C15N2) tracer dose studies of phenytoin. No significant (P less than .05) deep pool effect was detected.

The generalized truncated exponential distribution as a model for earthquake magnitudes

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-04-01

The random distribution of small, medium and large earthquake magnitudes follows an exponential distribution (ED) according to the Gutenberg-Richter relation. But a magnitude distribution is truncated in the range of very large magnitudes because the earthquake energy is finite and the upper tail of the exponential distribution does not fit well observations. Hence the truncated exponential distribution (TED) is frequently applied for the modelling of the magnitude distributions in the seismic hazard and risk analysis. The TED has a weak point: when two TEDs with equal parameters, except the upper bound magnitude, are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters, except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. It also applies to alternative distribution models. The presented generalized truncated exponential distribution (GTED) overcomes this weakness. The ED and the TED are special cases of the GTED. Different issues of the statistical inference are also discussed and an example of empirical data is presented in the current contribution.

CMB constraints on β-exponential inflationary models

NASA Astrophysics Data System (ADS)

Santos, M. A.; Benetti, M.; Alcaniz, J. S.; Brito, F. A.; Silva, R.

2018-03-01

We analyze a class of generalized inflationary models proposed in ref. [1], known as β-exponential inflation. We show that this kind of potential can arise in the context of brane cosmology, where the field describing the size of the extra-dimension is interpreted as the inflaton. We discuss the observational viability of this class of model in light of the latest Cosmic Microwave Background (CMB) data from the Planck Collaboration through a Bayesian analysis, and impose tight constraints on the model parameters. We find that the CMB data alone prefer weakly the minimal standard model (ΛCDM) over the β-exponential inflation. However, when current local measurements of the Hubble parameter, H0, are considered, the β-inflation model is moderately preferred over the ΛCDM cosmology, making the study of this class of inflationary models interesting in the context of the current H0 tension.

Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

NASA Astrophysics Data System (ADS)

Batac, Rene; Longjas, Anthony; Monterola, Christopher

2012-02-01

Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S-1.3 for the first layer to gamma distributions p(S)≈Sαexp(-S/S0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Non-minimally coupled f(R) cosmology

NASA Astrophysics Data System (ADS)

Thakur, Shruti; Sen, Anjan A.; Seshadri, T. R.

2011-02-01

We investigate the consequences of non-minimal gravitational coupling to matter and study how it differs from the case of minimal coupling by choosing certain simple forms for the nature of coupling. The values of the parameters are specified at z=0 (present epoch) and the equations are evolved backwards to calculate the evolution of cosmological parameters. We find that the Hubble parameter evolves more slowly in non-minimal coupling case as compared to the minimal coupling case. In both the cases, the universe accelerates around present time, and enters the decelerating regime in the past. Using the latest Union2 dataset for supernova Type Ia observations as well as the data for baryon acoustic oscillation (BAO) from SDSS observations, we constraint the parameters of Linder exponential model in the two different approaches. We find that there is an upper bound on model parameter in minimal coupling. But for non-minimal coupling case, there is range of allowed values for the model parameter.

Regularization techniques for backward--in--time evolutionary PDE problems

NASA Astrophysics Data System (ADS)

Gustafsson, Jonathan; Protas, Bartosz

2007-11-01

Backward--in--time evolutionary PDE problems have applications in the recently--proposed retrograde data assimilation. We consider the terminal value problem for the Kuramoto--Sivashinsky equation (KSE) in a 1D periodic domain as our model system. The KSE, proposed as a model for interfacial and combustion phenomena, is also often adopted as a toy model for hydrodynamic turbulence because of its multiscale and chaotic dynamics. Backward--in--time problems are typical examples of ill-posed problem, where disturbances are amplified exponentially during the backward march. Regularization is required to solve such problems efficiently and we consider approaches in which the original ill--posed problem is approximated with a less ill--posed problem obtained by adding a regularization term to the original equation. While such techniques are relatively well--understood for linear problems, they less understood in the present nonlinear setting. We consider regularization terms with fixed magnitudes and also explore a novel approach in which these magnitudes are adapted dynamically using simple concepts from the Control Theory.

Fractal dimension and universality in avascular tumor growth

NASA Astrophysics Data System (ADS)

Ribeiro, Fabiano L.; dos Santos, Renato Vieira; Mata, Angélica S.

2017-04-01

For years, the comprehension of the tumor growth process has been intriguing scientists. New research has been constantly required to better understand the complexity of this phenomenon. In this paper, we propose a mathematical model that describes the properties, already known empirically, of avascular tumor growth. We present, from an individual-level (microscopic) framework, an explanation of some phenomenological (macroscopic) aspects of tumors, such as their spatial form and the way they develop. Our approach is based on competitive interaction between the cells. This simple rule makes the model able to reproduce evidence observed in real tumors, such as exponential growth in their early stage followed by power-law growth. The model also reproduces (i) the fractal-space distribution of tumor cells and (ii) the universal growth behavior observed in both animals and tumors. Our analyses suggest that the universal similarity between tumor and animal growth comes from the fact that both can be described by the same dynamic equation—the Bertalanffy-Richards model—even if they do not necessarily share the same biological properties.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

PubMed

Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

PubMed Central

Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622

Cole-Davidson dynamics of simple chain models.

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

Dotson, Taylor C.; McCoy, John Dwane; Adolf, Douglas Brian

2008-10-01

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole-Davidson function was used to fit the response functions with extensive use being made of Cole-Cole plots in the fitting procedure. For the systems studied, the Cole-Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch-Williams-Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or freemore » rotation effects. The accuracy of the Cole-Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole-Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole-Davidson would provide a better frequency-domain description of the associated response function than the KWW function does.« less

Fuzzy Neural Networks for Decision Support in Negotiation

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

Sakas, D. P.; Vlachos, D. S.; Simos, T. E.

There is a large number of parameters which one can take into account when building a negotiation model. These parameters in general are uncertain, thus leading to models which represents them with fuzzy sets. On the other hand, the nature of these parameters makes them very difficult to model them with precise values. During negotiation, these parameters play an important role by altering the outcomes or changing the state of the negotiators. One reasonable way to model this procedure is to accept fuzzy relations (from theory or experience). The action of these relations to fuzzy sets, produce new fuzzy setsmore » which describe now the new state of the system or the modified parameters. But, in the majority of these situations, the relations are multidimensional, leading to complicated models and exponentially increasing computational time. In this paper a solution to this problem is presented. The use of fuzzy neural networks is shown that it can substitute the use of fuzzy relations with comparable results. Finally a simple simulation is carried in order to test the new method.« less

Evolution in leaps: The punctuated accumulation and loss of cultural innovations

PubMed Central

Kolodny, Oren; Creanza, Nicole; Feldman, Marcus W.

2015-01-01

Archaeological accounts of cultural change reveal a fundamental conflict: Some suggest that change is gradual, accelerating over time, whereas others indicate that it is punctuated, with long periods of stasis interspersed by sudden gains or losses of multiple traits. Existing models of cultural evolution, inspired by models of genetic evolution, lend support to the former and do not generate trajectories that include large-scale punctuated change. We propose a simple model that can give rise to both exponential and punctuated patterns of gain and loss of cultural traits. In it, cultural innovation comprises several realistic interdependent processes that occur at different rates. The model also takes into account two properties intrinsic to cultural evolution: the differential distribution of traits among social groups and the impact of environmental change. In our model, a population may be subdivided into groups with different cultural repertoires leading to increased susceptibility to cultural loss, whereas environmental change may lead to rapid loss of traits that are not useful in a new environment. Taken together, our results suggest the usefulness of a concept of an effective cultural population size. PMID:26598675

Evolution in leaps: The punctuated accumulation and loss of cultural innovations.

PubMed

Kolodny, Oren; Creanza, Nicole; Feldman, Marcus W

2015-12-08

Archaeological accounts of cultural change reveal a fundamental conflict: Some suggest that change is gradual, accelerating over time, whereas others indicate that it is punctuated, with long periods of stasis interspersed by sudden gains or losses of multiple traits. Existing models of cultural evolution, inspired by models of genetic evolution, lend support to the former and do not generate trajectories that include large-scale punctuated change. We propose a simple model that can give rise to both exponential and punctuated patterns of gain and loss of cultural traits. In it, cultural innovation comprises several realistic interdependent processes that occur at different rates. The model also takes into account two properties intrinsic to cultural evolution: the differential distribution of traits among social groups and the impact of environmental change. In our model, a population may be subdivided into groups with different cultural repertoires leading to increased susceptibility to cultural loss, whereas environmental change may lead to rapid loss of traits that are not useful in a new environment. Taken together, our results suggest the usefulness of a concept of an effective cultural population size.

Dependence of two-proton radioactivity on nuclear pairing models

NASA Astrophysics Data System (ADS)

Oishi, Tomohiro; Kortelainen, Markus; Pastore, Alessandro

2017-10-01

Sensitivity of two-proton emitting decay to nuclear pairing correlation is discussed within a time-dependent three-body model. We focus on the 6Be nucleus assuming α +p +p configuration, and its decay process is described as a time evolution of the three-body resonance state. For a proton-proton subsystem, a schematic density-dependent contact (SDDC) pairing model is employed. From the time-dependent calculation, we observed the exponential decay rule of a two-proton emission. It is shown that the density dependence does not play a major role in determining the decay width, which can be controlled only by the asymptotic strength of the pairing interaction. This asymptotic pairing sensitivity can be understood in terms of the dynamics of the wave function driven by the three-body Hamiltonian, by monitoring the time-dependent density distribution. With this simple SDDC pairing model, there remains an impossible trinity problem: it cannot simultaneously reproduce the empirical Q value, decay width, and the nucleon-nucleon scattering length. This problem suggests that a further sophistication of the theoretical pairing model is necessary, utilizing the two-proton radioactivity data as the reference quantities.

Markov chains at the interface of combinatorics, computing, and statistical physics

NASA Astrophysics Data System (ADS)

Streib, Amanda Pascoe

The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is always rapidly mixing for two general classes of positively biased { pxy}. More significantly, we also prove that the general conjecture is false by exhibiting values for the pxy, with 1/2 ≤ pxy ≤ 1 for all x < y, but for which the transposition chain will require exponential time to converge. Finally, we consider a model of colloids, which are binary mixtures of molecules with one type of molecule suspended in another. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters. This clustering has proved elusive to verify, since all local sampling algorithms are known to be inefficient at high density, and in fact a new nonlocal algorithm was recently shown to require exponential time in some cases. We characterize the high and low density phases for a general family of discrete interfering binary mixtures by showing that they exhibit a "clustering property" at high density and not at low density. The clustering property states that there will be a region that has very high area, very small perimeter, and high density of one type of molecule. Special cases of interfering binary mixtures include the Ising model at fixed magnetization and independent sets.

Development, triploblastism, physics of wetting and the Cambrian explosion.

PubMed

Fleury, Vincent

2013-09-01

The Cambrian explosion is characterized by the sudden outburst of organized animal plans, which occurred circa 530 M years ago. Around that time, many forms of animal life appeared, including several which have since disappeared. There is no general consensus about "why" this happened, and why it had any form of suddenness. However, all organized animal plans share a common feature: they are triploblastic, i.e., composed of 3 layers of tissue, endoderm, ectoderm and mesoderm. I show here that, within simple hypotheses, the formation of the mesoderm has intrinsically a physical exponential dynamics, leading rapidly to triploblastism, and eventually, to animal formation. A novel physico-mathematical framework including epithelium-mesenchyme transition, visco-elastic constitutive equations, and conservation laws, is presented which allows one to describe gastrulation as a self-wetting phenomenon of a soft solid onto itself. This phenomenon couples differentiation and migration during gastrulation, and leads in a closed form to an exponential scaling law for the formation of the mesoderm. Therefore, the Cambrian explosion might have started, actually, by a true viscoelastic "explosion": the exponential run-away of mesenchymal cells.

Fast dynamics in glass-forming polymers revisited

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

Colmenero, J.; Arbe, A.; Mijangos, C.

1997-12-31

The so called fast-dynamics of glass-forming systems as observed by time of flight (TOF) neutron scattering techniques is revisited. TOF-results corresponding to several glass-forming polymers with different chemical microstructure and glass-transition temperature are presented together with the theoretical framework proposed by the authors to interpret these results. The main conclusion is that the TOF-data can be explained in terms of quasiharmonic vibrations and the particular short time behavior of the segmental dynamics. The segmental dynamics display in the very short time range (t {approx} 2 ps) a crossover from a simple exponential behavior towards a non-exponential regime. The first exponentialmore » decay, which is controlled by C-C rotational barriers, can be understood as a trace of the behavior of the system in absence of the effects (correlations, cooperativity, memory effects {hor_ellipsis}) which characterize the dense supercooled liquid like state against the normal liquid state. The non-exponential regime at t > 2 ps corresponds to what is usually understood as {alpha} and {beta} relaxations. Some implications of these results are also discussed.« less

The ambient dose equivalent at flight altitudes: a fit to a large set of data using a Bayesian approach.

PubMed

Wissmann, F; Reginatto, M; Möller, T

2010-09-01

The problem of finding a simple, generally applicable description of worldwide measured ambient dose equivalent rates at aviation altitudes between 8 and 12 km is difficult to solve due to the large variety of functional forms and parametrisations that are possible. We present an approach that uses Bayesian statistics and Monte Carlo methods to fit mathematical models to a large set of data and to compare the different models. About 2500 data points measured in the periods 1997-1999 and 2003-2006 were used. Since the data cover wide ranges of barometric altitude, vertical cut-off rigidity and phases in the solar cycle 23, we developed functions which depend on these three variables. Whereas the dependence on the vertical cut-off rigidity is described by an exponential, the dependences on barometric altitude and solar activity may be approximated by linear functions in the ranges under consideration. Therefore, a simple Taylor expansion was used to define different models and to investigate the relevance of the different expansion coefficients. With the method presented here, it is possible to obtain probability distributions for each expansion coefficient and thus to extract reliable uncertainties even for the dose rate evaluated. The resulting function agrees well with new measurements made at fixed geographic positions and during long haul flights covering a wide range of latitudes.

Avian Egg Latebra as Brain Tissue Water Diffusion Model

PubMed Central

Maier, Stephan E.; Mitsouras, Dimitris; Mulkern, Robert V.

2013-01-01

Purpose Simplified models of non-monoexponential diffusion signal decay are of great interest to study the basic constituents of complex diffusion behaviour in tissues. The latebra, a unique structure uniformly present in the yolk of avian eggs, exhibits a non-monoexponential diffusion signal decay. This model is more complex than simple phantoms based on differences between water and lipid diffusion, but is also devoid of microscopic structures with preferential orientation or perfusion effects. Methods Diffusion scans with multiple b-values were performed on a clinical 3 Tesla system in raw and boiled chicken eggs equilibrated to room temperature. Diffusion encoding was applied over the ranges 5–5,000 and 5–50,000 s/mm2. A low read-out bandwidth and chemical shift was used for reliable lipid/water separation. Signal decays were fitted with exponential functions. Results The latebra, when measured over the 5–5,000 s/mm2 range, exhibited independent of preparation clearly biexponential diffusion, with diffusion parameters similar to those typically observed in in-vivo human brain. For the range 5–50,000 s/mm2 there was evidence of a small third, very slow diffusing water component. Conclusion The latebra of the avian egg contains membrane structures, which may explain a deviation from a simple monoexponential diffusion signal decay, which is remarkably similar to the deviation observed in brain tissue. PMID:24105853

Exact simulation of integrate-and-fire models with exponential currents.

PubMed

Brette, Romain

2007-10-01

Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

Non-Gaussian analysis of diffusion weighted imaging in head and neck at 3T: a pilot study in patients with nasopharyngeal carcinoma.

PubMed

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D

2014-01-01

To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Biological growth functions describe published site index curves for Lake States timber species.

Treesearch

Allen L. Lundgren; William A. Dolid

1970-01-01

Two biological growth functions, an exponential-monomolecular function and a simple monomolecular function, have been fit to published site index curves for 11 Lake States tree species: red, jack, and white pine, balsam fir, white and black spruce, tamarack, white-cedar, aspen, red oak, and paper birch. Both functions closely fit all published curves except those for...

Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

PubMed Central

Strauß, Magdalena E.; Mezzetti, Maura; Leorato, Samantha

2018-01-01

This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts. We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be precise and computationally efficient. Our implementations also account for spatially lagged regressors. We further allow for location-specific heterogeneity, which we model by including spatial splines. We conclude by comparing the performances of the different model specifications in applications to a real data set and by running simulations. Both the applications and the simulations suggest that the spatial splines are a flexible and efficient way to account for spatial heterogeneities governed by unknown mechanisms. PMID:29492375

Bayesian exponential random graph modelling of interhospital patient referral networks.

PubMed

Caimo, Alberto; Pallotti, Francesca; Lomi, Alessandro

2017-08-15

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among healthcare organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described can be reproduced with accuracy by specifying the system of local dependencies that produce - but at the same time are induced by - decentralised collaborative arrangements between hospitals. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Calculating Formulae of Proportion Factor and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Feng-Hua, Zhang; Gui-De, Zhou; Kun, Ma; Wen-Juan, Ma; Wen-Yuan, Cui; Bo, Zhang

2016-07-01

Previous studies have shown that, for the three main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the neutron exposure distribution (DNE) in the nucleosynthesis region can always be considered as an exponential function, i.e., ρAGB(τ) = C/τ0 exp(-τ/τ0) in an effective range of the neutron exposure values. However, the specific expressions of the proportion factor C and the mean neutron exposure τ0 in the exponential distribution function for different models are not completely determined in the related literature. Through dissecting the basic method to obtain the exponential DNE, and systematically analyzing the solution procedures of neutron exposure distribution functions in different stellar models, the general formulae, as well as their auxiliary equations, for calculating C and τ0 are derived. Given the discrete neutron exposure distribution Pk, the relationships of C and τ0 with the model parameters can be determined. The result of this study has effectively solved the problem to analytically calculate the DNE in the current low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.

A (137)Cs erosion model with moving boundary.

PubMed

Yin, Chuan; Ji, Hongbing

2015-12-01

A novel quantitative model of the relationship between diffused concentration changes and erosion rates using assessment of soil losses was developed. It derived from the analysis of surface soil (137)Cs flux variation under persistent erosion effect and based on the principle of geochemistry kinetics moving boundary. The new moving boundary model improves the basic simplified transport model (Zhang et al., 2008), and mainly applies to uniform rainfall areas which show a long-time soil erosion. The simulation results for this kind of erosion show under a long-time soil erosion, the influence of (137)Cs concentration will decrease exponentially with increasing depth. Using the new model fit to the measured (137)Cs depth distribution data in Zunyi site, Guizhou Province, China which has typical uniform rainfall provided a good fit with R(2) = 0.92. To compare the soil erosion rates calculated by the simple transport model and the new model, we take the Kaixian reference profile as example. The soil losses estimated by the previous simplified transport model are greater than those estimated by the new moving boundary model, which is consistent with our expectations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Application of artificial neural networks to identify equilibration in computer simulations

NASA Astrophysics Data System (ADS)

Leibowitz, Mitchell H.; Miller, Evan D.; Henry, Michael M.; Jankowski, Eric

2017-11-01

Determining which microstates generated by a thermodynamic simulation are representative of the ensemble for which sampling is desired is a ubiquitous, underspecified problem. Artificial neural networks are one type of machine learning algorithm that can provide a reproducible way to apply pattern recognition heuristics to underspecified problems. Here we use the open-source TensorFlow machine learning library and apply it to the problem of identifying which hypothetical observation sequences from a computer simulation are “equilibrated” and which are not. We generate training populations and test populations of observation sequences with embedded linear and exponential correlations. We train a two-neuron artificial network to distinguish the correlated and uncorrelated sequences. We find that this simple network is good enough for > 98% accuracy in identifying exponentially-decaying energy trajectories from molecular simulations.

Slow crack growth in glass in combined mode I and mode II loading

NASA Technical Reports Server (NTRS)

Shetty, D. K.; Rosenfield, A. R.

1991-01-01

Slow crack growth in soda-lime glass under combined mode I and mode II loading was investigated in precracked disk specimens in which pure mode I, pure mode II, and various combinations of mode I and mode II were achieved by loading in diametral compression at selected angles with respect to symmetric radial cracks. It is shown that slow crack growth under these conditions can be described by a simple exponential relationship with elastic strain energy release rate as the effective crack-driving force parameter. It is possible to interpret this equation in terms of theoretical models that treat subcritical crack growth as a thermally activated bond-rupture process with an activation energy dependent on the environment, and the elastic energy release rate as the crack-driving force parameter.

Using quantum dynamics simulations to follow the competition between charge migration and charge transfer in polyatomic molecules

NASA Astrophysics Data System (ADS)

Spinlove, K. E.; Vacher, M.; Bearpark, M.; Robb, M. A.; Worth, G. A.

2017-01-01

Recent work, particularly by Cederbaum and co-workers, has identified the phenomenon of charge migration, whereby charge flow occurs over a static molecular framework after the creation of an electronic wavepacket. In a real molecule, this charge migration competes with charge transfer, whereby the nuclear motion also results in the re-distribution of charge. To study this competition, quantum dynamics simulations need to be performed. To break the exponential scaling of standard grid-based algorithms, approximate methods need to be developed that are efficient yet able to follow the coupled electronic-nuclear motion of these systems. Using a simple model Hamiltonian based on the ionisation of the allene molecule, the performance of different methods based on Gaussian Wavepackets is demonstrated.

Deductibles in health insurance

NASA Astrophysics Data System (ADS)

Dimitriyadis, I.; Öney, Ü. N.

2009-11-01

This study is an extension to a simulation study that has been developed to determine ruin probabilities in health insurance. The study concentrates on inpatient and outpatient benefits for customers of varying age bands. Loss distributions are modelled through the Allianz tool pack for different classes of insureds. Premiums at different levels of deductibles are derived in the simulation and ruin probabilities are computed assuming a linear loading on the premium. The increase in the probability of ruin at high levels of the deductible clearly shows the insufficiency of proportional loading in deductible premiums. The PH-transform pricing rule developed by Wang is analyzed as an alternative pricing rule. A simple case, where an insured is assumed to be an exponential utility decision maker while the insurer's pricing rule is a PH-transform is also treated.

Floquet Supersymmetry

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Hsieh, Timothy H.

2018-05-01

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π . Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and π , which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.

Viscous bursting of suspended films

NASA Astrophysics Data System (ADS)

Debrégeas, G.; Martin, P.; Brochard-Wyart, F.

1995-11-01

Soap films break up by an inertial process. We present here the first observations on freely suspended films of long-chain polymers, where viscous effects are dominant and no surfactant is present. A hole is nucleated at time 0 and grows up to a radius R(t) at time t. A surprising feature is that the liquid from the hole is not collected into a rim (as it is in soap films): The liquid spreads out without any significant change of the film thickness. The radius R(t) grows exponentially with time, R~exp(t/τ) [while in soap films R(t) is linear]. The rise time τ~ηe/2γ where η is viscosity, e is thickness (in the micron range), and γ is surface tension. A simple model is developed to explain this growth law.

Modelling the Probability of Landslides Impacting Road Networks

NASA Astrophysics Data System (ADS)

Taylor, F. E.; Malamud, B. D.

2012-04-01

During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m2, which closely matches the value of A¯ L for the triggered landslide inventories. We further find that over the 500 iterations, the probability of a given number of road blocks occurring on any given iteration, p(NBL) as a function of NBL, follows reasonably well a three-parameter inverse gamma probability density distribution with an exponential rollover (i.e., the most frequent value) at NBL = 1.3. In this paper we have begun to calculate the probability of the number of landslides blocking roads during a triggering event, and have found that this follows an inverse-gamma distribution, which is similar to that found for the statistics of landslide areas resulting from triggers. As we progress to model more realistic road networks, this work will aid in both long-term and disaster management for road networks by allowing probabilistic assessment of road network potential damage during different magnitude landslide triggering event scenarios.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Rock size-frequency distributions on Mars and implications for Mars Exploration Rover landing safety and operations

NASA Astrophysics Data System (ADS)

Golombek, M. P.; Haldemann, A. F. C.; Forsberg-Taylor, N. K.; DiMaggio, E. N.; Schroeder, R. D.; Jakosky, B. M.; Mellon, M. T.; Matijevic, J. R.

2003-10-01

The cumulative fractional area covered by rocks versus diameter measured at the Pathfinder site was predicted by a rock distribution model that follows simple exponential functions that approach the total measured rock abundance (19%), with a steep decrease in rocks with increasing diameter. The distribution of rocks >1.5 m diameter visible in rare boulder fields also follows this steep decrease with increasing diameter. The effective thermal inertia of rock populations calculated from a simple empirical model of the effective inertia of rocks versus diameter shows that most natural rock populations have cumulative effective thermal inertias of 1700-2100 J m-2 s-0.5 K-1 and are consistent with the model rock distributions applied to total rock abundance estimates. The Mars Exploration Rover (MER) airbags have been successfully tested against extreme rock distributions with a higher percentage of potentially hazardous triangular buried rocks than observed at the Pathfinder and Viking landing sites. The probability of the lander impacting a >1 m diameter rock in the first 2 bounces is <3% and <5% for the Meridiani and Gusev landing sites, respectively, and is <0.14% and <0.03% for rocks >1.5 m and >2 m diameter, respectively. Finally, the model rock size-frequency distributions indicate that rocks >0.1 m and >0.3 m in diameter, large enough to place contact sensor instruments against and abrade, respectively, should be plentiful within a single sol's drive at the Meridiani and Gusev landing sites.

The Simple Map for Single-null Divertor Tokamak : How to Find Chaos

NASA Astrophysics Data System (ADS)

Martinez, Ilissa; Ali, Halima; Punjabi, Alkesh

2000-10-01

The Simple Map^1 represents the magnetic field inside a single-null divertor tokamak. The Simple map is given by the equations X_n+1=X_n-KYn (1-Y_n) and Y_n+1=Y_n+KX_n+1. We fix k at 0.6 and X0 at 0. We choose two different starting values of Y_0. These two values are very close together. These values of Y0 represent two field lines which start out very close together. We calculate the distance between two field lines as n is increased. This distance is given by d_n. For both equations given by the distance formula (d_n=[Y_n,2-Y_n,1)^2+(X_n,2-X_n,1)^2]. If dn increases exponentially as n is increased we find chaos, if dn does not increase exponentially then you have not found chaos. We have found chaos, Y0 must be less than one, but higher than 0.9971 for chaos. For Y0 between 0 and 0.9971, there is no chaos. This work is supported by US DOE OFES. Ms. Ilissa Martinez is a HU CFRT Summer Fusion High School Workshop Scholar from the Blanca Malaret High School in Puerto Rico. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Booze A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

A simplified 137Cs transport model for estimating erosion rates in undisturbed soil.

PubMed

Zhang, Xinbao; Long, Yi; He, Xiubin; Fu, Jiexiong; Zhang, Yunqi

2008-08-01

(137)Cs is an artificial radionuclide with a half-life of 30.12 years which released into the environment as a result of atmospheric testing of thermo-nuclear weapons primarily during the period of 1950s-1970s with the maximum rate of (137)Cs fallout from atmosphere in 1963. (137)Cs fallout is strongly and rapidly adsorbed by fine particles in the surface horizons of the soil, when it falls down on the ground mostly with precipitation. Its subsequent redistribution is associated with movements of the soil or sediment particles. The (137)Cs nuclide tracing technique has been used for assessment of soil losses for both undisturbed and cultivated soils. For undisturbed soils, a simple profile-shape model was developed in 1990 to describe the (137)Cs depth distribution in profile, where the maximum (137)Cs occurs in the surface horizon and it exponentially decreases with depth. The model implied that the total (137)Cs fallout amount deposited on the earth surface in 1963 and the (137)Cs profile shape has not changed with time. The model has been widely used for assessment of soil losses on undisturbed land. However, temporal variations of (137)Cs depth distribution in undisturbed soils after its deposition on the ground due to downward transport processes are not considered in the previous simple profile-shape model. Thus, the soil losses are overestimated by the model. On the base of the erosion assessment model developed by Walling, D.E., He, Q. [1999. Improved models for estimating soil erosion rates from cesium-137 measurements. Journal of Environmental Quality 28, 611-622], we discuss the (137)Cs transport process in the eroded soil profile and make some simplification to the model, develop a method to estimate the soil erosion rate more expediently. To compare the soil erosion rates calculated by the simple profile-shape model and the simple transport model, the soil losses related to different (137)Cs loss proportions of the reference inventory at the Kaixian site of the Three Gorge Region, China are estimated by the two models. The over-estimation of the soil loss by using the previous simple profile-shape model obviously increases with the time period from the sampling year to the year of 1963 and (137)Cs loss proportion of the reference inventory. As to 20-80% of (137)Cs loss proportions of the reference inventory at the Kaixian site in 2004, the annual soil loss depths estimated by the new simplified transport process model are only 57.90-56.24% of the values estimated by the previous model.

Proposal for a standardised identification of the mono-exponential terminal phase for orally administered drugs.

PubMed

Scheerans, Christian; Derendorf, Hartmut; Kloft, Charlotte

2008-04-01

The area under the plasma concentration-time curve from time zero to infinity (AUC(0-inf)) is generally considered to be the most appropriate measure of total drug exposure for bioavailability/bioequivalence studies of orally administered drugs. However, the lack of a standardised method for identifying the mono-exponential terminal phase of the concentration-time curve causes variability for the estimated AUC(0-inf). The present investigation introduces a simple method, called the two times t(max) method (TTT method) to reliably identify the mono-exponential terminal phase in the case of oral administration. The new method was tested by Monte Carlo simulation in Excel and compared with the adjusted r squared algorithm (ARS algorithm) frequently used in pharmacokinetic software programs. Statistical diagnostics of three different scenarios, each with 10,000 hypothetical patients showed that the new method provided unbiased average AUC(0-inf) estimates for orally administered drugs with a monophasic concentration-time curve post maximum concentration. In addition, the TTT method generally provided more precise estimates for AUC(0-inf) compared with the ARS algorithm. It was concluded that the TTT method is a most reasonable tool to be used as a standardised method in pharmacokinetic analysis especially bioequivalence studies to reliably identify the mono-exponential terminal phase for orally administered drugs showing a monophasic concentration-time profile.

An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.

Shift-Invariant Image Reconstruction of Speckle-Degraded Images Using Bispectrum Estimation

DTIC Science & Technology

1990-05-01

process with the requisite negative exponential pelf. I call this model the Negative Exponential Model ( NENI ). The NENI flowchart is seen in Figure 6...Figure ]3d-g. Statistical Histograms and Phase for the RPj NG EXP FDF MULT METHOD FILuteC 14a. Truth Object Speckled Via the NENI HISTOGRAM OF SPECKLE

Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays.

PubMed

Hu, Jin; Wang, Jun

2015-06-01

In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given. Copyright © 2015 Elsevier Ltd. All rights reserved.

An approximation method for improving dynamic network model fitting.

PubMed

Carnegie, Nicole Bohme; Krivitsky, Pavel N; Hunter, David R; Goodreau, Steven M

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, i.e., networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a non-negligible computational burden, is much easier. This paper examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail-networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.

Forecasting Daily Volume and Acuity of Patients in the Emergency Department.

PubMed

Calegari, Rafael; Fogliatto, Flavio S; Lucini, Filipe R; Neyeloff, Jeruza; Kuchenbecker, Ricardo S; Schaan, Beatriz D

2016-01-01

This study aimed at analyzing the performance of four forecasting models in predicting the demand for medical care in terms of daily visits in an emergency department (ED) that handles high complexity cases, testing the influence of climatic and calendrical factors on demand behavior. We tested different mathematical models to forecast ED daily visits at Hospital de Clínicas de Porto Alegre (HCPA), which is a tertiary care teaching hospital located in Southern Brazil. Model accuracy was evaluated using mean absolute percentage error (MAPE), considering forecasting horizons of 1, 7, 14, 21, and 30 days. The demand time series was stratified according to patient classification using the Manchester Triage System's (MTS) criteria. Models tested were the simple seasonal exponential smoothing (SS), seasonal multiplicative Holt-Winters (SMHW), seasonal autoregressive integrated moving average (SARIMA), and multivariate autoregressive integrated moving average (MSARIMA). Performance of models varied according to patient classification, such that SS was the best choice when all types of patients were jointly considered, and SARIMA was the most accurate for modeling demands of very urgent (VU) and urgent (U) patients. The MSARIMA models taking into account climatic factors did not improve the performance of the SARIMA models, independent of patient classification.

Forecasting Daily Volume and Acuity of Patients in the Emergency Department

PubMed Central

Fogliatto, Flavio S.; Neyeloff, Jeruza; Kuchenbecker, Ricardo S.; Schaan, Beatriz D.

2016-01-01

This study aimed at analyzing the performance of four forecasting models in predicting the demand for medical care in terms of daily visits in an emergency department (ED) that handles high complexity cases, testing the influence of climatic and calendrical factors on demand behavior. We tested different mathematical models to forecast ED daily visits at Hospital de Clínicas de Porto Alegre (HCPA), which is a tertiary care teaching hospital located in Southern Brazil. Model accuracy was evaluated using mean absolute percentage error (MAPE), considering forecasting horizons of 1, 7, 14, 21, and 30 days. The demand time series was stratified according to patient classification using the Manchester Triage System's (MTS) criteria. Models tested were the simple seasonal exponential smoothing (SS), seasonal multiplicative Holt-Winters (SMHW), seasonal autoregressive integrated moving average (SARIMA), and multivariate autoregressive integrated moving average (MSARIMA). Performance of models varied according to patient classification, such that SS was the best choice when all types of patients were jointly considered, and SARIMA was the most accurate for modeling demands of very urgent (VU) and urgent (U) patients. The MSARIMA models taking into account climatic factors did not improve the performance of the SARIMA models, independent of patient classification. PMID:27725842

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

A Decreasing Failure Rate, Mixed Exponential Model Applied to Reliability.

DTIC Science & Technology

1981-06-01

Trident missile systems have been observed. The mixed exponential distribu- tion has been shown to fit the life data for the electronic equipment on...these systems . This paper discusses some of the estimation problems which occur with the decreasing failure rate mixed exponential distribution when...assumption of constant or increasing failure rate seemed to be incorrect. 2. However, the design of this electronic equipment indicated that

Confronting quasi-exponential inflation with WMAP seven

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

Pal, Barun Kumar; Pal, Supratik; Basu, B., E-mail: barunp1985@rediffmail.com, E-mail: pal@th.physik.uni-bonn.de, E-mail: banasri@isical.ac.in

2012-04-01

We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.

Webcam classification using simple features

NASA Astrophysics Data System (ADS)

Pramoun, Thitiporn; Choe, Jeehyun; Li, He; Chen, Qingshuang; Amornraksa, Thumrongrat; Lu, Yung-Hsiang; Delp, Edward J.

2015-03-01

Thousands of sensors are connected to the Internet and many of these sensors are cameras. The "Internet of Things" will contain many "things" that are image sensors. This vast network of distributed cameras (i.e. web cams) will continue to exponentially grow. In this paper we examine simple methods to classify an image from a web cam as "indoor/outdoor" and having "people/no people" based on simple features. We use four types of image features to classify an image as indoor/outdoor: color, edge, line, and text. To classify an image as having people/no people we use HOG and texture features. The features are weighted based on their significance and combined. A support vector machine is used for classification. Our system with feature weighting and feature combination yields 95.5% accuracy.

Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface

NASA Astrophysics Data System (ADS)

Hayat, Tanzila; Nadeem, S.

2018-03-01

This paper examines the three dimensional Eyring-Powell fluid flow over an exponentially stretching surface with heterogeneous-homogeneous chemical reactions. A new model of heat flux suggested by Cattaneo and Christov is employed to study the properties of relaxation time. From the present analysis we observe that there is an inverse relationship between temperature and thermal relaxation time. The temperature in Cattaneo-Christov heat flux model is lesser than the classical Fourier's model. In this paper the three dimensional Cattaneo-Christov heat flux model over an exponentially stretching surface is calculated first time in the literature. For negative values of temperature exponent, temperature profile firstly intensifies to its most extreme esteem and after that gradually declines to zero, which shows the occurrence of phenomenon (SGH) "Sparrow-Gregg hill". Also, for higher values of strength of reaction parameters, the concentration profile decreases.

Renormalizing a viscous fluid model for large scale structure formation

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

Führer, Florian; Rigopoulos, Gerasimos, E-mail: fuhrer@thphys.uni-heidelberg.de, E-mail: gerasimos.rigopoulos@ncl.ac.uk

2016-02-01

Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher ordermore » vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.« less

The Spectrum And Morphology Of The Fermi Bubbles

DOE PAGES

Ackermann, M.

2014-09-05

The Fermi bubbles are two large structures in the gamma-ray sky extending to 55° above and below the Galactic center. We analyze 50 months of Fermi Large Area Telescope data between 100 MeV and 500 GeV above 10° in Galactic latitude to derive the spectrum and morphology of the Fermi bubbles. We thoroughly explore the systematic uncertainties that arise when modeling the Galactic diffuse emission through two separate approaches. The gamma-ray spectrum is well described by either a log parabola or a power law with an exponential cutoff. We exclude a simple power law with more than 7σ signi cance.more » The power law with an exponential cutoff has an index of 1:9±0:2 and a cutoff energy of 110 ± 50 GeV. We nd that the gamma-ray luminosity of the bubbles is 4:4+2:4 -0:9 X 1037 erg s -1. We confirm a signi cant enhancement of gamma-ray emission in the south-eastern part of the bubbles, but we do not nd signi cant evidence for a jet. No signi cant variation of the spectrum across the bubbles is detected. The width of the boundary of the bubbles is estimated to be 3:4+3:7 -2:6 deg. Both inverse Compton (IC) models and hadronic models including IC emission from secondary leptons t the gamma-ray data well. In the IC scenario, the synchrotron emission from the same population of electrons can also explain the WMAP and Planck microwave haze with a magnetic eld between 5 and 20 μG.« less

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

PubMed

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS

PubMed Central

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2015-01-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses. PMID:26166910

Verification of the exponential model of body temperature decrease after death in pigs.

PubMed

Kaliszan, Michal; Hauser, Roman; Kaliszan, Roman; Wiczling, Paweł; Buczyñski, Janusz; Penkowski, Michal

2005-09-01

The authors have conducted a systematic study in pigs to verify the models of post-mortem body temperature decrease currently employed in forensic medicine. Twenty-four hour automatic temperature recordings were performed in four body sites starting 1.25 h after pig killing in an industrial slaughterhouse under typical environmental conditions (19.5-22.5 degrees C). The animals had been randomly selected under a regular manufacturing process. The temperature decrease time plots drawn starting 75 min after death for the eyeball, the orbit soft tissues, the rectum and muscle tissue were found to fit the single-exponential thermodynamic model originally proposed by H. Rainy in 1868. In view of the actual intersubject variability, the addition of a second exponential term to the model was demonstrated to be statistically insignificant. Therefore, the two-exponential model for death time estimation frequently recommended in the forensic medicine literature, even if theoretically substantiated for individual test cases, provides no advantage as regards the reliability of estimation in an actual case. The improvement of the precision of time of death estimation by the reconstruction of an individual curve on the basis of two dead body temperature measurements taken 1 h apart or taken continuously for a longer time (about 4 h), has also been proved incorrect. It was demonstrated that the reported increase of precision of time of death estimation due to use of a multiexponential model, with individual exponential terms to account for the cooling rate of the specific body sites separately, is artifactual. The results of this study support the use of the eyeball and/or the orbit soft tissues as temperature measuring sites at times shortly after death. A single-exponential model applied to the eyeball cooling has been shown to provide a very precise estimation of the time of death up to approximately 13 h after death. For the period thereafter, a better estimation of the time of death is obtained from temperature data collected from the muscles or the rectum.

Effect of multiple perfusion components on pseudo-diffusion coefficient in intravoxel incoherent motion imaging

NASA Astrophysics Data System (ADS)

Kuai, Zi-Xiang; Liu, Wan-Yu; Zhu, Yue-Min

2017-11-01

The aim of this work was to investigate the effect of multiple perfusion components on the pseudo-diffusion coefficient D * in the bi-exponential intravoxel incoherent motion (IVIM) model. Simulations were first performed to examine how the presence of multiple perfusion components influences D *. The real data of livers (n  =  31), spleens (n  =  31) and kidneys (n  =  31) of 31 volunteers was then acquired using DWI for in vivo study and the number of perfusion components in these tissues was determined together with their perfusion fraction and D *, using an adaptive multi-exponential IVIM model. Finally, the bi-exponential model was applied to the real data and the mean, standard variance and coefficient of variation of D * as well as the fitting residual were calculated over the 31 volunteers for each of the three tissues and compared between them. The results of both the simulations and the in vivo study showed that, for the bi-exponential IVIM model, both the variance of D * and the fitting residual tended to increase when the number of perfusion components was increased or when the difference between perfusion components became large. In addition, it was found that the kidney presented the fewest perfusion components among the three tissues. The present study demonstrated that multi-component perfusion is a main factor that causes high variance of D * and the bi-exponential model should be used only when the tissues under investigation have few perfusion components, for example the kidney.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PubMed Central

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.

2014-01-01

Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318

Modeling Rabbit Responses to Single and Multiple Aerosol ...

EPA Pesticide Factsheets

Journal Article Survival models are developed here to predict response and time-to-response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple dose dataset to predict the probability of death through specifying dose-response functions and the time between exposure and the time-to-death (TTD). Among the models developed, the best-fitting survival model (baseline model) has an exponential dose-response model with a Weibull TTD distribution. Alternative models assessed employ different underlying dose-response functions and use the assumption that, in a multiple dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this paper. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high-dose rabbit datasets. More accurate survival models depend upon future development of dose-response datasets specifically designed to assess potential multiple dose effects on response and time-to-response. The process used in this paper to dev

Describing complex cells in primary visual cortex: a comparison of context and multi-filter LN models.

PubMed

Westö, Johan; May, Patrick J C

2018-05-02

Receptive field (RF) models are an important tool for deciphering neural responses to sensory stimuli. The two currently popular RF models are multi-filter linear-nonlinear (LN) models and context models. Models are, however, never correct and they rely on assumptions to keep them simple enough to be interpretable. As a consequence, different models describe different stimulus-response mappings, which may or may not be good approximations of real neural behavior. In the current study, we take up two tasks: First, we introduce new ways to estimate context models with realistic nonlinearities, that is, with logistic and exponential functions. Second, we evaluate context models and multi-filter LN models in terms of how well they describe recorded data from complex cells in cat primary visual cortex. Our results, based on single-spike information and correlation coefficients, indicate that context models outperform corresponding multi-filter LN models of equal complexity (measured in terms of number of parameters), with the best increase in performance being achieved by the novel context models. Consequently, our results suggest that the multi-filter LN-model framework is suboptimal for describing the behavior of complex cells: the context-model framework is clearly superior while still providing interpretable quantizations of neural behavior.

Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability

PubMed Central

Ihlen, Espen A. F.; van Schooten, Kimberley S.; Bruijn, Sjoerd M.; Pijnappels, Mirjam; van Dieën, Jaap H.

2017-01-01

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability. PMID:28900400

Lambert-Beer law in ocean waters: optical properties of water and of dissolved/suspended material, optical energy budgets.

PubMed

Stavn, R H

1988-01-15

The role of the Lambert-Beer law in ocean optics is critically examined. The Lambert-Beer law and the three-parameter model of the submarine light field are used to construct an optical energy budget for any hydrosol. It is further applied to the analytical exponential decay coefficient of the light field and used to estimate the optical properties and effects of the dissolved/suspended component in upper ocean layers. The concepts of the empirical exponential decay coefficient (diffuse attenuation coefficient) of the light field and a constant exponential decay coefficient for molecular water are analyzed quantitatively. A constant exponential decay coefficient for water is rejected. The analytical exponential decay coefficient is used to analyze optical gradients in ocean waters.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

The penny pusher: a cellular model of lens growth.

PubMed

Shi, Yanrong; De Maria, Alicia; Lubura, Snježana; Šikić, Hrvoje; Bassnett, Steven

2014-12-16

The mechanisms that regulate the number of cells in the lens and, therefore, its size and shape are unknown. We examined the dynamic relationship between proliferative behavior in the epithelial layer and macroscopic lens growth. The distribution of S-phase cells across the epithelium was visualized by confocal microscopy and cell populations were determined from orthographic projections of the lens surface. The number of S-phase cells in the mouse lens epithelium fell exponentially, to an asymptotic value of approximately 200 cells by 6 months. Mitosis became increasingly restricted to a 300-μm-wide swath of equatorial epithelium, the germinative zone (GZ), within which two peaks in labeling index were detected. Postnatally, the cell population increased to approximately 50,000 cells at 4 weeks of age. Thereafter, the number of cells declined, despite continued growth in lens dimensions. This apparently paradoxical observation was explained by a time-dependent increase in the surface area of cells at all locations. The cell biological measurements were incorporated into a physical model, the Penny Pusher. In this simple model, cells were considered to be of a single type, the proliferative behavior of which depended solely on latitude. Simulations using the Penny Pusher predicted the emergence of cell clones and were in good agreement with data obtained from earlier lineage-tracing studies. The Penny Pusher, a simple stochastic model, offers a useful conceptual framework for the investigation of lens growth mechanisms and provides a plausible alternative to growth models that postulate the existence of lens stem cells. Copyright 2015 The Association for Research in Vision and Ophthalmology, Inc.

Fast radiative transfer models for retrieval of cloud properties in the back-scattering region: application to DSCOVR-EPIC sensor

NASA Astrophysics Data System (ADS)

Molina Garcia, Victor; Sasi, Sruthy; Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego

2017-04-01

In this work, the requirements for the retrieval of cloud properties in the back-scattering region are described, and their application to the measurements taken by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) is shown. Various radiative transfer models and their linearizations are implemented, and their advantages and issues are analyzed. As radiative transfer calculations in the back-scattering region are computationally time-consuming, several acceleration techniques are also studied. The radiative transfer models analyzed include the exact Discrete Ordinate method with Matrix Exponential (DOME), the Matrix Operator method with Matrix Exponential (MOME), and the approximate asymptotic and equivalent Lambertian cloud models. To reduce the computational cost of the line-by-line (LBL) calculations, the k-distribution method, the Principal Component Analysis (PCA) and a combination of the k-distribution method plus PCA are used. The linearized radiative transfer models for retrieval of cloud properties include the Linearized Discrete Ordinate method with Matrix Exponential (LDOME), the Linearized Matrix Operator method with Matrix Exponential (LMOME) and the Forward-Adjoint Discrete Ordinate method with Matrix Exponential (FADOME). These models were applied to the EPIC oxygen-A band absorption channel at 764 nm. It is shown that the approximate asymptotic and equivalent Lambertian cloud models give inaccurate results, so an offline processor for the retrieval of cloud properties in the back-scattering region requires the use of exact models such as DOME and MOME, which behave similarly. The combination of the k-distribution method plus PCA presents similar accuracy to the LBL calculations, but it is up to 360 times faster, and the relative errors for the computed radiances are less than 1.5% compared to the results when the exact phase function is used. Finally, the linearized models studied show similar behavior, with relative errors less than 1% for the radiance derivatives, but FADOME is 2 times faster than LDOME and 2.5 times faster than LMOME.

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Fracture analysis of a central crack in a long cylindrical superconductor with exponential model

NASA Astrophysics Data System (ADS)

Zhao, Yu Feng; Xu, Chi

2018-05-01

The fracture behavior of a long cylindrical superconductor is investigated by modeling a central crack that is induced by electromagnetic force. Based on the exponential model, the stress intensity factors (SIFs) with the dimensionless parameter p and the length of the crack a/R for the zero-field cooling (ZFC) and field-cooling (FC) processes are numerically simulated using the finite element method (FEM) and assuming a persistent current flow. As the applied field Ba decreases, the dependence of p and a/R on the SIFs in the ZFC process is exactly opposite to that observed in the FC process. Numerical results indicate that the exponential model exhibits different characteristics for the trend of the SIFs from the results obtained using the Bean and Kim models. This implies that the crack length and the trapped field have significant effects on the fracture behavior of bulk superconductors. The obtained results are useful for understanding the critical-state model of high-temperature superconductors in crack problem.

Estimating time since infection in early homogeneous HIV-1 samples using a poisson model

PubMed Central

2010-01-01

Background The occurrence of a genetic bottleneck in HIV sexual or mother-to-infant transmission has been well documented. This results in a majority of new infections being homogeneous, i.e., initiated by a single genetic strain. Early after infection, prior to the onset of the host immune response, the viral population grows exponentially. In this simple setting, an approach for estimating evolutionary and demographic parameters based on comparison of diversity measures is a feasible alternative to the existing Bayesian methods (e.g., BEAST), which are instead based on the simulation of genealogies. Results We have devised a web tool that analyzes genetic diversity in acutely infected HIV-1 patients by comparing it to a model of neutral growth. More specifically, we consider a homogeneous infection (i.e., initiated by a unique genetic strain) prior to the onset of host-induced selection, where we can assume a random accumulation of mutations. Previously, we have shown that such a model successfully describes about 80% of sexual HIV-1 transmissions provided the samples are drawn early enough in the infection. Violation of the model is an indicator of either heterogeneous infections or the initiation of selection. Conclusions When the underlying assumptions of our model (homogeneous infection prior to selection and fast exponential growth) are met, we are under a very particular scenario for which we can use a forward approach (instead of backwards in time as provided by coalescent methods). This allows for more computationally efficient methods to derive the time since the most recent common ancestor. Furthermore, the tool performs statistical tests on the Hamming distance frequency distribution, and outputs summary statistics (mean of the best fitting Poisson distribution, goodness of fit p-value, etc). The tool runs within minutes and can readily accommodate the tens of thousands of sequences generated through new ultradeep pyrosequencing technologies. The tool is available on the LANL website. PMID:20973976

Conduit Stability and Collapse in Explosive Volcanic Eruptions: Coupling Conduit Flow and Failure Models

NASA Astrophysics Data System (ADS)

Mullet, B.; Segall, P.

2017-12-01

Explosive volcanic eruptions can exhibit abrupt changes in physical behavior. In the most extreme cases, high rates of mass discharge are interspaced by dramatic drops in activity and periods of quiescence. Simple models predict exponential decay in magma chamber pressure, leading to a gradual tapering of eruptive flux. Abrupt changes in eruptive flux therefore indicate that relief of chamber pressure cannot be the only control of the evolution of such eruptions. We present a simplified physics-based model of conduit flow during an explosive volcanic eruption that attempts to predict stress-induced conduit collapse linked to co-eruptive pressure loss. The model couples a simple two phase (gas-melt) 1-D conduit solution of the continuity and momentum equations with a Mohr-Coulomb failure condition for the conduit wall rock. First order models of volatile exsolution (i.e. phase mass transfer) and fragmentation are incorporated. The interphase interaction force changes dramatically between flow regimes, so smoothing of this force is critical for realistic results. Reductions in the interphase force lead to significant relative phase velocities, highlighting the deficiency of homogenous flow models. Lateral gas loss through conduit walls is incorporated using a membrane-diffusion model with depth dependent wall rock permeability. Rapid eruptive flux results in a decrease of chamber and conduit pressure, which leads to a critical deviatoric stress condition at the conduit wall. Analogous stress distributions have been analyzed for wellbores, where much work has been directed at determining conditions that lead to wellbore failure using Mohr-Coulomb failure theory. We extend this framework to cylindrical volcanic conduits, where large deviatoric stresses can develop co-eruptively leading to multiple distinct failure regimes depending on principal stress orientations. These failure regimes are categorized and possible implications for conduit flow are discussed, including cessation of eruption.

Supermassive black holes and their host galaxies. I. Bulge luminosities from dedicated near-infrared data

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

Läsker, Ronald; Van de Ven, Glenn; Ferrarese, Laura, E-mail: laesker@mpia.de

2014-01-01

In an effort to secure, refine, and supplement the relation between central supermassive black hole masses, M {sub •}, and the bulge luminosities of their host galaxies, L {sub bul}, we obtained deep, high spatial resolution K-band images of 35 nearby galaxies with securely measured M {sub •}, using the wide-field WIRCam imager at the Canada-France-Hawaii-Telescope. A dedicated data reduction and sky subtraction strategy was adopted to estimate the brightness and structure of the sky, a critical step when tracing the light distribution of extended objects in the near-infrared. From the final image product, bulge and total magnitudes were extractedmore » via two-dimensional profile fitting. As a first order approximation, all galaxies were modeled using a simple Sérsic-bulge+exponential-disk decomposition. However, we found that such models did not adequately describe the structure that we observed in a large fraction of our sample galaxies which often include cores, bars, nuclei, inner disks, spiral arms, rings, and envelopes. In such cases, we adopted profile modifications and/or more complex models with additional components. The derived bulge magnitudes are very sensitive to the details and number of components used in the models, although total magnitudes remain almost unaffected. Usually, but not always, the luminosities and sizes of the bulges are overestimated when a simple bulge+disk decomposition is adopted in lieu of a more complex model. Furthermore, we found that some spheroids are not well fit when the ellipticity of the Sérsic model is held fixed. This paper presents the details of the image processing and analysis, while we discuss how model-induced biases and systematics in bulge magnitudes impact the M {sub •}-L {sub bul} relation in a companion paper.« less

Supermassive Black Holes and Their Host Galaxies. I. Bulge Luminosities from Dedicated Near-infrared Data

NASA Astrophysics Data System (ADS)

Läsker, Ronald; Ferrarese, Laura; van de Ven, Glenn

2014-01-01

In an effort to secure, refine, and supplement the relation between central supermassive black hole masses, M •, and the bulge luminosities of their host galaxies, L bul, we obtained deep, high spatial resolution K-band images of 35 nearby galaxies with securely measured M •, using the wide-field WIRCam imager at the Canada-France-Hawaii-Telescope. A dedicated data reduction and sky subtraction strategy was adopted to estimate the brightness and structure of the sky, a critical step when tracing the light distribution of extended objects in the near-infrared. From the final image product, bulge and total magnitudes were extracted via two-dimensional profile fitting. As a first order approximation, all galaxies were modeled using a simple Sérsic-bulge+exponential-disk decomposition. However, we found that such models did not adequately describe the structure that we observed in a large fraction of our sample galaxies which often include cores, bars, nuclei, inner disks, spiral arms, rings, and envelopes. In such cases, we adopted profile modifications and/or more complex models with additional components. The derived bulge magnitudes are very sensitive to the details and number of components used in the models, although total magnitudes remain almost unaffected. Usually, but not always, the luminosities and sizes of the bulges are overestimated when a simple bulge+disk decomposition is adopted in lieu of a more complex model. Furthermore, we found that some spheroids are not well fit when the ellipticity of the Sérsic model is held fixed. This paper presents the details of the image processing and analysis, while we discuss how model-induced biases and systematics in bulge magnitudes impact the M •-L bul relation in a companion paper.

Foundations of the Bandera Abstraction Tools

NASA Technical Reports Server (NTRS)

Hatcliff, John; Dwyer, Matthew B.; Pasareanu, Corina S.; Robby

2003-01-01

Current research is demonstrating that model-checking and other forms of automated finite-state verification can be effective for checking properties of software systems. Due to the exponential costs associated with model-checking, multiple forms of abstraction are often necessary to obtain system models that are tractable for automated checking. The Bandera Tool Set provides multiple forms of automated support for compiling concurrent Java software systems to models that can be supplied to several different model-checking tools. In this paper, we describe the foundations of Bandera's data abstraction mechanism which is used to reduce the cardinality (and the program's state-space) of data domains in software to be model-checked. From a technical standpoint, the form of data abstraction used in Bandera is simple, and it is based on classical presentations of abstract interpretation. We describe the mechanisms that Bandera provides for declaring abstractions, for attaching abstractions to programs, and for generating abstracted programs and properties. The contributions of this work are the design and implementation of various forms of tool support required for effective application of data abstraction to software components written in a programming language like Java which has a rich set of linguistic features.

Molecular modeling of proteinlike inclusions in lipid bilayers: lipid-mediated interactions.

PubMed

Kik, Richard A; Leermakers, Frans A M; Kleijn, J Mieke

2010-02-01

We investigated the insertion of transmembrane structures in a lipid bilayer and their interactions using self-consistent field theory. The lipids are coarse-grained on a united-atom level and consist of a phosphatidylcholinelike headgroup and two hydrophobic tails. The inclusions, acting as simple models for proteins that span biological membranes, are rigid rods (radius R ) with a hydrophobic surface and hydrophilic end caps. The insertion free energy Omega of an individual rod is strongly regulated by the affinity between its hydrophobic surface and the lipid tails. This affinity also controls the best match of the hydrophobic length of the rod with that of the bilayer. The line tension tau(=Omega/2piR) is practically independent of R . The perturbations in the bilayer as a function of distance from the inclusion, have the shape of a damped oscillation. The wavelength and decay length are related to the elastic properties of the bilayer and do not depend on R . These results are used to analyze how the lipid matrix affects the interaction between transmembrane objects, for computational reasons considering the limit of R-->infinity . Contributions on different length scales can be distinguished: (i) a long-range elastic interaction, which is an exponentially decaying oscillation; (ii) an exponentially decaying repulsion on an intermediate length scale, resulting from the loss of conformational entropy of the lipid tails; and (iii) a short-range interaction due to the finite compressibility of the lipid tails, which manifests either as a depletion attraction if there is no affinity between the tails and the inclusions' surface or, otherwise, as an oscillatory structural force.

On the duration and intensity of cumulative advantage competitions

NASA Astrophysics Data System (ADS)

Jiang, Bo; Sun, Liyuan; Figueiredo, Daniel R.; Ribeiro, Bruno; Towsley, Don

2015-11-01

Network growth can be framed as a competition for edges among nodes in the network. As with various other social and physical systems, skill (fitness) and luck (random chance) act as fundamental forces driving competition dynamics. In the context of networks, cumulative advantage (CA)—the rich-get-richer effect—is seen as a driving principle governing the edge accumulation process. However, competitions coupled with CA exhibit non-trivial behavior and little is formally known about duration and intensity of CA competitions. By isolating two nodes in an ideal CA competition, we provide a mathematical understanding of how CA exacerbates the role of luck in detriment of skill. We show, for instance, that when nodes start with few edges, an early stroke of luck can place the less skilled in the lead for an extremely long period of time, a phenomenon we call ‘struggle of the fittest’. We prove that duration of a simple skill and luck competition model exhibit power-law tails when CA is present, regardless of skill difference, which is in sharp contrast to the exponential tails when fitness is distinct but CA is absent. We also prove that competition intensity is always upper bounded by an exponential tail, irrespective of CA and skills. Thus, CA competitions can be extremely long (infinite mean, depending on fitness ratio) but almost never very intense. The theoretical results are corroborated by extensive numerical simulations. Our findings have important implications to competitions not only among nodes in networks but also in contexts that leverage socio-physical models embodying CA competitions.

n-Iterative Exponential Forgetting Factor for EEG Signals Parameter Estimation

PubMed Central

Palma Orozco, Rosaura

2018-01-01

Electroencephalograms (EEG) signals are of interest because of their relationship with physiological activities, allowing a description of motion, speaking, or thinking. Important research has been developed to take advantage of EEG using classification or predictor algorithms based on parameters that help to describe the signal behavior. Thus, great importance should be taken to feature extraction which is complicated for the Parameter Estimation (PE)–System Identification (SI) process. When based on an average approximation, nonstationary characteristics are presented. For PE the comparison of three forms of iterative-recursive uses of the Exponential Forgetting Factor (EFF) combined with a linear function to identify a synthetic stochastic signal is presented. The one with best results seen through the functional error is applied to approximate an EEG signal for a simple classification example, showing the effectiveness of our proposal. PMID:29568310

Optimality of cycle time and inventory decisions in a two echelon inventory system with exponential price dependent demand under credit period

NASA Astrophysics Data System (ADS)

Krugon, Seelam; Nagaraju, Dega

2017-05-01

This work describes and proposes an two echelon inventory system under supply chain, where the manufacturer offers credit period to the retailer with exponential price dependent demand. The model is framed as demand is expressed as exponential function of retailer’s unit selling price. Mathematical model is framed to demonstrate the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. The major objective of the paper is to provide trade credit concept from the manufacturer to the retailer with exponential price dependent demand. The retailer would like to delay the payments of the manufacturer. At the first stage retailer and manufacturer expressions are expressed with the functions of ordering cost, carrying cost, transportation cost. In second stage combining of the manufacturer and retailer expressions are expressed. A MATLAB program is written to derive the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. From the optimality criteria derived managerial insights can be made. From the research findings, it is evident that the total cost of the supply chain is decreased with the increase in credit period under exponential price dependent demand. To analyse the influence of the model parameters, parametric analysis is also done by taking with help of numerical example.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

On stable exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Ernazarov, K. K.

2017-01-01

A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ˜ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.

The Secular Evolution Of Disc Galaxies And The Origin Of Exponential And Double Exponential Surface Density Profiles

NASA Astrophysics Data System (ADS)

Elmegreen, Bruce G.

2016-10-01

Exponential radial profiles are ubiquitous in spiral and dwarf Irregular galaxies, but the origin of this structural form is not understood. This talk will review the observations of exponential and double exponential disks, considering both the light and the mass profiles, and the contributions from stars and gas. Several theories for this structure will also be reviewed, including primordial collapse, bar and spiral torques, clump torques, galaxy interactions, disk viscosity and other internal processes of angular momentum exchange, and stellar scattering off of clumpy structure. The only process currently known that can account for this structure in the most theoretically difficult case is stellar scattering off disks clumps. Stellar orbit models suggest that such scattering can produce exponentials even in isolated dwarf irregulars that have no bars or spirals, little shear or viscosity, and profiles that go out too far for the classical Mestel case of primordial collapse with specific angular momentum conservation.

An exactly solvable, spatial model of mutation accumulation in cancer

NASA Astrophysics Data System (ADS)

Paterson, Chay; Nowak, Martin A.; Waclaw, Bartlomiej

2016-12-01

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

Pushing the Volcanic Explosivity Index to its limit and beyond: Constraints from exceptionally weak explosive eruptions at Kīlauea in 2008

USGS Publications Warehouse

Houghton, Bruce F.; Swanson, Don; Rausch, J.; Carey, R.J.; Fagents, S.A.; Orr, Tim R.

2013-01-01

Estimating the mass, volume, and dispersal of the deposits of very small and/or extremely weak explosive eruptions is difficult, unless they can be sampled on eruption. During explosive eruptions of Halema‘uma‘u Crater (Kīlauea, Hawaii) in 2008, we constrained for the first time deposits of bulk volumes as small as 9–300 m3 (1 × 104 to 8 × 105 kg) and can demonstrate that they show simple exponential thinning with distance from the vent. There is no simple fit for such products within classifications such as the Volcanic Explosivity Index (VEI). The VEI is being increasingly used as the measure of magnitude of explosive eruptions, and as an input for both hazard modeling and forecasting of atmospheric dispersal of tephra. The 2008 deposits demonstrate a problem for the use of the VEI, as originally defined, which classifies small, yet ballistic-producing, explosive eruptions at Kīlauea and other basaltic volcanoes as nonexplosive. We suggest a simple change to extend the scale in a fashion inclusive of such very small deposits, and to make the VEI more consistent with other magnitude scales such as the Richter scale for earthquakes. Eruptions of this magnitude constitute a significant risk at Kīlauea and elsewhere because of their high frequency and the growing number of “volcano tourists” visiting basaltic volcanoes.

[Shock shape representation of sinus heart rate based on cloud model].

PubMed

Yin, Wenfeng; Zhao, Jie; Chen, Tiantian; Zhang, Junjian; Zhang, Chunyou; Li, Dapeng; An, Baijing

2014-04-01

The present paper is to analyze the trend of sinus heart rate RR interphase sequence after a single ventricular premature beat and to compare it with the two parameters, turbulence onset (TO) and turbulence slope (TS). Based on the acquisition of sinus rhythm concussion sample, we in this paper use a piecewise linearization method to extract its linear characteristics, following which we describe shock form with natural language through cloud model. In the process of acquisition, we use the exponential smoothing method to forecast the position where QRS wave may appear to assist QRS wave detection, and use template to judge whether current cardiac is sinus rhythm. And we choose some signals from MIT-BIH Arrhythmia Database to detect whether the algorithm is effective in Matlab. The results show that our method can correctly detect the changing trend of sinus heart rate. The proposed method can achieve real-time detection of sinus rhythm shocks, which is simple and easily implemented, so that it is effective as a supplementary method.

Vortex with fourfold defect lines in a simple model of self-propelled particles

NASA Astrophysics Data System (ADS)

Seyed-Allaei, Hamid; Ejtehadi, Mohammad Reza

2016-03-01

We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. We derive hydrodynamical equations with an introduction of the "small deviation" technique to describe the vortex phase. The method is applicable to other systems as well. Finally, we compare the theory with the results of both computer simulations and an experiment using Quincke rotors. A good agreement between the three is observed.

Tipping Points, Great and Small

NASA Astrophysics Data System (ADS)

Morrison, Foster

2010-12-01

The Forum by Jordan et al. [2010] addressed environmental problems of various scales in great detail, but getting the critical message through to the formulators of public policies requires going back to basics, namely, that exponential growth (of a population, an economy, or most anything else) is not sustainable. When have you heard any politician or economist from anywhere across the ideological spectrum say anything other than that more growth is essential? There is no need for computer models to demonstrate “limits to growth,” as was done in the 1960s. Of course, as one seeks more details, the complexity of modeling will rapidly outstrip the capabilities of both observation and computing. This is common with nonlinear systems, even simple ones. Thus, identifying all possible “tipping points,” as suggested by Jordan et al. [2010], and then stopping just short of them, is impractical if not impossible. The main thing needed to avoid environmental disasters is a bit of common sense.

Effect of wet tropospheric path delays on estimation of geodetic baselines in the Gulf of California using the Global Positioning System

NASA Technical Reports Server (NTRS)

Tralli, David M.; Dixon, Timothy H.; Stephens, Scott A.

1988-01-01

Surface Meteorological (SM) and Water Vapor Radiometer (WVR) measurements are used to provide an independent means of calibrating the GPS signal for the wet tropospheric path delay in a study of geodetic baseline measurements in the Gulf of California using GPS in which high tropospheric water vapor content yielded wet path delays in excess of 20 cm at zenith. Residual wet delays at zenith are estimated as constants and as first-order exponentially correlated stochastic processes. Calibration with WVR data is found to yield the best repeatabilities, with improved results possible if combined carrier phase and pseudorange data are used. Although SM measurements can introduce significant errors in baseline solutions if used with a simple atmospheric model and estimation of residual zenith delays as constants, SM calibration and stochastic estimation for residual zenith wet delays may be adequate for precise estimation of GPS baselines. For dry locations, WVRs may not be required to accurately model tropospheric effects on GPS baselines.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

On Revenue-Optimal Dynamic Auctions for Bidders with Interdependent Values

NASA Astrophysics Data System (ADS)

Constantin, Florin; Parkes, David C.

In a dynamic market, being able to update one's value based on information available to other bidders currently in the market can be critical to having profitable transactions. This is nicely captured by the model of interdependent values (IDV): a bidder's value can explicitly depend on the private information of other bidders. In this paper we present preliminary results about the revenue properties of dynamic auctions for IDV bidders. We adopt a computational approach to design single-item revenue-optimal dynamic auctions with known arrivals and departures but (private) signals that arrive online. In leveraging a characterization of truthful auctions, we present a mixed-integer programming formulation of the design problem. Although a discretization is imposed on bidder signals the solution is a mechanism applicable to continuous signals. The formulation size grows exponentially in the dependence of bidders' values on other bidders' signals. We highlight general properties of revenue-optimal dynamic auctions in a simple parametrized example and study the sensitivity of prices and revenue to model parameters.

Measurements of strain at plate boundaries using space based geodetic techniques

NASA Technical Reports Server (NTRS)

Robaudo, Stefano; Harrison, Christopher G. A.

1993-01-01

We have used the space based geodetic techniques of Satellite Laser Ranging (SLR) and VLBI to study strain along subduction and transform plate boundaries and have interpreted the results using a simple elastic dislocation model. Six stations located behind island arcs were analyzed as representative of subduction zones while 13 sites located on either side of the San Andreas fault were used for the transcurrent zones. The length deformation scale was then calculated for both tectonic margins by fitting the relative strain to an exponentially decreasing function of distance from the plate boundary. Results show that space-based data for the transcurrent boundary along the San Andreas fault help to define better the deformation length scale in the area while fitting nicely the elastic half-space earth model. For subduction type bonndaries the analysis indicates that there is no single scale length which uniquely describes the deformation. This is mainly due to the difference in subduction characteristics for the different areas.

Monitoring Mars LOD Variations from a High Altitude Circular Equatorial Orbit: Theory and Simulation

NASA Astrophysics Data System (ADS)

Barriot, J.; Dehant, V.; Duron, J.

2003-12-01

We compute the perturbations of a high altitude circular equatorial orbit of a martian probe under the influence of an annual variation of the martian lenght of day. For this purpose, we use the first order perturbations of the newtonian equations of motion, where the small parameter is given from the hourglass model of Chao and Rubincam, which allow a simple computation of CO2 exchanges during the martian year. We are able to demonstrate that the perturbations contains two components: the first one is a sine/cosine modulation at the orbit frequency, the second one is composed of terms of the form exp(t)*sin(t), so the orbit may not stable in the long term (several martian years), with perturbations growing exponentially. We give the full theory and numbers.

Higher-Order Corrections to Timelike Jets

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

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

2011-02-01

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

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

PubMed

Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

2016-04-01

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

PubMed Central

Steimer, Andreas; Schindler, Kaspar

2015-01-01

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation. PMID:26203657

SPECTRUM AND MORPHOLOGY OF THE TWO BRIGHTEST MILAGRO SOURCES IN THE CYGNUS REGION: MGRO J2019+37 AND MGRO J2031+41

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

Abdo, A. A.; Abeysekara, U.; Linnemann, J. T.

2012-07-10

The Cygnus region is a very bright and complex portion of the TeV sky, host to unidentified sources and a diffuse excess with respect to conventional cosmic-ray propagation models. Two of the brightest TeV sources, MGRO J2019+37 and MGRO J2031+41, are analyzed using Milagro data with a new technique, and their emission is tested under two different spectral assumptions: a power law and a power law with an exponential cutoff. The new analysis technique is based on an energy estimator that uses the fraction of photomultiplier tubes in the observatory that detect the extensive air shower. The photon spectrum ismore » measured in the range 1-100 TeV using the last three years of Milagro data (2005-2008), with the detector in its final configuration. An F-test indicates that MGRO J2019+37 is better fit by a power law with an exponential cutoff than by a simple power law. The best-fitting parameters for the power law with exponential cutoff model are a normalization at 10 TeV of 7{sup +5}{sub -2} Multiplication-Sign 10{sup -10} s{sup -1} m{sup -2} TeV{sup -1}, a spectral index of 2.0{sup +0.5}{sub -1.0}, and a cutoff energy of 29{sup +50}{sub -16} TeV. MGRO J2031+41 shows no evidence of a cutoff. The best-fitting parameters for a power law are a normalization of 2.1{sup +0.6}{sub -0.6} Multiplication-Sign 10{sup -10} s{sup -1} m{sup -2} TeV{sup -1} and a spectral index of 3.22{sup +0.23}{sub -0.18}. The overall flux is subject to a {approx}30% systematic uncertainty. The systematic uncertainty on the power-law indices is {approx}0.1. Both uncertainties have been verified with cosmic-ray data. A comparison with previous results from TeV J2032+4130, MGRO J2031+41, and MGRO J2019+37 is also presented.« less

Spectrum and Morphology of the Two Brightest Milagro Sources in the Cygnus Region: MGRO J2019+37 and MGRO J2031+41

NASA Technical Reports Server (NTRS)

Abdo, A. A.; Abeysekara, U.; Allen, B, T.; Aune, T.; Berley, D.; Bonamente, E.; Christopher, G. E.; DeYoung, T.; Dingus, B. L.; Ellsworth, R. W.;

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms.

PubMed

Palombo, Marco; Gabrielli, Andrea; De Santis, Silvia; Capuani, Silvia

2012-03-01

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g. Copyright © 2012 Elsevier Inc. All rights reserved.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Growth and mortality of larval Myctophum affine (Myctophidae, Teleostei).

PubMed

Namiki, C; Katsuragawa, M; Zani-Teixeira, M L

2015-04-01

The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south-eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L(S)). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird-Gompertz model. The exponential model best fitted the data, and L(0) values from exponential and Laird-Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L(S)). The average growth rate (0·33 mm day(-1)) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area. © 2015 The Fisheries Society of the British Isles.

1/f oscillations in a model of moth populations oriented by diffusive pheromones

NASA Astrophysics Data System (ADS)

Barbosa, L. A.; Martins, M. L.; Lima, E. R.

2005-01-01

An individual-based model for the population dynamics of Spodoptera frugiperda in a homogeneous environment is proposed. The model involves moths feeding plants, mating through an anemotaxis search (i.e., oriented by odor dispersed in a current of air), and dying due to resource competition or at a maximum age. As observed in the laboratory, the females release pheromones at exponentially distributed time intervals, and it is assumed that the ranges of the male flights follow a power-law distribution. Computer simulations of the model reveal the central role of anemotaxis search for the persistence of moth population. Such stationary populations are exponentially distributed in age, exhibit random temporal fluctuations with 1/f spectrum, and self-organize in disordered spatial patterns with long-range correlations. In addition, the model results demonstrate that pest control through pheromone mass trapping is effective only if the amounts of pheromone released by the traps decay much slower than the exponential distribution for calling female.

Performance of time-series methods in forecasting the demand for red blood cell transfusion.

PubMed

Pereira, Arturo

2004-05-01

Planning the future blood collection efforts must be based on adequate forecasts of transfusion demand. In this study, univariate time-series methods were investigated for their performance in forecasting the monthly demand for RBCs at one tertiary-care, university hospital. Three time-series methods were investigated: autoregressive integrated moving average (ARIMA), the Holt-Winters family of exponential smoothing models, and one neural-network-based method. The time series consisted of the monthly demand for RBCs from January 1988 to December 2002 and was divided into two segments: the older one was used to fit or train the models, and the younger to test for the accuracy of predictions. Performance was compared across forecasting methods by calculating goodness-of-fit statistics, the percentage of months in which forecast-based supply would have met the RBC demand (coverage rate), and the outdate rate. The RBC transfusion series was best fitted by a seasonal ARIMA(0,1,1)(0,1,1)(12) model. Over 1-year time horizons, forecasts generated by ARIMA or exponential smoothing laid within the +/- 10 percent interval of the real RBC demand in 79 percent of months (62% in the case of neural networks). The coverage rate for the three methods was 89, 91, and 86 percent, respectively. Over 2-year time horizons, exponential smoothing largely outperformed the other methods. Predictions by exponential smoothing laid within the +/- 10 percent interval of real values in 75 percent of the 24 forecasted months, and the coverage rate was 87 percent. Over 1-year time horizons, predictions of RBC demand generated by ARIMA or exponential smoothing are accurate enough to be of help in the planning of blood collection efforts. For longer time horizons, exponential smoothing outperforms the other forecasting methods.

SU-E-T-259: Particle Swarm Optimization in Radial Dose Function Fitting for a Novel Iodine-125 Seed

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

Wu, X; Duan, J; Popple, R

2014-06-01

Purpose: To determine the coefficients of bi- and tri-exponential functions for the best fit of radial dose functions of the new iodine brachytherapy source: Iodine-125 Seed AgX-100. Methods: The particle swarm optimization (PSO) method was used to search for the coefficients of the biand tri-exponential functions that yield the best fit to data published for a few selected radial distances from the source. The coefficients were encoded into particles, and these particles move through the search space by following their local and global best-known positions. In each generation, particles were evaluated through their fitness function and their positions were changedmore » through their velocities. This procedure was repeated until the convergence criterion was met or the maximum generation was reached. All best particles were found in less than 1,500 generations. Results: For the I-125 seed AgX-100 considered as a point source, the maximum deviation from the published data is less than 2.9% for bi-exponential fitting function and 0.2% for tri-exponential fitting function. For its line source, the maximum deviation is less than 1.1% for bi-exponential fitting function and 0.08% for tri-exponential fitting function. Conclusion: PSO is a powerful method in searching coefficients for bi-exponential and tri-exponential fitting functions. The bi- and tri-exponential models of Iodine-125 seed AgX-100 point and line sources obtained with PSO optimization provide accurate analytical forms of the radial dose function. The tri-exponential fitting function is more accurate than the bi-exponential function.« less

Improving UWB-Based Localization in IoT Scenarios with Statistical Models of Distance Error.

PubMed

Monica, Stefania; Ferrari, Gianluigi

2018-05-17

Interest in the Internet of Things (IoT) is rapidly increasing, as the number of connected devices is exponentially growing. One of the application scenarios envisaged for IoT technologies involves indoor localization and context awareness. In this paper, we focus on a localization approach that relies on a particular type of communication technology, namely Ultra Wide Band (UWB). UWB technology is an attractive choice for indoor localization, owing to its high accuracy. Since localization algorithms typically rely on estimated inter-node distances, the goal of this paper is to evaluate the improvement brought by a simple (linear) statistical model of the distance error. On the basis of an extensive experimental measurement campaign, we propose a general analytical framework, based on a Least Square (LS) method, to derive a novel statistical model for the range estimation error between a pair of UWB nodes. The proposed statistical model is then applied to improve the performance of a few illustrative localization algorithms in various realistic scenarios. The obtained experimental results show that the use of the proposed statistical model improves the accuracy of the considered localization algorithms with a reduction of the localization error up to 66%.

Statistics of acoustic emissions and stress drops during granular shearing using a stick-slip fiber bundle mode

NASA Astrophysics Data System (ADS)

Cohen, D.; Michlmayr, G.; Or, D.

2012-04-01

Shearing of dense granular materials appears in many engineering and Earth sciences applications. Under a constant strain rate, the shearing stress at steady state oscillates with slow rises followed by rapid drops that are linked to the build up and failure of force chains. Experiments indicate that these drops display exponential statistics. Measurements of acoustic emissions during shearing indicates that the energy liberated by failure of these force chains has power-law statistics. Representing force chains as fibers, we use a stick-slip fiber bundle model to obtain analytical solutions of the statistical distribution of stress drops and failure energy. In the model, fibers stretch, fail, and regain strength during deformation. Fibers have Weibull-distributed threshold strengths with either quenched and annealed disorder. The shape of the distribution for drops and energy obtained from the model are similar to those measured during shearing experiments. This simple model may be useful to identify failure events linked to force chain failures. Future generalizations of the model that include different types of fiber failure may also allow identification of different types of granular failures that have distinct statistical acoustic emission signatures.

Relaxation processes in a low-order three-dimensional magnetohydrodynamics model

NASA Technical Reports Server (NTRS)

Stribling, Troy; Matthaeus, William H.

1991-01-01

The time asymptotic behavior of a Galerkin model of 3D magnetohydrodynamics (MHD) has been interpreted using the selective decay and dynamic alignment relaxation theories. A large number of simulations has been performed that scan a parameter space defined by the rugged ideal invariants, including energy, cross helicity, and magnetic helicity. It is concluded that time asymptotic state can be interpreted as a relaxation to minimum energy. A simple decay model, based on absolute equilibrium theory, is found to predict a mapping of initial onto time asymptotic states, and to accurately describe the long time behavior of the runs when magnetic helicity is present. Attention is also given to two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values 0(1). The faster of the two processes takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

NASA Astrophysics Data System (ADS)

Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar

2018-04-01

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

Following a trend with an exponential moving average: Analytical results for a Gaussian model

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Serror, Jeremy

2014-01-01

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

Too Big to Be Real? No Depleted Core in Holm 15A

NASA Astrophysics Data System (ADS)

Bonfini, Paolo; Dullo, Bililign T.; Graham, Alister W.

2015-07-01

Partially depleted cores, as measured by core-Sérsic model “break radii,” are typically tens to a few hundred parsecs in size. Here we investigate the unusually large ({R}γ \\prime =0.5 = 4.57 kpc) depleted core recently reported for Holm 15A, the brightest cluster galaxy of Abell 85. We model the one-dimensional (1D) light profile, and also the two-dimensional (2D) image (using Galfit-Corsair, a tool for fitting the core-Sérsic model in 2D). We find good agreement between the 1D and 2D analyses, with minor discrepancies attributable to intrinsic ellipticity gradients. We show that a simple Sérsic profile (with a low index n and no depleted core) plus the known outer exponential “halo” provide a good description of the stellar distribution. We caution that while almost every galaxy light profile will have a radius where the negative logarithmic slope of the intensity profile γ \\prime equals 0.5, this alone does not imply the presence of a partially depleted core within this radius.

Event-driven simulations of nonlinear integrate-and-fire neurons.

PubMed

Tonnelier, Arnaud; Belmabrouk, Hana; Martinez, Dominique

2007-12-01

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

A non-Gaussian option pricing model based on Kaniadakis exponential deformation

NASA Astrophysics Data System (ADS)

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

2017-09-01

A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements

NASA Astrophysics Data System (ADS)

Vincenzo, F.; Matteucci, F.; Spitoni, E.

2017-04-01

We present a theoretical method for solving the chemical evolution of galaxies by assuming an instantaneous recycling approximation for chemical elements restored by massive stars and the delay time distribution formalism for delayed chemical enrichment by Type Ia Supernovae. The galaxy gas mass assembly history, together with the assumed stellar yields and initial mass function, represents the starting point of this method. We derive a simple and general equation, which closely relates the Laplace transforms of the galaxy gas accretion history and star formation history, which can be used to simplify the problem of retrieving these quantities in the galaxy evolution models assuming a linear Schmidt-Kennicutt law. We find that - once the galaxy star formation history has been reconstructed from our assumptions - the differential equation for the evolution of the chemical element X can be suitably solved with classical methods. We apply our model to reproduce the [O/Fe] and [Si/Fe] versus [Fe/H] chemical abundance patterns as observed at the solar neighbourhood by assuming a decaying exponential infall rate of gas and different delay time distributions for Type Ia Supernovae; we also explore the effect of assuming a non-linear Schmidt-Kennicutt law, with the index of the power law being k = 1.4. Although approximate, we conclude that our model with the single-degenerate scenario for Type Ia Supernovae provides the best agreement with the observed set of data. Our method can be used by other complementary galaxy stellar population synthesis models to predict also the chemical evolution of galaxies.

An exponential model equation for thiamin loss in irradiated ground pork as a function of dose and temperature of irradiation

NASA Astrophysics Data System (ADS)

Fox, J. B.; Thayer, D. W.; Phillips, J. G.

The effect of low dose γ-irradiation on the thiamin content of ground pork was studied in the range of 0-14 kGy at 2°C and at radiation doses from 0.5 to 7 kGy at temperatures -20, 10, 0, 10 and 20°C. The detailed study at 2°C showed that loss of thiamin was exponential down to 0kGy. An exponential expression was derived for the effect of radiation dose and temperature of irradiation on thiamin loss, and compared with a previously derived general linear expression. Both models were accurate depictions of the data, but the exponential expression showed a significant decrease in the rate of loss between 0 and -10°C. This is the range over which water in meat freezes, the decrease being due to the immobolization of reactive radiolytic products of water in ice crystals.

Evaluation of regression and neural network models for solar forecasting over different short-term horizons

DOE PAGES

Inanlouganji, Alireza; Reddy, T. Agami; Katipamula, Srinivas

2018-04-13

Forecasting solar irradiation has acquired immense importance in view of the exponential increase in the number of solar photovoltaic (PV) system installations. In this article, analyses results involving statistical and machine-learning techniques to predict solar irradiation for different forecasting horizons are reported. Yearlong typical meteorological year 3 (TMY3) datasets from three cities in the United States with different climatic conditions have been used in this analysis. A simple forecast approach that assumes consecutive days to be identical serves as a baseline model to compare forecasting alternatives. To account for seasonal variability and to capture short-term fluctuations, different variants of themore » lagged moving average (LMX) model with cloud cover as the input variable are evaluated. Finally, the proposed LMX model is evaluated against an artificial neural network (ANN) model. How the one-hour and 24-hour models can be used in conjunction to predict different short-term rolling horizons is discussed, and this joint application is illustrated for a four-hour rolling horizon forecast scheme. Lastly, the effect of using predicted cloud cover values, instead of measured ones, on the accuracy of the models is assessed. Results show that LMX models do not degrade in forecast accuracy if models are trained with the forecast cloud cover data.« less

Evaluation of regression and neural network models for solar forecasting over different short-term horizons

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

Inanlouganji, Alireza; Reddy, T. Agami; Katipamula, Srinivas

Forecasting solar irradiation has acquired immense importance in view of the exponential increase in the number of solar photovoltaic (PV) system installations. In this article, analyses results involving statistical and machine-learning techniques to predict solar irradiation for different forecasting horizons are reported. Yearlong typical meteorological year 3 (TMY3) datasets from three cities in the United States with different climatic conditions have been used in this analysis. A simple forecast approach that assumes consecutive days to be identical serves as a baseline model to compare forecasting alternatives. To account for seasonal variability and to capture short-term fluctuations, different variants of themore » lagged moving average (LMX) model with cloud cover as the input variable are evaluated. Finally, the proposed LMX model is evaluated against an artificial neural network (ANN) model. How the one-hour and 24-hour models can be used in conjunction to predict different short-term rolling horizons is discussed, and this joint application is illustrated for a four-hour rolling horizon forecast scheme. Lastly, the effect of using predicted cloud cover values, instead of measured ones, on the accuracy of the models is assessed. Results show that LMX models do not degrade in forecast accuracy if models are trained with the forecast cloud cover data.« less

A Simple and Robust Statistical Test for Detecting the Presence of Recombination

PubMed Central

Bruen, Trevor C.; Philippe, Hervé; Bryant, David

2006-01-01

Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences is a difficult question. Here we develop a new statistic, Φw, that can be used to test for recombination. We show through simulation that our test can discriminate effectively between the presence and absence of recombination, even in diverse situations such as exponential growth (star-like topologies) and patterns of substitution rate correlation. A number of other tests, Max χ2, NSS, a coalescent-based likelihood permutation test (from LDHat), and correlation of linkage disequilibrium (both r2 and |D′|) with distance, all tend to underestimate the presence of recombination under strong population growth. Moreover, both Max χ2 and NSS falsely infer the presence of recombination under a simple model of mutation rate correlation. Results on empirical data show that our test can be used to detect recombination between closely as well as distantly related samples, regardless of the suspected rate of recombination. The results suggest that Φw is one of the best approaches to distinguish recurrent mutation from recombination in a wide variety of circumstances. PMID:16489234

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic pertubers

NASA Astrophysics Data System (ADS)

Kurz, Felix; Kampf, Thomas; Buschle, Lukas; Schlemmer, Heinz-Peter; Bendszus, Martin; Heiland, Sabine; Ziener, Christian

2016-12-01

In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

Estimation of renal allograft half-life: fact or fiction?

PubMed

Azancot, M Antonieta; Cantarell, Carme; Perelló, Manel; Torres, Irina B; Serón, Daniel; Seron, Daniel; Moreso, Francesc; Arias, Manuel; Campistol, Josep M; Curto, Jordi; Hernandez, Domingo; Morales, José M; Sanchez-Fructuoso, Ana; Abraira, Victor

2011-09-01

Renal allograft half-life time (t½) is the most straightforward representation of long-term graft survival. Since some statistical models overestimate this parameter, we compare different approaches to evaluate t½. Patients with a 1-year functioning graft transplanted in Spain during 1990, 1994, 1998 and 2002 were included. Exponential, Weibull, gamma, lognormal and log-logistic models censoring the last year of follow-up were evaluated. The goodness of fit of these models was evaluated according to the Cox-Snell residuals and the Akaike's information criterion (AIC) was employed to compare these models. We included 4842 patients. Real t½ in 1990 was 14.2 years. Median t½ (95% confidence interval) in 1990 and 2002 was 15.8 (14.2-17.5) versus 52.6 (35.6-69.5) according to the exponential model (P < 0.001). No differences between 1990 and 2002 were observed when t½ was estimated with the other models. In 1990 and 2002, t½ was 14.0 (13.1-15.0) versus 18.0 (13.7-22.4) according to Weibull, 15.5 (13.9-17.1) versus 19.1 (15.6-22.6) according to gamma, 14.4 (13.3-15.6) versus 18.3 (14.2-22.3) according to the log-logistic and 15.2 (13.8-16.6) versus 18.8 (15.3-22.3) according to the lognormal models. The AIC confirmed that the exponential model had the lowest goodness of fit, while the other models yielded a similar result. The exponential model overestimates t½, especially in cohorts of patients with a short follow-up, while any of the other studied models allow a better estimation even in cohorts with short follow-up.

Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised

NASA Technical Reports Server (NTRS)

Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.

1995-01-01

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.

Diffusion-weighted MR imaging of pancreatic cancer: A comparison of mono-exponential, bi-exponential and non-Gaussian kurtosis models.

PubMed

Kartalis, Nikolaos; Manikis, Georgios C; Loizou, Louiza; Albiin, Nils; Zöllner, Frank G; Del Chiaro, Marco; Marias, Kostas; Papanikolaou, Nikolaos

2016-01-01

To compare two Gaussian diffusion-weighted MRI (DWI) models including mono-exponential and bi-exponential, with the non-Gaussian kurtosis model in patients with pancreatic ductal adenocarcinoma. After written informed consent, 15 consecutive patients with pancreatic ductal adenocarcinoma underwent free-breathing DWI (1.5T, b-values: 0, 50, 150, 200, 300, 600 and 1000 s/mm 2 ). Mean values of DWI-derived metrics ADC, D, D*, f, K and D K were calculated from multiple regions of interest in all tumours and non-tumorous parenchyma and compared. Area under the curve was determined for all metrics. Mean ADC and D K showed significant differences between tumours and non-tumorous parenchyma (both P  < 0.001). Area under the curve for ADC, D, D*, f, K, and D K were 0.77, 0.52, 0.53, 0.62, 0.42, and 0.84, respectively. ADC and D K could differentiate tumours from non-tumorous parenchyma with the latter showing a higher diagnostic accuracy. Correction for kurtosis effects has the potential to increase the diagnostic accuracy of DWI in patients with pancreatic ductal adenocarcinoma.

Bi-periodicity evoked by periodic external inputs in delayed Cohen-Grossberg-type bidirectional associative memory networks

NASA Astrophysics Data System (ADS)

Cao, Jinde; Wang, Yanyan

2010-05-01

In this paper, the bi-periodicity issue is discussed for Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with time-varying delays and standard activation functions. It is shown that the model considered in this paper has two periodic orbits located in saturation regions and they are locally exponentially stable. Meanwhile, some conditions are derived to ensure that, in any designated region, the model has a locally exponentially stable or globally exponentially attractive periodic orbit located in it. As a special case of bi-periodicity, some results are also presented for the system with constant external inputs. Finally, four examples are given to illustrate the effectiveness of the obtained results.

Global exponential stability of bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model.

PubMed

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome.A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model.The overall tumor control rate was 94.1% in the 36-month (range 18-87 months) follow-up period (mean volume change of -43.3%). Volume regression (mean decrease of -50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of -3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9).Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

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

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

Study on the application of NASA energy management techniques for control of a terrestrial solar water heating system

NASA Technical Reports Server (NTRS)

Swanson, T. D.; Ollendorf, S.

1979-01-01

This paper addresses the potential for enhanced solar system performance through sophisticated control of the collector loop flow rate. Computer simulations utilizing the TRNSYS solar energy program were performed to study the relative effect on system performance of eight specific control algorithms. Six of these control algorithms are of the proportional type: two are concave exponentials, two are simple linear functions, and two are convex exponentials. These six functions are typical of what might be expected from future, more advanced, controllers. The other two algorithms are of the on/off type and are thus typical of existing control devices. Results of extensive computer simulations utilizing actual weather data indicate that proportional control does not significantly improve system performance. However, it is shown that thermal stratification in the liquid storage tank may significantly improve performance.

Edge Extraction by an Exponential Function Considering X-ray Transmission Characteristics

NASA Astrophysics Data System (ADS)

Kim, Jong Hyeong; Youp Synn, Sang; Cho, Sung Man; Jong Joo, Won

2011-04-01

3-D radiographic methodology has been into the spotlight for quality inspection of mass product or in-service inspection of aging product. To locate a target object in 3-D space, its characteristic contours such as edge length, edge angle, and vertices are very important. In spite of a simple geometry product, it is very difficult to get clear shape contours from a single radiographic image. The image contains scattering noise at the edges and ambiguity coming from X-Ray absorption within the body. This article suggests a concise method to extract whole edges from a single X-ray image. At the edge point of the object, the intensity of the X-ray decays exponentially as the X-ray penetrates the object. Considering this X-Ray decaying property, edges are extracted by using the least square fitting with the control of Coefficient of Determination.

Prediction of solar energetic particle event histories using real-time particle and solar wind measurements

NASA Technical Reports Server (NTRS)

Roelof, E. C.; Gold, R. E.

1978-01-01

The comparatively well-ordered magnetic structure in the solar corona during the decline of Solar Cycle 20 revealed a characteristic dependence of solar energetic particle injection upon heliographic longitude. When analyzed using solar wind mapping of the large scale interplanetary magnetic field line connection from the corona to the Earth, particle fluxes display an approximately exponential dependence on heliographic longitude. Since variations in the solar wind velocity (and hence the coronal connection longitude) can severely distort the simple coronal injection profile, the use of real-time solar wind velocity measurements can be of great aid in predicting the decay of solar particle events. Although such exponential injection profiles are commonplace during 1973-1975, they have also been identified earlier in Solar Cycle 20, and hence this structure may be present during the rise and maximum of the cycle, but somewhat obscured by greater temporal variations in particle injection.

Elastic Cheerios effect: Self-assembly of cylinders on a soft solid

NASA Astrophysics Data System (ADS)

Chakrabarti, Aditi; Ryan, Louis; Chaudhury, Manoj K.; Mahadevan, L.

2015-12-01

A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the "Cheerios Effect", which describes capillary interactions on a fluid interface. Our results show that the effective two-body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.

A comparison of modelling techniques used to characterise oxygen uptake kinetics during the on-transient of exercise.

PubMed

Bell, C; Paterson, D H; Kowalchuk, J M; Padilla, J; Cunningham, D A

2001-09-01

We compared estimates for the phase 2 time constant (tau) of oxygen uptake (VO2) during moderate- and heavy-intensity exercise, and the slow component of VO2 during heavy-intensity exercise using previously published exponential models. Estimates for tau and the slow component were different (P < 0.05) among models. For moderate-intensity exercise, a two-component exponential model, or a mono-exponential model fitted from 20 s to 3 min were best. For heavy-intensity exercise, a three-component model fitted throughout the entire 6 min bout of exercise, or a two-component model fitted from 20 s were best. When the time delays for the two- and three-component models were equal the best statistical fit was obtained; however, this model produced an inappropriately low DeltaVO2/DeltaWR (WR, work rate) for the projected phase 2 steady state, and the estimate of phase 2 tau was shortened compared with other models. The slow component was quantified as the difference between VO2 at end-exercise (6 min) and at 3 min (DeltaVO2 (6-3 min)); 259 ml x min(-1)), and also using the phase 3 amplitude terms (truncated to end-exercise) from exponential fits (409-833 ml x min(-1)). Onset of the slow component was identified by the phase 3 time delay parameter as being of delayed onset approximately 2 min (vs. arbitrary 3 min). Using this delay DeltaVO2 (6-2 min) was approximately 400 ml x min(-1). Use of valid consistent methods to estimate tau and the slow component in exercise are needed to advance physiological understanding.

Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

Robust Bayesian Fluorescence Lifetime Estimation, Decay Model Selection and Instrument Response Determination for Low-Intensity FLIM Imaging

PubMed Central

Rowley, Mark I.; Coolen, Anthonius C. C.; Vojnovic, Borivoj; Barber, Paul R.

2016-01-01

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting) with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET) experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters. PMID:27355322

Exponential inflation with F (R ) gravity

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.

2018-03-01

In this paper, we shall consider an exponential inflationary model in the context of vacuum F (R ) gravity. By using well-known reconstruction techniques, we shall investigate which F (R ) gravity can realize the exponential inflation scenario at leading order in terms of the scalar curvature, and we shall calculate the slow-roll indices and the corresponding observational indices, in the context of slow-roll inflation. We also provide some general formulas of the slow-roll and the corresponding observational indices in terms of the e -foldings number. In addition, for the calculation of the slow-roll and of the observational indices, we shall consider quite general formulas, for which it is not necessary for the assumption that all the slow-roll indices are much smaller than unity to hold true. Finally, we investigate the phenomenological viability of the model by comparing it with the latest Planck and BICEP2/Keck-Array observational data. As we demonstrate, the model is compatible with the current observational data for a wide range of the free parameters of the model.

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

NASA Astrophysics Data System (ADS)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Hypersurface Homogeneous Cosmological Model in Modified Theory of Gravitation

NASA Astrophysics Data System (ADS)

Katore, S. D.; Hatkar, S. P.; Baxi, R. J.

2016-12-01

We study a hypersurface homogeneous space-time in the framework of the f (R, T) theory of gravitation in the presence of a perfect fluid. Exact solutions of field equations are obtained for exponential and power law volumetric expansions. We also solve the field equations by assuming the proportionality relation between the shear scalar (σ ) and the expansion scalar (θ ). It is observed that in the exponential model, the universe approaches isotropy at large time (late universe). The investigated model is notably accelerating and expanding. The physical and geometrical properties of the investigated model are also discussed.

An analytic solution of the stochastic storage problem applicable to soil water

USGS Publications Warehouse

Milly, P.C.D.

1993-01-01

The accumulation of soil water during rainfall events and the subsequent depletion of soil water by evaporation between storms can be described, to first order, by simple accounting models. When the alternating supplies (precipitation) and demands (potential evaporation) are viewed as random variables, it follows that soil-water storage, evaporation, and runoff are also random variables. If the forcing (supply and demand) processes are stationary for a sufficiently long period of time, an asymptotic regime should eventually be reached where the probability distribution functions of storage, evaporation, and runoff are stationary and uniquely determined by the distribution functions of the forcing. Under the assumptions that the potential evaporation rate is constant, storm arrivals are Poisson-distributed, rainfall is instantaneous, and storm depth follows an exponential distribution, it is possible to derive the asymptotic distributions of storage, evaporation, and runoff analytically for a simple balance model. A particular result is that the fraction of rainfall converted to runoff is given by (1 - R−1)/(eα(1−R−1) − R−1), in which R is the ratio of mean potential evaporation to mean rainfall and a is the ratio of soil water-holding capacity to mean storm depth. The problem considered here is analogous to the well-known problem of storage in a reservoir behind a dam, for which the present work offers a new solution for reservoirs of finite capacity. A simple application of the results of this analysis suggests that random, intraseasonal fluctuations of precipitation cannot by themselves explain the observed dependence of the annual water balance on annual totals of precipitation and potential evaporation.

Performance and state-space analyses of systems using Petri nets

NASA Technical Reports Server (NTRS)

Watson, James Francis, III

1992-01-01

The goal of any modeling methodology is to develop a mathematical description of a system that is accurate in its representation and also permits analysis of structural and/or performance properties. Inherently, trade-offs exist between the level detail in the model and the ease with which analysis can be performed. Petri nets (PN's), a highly graphical modeling methodology for Discrete Event Dynamic Systems, permit representation of shared resources, finite capacities, conflict, synchronization, concurrency, and timing between state changes. By restricting the state transition time delays to the family of exponential density functions, Markov chain analysis of performance problems is possible. One major drawback of PN's is the tendency for the state-space to grow rapidly (exponential complexity) compared to increases in the PN constructs. It is the state space, or the Markov chain obtained from it, that is needed in the solution of many problems. The theory of state-space size estimation for PN's is introduced. The problem of state-space size estimation is defined, its complexities are examined, and estimation algorithms are developed. Both top-down and bottom-up approaches are pursued, and the advantages and disadvantages of each are described. Additionally, the author's research in non-exponential transition modeling for PN's is discussed. An algorithm for approximating non-exponential transitions is developed. Since only basic PN constructs are used in the approximation, theory already developed for PN's remains applicable. Comparison to results from entropy theory show the transition performance is close to the theoretic optimum. Inclusion of non-exponential transition approximations improves performance results at the expense of increased state-space size. The state-space size estimation theory provides insight and algorithms for evaluating this trade-off.

Model evaluation of plant metal content and biomass yield for the phytoextraction of heavy metals by switchgrass.

PubMed

Chen, Bo-Ching; Lai, Hung-Yu; Juang, Kai-Wei

2012-06-01

To better understand the ability of switchgrass (Panicum virgatum L.), a perennial grass often relegated to marginal agricultural areas with minimal inputs, to remove cadmium, chromium, and zinc by phytoextraction from contaminated sites, the relationship between plant metal content and biomass yield is expressed in different models to predict the amount of metals switchgrass can extract. These models are reliable in assessing the use of switchgrass for phytoremediation of heavy-metal-contaminated sites. In the present study, linear and exponential decay models are more suitable for presenting the relationship between plant cadmium and dry weight. The maximum extractions of cadmium using switchgrass, as predicted by the linear and exponential decay models, approached 40 and 34 μg pot(-1), respectively. The log normal model was superior in predicting the relationship between plant chromium and dry weight. The predicted maximum extraction of chromium by switchgrass was about 56 μg pot(-1). In addition, the exponential decay and log normal models were better than the linear model in predicting the relationship between plant zinc and dry weight. The maximum extractions of zinc by switchgrass, as predicted by the exponential decay and log normal models, were about 358 and 254 μg pot(-1), respectively. To meet the maximum removal of Cd, Cr, and Zn, one can adopt the optimal timing of harvest as plant Cd, Cr, and Zn approach 450 and 526 mg kg(-1), 266 mg kg(-1), and 3022 and 5000 mg kg(-1), respectively. Due to the well-known agronomic characteristics of cultivation and the high biomass production of switchgrass, it is practicable to use switchgrass for the phytoextraction of heavy metals in situ. Copyright © 2012 Elsevier Inc. All rights reserved.

The Population Tracking Model: A Simple, Scalable Statistical Model for Neural Population Data

PubMed Central

O'Donnell, Cian; alves, J. Tiago Gonç; Whiteley, Nick; Portera-Cailliau, Carlos; Sejnowski, Terrence J.

2017-01-01

Our understanding of neural population coding has been limited by a lack of analysis methods to characterize spiking data from large populations. The biggest challenge comes from the fact that the number of possible network activity patterns scales exponentially with the number of neurons recorded (∼2Neurons). Here we introduce a new statistical method for characterizing neural population activity that requires semi-independent fitting of only as many parameters as the square of the number of neurons, requiring drastically smaller data sets and minimal computation time. The model works by matching the population rate (the number of neurons synchronously active) and the probability that each individual neuron fires given the population rate. We found that this model can accurately fit synthetic data from up to 1000 neurons. We also found that the model could rapidly decode visual stimuli from neural population data from macaque primary visual cortex about 65 ms after stimulus onset. Finally, we used the model to estimate the entropy of neural population activity in developing mouse somatosensory cortex and, surprisingly, found that it first increases, and then decreases during development. This statistical model opens new options for interrogating neural population data and can bolster the use of modern large-scale in vivo Ca2+ and voltage imaging tools. PMID:27870612

Effect of artificial length scales in large eddy simulation of a neutral atmospheric boundary layer flow: A simple solution to log-layer mismatch

NASA Astrophysics Data System (ADS)

Chatterjee, Tanmoy; Peet, Yulia T.

2017-07-01

A large eddy simulation (LES) methodology coupled with near-wall modeling has been implemented in the current study for high Re neutral atmospheric boundary layer flows using an exponentially accurate spectral element method in an open-source research code Nek 5000. The effect of artificial length scales due to subgrid scale (SGS) and near wall modeling (NWM) on the scaling laws and structure of the inner and outer layer eddies is studied using varying SGS and NWM parameters in the spectral element framework. The study provides an understanding of the various length scales and dynamics of the eddies affected by the LES model and also the fundamental physics behind the inner and outer layer eddies which are responsible for the correct behavior of the mean statistics in accordance with the definition of equilibrium layers by Townsend. An economical and accurate LES model based on capturing the near wall coherent eddies has been designed, which is successful in eliminating the artificial length scale effects like the log-layer mismatch or the secondary peak generation in the streamwise variance.

Single-arm phase II trial design under parametric cure models.

PubMed

Wu, Jianrong

2015-01-01

The current practice of designing single-arm phase II survival trials is limited under the exponential model. Trial design under the exponential model may not be appropriate when a portion of patients are cured. There is no literature available for designing single-arm phase II trials under the parametric cure model. In this paper, a test statistic is proposed, and a sample size formula is derived for designing single-arm phase II trials under a class of parametric cure models. Extensive simulations showed that the proposed test and sample size formula perform very well under different scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models

PubMed Central

Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.

2017-01-01

Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior. PMID:28863161

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

PubMed

Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos

2017-01-01

The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Endogenous technological and demographic change under increasing water scarcity

NASA Astrophysics Data System (ADS)

Pande, S.; Ertsen, M.; Sivapalan, M.

2013-12-01

Many ancient civilizations such as the Indus Valley civilization dispersed under extreme dry conditions. Even contemporary societies such as the one in Murrumbidgee river basin, Australia, have started to witness a decline in overall population under increasing water scarcity. Skeptics of hydroclimatic determinism have often cautioned against the use of hydroclimatic change as the sole predictor of the fate of contemporary societies in water scarce regions by suggesting that technological change may ameliorate the effects of increasing water scarcity. We here develop a simple overlapping generations model of endogenous technological and demographic change. It models technological change not as an exogenous random sequence of events but as an endogenous process (as is widely accepted in contemporary literature) that depends on factors such as the investments that are (endogenously) made in a society, the endogenous diversification of a society into skilled and unskilled workers, individuals' patience in terms of its present consumption versus future consumption, the production technology and the (endogenous) interaction of these factors. The population growth rate is modeled to decline once consumption per capita crosses a ';survival' threshold. The model demonstrates that technological change may ameliorate the effects of increasing water scarcity but only to a certain extent in many cases. It is possible that technological change may allow a society to escape the effect of increasing water society, leading to an exponential rise in technology and population. However, such cases require that the rate of success of investment in technological advancement is high. In other more realistic cases of technological success, we find that endogenous technology change has an effect delaying the peak of population before it starts to decline. While the model is a rather simple model of societal growth, it is capable of replicating (not to scale) patterns of technological change (proxies of which in ancient technology include irrigation canals, metal tools, and the use of horses for labor while in contemporary societies its proxies may be the advent of drip irrigation, increasing reservoir storage capacity etc) and population change. It is capable of replicating the pattern of declining consumption per capita in presence of growth in aggregate production. It is also capable of modeling the exponential population rise even under increasing water scarcity. The results of the model suggest, as one of the many other possible explanations, that ancient societies that declined in the face of extreme water scarcity may have done so due to slower rate of success of investment in technological advancement. The model suggests that the population decline occurs after a prolonged decline in consumption per capita, which in turn is due to the joint effect of initially increasing population and increasing water scarcity. This is despite technological advancement and increase in aggregate production. Thus declining consumption per capita despite technological advancement and increase in aggregate production may serve as a useful predictor of upcoming decline in contemporary societies in water scarce basins.

Computing exponentially faster: implementing a non-deterministic universal Turing machine using DNA

PubMed Central

Currin, Andrew; Korovin, Konstantin; Ababi, Maria; Roper, Katherine; Kell, Douglas B.; Day, Philip J.

2017-01-01

The theory of computer science is based around universal Turing machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of classical UTMs. For the most important class of problem in computer science, non-deterministic polynomial complete problems, non-deterministic UTMs (NUTMs) are theoretically exponentially faster than both classical UTMs and quantum mechanical UTMs (QUTMs). However, no attempt has previously been made to build an NUTM, and their construction has been regarded as impossible. Here, we demonstrate the first physical design of an NUTM. This design is based on Thue string rewriting systems, and thereby avoids the limitations of most previous DNA computing schemes: all the computation is local (simple edits to strings) so there is no need for communication, and there is no need to order operations. The design exploits DNA's ability to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that the design works using both computational modelling and in vitro molecular biology experimentation: the design is thermodynamically favourable, microprogramming can be used to encode arbitrary Thue rules, all classes of Thue rule can be implemented, and non-deterministic rule implementation. In an NUTM, the resource limitation is space, which contrasts with classical UTMs and QUTMs where it is time. This fundamental difference enables an NUTM to trade space for time, which is significant for both theoretical computer science and physics. It is also of practical importance, for to quote Richard Feynman ‘there's plenty of room at the bottom’. This means that a desktop DNA NUTM could potentially utilize more processors than all the electronic computers in the world combined, and thereby outperform the world's current fastest supercomputer, while consuming a tiny fraction of its energy. PMID:28250099