Reconstruction of stochastic temporal networks through diffusive arrival times
National Research Council Canada - National Science Library
Xun Li; Xiang Li
2017-01-01
.... We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent...
On the Robustness of Temporal Properties for Stochastic Models
Directory of Open Access Journals (Sweden)
Ezio Bartocci
2013-08-01
Full Text Available Stochastic models such as Continuous-Time Markov Chains (CTMC and Stochastic Hybrid Automata (SHA are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Reconstruction of stochastic temporal networks through diffusive arrival times
Li, Xun; Li, Xiang
2017-01-01
Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687
Joint effects of habitat configuration and temporal stochasticity on population dynamics
Jennifer M. Fraterrigo; Scott M. Pearson; Monica G. Turner
2009-01-01
Habitat configuration and temporal stochasticity in the environment are recognized as important drivers of population structure, yet few studies have examined the combined influence of these factors....
Large scale stochastic spatio-temporal modelling with PCRaster
Karssenberg, Derek; Drost, Niels; Schmitz, Oliver; de Jong, Kor; Bierkens, Marc F. P.
2013-04-01
PCRaster is a software framework for building spatio-temporal models of land surface processes (http://www.pcraster.eu). Building blocks of models are spatial operations on raster maps, including a large suite of operations for water and sediment routing. These operations are available to model builders as Python functions. The software comes with Python framework classes providing control flow for spatio-temporal modelling, Monte Carlo simulation, and data assimilation (Ensemble Kalman Filter and Particle Filter). Models are built by combining the spatial operations in these framework classes. This approach enables modellers without specialist programming experience to construct large, rather complicated models, as many technical details of modelling (e.g., data storage, solving spatial operations, data assimilation algorithms) are taken care of by the PCRaster toolbox. Exploratory modelling is supported by routines for prompt, interactive visualisation of stochastic spatio-temporal data generated by the models. The high computational requirements for stochastic spatio-temporal modelling, and an increasing demand to run models over large areas at high resolution, e.g. in global hydrological modelling, require an optimal use of available, heterogeneous computing resources by the modelling framework. Current work in the context of the eWaterCycle project is on a parallel implementation of the modelling engine, capable of running on a high-performance computing infrastructure such as clusters and supercomputers. Model runs will be distributed over multiple compute nodes and multiple processors (GPUs and CPUs). Parallelization will be done by parallel execution of Monte Carlo realizations and sub regions of the modelling domain. In our approach we use multiple levels of parallelism, improving scalability considerably. On the node level we will use OpenCL, the industry standard for low-level high performance computing kernels. To combine multiple nodes we will use
Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures
Sivakumar, C.
2018-01-01
In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the early epochs. It provides persistent fluctuations in the number count vs. apparent magnitude relation, as expected from the observation of a fractal distribution of the galaxies. We also present a stochastic evolution of density perturbations in the early Universe.
Baselga, Andrés; Bonthoux, Sébastien; Balent, Gérard
2015-01-01
Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cover change that occurred between 1982 and 2007 on (i) the species composition (presence/absence) of bird assemblages and (ii) the spatial pattern of taxonomic beta diversity. We also compared the observed temporal change of bird assemblages with a null model accounting for the effect of stochastic dynamics on temporal beta diversity. Temporal assemblage dissimilarity was partitioned into two separate components, accounting for the replacement of species (i.e. turnover) and for the nested species losses (or gains) from one time to the other (i.e. nestedness-resultant dissimilarity), respectively. Neither the turnover nor the nestedness-resultant components of temporal variation were accurately explained by any of the measured variables accounting for land cover change (r(2)process could be driving the observed patterns, it is also possible that the observed changes in presence/absence species composition of local bird assemblages might be the consequence of stochastic processes in which species populations appeared and disappeared from specific localities in a random-like way. Our results might be case-specific, but if stochastic dynamics are generally dominant, the ability of correlative and mechanistic models to predict land cover change effects on species composition would be compromised.
Large scale stochastic spatio-temporal modelling with PCRaster
Karssenberg, D.J.; Drost, N.; Schmitz, O.; Jong, K. de; Bierkens, M.F.P.
2013-01-01
PCRaster is a software framework for building spatio-temporal models of land surface processes (http://www.pcraster.eu). Building blocks of models are spatial operations on raster maps, including a large suite of operations for water and sediment routing. These operations are available to model
Directory of Open Access Journals (Sweden)
Andrés Baselga
Full Text Available Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cover change that occurred between 1982 and 2007 on (i the species composition (presence/absence of bird assemblages and (ii the spatial pattern of taxonomic beta diversity. We also compared the observed temporal change of bird assemblages with a null model accounting for the effect of stochastic dynamics on temporal beta diversity. Temporal assemblage dissimilarity was partitioned into two separate components, accounting for the replacement of species (i.e. turnover and for the nested species losses (or gains from one time to the other (i.e. nestedness-resultant dissimilarity, respectively. Neither the turnover nor the nestedness-resultant components of temporal variation were accurately explained by any of the measured variables accounting for land cover change (r(2<0.06 in all cases. Additionally, the amount of spatial assemblage heterogeneity in the region did not significantly change between 1982 and 2007, and site-specific observed temporal dissimilarities were larger than null expectations in only 1% of sites for temporal turnover and 13% of sites for nestedness-resultant dissimilarity. Taken together, our results suggest that land cover change in this agricultural landscape had little impact on temporal beta diversity of bird assemblages. Although other unmeasured deterministic process could be driving the observed patterns, it is also possible that the observed changes in presence/absence species composition of local bird assemblages might be the consequence of stochastic processes in which species populations appeared and disappeared from specific
Modeling stochastic lead times in multi-echelon systems
Diks, EB Erik; Heijden, van der, ML
1997-01-01
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not c...
Modeling stochastic lead times in multi-echelon systems
Diks, E.B.; van der Heijden, Matthijs C.
1997-01-01
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well
Temporal and stochastic control of Staphylococcus aureus biofilm development.
Moormeier, Derek E; Bose, Jeffrey L; Horswill, Alexander R; Bayles, Kenneth W
2014-10-14
Biofilm communities contain distinct microniches that result in metabolic heterogeneity and variability in gene expression. Previously, these niches were visualized within Staphylococcus aureus biofilms by observing differential expression of the cid and lrg operons during tower formation. In the present study, we examined early biofilm development and identified two new stages (designated "multiplication" and "exodus") that were associated with changes in matrix composition and a distinct reorganization of the cells as the biofilm matured. The initial attachment and multiplication stages were shown to be protease sensitive but independent of most cell surface-associated proteins. Interestingly, after 6 h of growth, an exodus of the biofilm population that followed the transition of the biofilm to DNase I sensitivity was demonstrated. Furthermore, disruption of the gene encoding staphylococcal nuclease (nuc) abrogated this exodus event, causing hyperproliferation of the biofilm and disrupting normal tower development. Immediately prior to the exodus event, S. aureus cells carrying a nuc::gfp promoter fusion demonstrated Sae-dependent expression but only in an apparently random subpopulation of cells. In contrast to the existing model for tower development in S. aureus, the results of this study suggest the presence of a Sae-controlled nuclease-mediated exodus of biofilm cells that is required for the development of tower structures. Furthermore, these studies indicate that the differential expression of nuc during biofilm development is subject to stochastic regulatory mechanisms that are independent of the formation of metabolic microniches. Importance: In this study, we provide a novel view of four early stages of biofilm formation by the human pathogen Staphylococcus aureus. We identified an initial nucleoprotein matrix during biofilm development that is DNase I insensitive until a critical point when a nuclease-mediated exodus of the population is induced prior
Stochastic Urban Pluvial Flood Hazard Maps Based upon a Spatial-Temporal Rainfall Generator
Directory of Open Access Journals (Sweden)
Nuno Eduardo Simões
2015-06-01
Full Text Available It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2 located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions.
Analysis of Stochastic Radio Channels with Temporal Birth-Death Dynamics
DEFF Research Database (Denmark)
Jakobsen, Morten Lomholt; Pedersen, Troels; Fleury, Bernard Henri
2014-01-01
We employ the theory of spatial point processes to revisit and reinterpret a particular class of time-variant stochastic radio channel models. Common for all models in this class is that individual multipath components are emerging and vanishing in a temporal birth-death like manner, with the und......We employ the theory of spatial point processes to revisit and reinterpret a particular class of time-variant stochastic radio channel models. Common for all models in this class is that individual multipath components are emerging and vanishing in a temporal birth-death like manner...... novel assessment of the autocorrelation functions of random processes used in the general channel model description. Under simplifying assumptions the channel transfer function is shown to be wide-sense stationary in both time and frequency (despite the birth-death behavior of the overall channel...
De Ridder, Simon; Vandermarliere, Benjamin; Ryckebusch, Jan
2016-11-01
A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset (2015 Proc. 29th AAAI Conf. on Artificial Intelligence). We build on this methodology and extend it to also include the versatile stochastic block models (SBMs) as a parametric family for reconstructing the empirical networks. We use five different techniques for change point detection on prototypical temporal networks, including empirical and synthetic ones. We find that none of the considered methods can consistently outperform the others when it comes to detecting and locating the expected change points in empirical temporal networks. With respect to the precision and the recall of the results of the change points, we find that the method based on a degree-corrected SBM has better recall properties than other dedicated methods, especially for sparse networks and smaller sliding time window widths.
Stochastic recruitment leads to symmetry breaking in foraging populations
Biancalani, Tommaso; Dyson, Louise; McKane, Alan
2014-03-01
When an ant colony is faced with two identical equidistant food sources, the foraging ants are found to concentrate more on one source than the other. Analogous symmetry-breaking behaviours have been reported in various population systems, (such as queueing or stock market trading) suggesting the existence of a simple universal mechanism. Past studies have neglected the effect of demographic noise and required rather complicated models to qualitatively reproduce this behaviour. I will show how including the effects of demographic noise leads to a radically different conclusion. The symmetry-breaking arises solely due to the process of recruitment and ceases to occur for large population sizes. The latter fact provides a testable prediction for a real system.
Rossi, R.; Tarim, S.A.; Hnich, B.; Prestwich, S.
2010-01-01
In this paper we address the general multi-period production/inventory problem with non-stationary stochastic demand and supplier lead-time under service level constraints. A replenishment cycle policy (Rn,Sn) is modeled, where Rn is the nth replenishment cycle length and Sn is the respective
Causes of temporal variability of lead in domestic plumbing systems.
Schock, M R
1990-07-01
Sources of lead in drinking water are primarily lead pipe, lead/tin solder, and brass fixture materials.Lead levels in the water depend upon many solubility factors, such as pH, concentrations of substances such as inorganic carbonate, orthophosphate, chlorine, and silicate, the temperature, the nature of the pipe surface, etc. Physical factors, time, and chemical mass transfer are significant in governing lead levels in nonequilibrium systems. The diameter and length of lead pipe is extremely important, as well as the age and chemical history of the solder and brass fixtures. Analytical variability is not particularly significant relative to between-site and within-site variability. Knowledge of temporal variability at each site is necessary to define a statistically valid monitoring program. An analysis of published data covering repetitive measurements at a given site show that the variability of lead concentration at each site tends to be characterized by the frequent occurrence of 'spikes'. Variability expressed as approximate relative standard deviations tends to be of about 50 to 75% in untreated water, regardless of the mean lead concentration. The distributions are frequently nonnormal for small numbers of samples. Monitoring programs must incorporate controls for the causes of the within-site and between-site variability into their sampling design. The determination of necessary sampling frequency, sample number, and sample volume must be made with consideration of the system variability, or the results will be unrepresentative and irreproducible.
Supply Chain Model with Stochastic Lead Time, Trade-Credit Financing, and Transportation Discounts
Directory of Open Access Journals (Sweden)
Sung Jun Kim
2017-01-01
Full Text Available This model extends a two-echelon supply chain model by considering the trade-credit policy, transportations discount to make a coordination mechanism between transportation discounts, trade-credit financing, number of shipments, quality improvement of products, and reduced setup cost in such a way that the total cost of the whole system can be reduced, where the supplier offers trade-credit-period to the buyer. For buyer, the backorder rate is considered as variable. There are two investments to reduce setup cost and to improve quality of products. The model assumes lead time-dependent backorder rate, where the lead time is stochastic in nature. By using the trade-credit policy, the model gives how the credit-period would be determined to achieve the win-win outcome. An iterative algorithm is designed to obtain the global optimum results. Numerical example and sensitivity analysis are given to illustrate the model.
Spatio-temporal and stochastic modelling of severe acute respiratory syndrome
Directory of Open Access Journals (Sweden)
Poh-Chin Lai
2013-11-01
Full Text Available This study describes the development of a spatio-temporal disease model based on the episodes of severe acute respiratory syndrome (SARS that took place in Hong Kong in 2003. In contrast to conventional, deterministic modelling approaches, the model described here is predominantly spatial. It incorporates stochastic processing of environmental and social variables that interact in space and time to affect the patterns of disease transmission in a community. The model was validated through a comparative assessment between actual and modelled distribution of diseased locations. Our study shows that the inclusion of location-specific characteristics satisfactorily replicates the spatial dynamics of an infectious disease. The Pearson’s correlation coefficients for five trials based on 3-day aggregation of disease counts for 1-3, 4-6 and 7-9 day forecasts were 0.57- 0.95, 0.54-0.86 and 0.57-0.82, respectively, while the correlation based on 5-day aggregation for the 1-5 day forecast was 0.55- 0.94 and 0.58-0.81 for the 6-10 day forecast. The significant and strong relationship between actual results and forecast is encouraging for the potential development of an early warning system for detecting this type of disease outbreaks.
Stochastic integrated vendor–buyer model with unstable lead time and setup cost
Directory of Open Access Journals (Sweden)
Chandra K. Jaggi
2011-01-01
Full Text Available This paper presents a new vendor-buyer system where there are different objectives for both sides. The proposed method of this paper is different from the other previously published works since it considers different objectives for both sides. In this paper, the vendor’s emphasis is on the crashing of the setup cost, which not only helps him compete in the market but also provides better services to his customers; and the buyer’s aim is to reduce the lead time, which not only facilitates the buyer to fulfill the customers’ demand on time but also enables him to earn a good reputation in the market or vice versa. In the light of the above stated facts, an integrated vendor-buyer stochastic inventory model is also developed. The propsed model considers two cases for demand during lead time: Case (i Complete demand information, Case (ii Partial demand information. The proposed model jointly optimizes the buyer’s ordered quantity and lead time along with vendor’s setup cost and the number of shipments. The results are demonstrated with the help of numerical examples.
A new order splitting model with stochastic lead times for deterioration items
Sazvar, Zeinab; Akbari Jokar, Mohammad Reza; Baboli, Armand
2014-09-01
In unreliable supply environments, the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously is an attractive sourcing policy that has captured the attention of academic researchers and corporate managers alike. While various assumptions are considered in the models developed, researchers tend to overlook an important inventory category in order splitting models: deteriorating items. In this paper, we study an order splitting policy for a retailer that sells a deteriorating product. The inventory system is modelled as a continuous review system (s, Q) under stochastic lead time. Demand rate per unit time is assumed to be constant over an infinite planning horizon and shortages are backordered completely. We develop two inventory models. In the first model, it is assumed that all the requirements are supplied by only one source, whereas in the second, two suppliers are available. We use sensitivity analysis to determine the situations in which each sourcing policy is the most economic. We then study a real case from the European pharmaceutical industry to demonstrate the applicability and effectiveness of the proposed models. Finally, more promising directions are suggested for future research.
Gravenmier, Curtis A; Siddique, Miriam; Gatenby, Robert A
2017-05-15
While most cancers promote ingrowth of host blood vessels, the resulting vascular network usually fails to develop a mature organization, resulting in abnormal vascular dynamics with stochastic variations that include slowing, cessation, and even reversal of flow. Thus, substantial spatial and temporal variations in oxygen concentration are commonly observed in most cancers. Cancer cells, like all living systems, are subject to Darwinian dynamics such that their survival and proliferation are dependent on developing optimal phenotypic adaptations to local environmental conditions. Here, we consider the environmental stresses placed on tumors subject to profound, frequent, but stochastic variations in oxygen concentration as a result of temporal variations in blood flow. While vascular fluctuations will undoubtedly affect local concentrations of a wide range of molecules including growth factors (e.g., estrogen), substrate (oxygen, glucose, etc.), and metabolites ([Formula: see text], we focus on the selection forces that result solely from stochastic fluctuations in oxygen concentration. The glucose metabolism of cancer cells has been investigated for decades following observations that malignant cells ferment glucose regardless of oxygen concentration, a condition termed the Warburg effect. In contrast, normal cells cease fermentation under aerobic conditions and this physiological response is termed the Pasteur effect. Fermentation is markedly inefficient compared to cellular respiration in terms of adenosine triphosphate (ATP) production, generating just 2 ATP/glucose, whereas respiration generates 38 ATP/glucose. This inefficiency requires cancer cells to increase glycolytic flux, which subsequently increases acid production and can significantly acidify local tissue. Hence, it initially appears that cancer cells adopt a disadvantageous metabolic phenotype. Indeed, this metabolic "hallmark" of cancer is termed "energy dysregulation." However, if cancers arise
Stochastic dynamics of resistive switching: fluctuations lead to optimal particle number
Radtke, Paul K.; Hazel, Andrew L.; Straube, Arthur V.; Schimansky-Geier, Lutz
2017-09-01
Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies’ dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance.
Using stochastic models to incorporate spatial and temporal variability [Exercise 14
Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke
2003-01-01
To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...
DEFF Research Database (Denmark)
Hansen, Benni Winding; Kesäniemi, Jenni E; Mustonen, Marina
2014-01-01
variation: species with dispersive planktonic larvae are expected to be more likely to show temporal genetic variation than species with benthic or brooded non-dispersive larvae, due to differences in larval mortality and dispersal ability. We examined temporal genetic structure in populations of Pygospio...
Varouchakis, Emmanouil
2017-04-01
Reliable temporal modelling of groundwater level is significant for efficient water resources management in hydrological basins and for the prevention of possible desertification effects. In this work we propose a stochastic data driven approach of temporal monitoring and prediction that can incorporate auxiliary information. More specifically, we model the temporal (mean annual and biannual) variation of groundwater level by means of a discrete time autoregressive exogenous variable model (ARX model). The ARX model parameters and its predictions are estimated by means of the Kalman filter adaptation algorithm (KFAA). KFAA is suitable for sparsely monitored basins that do not allow for an independent estimation of the ARX model parameters. Three new modified versions of the original form of the ARX model are proposed and investigated: the first considers a larger time scale, the second a larger time delay in terms of the groundwater level input and the third considers the groundwater level difference between the last two hydrological years, which is incorporated in the model as a third input variable. We apply KFAA to time series of groundwater level values from Mires basin in the island of Crete. In addition to precipitation measurements, we use pumping data as exogenous variables. We calibrate the ARX model based on the groundwater level for the years 1981 to 2006 and use it to successfully predict the mean annual and biannual groundwater level for recent years (2007-2010).
A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall
Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.
2017-06-01
Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.
DEFF Research Database (Denmark)
Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten
gauges in the model area. The spatio-temporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatio-temporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying onprecipitation output......Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain...
spate: An R Package for Spatio-Temporal Modeling with a Stochastic Advection-Diffusion Process
Directory of Open Access Journals (Sweden)
Fabio Sigrist
2015-02-01
This package aims at providing tools for simulating and modeling of spatio-temporal processes using an SPDE based approach. The package contains functions for obtaining parametrizations, such as propagator or innovation covariance matrices, of the spatio-temporal model. This allows for building customized hierarchical Bayesian models using the SPDE based model at the process stage. The functions of the package then provide computationally efficient algorithms needed for doing inference with the hierarchical model. Furthermore, an adaptive Markov chain Monte Carlo (MCMC algorithm implemented in the package can be used as an algorithm for doing inference without any additional modeling. This function is flexible and allows for application specific customizing. The MCMC algorithm supports data that follow a Gaussian or a censored distribution with point mass at zero. Spatio-temporal covariates can be included in the model through a regression term.
Directory of Open Access Journals (Sweden)
Hardik Soni
2011-10-01
Full Text Available In today's global marketplace, individual firms do not compete as independent entities rather as an integral part of a supply chain. Uncertainty is the main attribute in managing the supply chains. Accordingly, we develop a (Q, R inventory model with service level constraint and variable lead-time in fuzzy-stochastic environment. In addition, the triangular fuzzy numbers counts upon lead-time are used to construct fuzzy-stochastic lead-time demand. Using credibility criterion, the expected shortages are calculated. Without loss of generality, we assume that all the observed values of the fuzzy random variable, representing the demand are triangular fuzzy numbers. Consequently, the value of total expected cost in the fuzzy sense is derived using the expected value criterion or credibility criterion. To determine an optimal policy, a numerical technique is presented and the results are analyzed using scan and zoom for constraint optimization. Finally, in order to demonstrate the accuracy and effectiveness of the proposed model, numerical example and sensitivity analysis are also included.
Stochastic and deterministic processes regulate spatio-temporal variation in seed bank diversity
Alejandro A. Royo; Todd E. Ristau
2013-01-01
Seed banks often serve as reservoirs of taxonomic and genetic diversity that buffer plant populations and influence post-disturbance vegetation trajectories; yet evaluating their importance requires understanding how their composition varies within and across spatial and temporal scales (α- and β-diversity). Shifts in seed bank diversity are strongly...
DEFF Research Database (Denmark)
Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten
2017-01-01
gauges in the model area. The spatiotemporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatiotemporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying on precipitation output......Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain...
Model Checking Discounted Temporal Properties
de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle Ida Antoinette; Jensen, K; Podelski, A.
2004-01-01
Temporal logic is two-valued: a property is either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a
Model Checking Discounted Temporal Properties
de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle Ida Antoinette
2005-01-01
Temporal logic is two-valued: a property is either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a
Fornix and medial temporal lobe lesions lead to comparable deficits in complex visual perception.
Lech, Robert K; Koch, Benno; Schwarz, Michael; Suchan, Boris
2016-05-04
Recent research dealing with the structures of the medial temporal lobe (MTL) has shifted away from exclusively investigating memory-related processes and has repeatedly incorporated the investigation of complex visual perception. Several studies have demonstrated that higher level visual tasks can recruit structures like the hippocampus and perirhinal cortex in order to successfully perform complex visual discriminations, leading to a perceptual-mnemonic or representational view of the medial temporal lobe. The current study employed a complex visual discrimination paradigm in two patients suffering from brain lesions with differing locations and origin. Both patients, one with extensive medial temporal lobe lesions (VG) and one with a small lesion of the anterior fornix (HJK), were impaired in complex discriminations while showing otherwise mostly intact cognitive functions. The current data confirmed previous results while also extending the perceptual-mnemonic theory of the MTL to the main output structure of the hippocampus, the fornix. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Multi-Objective Lead-Time Control Problem with Stochastic Constraints
Directory of Open Access Journals (Sweden)
M. Molavi
2014-10-01
Full Text Available This research intends to find out any development of a robust multi-objective for lead time optimal control problem in a multi-stage assembly system model. Assembly system modeling is possible by the help of the open queue network. A working station includes one or infinite servers and just manufacturing or assembly operations are performed therein. Each part has a separate entry process and independent of each other. It is completely based upon Poisson process.Serving Lead Time of Stations are also independent of each other and therefore exponential distribution of each parameter is controllable. All stations have bounded uncertain unrecyclable wastes which are completely independent in compliance with Erlang distribution. Uncertainty in the problem parameters has been suggested as robust multi-objective optimal control model in which we have three incompatible target functions including cyclic operation cost minimization, average lead time minimization and lead time variance. Finally, target progress method has been applied in order to achieve serving optimal speeds and solve discrete time of the main problem approximately. The proposed model could present a suitable solution even for the same problem as mentioned in other related papers along with some considerable results in parameter uncertainty conditions.
Mapping the spatio-temporal risk of lead exposure in apex species for more effective mitigation.
Mateo-Tomás, Patricia; Olea, Pedro P; Jiménez-Moreno, María; Camarero, Pablo R; Sánchez-Barbudo, Inés S; Rodríguez Martín-Doimeadios, Rosa C; Mateo, Rafael
2016-07-27
Effective mitigation of the risks posed by environmental contaminants for ecosystem integrity and human health requires knowing their sources and spatio-temporal distribution. We analysed the exposure to lead (Pb) in griffon vulture Gyps fulvus-an apex species valuable as biomonitoring sentinel. We determined vultures' lead exposure and its main sources by combining isotope signatures and modelling analyses of 691 bird blood samples collected over 5 years. We made yearlong spatially explicit predictions of the species risk of lead exposure. Our results highlight elevated lead exposure of griffon vultures (i.e. 44.9% of the studied population, approximately 15% of the European, showed lead blood levels more than 200 ng ml(-1)) partly owing to environmental lead (e.g. geological sources). These exposures to environmental lead of geological sources increased in those vultures exposed to point sources (e.g. lead-based ammunition). These spatial models and pollutant risk maps are powerful tools that identify areas of wildlife exposure to potentially harmful sources of lead that could affect ecosystem and human health. © 2016 The Author(s).
Mapping the spatio-temporal risk of lead exposure in apex species for more effective mitigation
Mateo-Tomás, Patricia; Olea, Pedro P.; Jiménez-Moreno, María; Camarero, Pablo R.; Sánchez-Barbudo, Inés S.; Rodríguez Martín-Doimeadios, Rosa C.; Mateo, Rafael
2016-01-01
Effective mitigation of the risks posed by environmental contaminants for ecosystem integrity and human health requires knowing their sources and spatio-temporal distribution. We analysed the exposure to lead (Pb) in griffon vulture Gyps fulvus—an apex species valuable as biomonitoring sentinel. We determined vultures' lead exposure and its main sources by combining isotope signatures and modelling analyses of 691 bird blood samples collected over 5 years. We made yearlong spatially explicit predictions of the species risk of lead exposure. Our results highlight elevated lead exposure of griffon vultures (i.e. 44.9% of the studied population, approximately 15% of the European, showed lead blood levels more than 200 ng ml−1) partly owing to environmental lead (e.g. geological sources). These exposures to environmental lead of geological sources increased in those vultures exposed to point sources (e.g. lead-based ammunition). These spatial models and pollutant risk maps are powerful tools that identify areas of wildlife exposure to potentially harmful sources of lead that could affect ecosystem and human health. PMID:27466455
Wu, Di; Torres, Elizabeth B.; Jose, Jorge V.
2015-03-01
ASD is a spectrum of neurodevelopmental disorders. The high heterogeneity of the symptoms associated with the disorder impedes efficient diagnoses based on human observations. Recent advances with high-resolution MEM wearable sensors enable accurate movement measurements that may escape the naked eye. It calls for objective metrics to extract physiological relevant information from the rapidly accumulating data. In this talk we'll discuss the statistical analysis of movement data continuously collected with high-resolution sensors at 240Hz. We calculated statistical properties of speed fluctuations within the millisecond time range that closely correlate with the subjects' cognitive abilities. We computed the periodicity and synchronicity of the speed fluctuations' from their power spectrum and ensemble averaged two-point cross-correlation function. We built a two-parameter phase space from the temporal statistical analyses of the nearest neighbor fluctuations that provided a quantitative biomarker for ASD and adult normal subjects and further classified ASD severity. We also found age related developmental statistical signatures and potential ASD parental links in our movement dynamical studies. Our results may have direct clinical applications.
Modeling and analysis for determining optimal suppliers under stochastic lead times
DEFF Research Database (Denmark)
Abginehchi, Soheil; Farahani, Reza Zanjirani
2010-01-01
systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q) policy has been assumed. When the inventory level depletes to a reorder level, the total...... order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost...
Cooperativity Leads to Temporally-Correlated Fluctuations in the Bacteriophage Lambda Genetic Switch
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Jacob Quinn Shenker
2015-04-01
Full Text Available Cooperative interactions are widespread in biochemical networks, providing the nonlinear response that underlies behavior such as ultrasensitivity and robust switching. We introduce a temporal correlation function—the conditional activity—to study the behavior of these phenomena. Applying it to the bistable genetic switch in bacteriophage lambda, we ﬁnd that cooperative binding between binding sites on the prophage DNA lead to non-Markovian behavior, as quantiﬁed by the conditional activity. Previously, the conditional activity has been used to predict allosteric pathways in proteins; here, we show that it identiﬁes the rare unbinding events which underlie induction from lysogeny to lysis.
Nigsch, Annette; Costard, Solenne; Jones, Bryony A; Pfeiffer, Dirk U; Wieland, Barbara
2013-03-01
African swine fever (ASF) is a notifiable viral pig disease with high mortality and serious socio-economic consequences. Since ASF emerged in Georgia in 2007 the disease has spread to several neighbouring countries and cases have been detected in areas bordering the European Union (EU). It is uncertain how fast the virus would be able to spread within the unrestricted European trading area if it were introduced into the EU. This project therefore aimed to develop a model for the spread of ASF within and between the 27 Member States (MS) of the EU during the high risk period (HRP) and to identify MS during that period would most likely contribute to ASF spread ("super-spreaders") or MS that would most likely receive cases from other MS ("super-receivers"). A stochastic spatio-temporal state-transition model using simulated individual farm records was developed to assess silent ASF virus spread during different predefined HRPs of 10-60 days duration. Infection was seeded into farms of different pig production types in each of the 27 MS. Direct pig-to-pig transmission and indirect transmission routes (pig transport lorries and professional contacts) were considered the main pathways during the early stages of an epidemic. The model was parameterised using data collated from EUROSTAT, TRACES, a questionnaire sent to MS, and the scientific literature. Model outputs showed that virus circulation was generally limited to 1-2 infected premises per outbreak (95% IQR: 1-4; maximum: 10) with large breeder farms as index case resulting in most infected premises. Seven MS caused between-MS spread due to intra-Community trade during the first 10 days after seeding infection. For a HRP of 60 days from virus introduction, movements of infected pigs will originate at least once from 16 MS, with 6 MS spreading ASF in more than 10% of iterations. Two thirds of all intra-Community spread was linked to six trade links only. Denmark, the Netherlands, Lithuania and Latvia were identified
Numerical methods for stochastic partial differential equations with white noise
Zhang, Zhongqiang
2017-01-01
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...
Bollhöfer, A.; Rosman, K. J. R.
2002-04-01
A recent survey by Bollhöfer and Rosman (2000, 2001) has defined the extent to which Pb isotopic ratios in aerosols vary on a global scale. However, it is also important for some applications to know how stable these signatures are. Here we report time series from 38 sites distributed worldwide in which aerosols have been sampled for periods of between 4 months and 4 yr. Apart from a few sites that have atypical conditions, European sites exhibit variations of <0.6% in the 206Pb/207Pb ratio. There is, however, evidence of seasonal variations at sampling sites closer to Eastern Europe that probably reflect an enhanced westward transport of pollution in winter. The variability in Canada and the United States is now larger than before due to a decrease of airborne Pb levels coupled with an increase in the variety of industrial sources. The temporal changes observed in the United States do not exhibit a seasonal pattern. One site in Winnipeg, Canada, showed an extremely large variation, probably the result of seasonal changes influencing the direction of movement of local smelting emissions. Temporal variations in mainland Australia are comparatively small, with a typical range of 0.2% in the 206Pb/207Pb ratio and isotopic ratios that indicate leaded petrol was still a major source of atmospheric Pb over the sampling period.
Spatio-temporal regulation of Hsp90-ligand complex leads to immune activation.
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Yasuaki eTamura
2016-05-01
Full Text Available Hsp90 is the most abundant cytosolic HSP and is known to act as a molecular chaperone. We found that an Hsp90-cancer antigen peptide complex was efficiently cross-presented by human monocyte-derived dendritic cells and induced peptide-specific cytotoxic T lymphocytes. Furthermore, we observed that the internalized Hsp90-peptide complex was strictly sorted to the Rab5+, EEA1+ static early endosome and the Hsp90-chaperoned peptide was processed and bound to MHC class I molecules through a endosome-recycling pathway. We also found that extracellular Hsp90 complexed with CpG-A or self-DNA stimulates production of a large amount of IFN-α from pDCs via static early endosome targeting. Thus, extracellular Hsp90 can target the antigen or nucleic acid to a static early endosome by spatio-temporal regulation. Moreover, we showed that Hsp90 associates with and delivers TLR7/9 from the ER to early endosomes for ligand recognition. Hsp90 inhibitor, geldanamycin derivative inhibited the Hsp90 association with TLR7/9, resulting in inhibition IFN-α production, leading to improvement of SLE symptoms. Interstingly, we observed that serum Hsp90 is clearly increased in patients with active SLE compared with that in patients with inactive disease. Serum Hsp90 detected in SLE patients binds to self-DNA and/or anti-DNA Ab, thus leading to stimulation of pDCs to produce IFN-α. Thus, Hsp90 plays a crucial role in the pathogenesis of SLE and that an Hsp90 inhibitor will therefore provide a new therapeutic approach to SLE and other nucleic acid-related autoimmune diseases. We will discuss how spatio-temporal regulation of Hsp90-ligand complexes within antigen-presenting cells affects the innate immunity and adaptive immunity.
Spatial and temporal variation in isotopic composition of atmospheric lead in Norwegian moss
Energy Technology Data Exchange (ETDEWEB)
Rosman, K.J.R.; Ly, C. [Curtin Univ. of Technology, Perth, Western Australia (Australia). Dept. of Applied Physics; Steinnes, E. [Norwegian Univ. of Science and Technology, Trondheim (Norway). Dept. of Chemistry
1998-09-01
Earlier studies using moss as a biomonitor of pollution have shown that long-range transport is a major source of pollution in Norway. Until now, the origin of these pollutants has been inferred from concentration measurements of various elements in moss and the climatology at each sampling site. Lead isotopes provide an opportunity to identify the sources and to quantify the contribution of each. This preliminary study reports measurements of lead isotopes in moss from selected sites along the full extent of Norway that reveal significant spatial and temporal variations. There are significant north-south trends that differ at coastal and inland sites and differ between sampling periods (1974--1994). These variations reflect the changing contributions from the different source regions as the regulation of pollution from automobiles and industry takes effect. Identifiable sources are the U.K. and possibly France, which is noticeable at coastal sites; western Europe at the southern end; and eastern Europe and Russia influencing the inland and northernmost sites.
Wildhaber, Mark L.; Wikle, Christopher K.; Moran, Edward H.; Anderson, Christopher J.; Franz, Kristie J.; Dey, Rima
2017-01-01
We present a hierarchical series of spatially decreasing and temporally increasing models to evaluate the uncertainty in the atmosphere – ocean global climate model (AOGCM) and the regional climate model (RCM) relative to the uncertainty in the somatic growth of the endangered pallid sturgeon (Scaphirhynchus albus). For effects on fish populations of riverine ecosystems, cli- mate output simulated by coarse-resolution AOGCMs and RCMs must be downscaled to basins to river hydrology to population response. One needs to transfer the information from these climate simulations down to the individual scale in a way that minimizes extrapolation and can account for spatio-temporal variability in the intervening stages. The goal is a framework to determine whether, given uncertainties in the climate models and the biological response, meaningful inference can still be made. The non-linear downscaling of climate information to the river scale requires that one realistically account for spatial and temporal variability across scale. Our down- scaling procedure includes the use of fixed/calibrated hydrological flow and temperature models coupled with a stochastically parameterized sturgeon bioenergetics model. We show that, although there is a large amount of uncertainty associated with both the climate model output and the fish growth process, one can establish significant differences in fish growth distributions between models, and between future and current climates for a given model.
Directory of Open Access Journals (Sweden)
Emil Bayramov
2016-05-01
Full Text Available The main goal of this research was to detect oil spills, to determine the oil spill frequencies and to approximate oil leak sources around the Oil Rocks Settlement, the Chilov and Pirallahi Islands in the Caspian Sea using 136 multi-temporal ENVISAT Advanced Synthetic Aperture Radar Wide Swath Medium Resolution images acquired during 2006–2010. The following oil spill frequencies were observed around the Oil Rocks Settlement, the Chilov and Pirallahi Islands: 2–10 (3471.04 sq km, 11–20 (971.66 sq km, 21–50 (692.44 sq km, 51–128 (191.38 sq km. The most critical oil leak sources with the frequency range of 41–128 were observed at the Oil Rocks Settlement. The exponential regression analysis between wind speeds and oil slick areas detected from 136 multi-temporal ENVISAT images revealed the regression coefficient equal to 63%. The regression model showed that larger oil spill areas were observed with decreasing wind speeds. The spatiotemporal patterns of currents in the Caspian Sea explained the multi-directional spatial distribution of oil spills around Oil Rocks Settlement, the Chilov and Pirallahi Islands. The linear regression analysis between detected oil spill frequencies and predicted oil contamination probability by the stochastic model showed the positive trend with the regression coefficient of 30%.
Cox process representation and inference for stochastic reaction-diffusion processes.
Schnoerr, David; Grima, Ramon; Sanguinetti, Guido
2016-05-25
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.
Energy Technology Data Exchange (ETDEWEB)
Driver, Jeffrey H., E-mail: jeff@risksciences.net [risksciences.net, LLC, 10009 Wisakon Trail, Manassas, VA 20111 (United States); Price, Paul S. [The Dow Chemical Company, 1803 Building, Midland, MI 48674 (United States); Van Wesenbeeck, Ian [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States); Ross, John H. [risksciences.net, LLC, 5150 Fair Oaks Blvd., Ste. 101-370, Carmichael, CA 95608 (United States); Gehen, Sean [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States); Holden, Larry R. [Larry R. Holden, Statistical Consulting, 1403 Post Oak Circle, College Station, TX (United States); Landenberger, Bryce [The Dow Chemical Company, 1803 Building, Midland, MI 48674 (United States); Hastings, Kerry; Yan, Zhongyu; Rasoulpour, Reza [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States)
2016-11-15
Dow AgroSciences (DAS) markets and sells 1,3-Dichloropropene (1,3-D), the active ingredient in Telone®, which is used as a pre-plant soil fumigant nematicide in economically important crops in California. 1,3-D has been regulated as a “probable human carcinogen” and the California Department of Pesticide Regulation limits use of 1,3-D based on human health risk assessments for bystanders. This paper presents a risk characterization for bystanders based on advances in the assessment of both exposure and hazard. The revised bystander risk assessment incorporates significant advances: 1) new data on residency duration and mobility in communities where 1,3-D is in high demand; 2) new information on spatial and temporal concentrations of 1,3-D in air based on multi-year modeling using a validated model; and 3) a new stochastic spatial and temporal model of long-term exposures. Predicted distributions of long-term, chronic exposures indicate that current, and anticipated uses of 1,3-D would result in lifetime average daily doses lower than 0.002 mg/kg/d, a dose associated with theoretical lifetime excess cancer risk of < 10{sup −} {sup 5} to > 95% of the local population based on a non-threshold risk assessment approach. Additionally, examination of 1,3-D toxicity studies including new chronic toxicity data and mechanism of action supports the use of a non-linear, threshold based risk assessment approach. The estimated maximum annual average daily dose of < 0.0016 mg/kg/d derived from the updated exposure assessment was then compared with a threshold point of departure. The calculated margin of exposure is > 1000-fold, a clear indication of acceptable risk for human health. In summary, the best available science supports 1,3-D's threshold nature of hazard and the revised exposure assessment supports that current agricultural uses of 1,3-D are associated with reasonable certainty of no harm, i.e., estimated long-term exposures pose insignificant health risks
Stochastic Models of Evolution
Bezruchko, Boris P.; Smirnov, Dmitry A.
To continue the discussion of randomness given in Sect. 2.2.1, we briefly touch on stochastic models of temporal evolution (random processes). They can be specified either via explicit definition of their statistical properties (probability density functions, correlation functions, etc., Sects. 4.1, 4.2 and 4.3) or via stochastic difference or differential equations. Some of the most widely known equations, their properties and applications are discussed in Sects. 4.4 and 4.5.
Cohen, Joel E; Saitoh, Takashi
2016-12-01
Taylor's law (TL) asserts that the variance in a species' population density is a power-law function of its mean population density: log(variance) = a + b × log(mean). TL is widely verified. We show here that empirical time series of density of the Hokkaido gray-sided vole, Myodes rufocanus, sampled 1962-1992 at 85 locations, satisfied temporal and spatial forms of TL. The slopes (b ± standard error) of the temporal and spatial TL were estimated to be 1.613 ± 0.141 and 1.430 ± 0.132, respectively. A previously verified autoregressive Gompertz model of the dynamics of these populations generated time series of density which reproduced the form of temporal and spatial TLs, but with slopes that were significantly steeper than the slopes estimated from data. The density-dependent components of the Gompertz model were essential for the temporal TL. Adding to the Gompertz model assumptions that populations with higher mean density have reduced variance of density-independent perturbations and that density-independent perturbations are spatially correlated among populations yielded simulated time series that satisfactorily reproduced the slopes from data. The slopes (b ± standard error) of the enhanced simulations were 1.619 ± 0.199 for temporal TL and 1.575 ± 0.204 for spatial TL. © 2016 by the Ecological Society of America.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
many leading experts in the field. During the program, the most recent developments, open questions and new ideas in stochastic thermodynamics were presented and discussed. From the talks and debates, the notion of information in stochastic thermodynamics, the fundamental properties of entropy production (rate) in non-equilibrium, the efficiency of small thermodynamic machines and the characteristics of optimal protocols for the applied (cyclic) forces were crystallizing as main themes. Surprisingly, the long-studied adiabatic piston, its peculiarities and its relation to stochastic thermodynamics were also the subject of intense discussions. The comment on the Nordita program Stochastic Thermodynamics published in this issue of Physica Scripta exploits the Jarzynski relation for determining free energy differences in the adiabatic piston. This scientific program and the contribution presented here were made possible by the financial and administrative support of The Nordic Institute for Theoretical Physics.
Pretegiani, Elena; Astefanoaei, Corina; Daye, Pierre M; FitzGibbon, Edmond J; Creanga, Dorina-Emilia; Rufa, Alessandra; Optican, Lance M
2015-01-28
We move our eyes to explore the world, but visual areas determining where to look next (action) are different from those determining what we are seeing (perception). Whether, or how, action and perception are temporally coordinated is not known. The preparation time course of an action (e.g., a saccade) has been widely studied with the gap/overlap paradigm with temporal asynchronies (TA) between peripheral target onset and fixation point offset (gap, synchronous, or overlap). However, whether the subjects perceive the gap or overlap, and when they perceive it, has not been studied. We adapted the gap/overlap paradigm to study the temporal coupling of action and perception. Human subjects made saccades to targets with different TAs with respect to fixation point offset and reported whether they perceived the stimuli as separated by a gap or overlapped in time. Both saccadic and perceptual report reaction times changed in the same way as a function of TA. The TA dependencies of the time change for action and perception were very similar, suggesting a common neural substrate. Unexpectedly, in the perceptual task, subjects misperceived lights overlapping by less than ∼100 ms as separated in time (overlap seen as gap). We present an attention-perception model with a map of prominence in the superior colliculus that modulates the stimulus signal's effectiveness in the action and perception pathways. This common source of modulation determines how competition between stimuli is resolved, causes the TA dependence of action and perception to be the same, and causes the misperception. Copyright © 2015 the authors 0270-6474/15/351493-12$15.00/0.
Astefanoaei, Corina; Daye, Pierre M.; FitzGibbon, Edmond J.; Creanga, Dorina-Emilia; Rufa, Alessandra; Optican, Lance M.
2015-01-01
We move our eyes to explore the world, but visual areas determining where to look next (action) are different from those determining what we are seeing (perception). Whether, or how, action and perception are temporally coordinated is not known. The preparation time course of an action (e.g., a saccade) has been widely studied with the gap/overlap paradigm with temporal asynchronies (TA) between peripheral target onset and fixation point offset (gap, synchronous, or overlap). However, whether the subjects perceive the gap or overlap, and when they perceive it, has not been studied. We adapted the gap/overlap paradigm to study the temporal coupling of action and perception. Human subjects made saccades to targets with different TAs with respect to fixation point offset and reported whether they perceived the stimuli as separated by a gap or overlapped in time. Both saccadic and perceptual report reaction times changed in the same way as a function of TA. The TA dependencies of the time change for action and perception were very similar, suggesting a common neural substrate. Unexpectedly, in the perceptual task, subjects misperceived lights overlapping by less than ∼100 ms as separated in time (overlap seen as gap). We present an attention-perception model with a map of prominence in the superior colliculus that modulates the stimulus signal's effectiveness in the action and perception pathways. This common source of modulation determines how competition between stimuli is resolved, causes the TA dependence of action and perception to be the same, and causes the misperception. PMID:25632126
... is serious about making sure companies that break the law are held accountable In the past year, EPA ... the health effects of lead in drinking water The law mandates no-lead products for drinking water after ...
Karal, David
2014-01-01
Stochastic Integrals David Karal Abstrakt In this thesis we study the Wiener process and stochastic integrals. The thesis defines the basic objects of stochastic analysis and the existence of the Wiener process and some of its properties are shown. This process is then used to con- struct the Itô stochastic integral, where the Wiener process acts as an integrator. The Itô stochastic integral is first defined for simple processes and subsequently extended to mathcalFt-progressively measurable ...
Preference Factoring for Stochastic Trees
Gordon Hazen
2000-01-01
Stochastic trees are extensions of decision trees that facilitate the modeling of temporal uncertainties. Their primary application has been to medical treatment decisions. It is often convenient to present stochastic trees in factored form, allowing loosely coupled pieces of the model to be formulated and presented separately. In this paper, we show how the notion of factoring can be extended as well to preference components of the stochastic model. We examine updateable-state utility, a fle...
EFFECTS OF LEAD AND CADMIUM UPON THE KIDNEY FUNCTION OF THE A TEMPORE NEWBORNS
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Marina Jonović
2002-09-01
Full Text Available The aim of this paper is to examine the subjection of the embryo and the newborn to lead and cadmium as well as the effects of these metals upon the kidney function in the children newly born on time. The hypothetical framework of the paper was that lead and cadmium that are trans placental transmitted to the embryo organism lead to the change of the kidney function in the sence of damages done to the tubular system and to the interstitium along with changes in the urine sediment and in the levels of urea and creatinine in the serum; thus induced effects can be detected in the first week of life of the newborn babies.The examination was done in 1995 at Gynecological and Obstetric Clinic in Niš. The examined and the control group consisted of 30 newborns on time. The clinic examination was done on all the newborns. Regarding the kidney function examination, on the forth day of life all the newborn children were subjected to the determination of the value of urea and creatinine in the vein blood, the urine examination, the physical and physical-chemical features of the urine (outlook, specific weight, color, pH, the chemical status of the urine, the microscopic examination of the urine sediment, the ultrasonic examination of the kidneys. On the basis of the carried out examination and obtained results we came to the following conclusions:The lead concentration in the air at the localities related to the examined group is above G VI while for the control one below GVI. The cadmium concentration in the air from the examined localities in both the groups are above GVI. The lead and cadmium concentrations in the sediment materials at the localities related to the examined and control group are below GVI.The lead concentration in the umbilical cord blood is higher in the control group with respect to the examined one though without statistic significance. The lead concentration in the human milk is higher in the control group than in the examined one
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
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Mark A. S. Laidlaw
2015-12-01
Full Text Available Background: The age standardised death rate from motor neuron disease (MND has increased from 1.29 to 2.74 per 100,000, an increase of 112.4% between 1959 and 2013. It is clear that genetics could not have played a causal role in the increased rate of MND deaths over such a short time span. We postulate that environmental factors are responsible for this rate increase. We focus on lead additives in Australian petrol as a possible contributing environmental factor. Methods: The associations between historical petrol lead emissions and MND death trends in Australia between 1962 and 2013 were examined using linear regressions. Results: Regression results indicate best fit correlations between a 20 year lag of petrol lead emissions and age-standardised female death rate (R2 = 0.86, p = 4.88 × 10−23, male age standardised death rate (R2 = 0.86, p = 9.4 × 10−23 and percent all cause death attributed to MND (R2 = 0.98, p = 2.6 × 10−44. Conclusion: Legacy petrol lead emissions are associated with increased MND death trends in Australia. Further examination of the 20 year lag between exposure to petrol lead and the onset of MND is warranted.
Laidlaw, Mark A S; Rowe, Dominic B; Ball, Andrew S; Mielke, Howard W
2015-12-19
The age standardised death rate from motor neuron disease (MND) has increased from 1.29 to 2.74 per 100,000, an increase of 112.4% between 1959 and 2013. It is clear that genetics could not have played a causal role in the increased rate of MND deaths over such a short time span. We postulate that environmental factors are responsible for this rate increase. We focus on lead additives in Australian petrol as a possible contributing environmental factor. The associations between historical petrol lead emissions and MND death trends in Australia between 1962 and 2013 were examined using linear regressions. Regression results indicate best fit correlations between a 20 year lag of petrol lead emissions and age-standardised female death rate (R² = 0.86, p = 4.88 × 10(-23)), male age standardised death rate (R² = 0.86, p = 9.4 × 10(-23)) and percent all cause death attributed to MND (R² = 0.98, p = 2.6 × 10(-44)). Legacy petrol lead emissions are associated with increased MND death trends in Australia. Further examination of the 20 year lag between exposure to petrol lead and the onset of MND is warranted.
Martínez-Cruz, B; Godoy, J A; Negro, J J
2007-02-01
The fragmentation of a population may have important consequences for population genetic diversity and structure due to the effects of genetic drift and reduced gene flow. We studied the genetic consequences of the fragmentation of the Spanish imperial eagle (Aquila adalberti) population into small patches through a temporal analysis. Thirty-four museum individuals representing the population predating the fragmentation were analysed for a 345-bp segment of the mitochondrial control region and a set of 10 nuclear microsatellite loci. Data from a previous study on the current population (N = 79) were re-analysed for this subset of 10 microsatellite markers and results compared to those obtained from the historical sample. Three shared mitochondrial haplotypes were found in both populations, although fluctuations in haplotype frequencies and the occurrence of a fourth haplotype in the historical population resulted in lower current levels of haplotype and nucleotide diversity. However, microsatellite markers revealed undiminished levels of nuclear diversity. No evidence for genetic structure was observed for the historical Spanish imperial eagle population, suggesting that the current pattern of structure is the direct consequence of population fragmentation. Temporal fluctuations in mitochondrial and microsatellite allelic frequencies were found between the historical and the current population as well as for each pairwise comparison between historical and current Centro and historical and current Parque Nacional de Doñana nuclei. Our results indicate an ancestral panmictic situation for the species that management policies should aim to restore. A historical analysis like the one taken here provides the baseline upon which the relative role of recent drift in shaping current genetic patterns in endangered species can be evaluated and this knowledge is used to guide conservation actions.
Snitz, Beth E.; Small, Brent J.; Wang, Tianxiu; Chang, Chung-Chou H.; Hughes, Tiffany F.; Ganguli, Mary
2015-01-01
Objective The relationship between subjective memory complaints (SM) and objective memory (OM) performance in aging has been variably characterized in a substantial literature, to date. In particular, cross-sectional studies often observe weak or no associations. We investigated whether subjective memory complaints and objectively measured cognition influence each other over time, and if so, which is the stronger pathway of change – objective to subjective, or subjective to objective – or whether they are both important. Method Using bivariate latent change score modeling in data from a population study (N=1980) over 5 annual assessment cycles, we tested 4 corresponding hypotheses: 1) no coupling between SM and OM over time; 2) SM as leading indicator of change in OM; 3) OM as leading indicator of change in SM; 4) dual coupling over time, with both SM and OM leading subsequent change in the other. We also extended objective cognition to two other domains, language and executive functions. Results The dual-coupling models best fit the data for all three objective cognitive domains. The SM – OM temporal dynamics differ qualitatively compared to other domains, potentially reflecting changes in insight and self-awareness specific to memory impairment. Conclusions Subjective memory and objective cognition reciprocally influence each other over time. The temporal dynamics between subjective and objective cognition in aging are nuanced, and must be carefully disentangled to shed light on the underlying processes. PMID:26477680
Stochastic volatility selected readings
Shephard, Neil
2005-01-01
Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major issues involved. General Introduction N. Shephard. Part I: Model Building. 1. A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, (P. K. Clark). 2. Financial Returns Modelled by the Product of Two Stochastic Processes: A Study of Daily Sugar Prices, 1961-7, S. J. Taylor. 3. The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices, B. Rosenberg. 4. The Pricing of Options on Assets with Stochastic Volatilities, J. Hull and A. White. 5. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model, F. X. Diebold and M. Nerlove. 6. Multivariate Stochastic Variance Models. 7. Stochastic Autoregressive...
... Test Safety Alert: Learn about CDC Recommendations Second Informational Call (CDC-RFA-17-1701PPHF17), April 5, 2017, ... CLPPP CAP Healthy Homes Assessment Tools Lead Health Literacy Initiative Refugee Tool Kit Resources Healthy Homes and ...
Liss, Alexander
Extreme weather events, such as heat waves and cold spells, cause substantial excess mortality and morbidity in the vulnerable elderly population, and cost billions of dollars. The accurate and reliable assessment of adverse effects of extreme weather events on human health is crucial for environmental scientists, economists, and public health officials to ensure proper protection of vulnerable populations and efficient allocation of scarce resources. However, the methodology for the analysis of large national databases is yet to be developed. The overarching objective of this dissertation is to examine the effect of extreme weather on the elderly population of the Conterminous US (ConUS) with respect to seasonality in temperature in different climatic regions by utilizing heterogeneous high frequency and spatio-temporal resolution data. To achieve these goals the author: 1) incorporated dissimilar stochastic high frequency big data streams and distinct data types into the integrated data base for use in analytical and decision support frameworks; 2) created an automated climate regionalization system based on remote sensing and machine learning to define climate regions for the Conterminous US; 3) systematically surveyed the current state of the art and identified existing gaps in the scientific knowledge; 4) assessed the dose-response relationship of exposure to temperature extremes on human health in relatively homogeneous climate regions using different statistical models, such as parametric and non-parametric, contemporaneous and asynchronous, applied to the same data; 5) assessed seasonal peak timing and synchronization delay of the exposure and the disease within the framework of contemporaneous high frequency harmonic time series analysis and modification of the effect by the regional climate; 6) modeled using hyperbolic functional form non-linear properties of the effect of exposure to extreme temperature on human health. The proposed climate
Stochastic inflationary scalar electrodynamics
Prokopec, T.; Tsamis, N.C.; Woodard, R.P.
2008-01-01
We stochastically formulate the theory of scalar quantum electrodynamics on a de Sitter background. This reproduces the leading infrared logarithms at each loop order. It also allows one to sum the series of leading infrared logarithms to obtain explicit, nonperturbative results about the late time
Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.
Komorowski, Michał; Costa, Maria J; Rand, David A; Stumpf, Michael P H
2011-05-24
We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Goovaerts, Pierre
2017-03-01
Since Flint returned to its pre-crisis source of drinking water close to 25,000 water samples have been collected and tested for lead and copper in >10,000 residences. This paper presents the first analysis and time trend modeling of lead data, providing new insights about the impact of this intervention. The analysis started with geocoding all water lead levels (WLL) measured during an 11-month period following the return to the Detroit water supply. Each data was allocated to the corresponding tax parcel unit and linked to secondary datasets, such as the composition of service lines, year built, or census tract poverty level. Only data collected on residential parcels within the City limits were used in the analysis. One key feature of Flint data is their collection through two different sampling initiatives: (i) voluntary or homeowner-driven sampling whereby concerned citizens decided to acquire a testing kit and conduct sampling on their own (non-sentinel sites), and (ii) State-controlled sampling where data were collected bi-weekly at selected sites after training of residents by technical teams (sentinel sites). Temporal trends modeled from these two datasets were found to be statistically different with fewer sentinel data exceeding WLL thresholds ranging from 10 to 50μg/L. Even after adjusting for housing characteristics the odds ratio (OR) of measuring WLL above 15μg/L at non-sentinel sites is significantly >1 (OR=1.480) and it increases with the threshold (OR=2.055 for 50μg/L). Joinpoint regression showed that the city-wide percentage of WLL data above 15μg/L displayed four successive trends since the return to Detroit Water System. Despite the recent improvement in water quality, the culprit for differences between sampling programs needs to be identified as it impacts exposure assessment and might influence whether there is compliance or not with the Lead and Copper Rule. Copyright © 2016 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Boyle, E.A.; Bergquist, B.A.; Kayser, R.A.; Mahowald, N. [MIT, Cambridge, MA (US)
2005-02-15
Trace metal clean techniques were used to sample Hawaii Ocean Time-series (HOT) station ALOHA on seven occasions between November 1998 and October 2002. On three occasions, full water column profile samples were obtained; on the other four occasions, surface and near-surface euphotic zone profiles were obtained. Low Fe concentrations (< 0.1 nmol kg{sup -1}) are seen in the lower euphotic zone, and Fe concentrations increase to a maximum in intermediate waters. In the deepwaters (> 2500 m), the concentrations we observe (0.4-0.5 nmol kg{sup -1}) are significantly lower than some other deep North Pacific stations but are similar to values that have been reported for a station 350 miles to the northeast. We attribute these low deepwater values to transport of low-Fe Antarctic Bottom Water into the basin and a balance between Fe regeneration and scavenging in the deep water. Near-surface waters have higher Fe levels than observed in the lower euphotic zone. Significant temporal variability is seen in near-surface Fe concentrations (ranging from 0.2-0.7 nmol kg{sup -1}); we attribute these surface Fe fluctuations to variable dust deposition, biological uptake, and changes in the mixed layer depth. This variability could occur only if the surface layer Fe residence time is less than a few, years, and based on that constraint, it appears that a higher percentage of the total Fe must be released from North Pacific aerosols compared to North Atlantic aerosols. We attribute the surface water Pb decrease to the elimination of leaded gasoline in Japan and to some extent by the U.S. and Canada. We attribute most of the remaining Pb in Pacific surface waters to Asian emissions, more likely due to high-temperature industrial activities such as coal burning rather than to leaded gasoline consumption.
Stochastic ontogenetic allometry: the statistical dynamics of relative growth.
Papadopoulos, Anthony
2011-01-01
In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, θt = log(a) b + kφ(t), where θt ≡ θ(t) and φt ≡ φ(t) are the logarithmic sizes of two traits at any given time t. Realistically, however, stochasticity is an inherent property of ontogenetic allometry. Due to the inherent stochasticity in both θt and φt, the ontogenetic allometry coefficients, log(a) b and k, can vary with t and have intricate temporal distributions that are governed by the central and mixed moments of the random ontogenetic growth functions, θt and φt. Unfortunately, there is no probabilistic model for analyzing these informative ontogenetic statistical moments. This study treats θt and φt as correlated stochastic processes to formulate the exact probabilistic version of each of the ontogenetic allometry coefficients. In particular, the statistical dynamics of relative growth is addressed by analyzing the allometric growth factors that affect the temporal distribution of the probabilistic version of the relative growth rate, k ≡ Dt(u)/Dt(v), where is the expected value of the ratio of stochastic θt to stochastic φt, and u and v are the numerator and the denominator of , respectively. These allometric growth factors, which provide important insight into ontogenetic allometry but appear only when stochasticity is introduced, describe the central and mixed moments of θt and φt as differentiable real-valued functions of t. Failure to account for the inherent stochasticity in both θt and φt leads not only to the miscalculation of k, but also to the omission of all of the informative ontogenetic statistical moments that affect the size of traits and the timing and rate of development of traits. Furthermore, even though the stochastic process θt and the stochastic process φt are linearly related, k can vary with t.
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
McKean, Henry P
2005-01-01
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen
Demirel, M.C.; Booij, Martijn J.; Hoekstra, Arjen Ysbert
2013-01-01
The aim of this paper is to assess the relative importance of low flow indicators for the River Rhine and to identify their appropriate temporal lag and resolution. This is done in the context of low flow forecasting with lead times of 14 and 90 days. First, the Rhine basin is subdivided into seven
Koh, Dong-Hee; Nam, Jun-Mo; Graubard, Barry I.; Chen, Yu-Cheng; Locke, Sarah J.; Friesen, Melissa C.
2014-01-01
Objectives: The published literature provides useful exposure measurements that can aid retrospective exposure assessment efforts, but the analysis of this data is challenging as it is usually reported as means, ranges, and measures of variability. We used mixed-effects meta-analysis regression models, which are commonly used to summarize health risks from multiple studies, to predict temporal trends of blood and air lead concentrations in multiple US industries from the published data while accounting for within- and between-study variability in exposure. Methods: We extracted the geometric mean (GM), geometric standard deviation (GSD), and number of measurements from journal articles reporting blood and personal air measurements from US worksites. When not reported, we derived the GM and GSD from other summary measures. Only industries with measurements in ≥2 time points and spanning ≥10 years were included in our analyses. Meta-regression models were developed separately for each industry and sample type. Each model used the log-transformed GM as the dependent variable and calendar year as the independent variable. It also incorporated a random intercept that weighted each study by a combination of the between- and within-study variances. The within-study variances were calculated as the squared log-transformed GSD divided by the number of measurements. Maximum likelihood estimation was used to obtain the regression parameters and between-study variances. Results: The blood measurement models predicted statistically significant declining trends of 2–11% per year in 8 of the 13 industries. The air measurement models predicted a statistically significant declining trend (3% per year) in only one of the seven industries; an increasing trend (7% per year) was also observed for one industry. Of the five industries that met our inclusion criteria for both air and blood, the exposure declines per year tended to be slightly greater based on blood measurements than
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost P.; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution
Lukacs, Eugene; Lukacs, E
1975-01-01
Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the po
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Stochastic Constraint Programming
Walsh, Toby
2009-01-01
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number...
Göttlich, Martin; Heldmann, Marcus; Göbel, Anna; Dirk, Anna-Luise; Brabant, Georg; Münte, Thomas F
2015-06-01
Adult onset hyperthyroidism may impact on different cognitive domains, including attention and concentration, memory, perceptual function, language and executive function. Previous PET studies implicated changed functionality of limbic regions, the temporal and frontal lobes in hyperthyroidism, whereas it is unknown whether cognitive effects of hyperthyroidism may be due to changed brain connectivity. This study aimed to investigate the effect of experimentally induced short-term hyperthyroidism thyrotoxicosis on resting-state functional connectivity using functional magnetic resonance imaging. Twenty-nine healthy male right-handed subjects were examined twice, once prior and once after 8 weeks of oral administration of 250 μg levothyroxine per day. Resting-state fMRI was subjected to graph-theory based analysis methods to investigate whole-brain intrinsic functional connectivity. Despite a lack of subjective changes noticed by the subjects significant thyrotoxicosis was confirmed in all subjects. This induced a significant increase in resting-state functional connectivity specifically in the rostral temporal lobes (0.05 FDR corrected at the cluster level), which is caused by an increased connectivity to the cognitive control network. The increased connectivity between temporal poles and the cognitive control network shown here under experimental conditions supports an important function of thyroid hormones in the regulation of paralimbic structures. Copyright © 2015 Elsevier Ltd. All rights reserved.
Hnat, B.; Chapman, S. C.; Kiyani, K. H.
2010-12-01
The power spectral density of magnetic field components in the fast solar wind on magnetohydrodynamic scales typically shows two power law regions, identified with an inertial range of turbulence, and at lower frequencies, a ~1/f range of coronal origin. The power spectral density of field magnitude shows a single power law region across these scales. We present the first scale-by-scale quantitative comparison of the averaged statistical properties of magnetic field magnitude and component fluctuations over timescales of ~2 minutes to 5.6 hours observed in-situ in the fast quiet solar wind at solar minimum at 1AU with the ACE spacecraft. Fluctuations in the field components show an 'inertial range' of scaling up to ~30 minutes and beyond this, uncorrelated Gaussian statistics. In contrast, the magnetic field magnitude fluctuations show a single scaling behaviour up to 5 hours and are non-Gaussian over this entire range of scales. Thus unlike for the components, a single stochastic process could account for the fluctuations in field magnitude over both the inertial range and 1/f range of timescales the fast solar wind.
Directory of Open Access Journals (Sweden)
Heather Moody
2017-11-01
Full Text Available Objective: The purpose of this research is to geographically model airborne lead emission concentrations and total lead deposition in the Detroit Metropolitan Area (DMA from 2006 to 2013. Further, this study characterizes the racial and socioeconomic composition of recipient neighborhoods and estimates the potential for IQ (Intelligence Quotient loss of children residing there. Methods: Lead emissions were modeled from emitting facilities in the DMA using AERMOD (American Meteorological Society/Environmental Protection Agency Regulatory Model. Multilevel modeling was used to estimate local racial residential segregation, controlling for poverty. Global Moran’s I bivariate spatial autocorrelation statistics were used to assess modeled emissions with increasing segregation. Results: Lead emitting facilities were primarily located in, and moving to, highly black segregated neighborhoods regardless of poverty levels—a phenomenon known as environmental injustice. The findings from this research showed three years of elevated airborne emission concentrations in these neighborhoods to equate to a predicted 1.0 to 3.0 reduction in IQ points for children living there. Across the DMA there are many areas where annual lead deposition was substantially higher than recommended for aquatic (rivers, lakes, etc. and terrestrial (forests, dunes, etc. ecosystems. These lead levels result in decreased reproductive and growth rates in plants and animals, and neurological deficits in vertebrates. Conclusions: This lead-hazard and neighborhood context assessment will inform future childhood lead exposure studies and potential health consequences in the DMA.
Stochastic Analysis : A Series of Lectures
Dozzi, Marco; Flandoli, Franco; Russo, Francesco
2015-01-01
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Stochastic Differential Equations
Cecconi, Jaures
2011-01-01
C. Doleans-Dade: Stochastic processes and stochastic differential equations.- A. Friedman: Stochastic differential equations and applications.- D.W. Stroock, S.R.S. Varadhan: Theory of diffusion processes.- G.C. Papanicolaou: Wave propagation and heat conduction in a random medium.- C. Dewitt Morette: A stochastic problem in Physics.- G.S. Goodman: The embedding problem for stochastic matrices.
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
Intermittent stochastic fields and space-time symmetry
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Schmiegel, Jürgen
We present a spatio-temporal modelling framework for stochastic fields that obey exact symmetry in space and time, i.e. the field amplitude considered as a stochastic process in time at a fixed position in space is identical, as a stochastic process, to the field amplitude considered as a stochas...... as a stochastic process in space at a fixed time point. The stochastic fields are given in explicit form and include intermittency as a basic ingredient. A causal version is discussed with respect to turbulence modelling and in relation to Taylor’s Frozen Flow Hypothesis....
Energy Technology Data Exchange (ETDEWEB)
Vega-Sánchez, Miguel E. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Loqué, Dominique [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Lao, Jeemeng [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Catena, Michela [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Verhertbruggen, Yves [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Herter, Thomas [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Yang, Fan [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Harholt, Jesper [Department of Plant and Environmental Sciences, University of Copenhagen, Frederiksberg C Denmark; Ebert, Berit [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Department of Plant and Environmental Sciences, University of Copenhagen, Frederiksberg C Denmark; Baidoo, Edward E. K. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Keasling, Jay D. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Department of Chemical and Biomolecular Engineering, and Department of Bioengineering, University of California, Berkeley CA USA; Scheller, Henrik V. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Department of Plant and Microbial Biology, University of California, Berkeley CA USA; Heazlewood, Joshua L. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Ronald, Pamela C. [Joint BioEnergy Institute and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley CA USA; Department of Plant Pathology and the Genome Center, University of California, Davis CA USA
2015-01-14
Reduced cell wall recalcitrance and increased C6 monosaccharide content are desirable traits for future biofuel crops, as long as these biomass modifications do not significantly alter normal growth and development. Mixed-linkage glucan (MLG), a cell wall polysaccharide only present in grasses and related species among flowering plants, is comprised of glucose monomers linked by both β-1,3 and β-1,4 bonds. Previous data have shown that constitutive production of MLG in barley (Hordeum vulgare) severely compromises growth and development. Here, we used spatio-temporal strategies to engineer Arabidopsis thaliana plants to accumulate significant amounts of MLG in the cell wall by expressing the rice CslF6 MLG synthase using secondary cell wall and senescence-associated promoters. Results using secondary wall promoters were suboptimal. When the rice MLG synthase was expressed under the control of a senescence-associated promoter, we obtained up to four times more glucose in the matrix cell wall fraction and up to a 42% increase in saccharification compared to control lines. Importantly, these plants grew and developed normally. The induction of MLG deposition at senescence correlated with an increase of gluconic acid in cell wall extracts of transgenic plants in contrast to the other approaches presented in this study. MLG produced in Arabidopsis has an altered structure compared to the grass glucan, which likely affects its solubility, while its molecular size is unaffected. The induction of cell wall polysaccharide biosynthesis in senescing tissues offers a novel engineering alternative to enhance cell wall properties of lignocellulosic biofuel crops.
Energy Technology Data Exchange (ETDEWEB)
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Verification of Stochastic Process Calculi
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya
process calculi. The description of a system in the syntax of a particular stochastic process calculus can be analysed in a compositional way, without expanding the state space by explicitly resolving all the interdependencies between the subsystems which may lead to the state space explosion problem...
Stochastic models of cell motility
DEFF Research Database (Denmark)
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Stochastic Temporal Properties of the SASE FEL
Energy Technology Data Exchange (ETDEWEB)
Krinsky, S.
2009-08-23
We review the statistical description of the chaotic time evolution of the radiation from a self-amplified spontaneous-emission free-electron laser in the linear region before saturation. A high-gain, self-amplified spontaneous-emission (SASE) free-electron laser (FEL) [1, 2], based on modern beam technology, has the advantage of operating without a resonator and hence is capable of generating coherent radiation with wavelength down to the x-ray region. The LCLS at SLAC has recently achieved high gain and saturation at 1.5 {angstrom} [3]. A review of SASE theory can be found in ref. [4]. In this paper, we have considered the linear regime before saturation. In the nonlinear saturation regime, SASE is no longer a Gaussian process and analytic treatment is very difficult. A valuable numerical simulation analysis of the statistical behavior in the nonlinear regime can be found in ref. [10,11].
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
Description of radiation- and ultrasound-induced cell death by a stochastic process.
Sontag, Werner; Kruglikov, I L
2009-02-01
Cell survival is a stochastic process with the stochastic component being strongly dependent on the irradiation conditions. This process is described by a stochastic model which allows differentiation between the deterministic and stochastic components of survival. The proposed model is tested for four irradiation experiments (2 with ionizing radiation and 2 with ultrasound) and very good agreement with experimental results is demonstrated. It identifies the higher stochasticity of the cell survival for the temporally varying radiation fields and provides the possibility to compare the stochasticity of survival in different radiation fields.
Dzhunushaliev, Vladimir
2010-01-01
Stochastic Einstein equations are considered when 3D space metric $\\gamma_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed. The connection between general relativity and Ricci flows is discussed.
Stochastically lighting up galaxies: Statistical implications of stellar clustering
da Silva, Robert Louis
Stars form discretely. At the very least, they form in units of individual stars. However, their discreteness likely extends to much larger spatially and temporally correlated structures known as star clusters. This discreteness has a profound impact on the light that a population of stars will produce even at fixed star formation rate. Ignoring the effects of this clustering when analyzing observations can lead to significant errors and biases. This work presents an exploration of the effects of this clustering, the foundation of which is the construction of SLUG, a code which Stochastically Lights Up Galaxies. It accounts for the effects of clustering by populating composite stellar populations ("galaxies") one cluster at a time where each cluster is filled by individual stars whose evolution is tracked. This is the first code capable of exploring stochasticity for stellar populations composed of clusters and led to several significant insights in the field. Most notably, the scatter of luminosities due to stochastically placing clusters over the star formation history of a population greatly exceeds the effects of stochastically sampling a population with a stellar initial mass function. This has profound implications for interpretations of star formation rates, deriving initial mass functions, and the star formation rate distribution of the universe. We also explore the statistics of luminosities of clusters themselves, deriving an analytical method (CLOC) for calculating the full distribution of cluster order statistics roughly one billion times faster than a suite of Monte Carlo simulations. This giant leap forward in speed provides the groundwork for a previously impossible robust exploration of the relevant parameter space (e.g. dust opacity distributions, cluster mass function shape and cutoffs, and cluster disruption parameters).
Statistical methods for spatio-temporal systems
Finkenstadt, Barbel
2006-01-01
Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities.Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time co...
Stochastic physical ecohydrologic-based model for estimating irrigation requirement
Alizadeh, H.; Mousavi, S. J.
2012-04-01
Climate uncertainty affects both natural and managed hydrological systems. Therefore, methods which could take this kind of uncertainty into account are of primal importance for management of ecosystems, especially agricultural ecosystems. One of the famous problems in these ecosystems is crop water requirement estimation under climatic uncertainty. Both deterministic physically-based methods and stochastic time series modeling have been utilized in the literature. Like other fields of hydroclimatic sciences, there is a vast area in irrigation process modeling for developing approaches integrating physics of the process and statistics aspects. This study is about deriving closed-form expressions for probability density function (p.d.f.) of irrigation water requirement using a stochastic physically-based model, which considers important aspects of plant, soil, atmosphere and irrigation technique and policy in a coherent framework. An ecohydrologic stochastic model, building upon the stochastic differential equation of soil moisture dynamics at root zone, is employed as a basis for deriving the expressions considering temporal stochasticity of rainfall. Due to distinguished nature of stochastic processes of micro and traditional irrigation applications, two different methodologies have been used. Micro-irrigation application has been modeled through dichotomic process. Chapman-Kolomogrov equation of time integral of the dichotomic process for transient condition has been solved to derive analytical expressions for probability density function of seasonal irrigation requirement. For traditional irrigation, irrigation application during growing season has been modeled using a marked point process. Using the renewal theory, probability mass function of seasonal irrigation requirement, which is a discrete-value quantity, has been analytically derived. The methodology deals with estimation of statistical properties of the total water requirement in a growing season that
Stochastic evolution of the Universe: A possible dynamical process ...
Indian Academy of Sciences (India)
In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the ...
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
Stochastic Hierarchical Systems: Excitable Dynamics
Leonhardt, Helmar; Zaks, Michael A.; Falcke, Martin; Schimansky-Geier, Lutz
2008-01-01
We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive...
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter
2017-06-04
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Campo, M. A.; Lopez, J. J.; Rebole, J. P.
2012-04-01
This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series
Directory of Open Access Journals (Sweden)
Bernadete M Boff
2002-06-01
Full Text Available OBJETIVO: Identificar os agravos à saúde subjacentes à concessão de benefício por incapacidade temporária, na população trabalhadora segurada. MÉTODOS: Foram recuperados do banco de dados do Instituto Nacional de Seguro Social (INSS todos os benefícios do tipo auxílio-doença previdenciário (E-31 concedidos no ano de 1998 aos trabalhadores de Porto Alegre, RS. Os Códigos de Classificação Internacional de Doenças atribuídos à condição subjacente à incapacidade no exame pericial inicial (aX1 foram utilizados para descrever as principais causas e os grupos de causas subjacentes à incapacidade. RESULTADOS: Foram concedidos 6.898 benefícios E-31: 1.486 (22% por "causas externas"; 1.181 (17% por "convalescência após cirurgia" (34% por causas gastrointestinais, 26% genitourinárias, 11% osteomusculares e 10% por causas externas; e 4.119 (61% por "condições clínicas" (24,8% por doenças osteomusculares, 18,9% por doenças mentais e 16,2% por doenças cardiovasculares. Comparadas a estudo realizado no Brasil em 1986, as causas externas passaram da quarta para a primeira posição como determinante de incapacidade temporária para o trabalho. CONCLUSÃO: Acidentes e violências, doenças osteomusculares e doenças mentais -- as três primeiras causas de incapacidade identificadas -- estão potencialmente associadas à piora da qualidade de vida e de trabalho registrada no período e merecem atenção prioritária (preventiva e assistencial do Sistema Único de Saúde (SUS. O estudo demonstra a viabilidade da utilização do banco de dados do INSS para estudos de morbidade.INTRODUCTION: To identify health conditions leading to benefits due to temporary work disability in a population of insured workers. METHODS: International Classification of Diseases (ICD codes for conditions resulting in temporary work-disability (E-31 were retrieved from the National Institute of Social Security (INSS data bank in Porto Alegre, Brazil, in
Fundamentals of Stochastic Networks
Ibe, Oliver C
2011-01-01
An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physi
Deterministic and stochastic aspects of the transition to turbulence
Song, Baofang
2014-01-01
The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear cut instability mechanism, the spatio-temporal intermittent character and extremely long lived transients are some of the major difficulties encountered in these flows and have hindered progress towards understanding the transition process. We will show for the case of pipe flow that concepts from nonlinear dynamics and statistical physics can help to explain the onset of turbulence. In particular the turbulent structures ('puffs') observed close to onset are spatially localized chaotic transients and their lifetimes increase super exponentially with Reynolds number. At the same time fluctuations of individual turbulent puffs can (although very rarely) lead to the nucleation of new puffs. The competition between these two stochastic processes gives rise to a non-equilibrium phase transition where turbulence changes from a super-transient to a sustained state.
Stochastic phase transition operator.
Yamanobe, Takanobu
2011-07-01
In this study a Markov operator is introduced that represents the density evolution of an impulse-driven stochastic biological oscillator. The operator's stochastic kernel is constructed using the asymptotic expansion of stochastic processes instead of solving the Fokker-Planck equation. The Markov operator is shown to successfully approximate the density evolution of the biological oscillator considered. The response of the oscillator to both periodic and time-varying impulses can be analyzed using the operator's transient and stationary properties. Furthermore, an unreported stochastic dynamic bifurcation for the biological oscillator is obtained by using the eigenvalues of the product of the Markov operators.
Stochastic hierarchical systems: excitable dynamics.
Leonhardt, Helmar; Zaks, Michael A; Falcke, Martin; Schimansky-Geier, Lutz
2008-10-01
We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations, and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto model is shown.
Stochastic goal-oriented error estimation with memory
Ackmann, Jan; Marotzke, Jochem; Korn, Peter
2017-11-01
We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.
Robustness analysis of stochastic biochemical systems.
Directory of Open Access Journals (Sweden)
Milan Ceska
Full Text Available We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Evolution with Stochastic Fitness and Stochastic Migration
Rice, Sean H.; Papadopoulos, Anthony
2009-01-01
Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory
Indian Academy of Sciences (India)
andoh
input signals, consisting of random square waves. We find that, in an optimal band of noise, the output consistently is a logical combination of the input signals: Logical Stochastic Resonance. (LSR) with K. Murali, W.L. Ditto, A. Bulsara. Physical Review Letters, March 2009. Sudeshna Sinha. Logical Stochastic Resonance ...
Stochastic Convection Parameterizations
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
A Stochastic Employment Problem
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Constructing Stochastic Models for Dipole Fluctuations from Paleomagnetic Observations
Buffett, Bruce; Puranam, Abhijit
2017-01-01
Records of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we construct a stochastic model...
Stochastic flux freezing and magnetic dynamo.
Eyink, Gregory L
2011-05-01
Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered. © 2011 American Physical Society
PC analysis of stochastic differential equations driven by Wiener noise
Le Maitre, Olivier
2015-03-01
A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.
Stochastic processes in gravitropism.
Meroz, Yasmine; Bastien, Renaud
2014-01-01
In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles) to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i) dynamic sensing, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification, and integration of the signal. (ii) The role of the cytoskeleton in signal-to-noise modulation and (iii) in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
Stochastic Processes in Electrochemistry.
Singh, Pradyumna S; Lemay, Serge G
2016-05-17
Stochastic behavior becomes an increasingly dominant characteristic of electrochemical systems as we probe them on the smallest scales. Advances in the tools and techniques of nanoelectrochemistry dictate that stochastic phenomena will become more widely manifest in the future. In this Perspective, we outline the conceptual tools that are required to analyze and understand this behavior. We draw on examples from several specific electrochemical systems where important information is encoded in, and can be derived from, apparently random signals. This Perspective attempts to serve as an accessible introduction to understanding stochastic phenomena in electrochemical systems and outlines why they cannot be understood with conventional macroscopic descriptions.
Fundamentals of Stochastic Filtering
Crisan, Dan
2008-01-01
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Stochasticity or the fatal 'imperfection' of cloning
Indian Academy of Sciences (India)
Unknown
will be aborted. Near-threshold levels of essential gene products may lead stochastically to opposite outcomes in the same individual. In this case, the genetic background cannot be used as a possible explanation. Local differ- ences may exert an effect on the outcome (figure 5). Mouse is by far less dosage sensitive than ...
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
Stochastic calculus with infinitesimals
Herzberg, Frederik
2013-01-01
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Logical Stochastic Optimization
Saad, Emad
2013-01-01
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the language of probability answer set programming to allow minimization or maximization of some desired criteria under the probabilistic environments. We show the application of the proposed logical stochastic optimization framework under the probability answ...
Research in Stochastic Processes
1988-08-31
completed the following reports. 1. A vector bimeasure integral with some applications [1]. A Fubini type theorem is obtained for a class of vector...extended neurons and assemblies of neurons. Fluctuation theorems for large systems of interacting diffusions. Stochastic analysis on canonical Hilbert...dimensional (nuclear space valued) diffusions. 3. Discontinuous stochastic differential equations in duals of nuclear spaces. 4. Fluctuation theorems for large
Stochastic evolution of the Universe: A possible dynamical process ...
Indian Academy of Sciences (India)
C Sivakumar
2017-12-11
type equations [25,29] or stochastic differential equations (SDE). We argue that, such dynamical processes may lead to a fractal distribu- tion (or a scale invariant inhomogeneous distribution) of galaxies, because dynamical ...
Stochasticity in reproductive opportunity and the evolution of egg limitation in insects.
Rosenheim, Jay A
2011-08-01
Is reproduction by adult female insects limited by the finite time available to locate hosts (time limitation) or by the finite supply of eggs (egg limitation)? An influential model predicted that stochasticity in reproductive opportunity favors elevated fecundity, rendering egg limitation sufficiently rare that its importance would be greatly diminished. Here, I use models to explore how stochasticity shapes fecundity, the likelihood of egg limitation, and the ecological importance of egg limitation. The models make three predictions. First, whereas spatially stochastic environments favor increased fecundity, temporally stochastic environments favor increases, decreases, or intermediate maxima in fecundity, depending on egg costs. Second, even when spatially or temporally stochastic environments favor life histories with less-frequent egg limitation, stochasticity still increases the proportion of all eggs laid in the population that is laid by females destined to become egg limited. This counterintuitive result is explained by noting that stochasticity concentrates reproduction in the hands of a few females that are likely to become egg limited. Third, spatially or temporally stochastic environments amplify the constraints imposed by time and eggs on total reproduction by the population. I conclude that both egg and time constraints are fundamental in shaping insect reproductive behavior and population dynamics in stochastic environments. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.
Powell, Philip A; Simpson, Jane; Overton, Paul G
2013-01-01
Research has shown that feelings of self-disgust may have a functional role in the genesis of depression by partially mediating the cross-sectional relationship between dysfunctional thoughts and depressive symptoms. However, there are many outstanding issues regarding these hypothesised associations. First, it is not yet clear whether self-disgust is a temporal antecedent, concomitant, or consequence of depressive experience. Second, it is not known whether the hypothesised mediation sequence is valid over time. Third, the relative contribution of disgust towards different aspects of the self has not yet been examined. In the present longitudinal study, participants completed measures of dysfunctional cognitions, self-disgust and depressive symptoms at baseline, and at six and 12-month follow-ups. Analysis showed that self-disgust is best considered as antecedent to depressive symptoms; the hypothesised mediation model was partially supported, but is too simplistic; and disgust towards physical aspects of the self, rather than behaviour, was more important as a temporal predictor of depressive symptoms. The current results help elucidate the role of self-disgust as an antecedent of depressive experience.
Acoustic wave propagation and stochastic effects in metamaterial absorbers
DEFF Research Database (Denmark)
Christensen, Johan; Willatzen, Morten
2014-01-01
We show how stochastic variations of the effective parameters of anisotropic structured metamaterials can lead to increased absorption of sound. For this, we derive an analytical model based on the Bourret approximation and illustrate the immediate connection between material disorder and attenua......We show how stochastic variations of the effective parameters of anisotropic structured metamaterials can lead to increased absorption of sound. For this, we derive an analytical model based on the Bourret approximation and illustrate the immediate connection between material disorder...
Stochastic phenomena in a fiber Raman amplifier
Kalashnikov, Vladimir; Ania-Castanón, Juan Diego; Jacobsen, Gunnar; Popov, Sergei
2016-01-01
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering-based nonlinearity, the random birefringence of a fiber, and the pump-to-signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence-induced resonance-like enhancement of the gain fluctuations (stochastic anti-resonance) accompanied by pulse broadening and rare events in the form of low power outpu...
Computational stochastic model of ions implantation
Energy Technology Data Exchange (ETDEWEB)
Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
Smolin, Lee
2015-11-01
Two people may claim both to be naturalists, but have divergent conceptions of basic elements of the natural world which lead them to mean different things when they talk about laws of nature, or states, or the role of mathematics in physics. These disagreements do not much affect the ordinary practice of science which is about small subsystems of the universe, described or explained against a background, idealized to be fixed. But these issues become crucial when we consider including the whole universe within our system, for then there is no fixed background to reference observables to. I argue here that the key issue responsible for divergent versions of naturalism and divergent approaches to cosmology is the conception of time. One version, which I call temporal naturalism, holds that time, in the sense of the succession of present moments, is real, and that laws of nature evolve in that time. This is contrasted with timeless naturalism, which holds that laws are immutable and the present moment and its passage are illusions. I argue that temporal naturalism is empirically more adequate than the alternatives, because it offers testable explanations for puzzles its rivals cannot address, and is likely a better basis for solving major puzzles that presently face cosmology and physics. This essay also addresses the problem of qualia and experience within naturalism and argues that only temporal naturalism can make a place for qualia as intrinsic qualities of matter.
Stochastic Indicators for Waste Site Characterization
Christakos, George; Hristopulos, Dionissios T.
1996-08-01
Site characterization is an important prerequisite of risk assessment and remediation strategies. Evaluation of the health effects of groundwater and soil contamination depends on the adequate analysis of spatial heterogeneity, exceedance levels, and uncertainties. In this work we formulate and calculate stochastic indicators that provide a rigorous characterization of exposure levels in sites with heterogeneous contaminant distributions and offer valuable information for a cost-effective cleanup analysis. These site indicators are general and can be used for different types and distributions of groundwater and soil contaminants. Important properties of the stochastic indicators are examined which can evaluate the potential for contamination at large scales, and improve understanding of threatened and damaged ecosystems. Analytically tractable formulas are derived that allow the practical estimation of site indicators on the basis of experimental data. Scale and modeling effects on contaminant level analysis are examined in terms of the stochastic indicators. Site cleanup costs depend directly on inferred characteristics of the stochastic indicators, which thus can play an important role in waste site management. Applications are discussed that offer insight regarding certain aspects of stochastic site characterization. Analytical methods of site characterization are compared to numerical simulations. It is shown that the latter can provide a practical alternative to the former, but they could lead to inaccurate results if they are not interpreted carefully.
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Székely, Tamás; Burrage, Kevin; Zygalakis, Konstantinos C; Barrio, Manuel
2014-06-18
Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie's stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.
Redefining the merit order of stochastic generation in forward markets
DEFF Research Database (Denmark)
Morales, Juan M.; Zugno, Marco; Pineda Morente, Salvador
2014-01-01
This letter proposes a new merit order for the dispatch of stochastic production in forward markets (e.g., day-ahead markets). The proposed merit order considers not only the marginal cost of the stochastic generating unit, which is often very low or zero, but also the projected cost of balancing...... its energy deviations during the real-time operation of the power system. We show, through an illustrative example, that the proposed merit order leads to increased market efficiency as the penetration of stochastic generation in the electricity market grows.......This letter proposes a new merit order for the dispatch of stochastic production in forward markets (e.g., day-ahead markets). The proposed merit order considers not only the marginal cost of the stochastic generating unit, which is often very low or zero, but also the projected cost of balancing...
Redefining the merit order of stochastic generation in forward markets
DEFF Research Database (Denmark)
Morales González, Juan Miguel; Zugno, Marco; Pineda Morente, Salvador
2014-01-01
This letter proposes a new merit order for the dispatch of stochastic production in forward markets (e.g., dayahead markets). The proposed merit order considers not only the marginal cost of the stochastic generating unit, which is often very low or zero, but also the projected cost of balancing ...... its energy deviations during the real-time operation of the power system.We show, through an illustrative example, that the proposed merit order leads to increased market efficiency as the penetration of stochastic generation in the electricity market grows.......This letter proposes a new merit order for the dispatch of stochastic production in forward markets (e.g., dayahead markets). The proposed merit order considers not only the marginal cost of the stochastic generating unit, which is often very low or zero, but also the projected cost of balancing...
Stochastic Samples versus Vacuum Expectation Values in Cosmology
Tsamis, N C; Woodard, R P
2010-01-01
Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some things, such as the stress tensor, we argue that operators exist for which there is no essential problem. We quantify this by examining the stochastic properties of a noninteracting, massless, minimally coupled scalar on a locally de Sitter background. The square of the stochastic realization of this field seems to provide an example of great relevance for which expectation values are not misleading. We also examine the frequently expressed concern that significant back-reaction from expectation values necessarily implies large stochastic fluctuations between nearby spatial points. Rather than viewing the stochastic formalism in opposition to expectation values, we argue that it provides a marvelously simple way of capturing the leading infrared logarithm corrections to the...
Directory of Open Access Journals (Sweden)
J. Alonso Díaz
2004-12-01
Full Text Available At the present work, limpet (Patella vulgata L. and seaweed (Ulva lactuca specimens have been monthly sampled at the same point from the Vigo estuary, during a year. Heavy metal (cadmium and lead content has been determined by means of differential pulse anodic stripping voltammetry in both limpet and seaweed tissues, as well as in seawater. The obtained results have shown the main heavy metal content in limpet soft tissues with respect to shell, with maximum concentrations of 3 ppm (limpet shell for lead, whereas the highest content for cadmium was identified in seaweed samples (1.1 ppm. The statistical study revealed the existence of a clear correlation between cadmium and lead concentrations in seaweed samples.En el presente trabajo se han recogido muestras de lapa (Patella vulgata L. y alga verde (Ulva lactuca en un mismo punto de muestreo de la ría de Vigo, con una periodicidad mensual, a lo largo de un año, analizándose por medio de voltamperometría de redisolución anódica la concentración en dos metales pesados con claras repercusiones toxicológicas, cadmio y plomo, en estas muestras, así como en el agua marina. Los resultados obtenidos mostraron la mayor concentración de ambos metales en los tejidos blandos de las lapas frente a las valvas de estos moluscos, con valores máximos en el caso del plomo próximos a 3 ppm (valva de lapa, mientras que para el cadmio se situó en torno a 1,1 ppm (alga verde. El estudio estadístico permitió poner en evidencia una clara correlación estadística entre los valores de cadmio y plomo cuantificados en las muestras de algas.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Positive temporal dependence of the biological clock implies hyperbolic discounting
Directory of Open Access Journals (Sweden)
Debajyoti eRay
2011-01-01
Full Text Available Temporal preferences of animals and humans often exhibit inconsistencies, whereby an earlier, smaller reward may be preferred when it occurs immediately but not when it is delayed. Such choices reflect hyperbolic discounting of future rewards, rather than the exponential discounting required for temporal consistency. Simultaneously, however, evidence has emerged that suggests that animals and humans have an internal representation of time that often differs from the calendar time used in detection of temporal inconsistencies. Here, we prove that temporal inconsistencies emerge if fixed durations in calendar time are experienced as positively related (positive quadrant dependent. Hence, what are time-consistent choices within the time framework of the decision maker appear as time-inconsistent to an outsider who analyzes choices in calendar time. As the biological clock becomes more variable, the fit of the hyperbolic discounting model improves. A recent alternative explanation for temporal choice inconsistencies builds on persistent under-estimation of the length of distant time intervals. By increasing the expected speed of our stochastic biological clock for time farther into the future, we can emulate this explanation. Ours is therefore an encompassing theoretical framework that predicts context-dependent degrees of intertemporal choice inconsistencies, to the extent that context can generate changes in autocorrelation, variability, and expected speed of the biological clock. Our finding should lead to novel experiments that will clarify the role of time perception in impulsivity, with critical implications for, among others, our understanding of aging, drug abuse and pathological gambling.
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Energy Technology Data Exchange (ETDEWEB)
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Schrager, D.F.
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...... a section on that topic can be found in appendix....
Stochastic Effects in Computational Biology of Space Radiation Cancer Risk
Cucinotta, Francis A.; Pluth, Janis; Harper, Jane; O'Neill, Peter
2007-01-01
Estimating risk from space radiation poses important questions on the radiobiology of protons and heavy ions. We are considering systems biology models to study radiation induced repair foci (RIRF) at low doses, in which less than one-track on average transverses the cell, and the subsequent DNA damage processing and signal transduction events. Computational approaches for describing protein regulatory networks coupled to DNA and oxidative damage sites include systems of differential equations, stochastic equations, and Monte-Carlo simulations. We review recent developments in the mathematical description of protein regulatory networks and possible approaches to radiation effects simulation. These include robustness, which states that regulatory networks maintain their functions against external and internal perturbations due to compensating properties of redundancy and molecular feedback controls, and modularity, which leads to general theorems for considering molecules that interact through a regulatory mechanism without exchange of matter leading to a block diagonal reduction of the connecting pathways. Identifying rate-limiting steps, robustness, and modularity in pathways perturbed by radiation damage are shown to be valid techniques for reducing large molecular systems to realistic computer simulations. Other techniques studied are the use of steady-state analysis, and the introduction of composite molecules or rate-constants to represent small collections of reactants. Applications of these techniques to describe spatial and temporal distributions of RIRF and cell populations following low dose irradiation are described.
Evoking prescribed spike times in stochastic neurons
Doose, Jens; Lindner, Benjamin
2017-09-01
Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.
Stochastic exposure kinetics of EUV photoresists: a simulation study
Mack, Chris A.; Thackeray, James W.; Biafore, John J.; Smith, Mark D.
2011-04-01
BACKGROUND: The stochastic nature of extreme ultraviolet (EUV) resist exposure leads to variations in the resulting acid concentration, which leads to line-edge roughness (LER) of the resulting features. METHODS: Using a stochastic resist simulator, we predicted the mean and standard deviation of the acid concentration for an open-frame exposure and fit the results to analytical expressions. RESULTS: The EUV resist exposure mechanism of the PROLTIH Stochastic Resist Simulator is first order, and an analytical expression for the exposure rate constant C allows prediction of the mean acid concentration of an open-frame exposure to about 1% accuracy over a wide range of parameter values. A second analytical expression for the standard deviation of the acid concentration also matched the output of PROLITH to within about 1%. CONCLUSIONS: Predicting the stochastic uncertainty in acid concentration for EUV resists allows optimization of resist processing and formulations, and may form the basis of a comprehensive LER model.
Skorokhod, A. V.
1982-12-01
CONTENTSIntroduction § 1. The finite-dimensional case § 2. Stochastic semigroups in the L2-strong theory § 3. Homogeneous strongly continuous semigroups with the group of the first moments § 4. Stochastic equations of diffusion type with constant coefficients § 5. Continuous homogeneous stochastic semigroups in the presence of two moments References
Fluctuation theorems for stochastic dynamics
Harris, R. J.; Schütz, G. M.
2007-07-01
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.
ARIMA-Based Time Series Model of Stochastic Wind Power Generation
DEFF Research Database (Denmark)
Chen, Peiyuan; Pedersen, Troels; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from...... the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation...... and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power...
Stochastic and deterministic assembly processes in subsurface microbial communities.
Stegen, James C; Lin, Xueju; Konopka, Allan E; Fredrickson, James K
2012-09-01
A major goal of microbial community ecology is to understand the forces that structure community composition. Deterministic selection by specific environmental factors is sometimes important, but in other cases stochastic or ecologically neutral processes dominate. Lacking is a unified conceptual framework aiming to understand why deterministic processes dominate in some contexts but not others. Here we work toward such a framework. By testing predictions derived from general ecological theory we aim to uncover factors that govern the relative influences of deterministic and stochastic processes. We couple spatiotemporal data on subsurface microbial communities and environmental parameters with metrics and null models of within and between community phylogenetic composition. Testing for phylogenetic signal in organismal niches showed that more closely related taxa have more similar habitat associations. Community phylogenetic analyses further showed that ecologically similar taxa coexist to a greater degree than expected by chance. Environmental filtering thus deterministically governs subsurface microbial community composition. More importantly, the influence of deterministic environmental filtering relative to stochastic factors was maximized at both ends of an environmental variation gradient. A stronger role of stochastic factors was, however, supported through analyses of phylogenetic temporal turnover. Although phylogenetic turnover was on average faster than expected, most pairwise comparisons were not themselves significantly non-random. The relative influence of deterministic environmental filtering over community dynamics was elevated, however, in the most temporally and spatially variable environments. Our results point to general rules governing the relative influences of stochastic and deterministic processes across micro- and macro-organisms.
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
Robustness of Populations in Stochastic Environments
DEFF Research Database (Denmark)
Gießen, Christian; Kötzing, Timo
2016-01-01
We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend...... these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size Θ(logn)) can make evolutionary algorithms perform well for high noise levels, well outside...... the abilities of the (1+1) EA. Larger population sizes are even more beneficial; we consider both parent and offspring populations. In this sense, populations are robust in these stochastic settings....
Advances in stochastic and deterministic global optimization
Zhigljavsky, Anatoly; Žilinskas, Julius
2016-01-01
Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and mu...
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Stochastic dynamics and the evolution of mutations in stem cells
Directory of Open Access Journals (Sweden)
Dingli David
2011-06-01
Full Text Available Abstract Stem cells are the target of mutations that can lead to life threatening diseases. However, stem cell populations tend to be small and therefore clonal expansion of mutant cells is highly sensitive to stochastic fluctuations. The evolutionary dynamics of mutations in these cells is discussed, taking into consideration the impact of such mutations on the reproductive fitness of cells. We show how stochastic effects can explain clinical observations, including extinction of acquired clonal stem cell disorders.
Generic Properties of Stochastic Entropy Production
Pigolotti, Simone; Neri, Izaak; Roldán, Édgar; Jülicher, Frank
2017-10-01
We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non-steady-state conditions.
Network interdiction and stochastic integer programming
2003-01-01
On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....
Constructing stochastic models for dipole fluctuations from paleomagnetic observations
Buffett, Bruce; Puranam, Abhijit
2017-11-01
Records of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we construct a stochastic model from two recent inversions of paleomagnetic observations for the axial dipole moment. An estimate of the noise term in the stochastic model is recovered from a high-resolution inversion (CALS10k.2), while the drift term is estimated from the low-frequency part of the power spectrum for a long, but lower-resolution inversion (PADM2M). Realizations of the resulting stochastic model yield a composite, broadband power spectrum that agrees well with the spectra from both PADM2M and CALS10k.2. A simple generalization of the stochastic model permits predictions for the mean rate of magnetic reversals. We show that the reversal rate depends on the time-averaged dipole moment, the variance of the dipole moment and a slow timescale that characterizes the adjustment of the dipole toward the time-averaged value. Predictions of the stochastic model give a mean rate of 4.2 Myr-1, which is in good agreement with observations from marine magnetic anomalies.
Stochastic evolutions of dynamic traffic flow modeling and applications
Chen, Xiqun (Michael); Shi, Qixin
2015-01-01
This book reveals the underlying mechanisms of complexity and stochastic evolutions of traffic flows. Using Eulerian and Lagrangian measurements, the authors propose lognormal headway/spacing/velocity distributions and subsequently develop a Markov car-following model to describe drivers’ random choices concerning headways/spacings, putting forward a stochastic fundamental diagram model for wide scattering flow-density points. In the context of highway onramp bottlenecks, the authors present a traffic flow breakdown probability model and spatial-temporal queuing model to improve the stability and reliability of road traffic flows. This book is intended for researchers and graduate students in the fields of transportation engineering and civil engineering.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Stochastic calculus and applications
Cohen, Samuel N
2015-01-01
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... is still undergoing rapid development. Turbulence and wind energy are vast and complicated subjects. Turbulence has structures across a wide range of length and time scales, structures which cannot be captured by a Gaussian process that relies on only second order properties. Concerning wind energy, a wind...... turbine operates in the turbulent atmospheric boundary layer. In this respect, three regimes are of particular interest: modelling the turbulent wind before it interacts with the wind turbine (e.g. to be used in load simulations), modelling of the interaction of the wind with the wind turbine (e...
Isotropic stochastic rotation dynamics
Mühlbauer, Sebastian; Strobl, Severin; Pöschel, Thorsten
2017-12-01
Stochastic rotation dynamics (SRD) is a widely used method for the mesoscopic modeling of complex fluids, such as colloidal suspensions or multiphase flows. In this method, however, the underlying Cartesian grid defining the coarse-grained interaction volumes induces anisotropy. We propose an isotropic, lattice-free variant of stochastic rotation dynamics, termed iSRD. Instead of Cartesian grid cells, we employ randomly distributed spherical interaction volumes. This eliminates the requirement of a grid shift, which is essential in standard SRD to maintain Galilean invariance. We derive analytical expressions for the viscosity and the diffusion coefficient in relation to the model parameters, which show excellent agreement with the results obtained in iSRD simulations. The proposed algorithm is particularly suitable to model systems bound by walls of complex shape, where the domain cannot be meshed uniformly. The presented approach is not limited to SRD but is applicable to any other mesoscopic method, where particles interact within certain coarse-grained volumes.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Stochastic conditional intensity processes
DEFF Research Database (Denmark)
Bauwens, Luc; Hautsch, Nikolaus
2006-01-01
In this article, we introduce the so-called stochastic conditional intensity (SCI) model by extending Russell’s (1999) autoregressive conditional intensity (ACI) model by a latent common dynamic factor that jointly drives the individual intensity components. We show by simulations that the propos...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...
Lenczewski, Romuald
2001-01-01
By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time filtration makes the integrands similar to adapted processes, whereas ``quantum'' color filtration produces their deviations from adaptedness. An important feature of this calculus, which we call filtered stochastic calculus, is that it provides an explicit interpo...
McDonnell, Mark D; Amblard, Pierre-Olivier; Stocks, Nigel G.
2009-01-01
We introduce and define the concept of a stochastic pooling network (SPN), as a model for sensor systems where redundancy and two forms of 'noise' -- lossy compression and randomness -- interact in surprising ways. Our approach to analyzing SPNs is information theoretic. We define an SPN as a network with multiple nodes that each produce noisy and compressed measurements of the same information. An SPN must combine all these measurements into a single further compressed network output, in a w...
Stochastic Thermodynamics of Learning
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Preconditioned Stochastic Gradient Descent.
Li, Xi-Lin
2017-03-09
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts in this direction either aim at solving specialized problems, or result in significantly more complicated methods than SGD. This paper proposes a new method to adaptively estimate a preconditioner, such that the amplitudes of perturbations of preconditioned stochastic gradient match that of the perturbations of parameters to be optimized in a way comparable to Newton method for deterministic optimization. Unlike the preconditioners based on secant equation fitting as done in deterministic quasi-Newton methods, which assume positive definite Hessian and approximate its inverse, the new preconditioner works equally well for both convex and nonconvex optimizations with exact or noisy gradients. When stochastic gradient is used, it can naturally damp the gradient noise to stabilize SGD. Efficient preconditioner estimation methods are developed, and with reasonable simplifications, they are applicable to large-scale problems. Experimental results demonstrate that equipped with the new preconditioner, without any tuning effort, preconditioned SGD can efficiently solve many challenging problems like the training of a deep neural network or a recurrent neural network requiring extremely long-term memories.
Spatio-Temporal Modeling of Neuron Fields
DEFF Research Database (Denmark)
Lund, Adam
The starting point and focal point for this thesis was stochastic dynamical modelling of neuronal imaging data with the declared objective of drawing inference, within this model framework, in a large-scale (high-dimensional) data setting. Implicitly this objective entails carrying out three......-temporal array data. This framework was developed with neuron field models in mind but may in turn be applied to other settings conforming to the spatio-temporal array data setup....
Stochastic modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic Modeling Of Biochemical Reactions
2006-11-01
STOCHASTIC MODELING OF BIOCHEMICAL REACTIONS Abhyudai Singh and João Pedro Hespanha* Department of Electrical and Computer Engineering University of...procedure for con- structing approximate stochastic models for chemical reactions used for modeling biochemical processes such as gene regulatory networks... biochemical reactions , the modeling tools developed in this paper can be applied to a very general class of stochastic systems, in particular
Stochastic modelling in disability insurance
Löfdahl, Björn
2013-01-01
This thesis consists of two papers related to the stochastic modellingof disability insurance. In the first paper, we propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into con...
Stochastic integration by parts and functional Itô calculus
Vives, Josep
2016-01-01
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...
Applications of Little's Law to stochastic models of gene expression
Elgart, Vlad; Kulkarni, Rahul V
2010-01-01
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The de...
Doubly stochastic coherence in complex neuronal networks
Gao, Yang; Wang, Jianjun
2012-11-01
A system composed of coupled FitzHugh-Nagumo neurons with various topological structures is investigated under the co-presence of two independently additive and multiplicative Gaussian white noises, in which particular attention is paid to the neuronal networks spiking regularity. As the additive noise intensity and the multiplicative noise intensity are simultaneously adjusted to optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of doubly stochastic coherence. The network topology randomness exerts different influences on the temporal coherence of the spiking oscillation for dissimilar coupling strength regimes. At a small coupling strength, the spiking regularity shows nearly no difference in the regular, small-world, and completely random networks. At an intermediate coupling strength, the temporal periodicity in a small-world neuronal network can be improved slightly by adding a small fraction of long-range connections. At a large coupling strength, the dynamical behavior of the neurons completely loses the resonance property with regard to the additive noise intensity or the multiplicative noise intensity, and the spiking regularity decreases considerably with the increase of the network topology randomness. The network topology randomness plays more of a depressed role than a favorable role in improving the temporal coherence of the spiking oscillation in the neuronal network research study.
Time series analysis of temporal networks
Sikdar, Sandipan; Ganguly, Niloy; Mukherjee, Animesh
2016-01-01
A common but an important feature of all real-world networks is that they are temporal in nature, i.e., the network structure changes over time. Due to this dynamic nature, it becomes difficult to propose suitable growth models that can explain the various important characteristic properties of these networks. In fact, in many application oriented studies only knowing these properties is sufficient. For instance, if one wishes to launch a targeted attack on a network, this can be done even without the knowledge of the full network structure; rather an estimate of some of the properties is sufficient enough to launch the attack. We, in this paper show that even if the network structure at a future time point is not available one can still manage to estimate its properties. We propose a novel method to map a temporal network to a set of time series instances, analyze them and using a standard forecast model of time series, try to predict the properties of a temporal network at a later time instance. To our aim, we consider eight properties such as number of active nodes, average degree, clustering coefficient etc. and apply our prediction framework on them. We mainly focus on the temporal network of human face-to-face contacts and observe that it represents a stochastic process with memory that can be modeled as Auto-Regressive-Integrated-Moving-Average (ARIMA). We use cross validation techniques to find the percentage accuracy of our predictions. An important observation is that the frequency domain properties of the time series obtained from spectrogram analysis could be used to refine the prediction framework by identifying beforehand the cases where the error in prediction is likely to be high. This leads to an improvement of 7.96% (for error level ≤20%) in prediction accuracy on an average across all datasets. As an application we show how such prediction scheme can be used to launch targeted attacks on temporal networks. Contribution to the Topical Issue
Hardwick, Robert J.; Vennin, Vincent; Byrnes, Christian T.; Torrado, Jesús; Wands, David
2017-10-01
We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Understanding Stochastic Subspace Identification
DEFF Research Database (Denmark)
Brincker, Rune; Andersen, Palle
2006-01-01
The data driven Stochastic Subspace Identification techniques is considered to be the most powerful class of the known identification techniques for natural input modal analysis in the time domain. However, the techniques involves several steps of "mysterious mathematics" that is difficult...... to follow and to understand for people with a classical background in structural dynamics. Also the connection to the classical correlation driven time domain techniques is not well established. The purpose of this paper is to explain the different steps in the SSI techniques of importance for modal...
The stochastic quality calculus
DEFF Research Database (Denmark)
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A
2016-01-01
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...
de Vries, Daniel H
2017-01-01
After major flooding associated with Hurricane Floyd (1999) in North Carolina, mitigation managers seized upon the "window of opportunity" to woo residents to accept residential buyout offers despite sizable community resistance. I present a theoretical explanation of how post-crisis periods turn into "opportunities" based on a temporal referential theory that complements alternative explanations based on temporal coincidence, panarchy, and shock-doctrine theories. Results from fieldwork conducted from 2002 to 2004 illustrate how several temporal influences compromised collective calibration of "normalcy" in local cultural models, leading to an especially heightened vulnerability to collective surprise. Four factors particularly influenced this temporal vulnerability: 1) epistemological uncertainty of floodplain dynamics due to colonization; 2) cultural practices that maintained a casual amnesia; 3) meaning attributed to stochastic timing of floods; and 4) competitive impact of referential flood baseline attractors.
Directory of Open Access Journals (Sweden)
Wenlei Bai
2017-12-01
Full Text Available The deterministic methods generally used to solve DC optimal power flow (OPF do not fully capture the uncertainty information in wind power, and thus their solutions could be suboptimal. However, the stochastic dynamic AC OPF problem can be used to find an optimal solution by fully capturing the uncertainty information of wind power. That uncertainty information of future wind power can be well represented by the short-term future wind power scenarios that are forecasted using the generalized dynamic factor model (GDFM—a novel multivariate statistical wind power forecasting model. Furthermore, the GDFM can accurately represent the spatial and temporal correlations among wind farms through the multivariate stochastic process. Fully capturing the uncertainty information in the spatially and temporally correlated GDFM scenarios can lead to a better AC OPF solution under a high penetration level of wind power. Since the GDFM is a factor analysis based model, the computational time can also be reduced. In order to further reduce the computational time, a modified artificial bee colony (ABC algorithm is used to solve the AC OPF problem based on the GDFM forecasting scenarios. Using the modified ABC algorithm based on the GDFM forecasting scenarios has resulted in better AC OPF’ solutions on an IEEE 118-bus system at every hour for 24 h.
An energy-conserving method for stochastic Maxwell equations with multiplicative noise
Hong, Jialin; Ji, Lihai; Zhang, Liying; Cai, Jiaxiang
2017-12-01
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic multi-symplectic conservation law), and the energy of system is a conservative quantity almost surely. We propose a stochastic multi-symplectic energy-conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time. Numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy. The mean square convergence result of the method in temporal direction is tested numerically, and numerical comparisons with finite difference method are also investigated.
Stochastic Blind Motion Deblurring
Xiao, Lei
2015-05-13
Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.
AA, stochastic precooling pickup
CERN PhotoLab
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...
Stochastic ferromagnetism analysis and numerics
Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas
2013-01-01
This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.
Some stochastic aspects of quantization
Indian Academy of Sciences (India)
From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson's stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic ﬁeld equations via the Poisson process and how to describe a ...
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept...
Strong and weak approximation of semilinear stochastic evolution equations
Kruse, Raphael
2014-01-01
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Variance decomposition in stochastic simulators
Le Maître, O. P.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Application of Stochastic Index Numbers in Inflation Measurement – the Case of Poland
Directory of Open Access Journals (Sweden)
Jacek Białek
2014-06-01
Full Text Available The stochastic approach is a specific way of viewing index numbers, in which uncertainty and statistical properties play a central role. This approach, applied to the prices, treats the underlying rate of infl ation as an unknown parameter that has to be estimated from the individual prices. Thus, the stochastic approach provils the whole probability distribution of inflation. In this paper we present and discuss several basic stochastic index numbers. We propose a simple stochastic model, which leads to a price index formula being a mixture of the previously presented specifi cations. We verify the considered indices on a real data set.
Hourly temporal distribution of wind
Deligiannis, Ilias; Dimitriadis, Panayiotis; Koutsoyiannis, Demetris
2016-04-01
The wind process is essential for hydrometeorology and additionally, is one of the basic renewable energy resources. Most stochastic forecast models are limited up to daily scales disregarding the hourly scale which is significant for renewable energy management. Here, we analyze hourly wind timeseries giving emphasis on the temporal distribution of wind within the day. We finally present a periodic model based on statistical as well as hydrometeorological reasoning that shows good agreement with data. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.
Constructing stochastic models for dipole fluctuations from paleomagnetic observations
Buffett, B; Puranam, A
2017-01-01
© 2017 Elsevier B.V. Records of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we constru...
A Generic Stochastic Template Bank Placement Algorithm
Frei, Melissa; Fotopoulos, N.; Priviteria, S.
2012-01-01
Black hole binary (BBH) systems represent strong candidates for gravitational wave (GW) detection by GW detectors LIGO and Virgo. BBH searches are template based searches where the templates describe potential GWs. Most BBH sources are spinning strongly enough to affect orbital dynamics though past searches have all been for non-spinning systems. Neglecting spin results in a significant decrease in a BBH search's sensitivity to spinning systems while the inclusion of leading order, single parameter spin corrections regain much of that sensitivity. BBH templates in past searches were chosen so that the overlap between neighboring templates was 97%. The optimal placement of non-spinning, inspiral templates is known but does not work for systems described by more parameters. For spinning systems, the placement metric is not known and stochastic methods like the one described in this poster are necessary. The method described here is based on previous stochastic work. It represents a fast, flexible, open-source tool using publicly available LIGO Algorithms Library (LAL) to generate stochastic banks for any template family no matter the number of parameters used to describe it. The method shows more efficient coverage of the parameter space of interest than a discrete stacking of a two-dimensional bank in a third direction.
Stochastic phenomena in a fiber Raman amplifier
Energy Technology Data Exchange (ETDEWEB)
Kalashnikov, Vladimir [Aston Institute of Photonic Technologies, Aston University, Birmingham (United Kingdom); Institute of Photonics, Vienna University of Technology (Austria); Sergeyev, Sergey V. [Aston Institute of Photonic Technologies, Aston University, Birmingham (United Kingdom); Ania-Castanon, Juan Diego [Instituto de Optica CSIC, Madrid (Spain); Jacobsen, Gunnar [Acreo, Kista (Sweden); Popov, Sergei [Royal Institute of Technology (KTH), Stockholm (Sweden)
2017-01-15
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering-based nonlinearity, the random birefringence of a fiber, and the pump-to-signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence-induced resonance-like enhancement of the gain fluctuations (stochastic anti-resonance) accompanied by pulse broadening and rare events in the form of low power output signals having probability heavily deviated from the Gaussian distribution. (copyright 2016 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A stochastic model for retinocollicular map development
Directory of Open Access Journals (Sweden)
Tsigankov Dmitry N
2004-08-01
Full Text Available Abstract Background We examine results of gain-of-function experiments on retinocollicular maps in knock-in mice [Brown et al. (2000 Cell 102:77]. In wild-type mice the temporal-nasal axis of retina is mapped to the rostral-caudal axis of superior colliculus. The established map is single-valued, which implies that each point in retina maps to a unique termination zone in superior colliculus. In homozygous Isl2/EphA3 knock-in mice the map is double-valued, which means that each point on retina maps to two termination zones in superior colliculus. This is because about 50 percent of cells in retina express Isl2, and two types of projections, wild-type and Isl2/EphA3 positive, form two branches of the map. In heterozygous Isl2/EphA3 knock-ins the map is intermediate between the homozygous and wild-type: it is single-valued in temporal and double-valued in the nasal parts of retina. In this study we address possible reasons for such a bifurcation of the map. Results We study the map formation using stochastic model based on Markov chains. In our model the map undergoes a series of reconstructions with probabilities dependent upon a set of chemical cues. Our model suggests that the map in heterozygotes is single-valued in temporal region of retina for two reasons. First, the inhomogeneous gradient of endogenous receptor in retina makes the impact of exogenous receptor less significant in temporal retina. Second, the gradient of ephrin in the corresponding region of superior colliculus is smaller, which reduces the chemical signal-to-noise ratio. We predict that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should extend to a larger portion of temporal retina, i.e. the point of transition between single-and doulble-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. Conclusions We present a theoretical model for retinocollicular map development, which can account for
Stochastic Gabor reflectivity and acoustic impedance inversion
Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John
2018-02-01
To delineate subsurface lithology to estimate petrophysical properties of a reservoir, it is possible to use acoustic impedance (AI) which is the result of seismic inversion. To change amplitude to AI, removal of wavelet effects from the seismic signal in order to get a reflection series, and subsequently transforming those reflections to AI, is vital. To carry out seismic inversion correctly it is important to not assume that the seismic signal is stationary. However, all stationary deconvolution methods are designed following that assumption. To increase temporal resolution and interpretation ability, amplitude compensation and phase correction are inevitable. Those are pitfalls of stationary reflectivity inversion. Although stationary reflectivity inversion methods are trying to estimate reflectivity series, because of incorrect assumptions their estimations will not be correct, but may be useful. Trying to convert those reflection series to AI, also merging with the low frequency initial model, can help us. The aim of this study was to apply non-stationary deconvolution to eliminate time variant wavelet effects from the signal and to convert the estimated reflection series to the absolute AI by getting bias from well logs. To carry out this aim, stochastic Gabor inversion in the time domain was used. The Gabor transform derived the signal’s time–frequency analysis and estimated wavelet properties from different windows. Dealing with different time windows gave an ability to create a time-variant kernel matrix, which was used to remove matrix effects from seismic data. The result was a reflection series that does not follow the stationary assumption. The subsequent step was to convert those reflections to AI using well information. Synthetic and real data sets were used to show the ability of the introduced method. The results highlight that the time cost to get seismic inversion is negligible related to general Gabor inversion in the frequency domain. Also
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Stochastic population theories
Ludwig, Donald
1974-01-01
These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the Na...
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Stochastic project networks temporal analysis, scheduling and cost minimization
Neumann, Klaus
1990-01-01
Project planning, scheduling, and control are regularly used in business and the service sector of an economy to accomplish outcomes with limited resources under critical time constraints. To aid in solving these problems, network-based planning methods have been developed that now exist in a wide variety of forms, cf. Elmaghraby (1977) and Moder et al. (1983). The so-called "classical" project networks, which are used in the network techniques CPM and PERT and which represent acyclic weighted directed graphs, are able to describe only projects whose evolution in time is uniquely specified in advance. Here every event of the project is realized exactly once during a single project execution and it is not possible to return to activities previously carried out (that is, no feedback is permitted). Many practical projects, however, do not meet those conditions. Consider, for example, a production process where some parts produced by a machine may be poorly manufactured. If an inspection shows that a part does no...
Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs
2011-04-01
adl`ag, and Markov time properties, and prove that the semantics of our logic is measurable. We present compositional proof rules, including rules for stochastic differential equations, and prove soundness.
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
DEFF Research Database (Denmark)
Gidofalvi, Gyozo; Pedersen, Torben Bach
2005-01-01
Recent advances in communication and information technology, such as the increasing accuracy of GPS technology and the miniaturization of wireless communication devices pave the road for Location-Based Services (LBS). To achieve high quality for such services, spatio-temporal data mining techniques...... are needed. In this paper, we describe experiences with spatio-temporal rule mining in a Danish data mining company. First, a number of real world spatio-temporal data sets are described, leading to a taxonomy of spatio-temporal data. Second, the paper describes a general methodology that transforms...... the spatio-temporal rule mining task to the traditional market basket analysis task and applies it to the described data sets, enabling traditional association rule mining methods to discover spatio-temporal rules for LBS. Finally, unique issues in spatio-temporal rule mining are identified and discussed....
Stochastic Collapsed Variational Bayesian Inference for Latent Dirichlet Allocation
Foulds, J.; Boyles, L.; DuBois, C.; Smyth, P.; Welling, M.; Dhillon, I.S.; Koren, Y.; Ghani, R.; Senator, T.E.; Bradley, P.; Parekh, R.; He, J.; Grossman, R.L.; Uthurusamy, R.
2013-01-01
There has been an explosion in the amount of digital text information available in recent years, leading to challenges of scale for traditional inference algorithms for topic models. Recent advances in stochastic variational inference algorithms for latent Dirichlet allocation (LDA) have made it
Approximation methods for stochastic petri nets
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay
DEFF Research Database (Denmark)
Tryggestad, Kjell; Justesen, Lise; Mouritsen, Jan
2013-01-01
Purpose – The purpose of this paper is to explore how animals can become stakeholders in interaction with project management technologies and what happens with project temporalities when new and surprising stakeholders become part of a project and a recognized matter of concern to be taken...... into account. Design/methodology/approach – The paper is based on a qualitative case study of a project in the building industry. The authors use actor-network theory (ANT) to analyze the emergence of animal stakeholders, stakes and temporalities. Findings – The study shows how project temporalities can...... multiply in interaction with project management technologies and how conventional linear conceptions of project time may be contested with the emergence of new non-human stakeholders and temporalities. Research limitations/implications – The study draws on ANT to show how animals can become stakeholders...
Computational methods in stochastic dynamics
Papadrakakis, Manolis; Papadopoulos, Vissarion
2011-01-01
Covering what is an emerging frontier in research, this book focuses on advanced computational methods and software tools. These can be of huge assistance in tackling complex problems in stochastic dynamic and seismic analysis as well as structure design.
Stochastic Climate Theory and Modelling
Franzke, Christian L E; Berner, Judith; Williams, Paul D; Lucarini, Valerio
2014-01-01
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochast...
Path Loss Models Based on Stochastic Rays
Hu, Luoquan; Yu, Han; Chen, Yifan
2007-01-01
In this paper, two-dimensional percolation lattices are applied to describe wireless propagation environment, and stochastic rays are employed to model the trajectories of radio waves. We first derive the probability that a stochastic ray undergoes certain number of collisions at a specific spatial location. Three classes of stochastic rays with different constraint conditions are considered: stochastic rays of random walks, and generic stochastic rays with two different anomalous levels. Sub...
Stochastic Programming with Cauchy Distribution
Directory of Open Access Journals (Sweden)
Manas Kumar Pal
2015-12-01
Full Text Available The aim of this paper is to derive a method for solving a stochastic linear programming problem with Cauchy distribution. Assuming that the coefficients are distributed as Cauchy random variables, the stochastic linear programming is converted to a deterministic non-linear programming problem by a suitable transformation. Then an algorithm can be used to solve the resulting deterministic problem .A numerical example can be considered to illustrate the above methodology.
On solving stochastic MADM problems
Directory of Open Access Journals (Sweden)
Văduva Ion
2009-01-01
Full Text Available The paper examines a MADM problem with stochastic attributes. The transformation of a stochastic MADM problem into a cardinal problem is done by the standardization of the probability distribution of each attribute X and calculating the information of each attribute as Shannon's entropy or Onicescu's informational energy. Some well known (performant methods to solve a cardinal MADM problem are presented and a method for combining results of several methods to give a final MADM solution is discussed.
Stochastic Analysis and Related Topics
Ustunel, Ali
1988-01-01
The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.
Stochastic force in gravitational systems
Del Popolo, A.
2001-01-01
In this paper I study the probability distribution of the gravitational force in gravitational systems through numerical experiments. I show that Kandrup's (1980) and Antonuccio-Delogu & Atrio-Barandela's (1992) theories describe correctly the stochastic force probability distribution respectively in inhomogeneous and clustered systems. I find equations for the probability distribution of stochastic forces in finite systems, both homogeneous and clustered, which I use to compare the theoretic...
Stochastic optimization: beyond mathematical programming
CERN. Geneva
2015-01-01
Stochastic optimization, among which bio-inspired algorithms, is gaining momentum in areas where more classical optimization algorithms fail to deliver satisfactory results, or simply cannot be directly applied. This presentation will introduce baseline stochastic optimization algorithms, and illustrate their efficiency in different domains, from continuous non-convex problems to combinatorial optimization problem, to problems for which a non-parametric formulation can help exploring unforeseen possible solution spaces.
Strategy-Proof Stochastic Assignment
Erdil, A.
2013-01-01
I study strategy-proof assignment mechanisms where the agents reveal their preference rankings over the available objects. A stochastic mechanism returns lotteries over deterministic assignments, and mechanisms are compared according to first-order stochastic dominance. I show that non-wasteful strategy-proof mechanisms are not dominated by strategy-proof mechanisms, however nonwastefulness is highly restrictive when the mechanism involves randomization. In fact, the Random Priority mechanism...
Using copulas for modeling stochastic dependence in power system uncertainty analysis
Papaefthymiou, G.; Kurowicka, D.
2009-01-01
The increasing penetration of renewable generation in power systems necessitates the modeling of this stochastic system infeed in operation and planning studies. The system analysis leads to multivariate uncertainty analysis problems, involving non-Normal correlated random variables. In this
Phenomenology of stochastic exponential growth
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.
Mean Field Games for Stochastic Growth with Relative Utility
Energy Technology Data Exchange (ETDEWEB)
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Stochastic Optimal Prediction with Application to Averaged Euler Equations
Energy Technology Data Exchange (ETDEWEB)
Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-04-24
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.
Nonlinear stochastic Markov processes and modeling uncertainty in populations.
Banks, H Thomas; Hu, Shuhua
2012-01-01
We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.
Adaptation in stochastic environments
Clark, Colib
1993-01-01
The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "Cha...
AA, stochastic precooling kicker
CERN PhotoLab
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling", while a shutter shielded the deeply cooled antiproton stack from the violent action of the precooling kicker. In this picture, the injection orbit is to the left, the stack orbit to the far right, the separating shutter is in open position. After several seconds of precooling (in momentum and in the vertical plane), the shutter was opened briefly, so that by means of RF the precooled antiprotons could be transferred to the stack tail, where they were subjected to further cooling in momentum and both transverse planes, until they ended up, deeply cooled, in the stack core. The fast shutter, which had to open and close in a fraction of a second was an essential item of the cooling scheme and a mechanical masterpiece. Here the shutter is in the open position. The precooling pickups were of the same design, with the difference that the kickers had cooling circuits and the pickups not. 8401150 shows a precooling pickup with the shutte...
Stacking with Stochastic Cooling
Caspers, Friedhelm
2004-01-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles seen by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly protected from the Schottky noise of the stack. Vice versa the stack has to be efficiently shielded against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105, the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters)....
Kallianpur, Gopinath; Hida, Takeyuki
1987-01-01
The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis cipline with its own repertoire of techniques. The purpose of the Workshop on sto chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important f...
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Stochastic analysis in production process and ecology under uncertainty
Bieda, Bogusław
2014-01-01
The monograph addresses a problem of stochastic analysis based on the uncertainty assessment by simulation and application of this method in ecology and steel industry under uncertainty. The first chapter defines the Monte Carlo (MC) method and random variables in stochastic models. Chapter two deals with the contamination transport in porous media. Stochastic approach for Municipal Solid Waste transit time contaminants modeling using MC simulation has been worked out. The third chapter describes the risk analysis of the waste to energy facility proposal for Konin city, including the financial aspects. Environmental impact assessment of the ArcelorMittal Steel Power Plant, in Kraków - in the chapter four - is given. Thus, four scenarios of the energy mix production processes were studied. Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing t...
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Spatio-temporal data analytics for wind energy integration
Yang, Lei; Zhang, Junshan
2014-01-01
This SpringerBrief presents spatio-temporal data analytics for wind energy integration using stochastic modeling and optimization methods. It explores techniques for efficiently integrating renewable energy generation into bulk power grids. The operational challenges of wind, and its variability are carefully examined. A spatio-temporal analysis approach enables the authors to develop Markov-chain-based short-term forecasts of wind farm power generation. To deal with the wind ramp dynamics, a support vector machine enhanced Markov model is introduced. The stochastic optimization of economic di
Stochastic bursting synchronization in a population of subthreshold Izhikevich neurons
Kim, Sang-Yoon; Kim, Youngnam; Hong, Duk-Geun; Kim, Jean; Lim, Woochang
2012-05-01
We consider a population of subthreshold Izhikevich neurons that cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings ( i.e., discrete groups or bursts of noise-induced spikes). We investigate stochastic bursting synchronization by varying the noise intensity. Through competition between the constructive and the destructive roles of noise, collective coherence between noise-induced burstings is found to occur over a large range of intermediate noise intensities. This kind of stochastic bursting synchronization is well characterized by using the techniques of statistical mechanics and nonlinear dynamics, such as the order parameter, the raster plot of neural spikes, the time series of the ensemble-averaged global potential, and the phase portraits of limit cycles. In contrast to spiking neurons showing only spike synchronization (characterizing a temporal relationship between spikes), bursting neurons are found to exhibit both spike synchronization and burst synchronization (characterizing a temporal relationship between the onset times of the active phases of repetitive spikings). The degree of stochastic bursting synchronization is also measured in terms of a synchronization measure that reflects the resemblance of the global potential to the individual potential.
Stochastic S-system modeling of gene regulatory network.
Chowdhury, Ahsan Raja; Chetty, Madhu; Evans, Rob
2015-10-01
Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomyces cerevisiae yeast, and (2) the SOS DNA repair network in Escherichia coli.
Slow update stochastic simulation algorithms for modeling complex biochemical networks.
Ghosh, Debraj; De, Rajat K
2017-10-30
The stochastic simulation algorithm (SSA) based modeling is a well recognized approach to predict the stochastic behavior of biological networks. The stochastic simulation of large complex biochemical networks is a challenge as it takes a large amount of time for simulation due to high update cost. In order to reduce the propensity update cost, we proposed two algorithms: slow update exact stochastic simulation algorithm (SUESSA) and slow update exact sorting stochastic simulation algorithm (SUESSSA). We applied cache-based linear search (CBLS) in these two algorithms for improving the search operation for finding reactions to be executed. Data structure used for incorporating CBLS is very simple and the cost of maintaining this during propensity update operation is very low. Hence, time taken during propensity updates, for simulating strongly coupled networks, is very fast; which leads to reduction of total simulation time. SUESSA and SUESSSA are not only restricted to elementary reactions, they support higher order reactions too. We used linear chain model and colloidal aggregation model to perform a comparative analysis of the performances of our methods with the existing algorithms. We also compared the performances of our methods with the existing ones, for large biochemical networks including B cell receptor and FcϵRI signaling networks. Copyright © 2017 Elsevier B.V. All rights reserved.
A Stochastic Collocation Algorithm for Uncertainty Analysis
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories
Krommes, J. A.; Reiman, A. H.
2008-11-01
The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.
Soil Erosion as a stochastic process
Casper, Markus C.
2015-04-01
corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Relativistic analysis of stochastic kinematics
Giona, Massimiliano
2017-10-01
The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.
Measurable Stochastics for Brane Calculus
Directory of Open Access Journals (Sweden)
Giorgio Bacci
2010-10-01
Full Text Available We give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare. In this presentation, the semantics of a Brane process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a labelled transition system for Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics. Then, brane systems are presented as Markov processes over the measurable space generated by terms up-to syntactic congruence, and where the measures are indexed by the actions of this new LTS. Finally, we provide a SOS presentation of this stochastic semantics, which is compositional and syntax-driven.
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-03-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.
Fundamentals of stochastic nature sciences
Klyatskin, Valery I
2017-01-01
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...
Das, Iswar Das; Das, Iswar; Kumar, Gaurev; Stein, A.; Bagchi, Arunabha; Dadhwal, Vinay K.
2011-01-01
Little is known about the quantitative vulnerability analysis to landslides as not many attempts have been made to assess it comprehensively. This study assesses the spatio-temporal vulnerability of elements at risk to landslides in a stochastic framework. The study includes buildings, persons
Stochastic acceleration by a single wave in a magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Smith, R.
1977-09-22
A particularly simple problem exhibiting stochasticity is the motion of a charged particle in a uniform magnetic field and a single wave. Detailed studies of this wave-particle interaction show the following features. An electrostatic wave propagating obliquely to the magnetic field causes stochastic motion if the wave amplitude exceeds a certain threshold. The overlap of cyclotron resonances then destroys a constant of the motion, allowing strong particle acceleration. A wave of large enough amplitude would thus suffer severe damping and lead to rapid heating of a particle distribution. The stochastic motion resembles a diffusion process even though the wave spectrum contains only a single wave. The motion of ions in a nonuniform magnetic field and a single electrostatic wave is treated in our study of a possible saturation mechanism of the dissipative trapped-ion instability in a tokamak. A theory involving the overlap of bounce resonances predicts the main features found in the numerical integration of the equations of motion. Ions in a layer near the trapped-circulating boundary move stochastically. This motion leads to nonlinear stabilization mechanisms which are described qualitatively.
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Stochastic Optimization of Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Birge, John R. [University of Chicago
2014-03-20
This project focused on methodologies for the solution of stochastic optimization problems based on relaxation and penalty methods, Monte Carlo simulation, parallel processing, and inverse optimization. The main results of the project were the development of a convergent method for the solution of models that include expectation constraints as in equilibrium models, improvement of Monte Carlo convergence through the use of a new method of sample batch optimization, the development of new parallel processing methods for stochastic unit commitment models, and the development of improved methods in combination with parallel processing for incorporating automatic differentiation methods into optimization.
QB1 - Stochastic Gene Regulation
Energy Technology Data Exchange (ETDEWEB)
Munsky, Brian [Los Alamos National Laboratory
2012-07-23
Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Algebraic and stochastic coding theory
Kythe, Dave K
2012-01-01
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
Stochastic model in microwave propagation
Energy Technology Data Exchange (ETDEWEB)
Ranfagni, A. [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy); Mugnai, D., E-mail: d.mugnai@ifac.cnr.it [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)
2011-11-28
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
Hamiltonian theory of stochastic acceleration.
Makhnovskii, Yurii A; Pollak, Eli
2006-04-01
Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle's momentum and coordinate. Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling. Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this paper does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in time without bound.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Recursive utility using the stochastic maximum principle
National Research Council Canada - National Science Library
Aase, Knut K
2016-01-01
.... We use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations, and works when the economy is not Markovian, which can be the case with recursive utility...
Lead is a metal that occurs naturally in the earth's crust. Lead can be found in all parts of our ... from human activities such as mining and manufacturing. Lead used to be in paint; older houses may ...
Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations
Directory of Open Access Journals (Sweden)
Bo Zhu
2012-01-01
Full Text Available We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input...
The Share-a-Ride problem with stochastic travel times and stochastic delivery locations
Li, Baoxiang; Krushinsky, Dmitry; Van Woensel, Tom; Reijers, Hajo A.
2016-01-01
We consider two stochastic variants of the Share-a-Ride problem: one with stochastic travel times and one with stochastic delivery locations. Both variants are formulated as a two-stage stochastic programming model with recourse. The objective is to maximize the expected profit of serving a set of
Stochastic delay accelerates signaling in gene networks.
Josić, Krešimir; López, José Manuel; Ott, William; Shiau, LieJune; Bennett, Matthew R
2011-11-01
The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases.
Energy Technology Data Exchange (ETDEWEB)
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)
2017-08-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Gutierrez T, C.; Hernandez A, O. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)
1999-07-01
The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
Quantum stochastic calculus with maximal operator domains
Lindsay, J. Martin; Attal, Stéphane
2004-01-01
Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Itô formulas for op...
Directory of Open Access Journals (Sweden)
Marco S Nobile
Full Text Available Tau-leaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tau-leaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU provides power-efficient high-performance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tau-leaping simulations, by fully exploiting the Nvidia's Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tau-leaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPU-based tau-leaping implementation when the number of parallel simulations increases, with a break-even directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep analysis to study the oscillatory regimes in the Ras/cAMP/PKA pathway in S. cerevisiae.
Nobile, Marco S; Cazzaniga, Paolo; Besozzi, Daniela; Pescini, Dario; Mauri, Giancarlo
2014-01-01
Tau-leaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tau-leaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU) provides power-efficient high-performance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tau-leaping simulations, by fully exploiting the Nvidia's Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tau-leaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPU-based tau-leaping implementation when the number of parallel simulations increases, with a break-even directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep analysis to study the oscillatory regimes in the Ras/cAMP/PKA pathway in S. cerevisiae.
Symmetrized solutions for nonlinear stochastic differential equations
Directory of Open Access Journals (Sweden)
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
Variational principles for stochastic soliton dynamics
Holm, Darryl D.; Tyranowski, Tomasz M.
2016-01-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa–Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler–Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling. PMID:27118922
A stochastic causality-based process algebra
Brinksma, Hendrik; Katoen, Joost P.; Langerak, Romanus; Latella, Diego
1995-01-01
This paper discusses stochastic extensions of a simple process algebra in a causality-based setting. Atomic actions are supposed to happen after a delay that is determined by a stochastic variable with a certain distribution. A simple stochastic type of event structures is discussed, restricting the
Symmetry Reduction For Stochastic Hybrid Systems
Bujorianu, L.M.; Katoen, Joost P.
2008-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA).
Symmetry reduction for stochastic hybrid systems
Bujorianu, L.M.; Katoen, Joost P.
2009-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we
Stochastic Volatility and DSGE Models
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains an introduct......In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Stochastic control of traffic patterns
DEFF Research Database (Denmark)
Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer
2013-01-01
A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage...
Stochastic vehicle routing with recourse
DEFF Research Database (Denmark)
Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand inst...
CHARACTERISTIC RADICALS OF STOCHASTIC MATRICES,
The paper investigates the distribution on a complex plane of characteristic radicals of stochastic matrices of the n-th order. The results obtained...can be interpreted as theorems on the relative distribution of characteristic radicals of an arbitrary matrix with non-negative elements. (Author)
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Stochastic modeling of soil salinity
Suweis, S.; Rinaldo, A.; Zee, van der S.E.A.T.M.; Daly, E.; Maritan, A.
2010-01-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Integral characteristics: a key to understanding structure formation in stochastic dynamic systems
Klyatskin, Valery I.
2011-05-01
Some general problems concerning the stochastic approach are discussed in relation to parametrically excited stochastic dynamic systems described by partial differential equations. Such problems arise in hydrodynamics, magnetohydrodynamics, and astro, plasma, and radio physics and share the feature that the statistical characteristics of their solutions (moments, correlation and spectral functions, and so on) increasing exponentially with time, whereas some solution implementations lead to the formation of random structures with probability one as a result of clustering. The goal of this paper is to use the ideas of stochastic topography to find conditions under which such structures arise.
Optically levitated nanoparticle as a model system for stochastic bistable dynamics
Ricci, F.; Rica, R. A.; Spasenović, M.; Gieseler, J.; Rondin, L.; Novotny, L.; Quidant, R.
2017-05-01
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
Dynamics of the stochastic chemostat with Monod-Haldane response function.
Wang, Liang; Jiang, Daqing; Wolkowicz, Gail S K; O'Regan, Donal
2017-10-20
The stochastic chemostat model with Monod-Haldane response function is perturbed by environmental white noise. This model has a global positive solution. We demonstrate that there is a stationary distribution of the stochastic model and the system is ergodic under appropriate conditions, on the basis of Khasminskii's theory on ergodicity. Sufficient criteria for extinction of the microbial population in the stochastic system are established. These conditions depend strongly on the Brownian motion. We find that even small scale white noise can promote the survival of microorganism populations, while large scale noise can lead to extinction. Numerical simulations are carried out to illustrate our theoretical results.
Classification in postural style based on stochastic process modeling.
Denis, Christophe
2014-01-01
We address the statistical challenge of classifying subjects as hemiplegic, vestibular or normal based on complex trajectories obtained through two experimental protocols designed to evaluate potential deficits in postural control. The classification procedure involves a dimension reduction step where the complex trajectories are summarized by finite-dimensional summary measures based on a stochastic process model for a real-valued trajectory. This allows us to retrieve from the trajectories information relative to their temporal dynamic. A leave-one-out evaluation yields a 79% performance of correct classification for a total of n=70 subjects, with 22 hemiplegic (31%), 16 vestibular (23%) and 32 normal (46%) subjects.
Algorithmic advances in stochastic programming
Energy Technology Data Exchange (ETDEWEB)
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
Infinite-degree-corrected stochastic block model
DEFF Research Database (Denmark)
Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten
2014-01-01
, Phys. Rev. E 83, 016107 (2011)] incorporates a node degree correction to model degree heterogeneity within each group. Although this demonstrably leads to better performance on several networks, it is not obvious whether modeling node degree is always appropriate or necessary. We formulate the degree...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...... in the network that can be used to quantify the model’s predictive performance. On synthetic data we demonstrate that including the degree correction yields better performance on both recovering the true group structure and predicting missing links when degree heterogeneity is present, whereas performance...
Stochastic models for surface diffusion of molecules
Energy Technology Data Exchange (ETDEWEB)
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Yu, Yueyue; Cai, Ming; Ren, Rongcai
2017-08-01
We consider three indices to measure the polar stratospheric mass and stratospheric meridional mass circulation variability: anomalies of (1) total mass in the polar stratospheric cap (60-90°N, above the isentropic surface 400 K, PSM), (2) total adiabatic mass transport across 60°N into the polar stratosphere cap (AMT), (3) and total diabetic mass transport across 400 K from the polar stratosphere into the troposphere below (DMT). It is confirmed that the negative stratospheric Northern Annular Mode (NAM) and PSM indices have a nearly indistinguishable temporal evolution and a similar red-noise-like spectrum with a de-correlation timescale of 4 weeks. This enables us to examine the low-frequency nature of the NAM in the framework of mass circulation, namely, d/{dt}{PSM}={AMT} - {DMT} . The DMT index tends to be positively correlated with the PSM with a red-noise-like spectrum, representing slow radiative cooling processes giving rise to a de-correlation timescale of 3-4 weeks. The AMT is nearly perfectly correlated with the day-to-day tendency of PSM, reflecting a robust quasi 90° out-of-phase relation between the AMT and PSM at all frequency bands. Variations of vertically westward tilting of planetary waves contribute mainly to the high-frequency portion of AMT. It is the wave amplitude's slow vacillation that plays the leading role in the quasi 90° out-of-phase relation between the AMT and PSM. Based on this, we put forward a linear stochastic model with a low-frequency amplification feedback from low-frequency amplitude vacillations of planetary waves to explain the amplified low-frequency response of PSM/NAM to a stochastic forcing from the westward tilting variability.
Forward, backward, and weighted stochastic bridges
Drummond, Peter D.
2017-10-01
We define stochastic bridges as conditional distributions of stochastic paths that leave a specified point in phase-space in the past and arrive at another one in the future. These can be defined relative to either forward or backward stochastic differential equations and with the inclusion of arbitrary path-dependent weights. The underlying stochastic equations are not the same except in linear cases. Accordingly, we generalize the theory of stochastic bridges to include time-reversed and weighted stochastic processes. We show that the resulting stochastic bridges are identical, whether derived from a forward or a backward time stochastic process. A numerical algorithm is obtained to sample these distributions. This technique, which uses partial stochastic equations, is robust and easily implemented. Examples are given, and comparisons are made to previous work. In stochastic equations without a gradient drift, our results confirm an earlier conjecture, while generalizing this to cases with path-dependent weights. An example of a two-dimensional stochastic equation with no potential solution is analyzed and numerically solved. We show how this method can treat unexpectedly large excursions occurring during a tunneling or escape event, in which a system escapes from one quasistable point to arrive at another one at a later time.
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, Luminita Manuela
2012-01-01
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...
Momentum Maps and Stochastic Clebsch Action Principles
Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.
2017-11-01
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.
Millman, Daniel Raul
Computational fluid dynamics (CFD) methods have been coupled with structural solvers to provide accurate predictions of limit cycle oscillations (LCO). There is, however, a growing interest in understanding how uncertainties in flight conditions and structural parameters affect the character of an LCO response, leading to failure of an aeroelastic system. Uncertainty quantification of a stochastic system (parametric uncertainty) with stochastic inputs (initial condition uncertainty) has traditionally been analyzed with Monte Carlo simulations (MCS). Probability density functions (PDF) of the LCO response are obtained from the MCS to estimate the probability of failure. A CFD solution, however, can take days to weeks to obtain a single response, making the MCS method intractable for large problems. A candidate approach to efficiently estimate the PDF of an LCO response is the stochastic projection method. The classical stochastic projection method is a polynomial chaos expansion (PCE). The PCE approximates the response in the stochastic domain through a Fourier type expansion of the Wiener-Hermite polynomials. An LCO response can be characterized as a subcritical or supercritical bifurcation, and bifurcations are shown to be discontinuities in the stochastic domain. The PCE method, then, would be too inefficient for estimating the LCO response surface. The objective of this research is to extend the stochastic projection method to include the construction of B-spline surfaces in the stochastic domain. The multivariate B-spline problem is solved to estimate the LCO response surface. An MCS is performed on this response surface to estimate the PDF of the LCO response. The probability of failure is then computed from the PDF. The stochastic projection method via B-splines is applied to the problem of estimating the PDF of a subcritical LCO response of a nonlinear airfoil in inviscid transonic flow. The stochastic algorithm provides a conservative estimate of the
Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers
Churkin, D. V.; Sugavanam, S.; Tarasov, N.; Khorev, S.; Smirnov, S. V.; Kobtsev, S. M.; Turitsyn, S. K.
2015-01-01
Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. The complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discovered that while radiation of partially mode-locked fibre lasers is stochastic and intermittent on a short time scale, it exhibits non-trivial periodicity and long-scale correlations over slow evolution from one round-trip to another. A new technique for evolution mapping of intensity autocorrelation function has enabled us to reveal a variety of localized spatio-temporal structures and to experimentally study their symbiotic co-existence with stochastic radiation. Real-time characterization of dynamical spatio-temporal regimes of laser operation is set to bring new insights into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems. PMID:25947951
Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers.
Churkin, D V; Sugavanam, S; Tarasov, N; Khorev, S; Smirnov, S V; Kobtsev, S M; Turitsyn, S K
2015-05-07
Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. The complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discovered that while radiation of partially mode-locked fibre lasers is stochastic and intermittent on a short time scale, it exhibits non-trivial periodicity and long-scale correlations over slow evolution from one round-trip to another. A new technique for evolution mapping of intensity autocorrelation function has enabled us to reveal a variety of localized spatio-temporal structures and to experimentally study their symbiotic co-existence with stochastic radiation. Real-time characterization of dynamical spatio-temporal regimes of laser operation is set to bring new insights into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems.
Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes
Directory of Open Access Journals (Sweden)
Victor Dévoué
2016-01-01
Full Text Available We study some nonlinear stochastic Cauchy problems in the framework of the (C,E,P-algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist.
Anomalous scaling of stochastic processes and the Moses effect.
Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H
2017-04-01
The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.
Size and stochasticity in irrigated social-ecological systems
Puy, Arnald; Muneepeerakul, Rachata; Balbo, Andrea L.
2017-03-01
This paper presents a systematic study of the relation between the size of irrigation systems and the management of uncertainty. We specifically focus on studying, through a stylized theoretical model, how stochasticity in water availability and taxation interacts with the stochastic behavior of the population within irrigation systems. Our results indicate the existence of two key population thresholds for the sustainability of any irrigation system: or the critical population size required to keep the irrigation system operative, and N* or the population threshold at which the incentive to work inside the irrigation system equals the incentives to work elsewhere. Crossing irretrievably leads to system collapse. N* is the population level with a sub-optimal per capita payoff towards which irrigation systems tend to gravitate. When subjected to strong stochasticity in water availability or taxation, irrigation systems might suffer sharp population drops and irreversibly disintegrate into a system collapse, via a mechanism we dub ‘collapse trap’. Our conceptual study establishes the basis for further work aiming at appraising the dynamics between size and stochasticity in irrigation systems, whose understanding is key for devising mitigation and adaptation measures to ensure their sustainability in the face of increasing and inevitable uncertainty.
Anomalous scaling of stochastic processes and the Moses effect
Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.
2017-04-01
The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.
Impact of a refined airborne LiDAR stochastic model for natural hazard applications
Glennie, C. L.; Bolkas, D.; Fotopoulos, G.
2016-12-01
Airborne Light Detection and Ranging (LiDAR) is often employed to derive multi-temporal Digital Elevation Models (DEMs), that are used to estimate vertical displacement resulting from natural hazards such as landslides, rockfalls and erosion. Vertical displacements are estimated by computing the difference between two DEMs separated by a specified time period and applying a threshold to remove the inherent noise. Thus, reliable information about the accuracy of DEMs is essential. The assessment of airborne LiDAR errors is typically based on (i) independent ground control points (ii) forward error propagation utilizing the LiDAR geo-referencing equation. The latter approach is dependent on the stochastic model information of the LiDAR measurements. Furthermore, it provides the user with point-by-point accuracy estimation. In this study, a refined stochastic model is obtained through variance component estimation (VCE) for a dataset in Houston, Texas. Results show that initial stochastic information was optimistic by 35% for both horizontal coordinates and ellipsoidal heights. To assess the impact of a refined stochastic model, surface displacement simulations are evaluated. The simulations include scenarios with topographic slopes that vary from 10º to 60º, and vertical displacement of ±1 to ±5 m. Results highlight the cases where a reliable stochastic model is important. A refined stochastic model can be used in practical applications for determining appropriate noise thresholds in vertical displacement, improve quantitative analysis, and enhance relevant decision-making.
... or dust from lead-based paint. Toys and furniture painted before 1976. Painted toys and decorations made ... by decades of car exhaust or years of house paint scrapings. Lead is more common in soil ...
... a hard, durable surface. In 1977, federal regulations banned lead from paint for general use. But homes ... OTHERS: Lead has recently been found in some plastic mini-blinds and vertical blinds which were made ...
DEFF Research Database (Denmark)
Larsen, Mette Vinther; Rasmussen, Jørgen Gulddahl
2015-01-01
This first chapter presents the exploratory and curious approach to leading as relational processes – an approach that pervades the entire book. We explore leading from a perspective that emphasises the unpredictable challenges and triviality of everyday life, which we consider an interesting......, relevant and realistic way to examine leading. The chapter brings up a number of concepts and contexts as formulated by researchers within the field, and in this way seeks to construct a first understanding of relational leading....
Stochastic heating in laser interaction with ultra-thin foils
Luis Martins, Joana; Siminos, Evangelos; Fulop, Tunde
2017-10-01
Stochastic heating of electrons in multiple counter-propagating electromagnetic waves has been investigated theoretically and numerically in numerous works since the 80s (e.g. Ref.). Stochastic heating has been invoked as a possible mechanism responsible for electron heating in scenarios such as laser interaction with thin foils for ion acceleration and electron heating in beat-wave injection. However, a clear experimental verification of this heating process has not been done, to our knowledge. In this work, we examine electron heating during the interaction of multiple laser pulses with ultra-thin foils (a few atomic layers wide) through numerical particle-in-cell and particle-particle simulations. Such targets could prevent the development of instabilities/processes which could hinder the interpretation of observations. We include realistic temporally and spatially finite laser pulses and targets and explore in detail possible setups for an experimental observation of stochastic heating, analyzing signatures in the electron energy spectra, angular distribution, and radiation emission.
Stochastic time models of syllable structure.
Shaw, Jason A; Gafos, Adamantios I
2015-01-01
Drawing on phonology research within the generative linguistics tradition, stochastic methods, and notions from complex systems, we develop a modelling paradigm linking phonological structure, expressed in terms of syllables, to speech movement data acquired with 3D electromagnetic articulography and X-ray microbeam methods. The essential variable in the models is syllable structure. When mapped to discrete coordination topologies, syllabic organization imposes systematic patterns of variability on the temporal dynamics of speech articulation. We simulated these dynamics under different syllabic parses and evaluated simulations against experimental data from Arabic and English, two languages claimed to parse similar strings of segments into different syllabic structures. Model simulations replicated several key experimental results, including the fallibility of past phonetic heuristics for syllable structure, and exposed the range of conditions under which such heuristics remain valid. More importantly, the modelling approach consistently diagnosed syllable structure proving resilient to multiple sources of variability in experimental data including measurement variability, speaker variability, and contextual variability. Prospects for extensions of our modelling paradigm to acoustic data are also discussed.
Stochastic Time Models of Syllable Structure
Shaw, Jason A.; Gafos, Adamantios I.
2015-01-01
Drawing on phonology research within the generative linguistics tradition, stochastic methods, and notions from complex systems, we develop a modelling paradigm linking phonological structure, expressed in terms of syllables, to speech movement data acquired with 3D electromagnetic articulography and X-ray microbeam methods. The essential variable in the models is syllable structure. When mapped to discrete coordination topologies, syllabic organization imposes systematic patterns of variability on the temporal dynamics of speech articulation. We simulated these dynamics under different syllabic parses and evaluated simulations against experimental data from Arabic and English, two languages claimed to parse similar strings of segments into different syllabic structures. Model simulations replicated several key experimental results, including the fallibility of past phonetic heuristics for syllable structure, and exposed the range of conditions under which such heuristics remain valid. More importantly, the modelling approach consistently diagnosed syllable structure proving resilient to multiple sources of variability in experimental data including measurement variability, speaker variability, and contextual variability. Prospects for extensions of our modelling paradigm to acoustic data are also discussed. PMID:25996153
Stochastic problems in population genetics
Maruyama, Takeo
1977-01-01
These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura...
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Stochastic integration and differential equations
Protter, Philip E
2003-01-01
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...
Stochastic stability of traffic maps
Blank, Michael
2012-12-01
We study the ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using connections to topological Markov chains we obtain nontrivial invariant measures, prove their stochastic stability and calculate the topological entropy. Technically these results in the deterministic setting are related to the construction of measures of maximal entropy via measures uniformly distributed on periodic points of a given period, while in the random setting we construct (spatially) Markov invariant measures directly. In distinction to conventional results the limiting measures in the non-lattice case are non-ergodic. The average velocity of individual ‘vehicles’ as a function of their density and its stochastic stability is studied as well.
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Stochastic Modeling of Soil Salinity
Suweis, S; Van der Zee, S E A T M; Daly, E; Maritan, A; Porporato, A; 10.1029/2010GL042495
2012-01-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long-term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in long-term soil salinization trend...
Alekseev, Oleg; Mineev-Weinstein, Mark
2016-12-01
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The classical point for the action, defined as a minus logarithm of the growth probability, describes the most probable scenario and reproduces the Laplacian growth equation, which embraces numerous fundamental free boundary dynamics in nonequilibrium physics. For nonclassical scenarios we introduce virtual point sources, in which presence the action becomes the Kullback-Leibler entropy. Strikingly, this entropy is shown to be the sum of electrostatic energies of layers grown per elementary time unit. Hence the growth probability of the presented nonequilibrium process obeys the Gibbs-Boltzmann statistics, which, as a rule, is not applied out from equilibrium. Each layer's probability is expressed as a product of simple factors in an auxiliary complex plane after a properly chosen conformal map. The action at this plane is a sum of Robin functions, which solve the Liouville equation. At the end we establish connections of our theory with the τ function of the integrable Toda hierarchy and with the Liouville theory for noncritical quantum strings.
McMahon, Jay W.
2017-10-01
The YORP effect is one of the dominant processes that controls the dynamical evolution of small asteroids in the inner solar system. It has recently been hypothesized that as an asteroid’s spin rate increases due to YORP, the shape will change, which in turn causes the YORP coefficient to drastically change before reaching the spin limit - thus making the classical YORP cycles “stochastic”. This work examines how the YORP coefficient changes when the shape change due to spin up is constrained by a simple geophysical model that represents the effect of a cohesive rubble pile. Two processes are investigated: the relaxation of the asteroid shape, and the motion of boulders on the surface. In both cases the changes are modeled so that the resulting shape respects various arbitrary slope limits. Simulations of this process appear to stop the drastic change in YORP coefficients that leads to the idea of “stochastic” YORP, except in carefully prescribed worst case scenarios. Results are presented specifically based on the current radar and lightcurve derived shape model of Bennu.
Stochastic Models of Polymer Systems
2016-01-01
information about the behavior of the algorithm. At the same time, we were also able to formulate various acceleration techniques in precise math terms...peer-reviewed journals : Number of Papers published in non peer-reviewed journals : Final Report: Stochastic Models of Polymer Systems Report Title...the algorithm. At the same time, we were also able to formulate various acceleration techniques in precise math terms (e.g. formulate them as
Stochastic Energetics of Quantum Transport
Ghosh, Pulak Kumar; Ray, Deb Shankar
2006-01-01
We examine the stochastic energetics of directed quantum transport due to rectification of non-equilibrium thermal fluctuations. We calculate the quantum efficiency of a ratchet device both in presence and absence of an external load to characterize two quantifiers of efficiency. It has been shown that the quantum current as well as efficiency in absence of load (Stokes efficiency) is higher as compared to classical current and efficiency, respectively, at low temperature. The conventional ef...
Stochastic processes and filtering theory
Jazwinski, Andrew H
1970-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
Foundations of infinitesimal stochastic analysis
Stroyan, KD
2011-01-01
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2008-05-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out
Stochastic analysis of biochemical systems
Anderson, David F
2015-01-01
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...
Mechanical Autonomous Stochastic Heat Engine.
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Stochastic estimation of microactuator buckling
Energy Technology Data Exchange (ETDEWEB)
Bahrami, Mohsen; Tayefeh, Mohsen [Department of Mechanical Engineering, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of)
2006-04-01
In order to make a robust design of microsystems, it is important to analyze the electrical, thermal and mechanical fields including the actual input parameters. These microdevices, which typically are made of brittle materials such as polysilicon, show wide scatter (stochastic behavior) in properties as well as substantial uncertainty in the shape and geometry because of manufacturing processes. These behaviors necessitate either costly and time-consuming trial-and-error designs or, more efficiently, the development of a probabilistic design methodology for MEMS. Computer aided MEMS simulations regarding performance, power consumption, and reliability is an important design task due to high prototyping costs. Since microbeams have a wide range of applications in MEMS actuation mechanisms, analysis of the thermomechanical behavior of these actuators is very important. In the present work, assessing meaningful uncertainties involved in thermally driven microbeams, the stochastic finite element model (SFEM) is developed and implemented. The analysis shows a large deviation in buckling temperature and thermal stresses for reasonable probability density functions of characteristic parameters. Although computationally significantly more expensive than deterministic electromechanical simulation, the work illustrates the requirement of stochastic modeling for true estimation of microsystems' performance.
Multiple fields in stochastic inflation
Energy Technology Data Exchange (ETDEWEB)
Assadullahi, Hooshyar [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Noorbala, Mahdiyar [Department of Physics, University of Tehran,P.O. Box 14395-547, Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Vennin, Vincent; Wands, David [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)
2016-06-24
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
Information Anatomy of Stochastic Equilibria
Directory of Open Access Journals (Sweden)
Sarah Marzen
2014-08-01
Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.
On square-wave-driven stochastic resonance for energy harvesting in a bistable system
Directory of Open Access Journals (Sweden)
Dongxu Su
2014-11-01
Full Text Available Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.
On square-wave-driven stochastic resonance for energy harvesting in a bistable system
Energy Technology Data Exchange (ETDEWEB)
Su, Dongxu, E-mail: sudx@iis.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, Tokyo 1538505 (Japan); Zheng, Rencheng; Nakano, Kimihiko [Institute of Industrial Science, The University of Tokyo, Tokyo 1538505 (Japan); Cartmell, Matthew P [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2014-11-15
Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.
Double diffusivity model under stochastic forcing
Chattopadhyay, Amit K.; Aifantis, Elias C.
2017-05-01
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into
Stochastic Parametrization for the Impact of Neglected Variability Patterns
Kaiser, Olga; Hien, Steffen; Achatz, Ulrich; Horenko, Illia
2017-04-01
An efficient description of the gravity wave variability and the related spontaneous emission processes requires an empirical stochastic closure for the impact of neglected variability patterns (subgridscales or SGS). In particular, we focus on the analysis of the IGW emission within a tangent linear model which requires a stochastic SGS parameterization for taking the self interaction of the ageostrophic flow components into account. For this purpose, we identify the best SGS model in terms of exactness and simplicity by deploying a wide range of different data-driven model classes, including standard stationary regression models, autoregression and artificial neuronal networks models - as well as the family of nonstationary models like FEM-BV-VARX model class (Finite Element based vector autoregressive time series analysis with bounded variation of the model parameters). The models are used to investigate the main characteristics of the underlying dynamics and to explore the significant spatial and temporal neighbourhood dependencies. The best SGS model in terms of exactness and simplicity is obtained for the nonstationary FEM-BV-VARX setting, determining only direct spatial and temporal neighbourhood as significant - and allowing to drastically reduce the number of informations that are required for the optimal SGS. Additionally, the models are characterized by sets of vector- and matrix-valued parameters that must be inferred from big data sets provided by simulations - making it a task that can not be solved without deploying high-performance computing facilities (HPC).
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Stochastic Modeling of Radioactive Material Releases
Energy Technology Data Exchange (ETDEWEB)
Andrus, Jason [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pope, Chad [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Stochastic dynamics for reinfection by transmitted diseases
Barros, Alessandro S.; Pinho, Suani T. R.
2017-06-01
The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ 1 ).
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Stochastic synaptic plasticity with memristor crossbar arrays
Naous, Rawan
2016-11-01
Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.
Stochastic predictive control with adaptive model maintenance
Bavdekar, VA; Ehlinger, V; Gidon, D; Mesbah, A.
2016-01-01
© 2016 IEEE. The closed-loop performance of model-based controllers often degrades over time due to increased model uncertainty. Some form of model maintenance must be performed to regularly adapt the system model using closed-loop data. This paper addresses the problem of control-oriented model adaptation in the context of predictive control of stochastic linear systems. A stochastic predictive control approach is presented that integrates stochastic optimal control with control-oriented inp...
Ant colony optimization and stochastic gradient descent.
Meuleau, Nicolas; Dorigo, Marco
2002-01-01
In this article, we study the relationship between the two techniques known as ant colony optimization (ACO) and stochastic gradient descent. More precisely, we show that some empirical ACO algorithms approximate stochastic gradient descent in the space of pheromones, and we propose an implementation of stochastic gradient descent that belongs to the family of ACO algorithms. We then use this insight to explore the mutual contributions of the two techniques.
Ambit processes and stochastic partial differential equations
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....
Loss Aversion, Stochastic Compensation, and Team Incentives
大洞, 公平; Murooka, Takeshi
2013-01-01
We investigate moral-hazard problems with limited liability where agents have expectation-based reference-dependent preferences. We show that stochastic compensation for low performance can be optimal. Because of loss aversion, the agents have first-order risk aversion to wage uncertainty. This causes the agents to work harder when their low performance is stochastically compensated. We also examine team incentives for credibly employing such stochastic compensation. In an optimal contract, l...
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan
2018-01-01
The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.
Derivation of stochastic partial differential equations for size- and age-structured populations.
Allen, Edward J
2009-01-01
Stochastic partial differential equations (SPDEs) for size-structured and age- and size-structured populations are derived from basic principles, i.e. from the changes that occur in a small time interval. Discrete stochastic models of size-structured and age-structured populations are constructed, carefully taking into account the inherent randomness in births, deaths, and size changes. As the time interval decreases, the discrete stochastic models lead to systems of Itô stochastic differential equations. As the size and age intervals decrease, SPDEs are derived for size-structured and age- and size-structured populations. Comparisons between numerical solutions of the SPDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations.
Chen, Lihong; Wei, Fengying
2017-10-01
In this paper, the dynamics of a stochastic susceptible-infected-removed model in a population with varying size is investigated. We firstly show that the stochastic epidemic model has a unique global positive solution with any positive initial value. Then we verify that random perturbations lead to extinction when some conditions are being valid. Moreover, we prove that the solution of the stochastic epidemic model is persistent in the mean by building up a suitable Lyapunov function and using generalized Itô's formula. Further, the stochastic epidemic model admits a stationary distribution around the endemic equilibrium when parameters satisfy some sufficient conditions. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.
Adaptive stochastic Galerkin FEM with hierarchical tensor representations
Eigel, Martin
2016-01-08
PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.
Pricing vulnerable options with stochastic volatility
Wang, Guanying; Wang, Xingchun; Zhou, Ke
2017-11-01
In this paper, we investigate the pricing issue of vulnerable options with stochastic volatility by decomposing stochastic volatility into the long-term and short-term volatility. We describe the short-term fluctuation of stochastic volatility using a mean-reverting process, and assume the long-term volatility to be a constant. Based on the proposed model, we derive a pricing formula of vulnerable options in a special case. Numerical results are presented to illustrate the impacts of two stochastic volatility components on vulnerable option prices.
Stochastic versus deterministic systems of differential equations
Ladde, G S
2003-01-01
This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/flu
Treatment of Temporal Bone Fractures.
Diaz, Rodney C; Cervenka, Brian; Brodie, Hilary A
2016-10-01
Traumatic injury to the temporal bone can lead to significant morbidity or mortality and knowledge of the pertinent anatomy, pathophysiology of injury, and appropriate management strategies is critical for successful recovery and rehabilitation of such injured patients. Most temporal bone fractures are caused by motor vehicle accidents. Temporal bone fractures are best classified as either otic capsule sparing or otic capsule disrupting-type fractures, as such classification correlates well with risk of concomitant functional complications. The most common complications of temporal bone fractures are facial nerve injury, cerebrospinal fluid (CSF) leak, and hearing loss. Assessment of facial nerve function as soon as possible following injury greatly facilitates clinical decision making. Use of prophylactic antibiotics in the setting of CSF leak is controversial; however, following critical analysis and interpretation of the existing classic and contemporary literature, we believe its use is absolutely warranted.
Treatment of Temporal Bone Fractures
Diaz, Rodney C.; Cervenka, Brian; Brodie, Hilary A.
2016-01-01
Traumatic injury to the temporal bone can lead to significant morbidity or mortality and knowledge of the pertinent anatomy, pathophysiology of injury, and appropriate management strategies is critical for successful recovery and rehabilitation of such injured patients. Most temporal bone fractures are caused by motor vehicle accidents. Temporal bone fractures are best classified as either otic capsule sparing or otic capsule disrupting-type fractures, as such classification correlates well with risk of concomitant functional complications. The most common complications of temporal bone fractures are facial nerve injury, cerebrospinal fluid (CSF) leak, and hearing loss. Assessment of facial nerve function as soon as possible following injury greatly facilitates clinical decision making. Use of prophylactic antibiotics in the setting of CSF leak is controversial; however, following critical analysis and interpretation of the existing classic and contemporary literature, we believe its use is absolutely warranted. PMID:27648399
Predicting population extinction or disease outbreaks with stochastic models
Directory of Open Access Journals (Sweden)
Linda J. S. Allen
2017-01-01
Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.
Dynamic two state stochastic models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Niels Jacob; Madsen, Henrik
2009-01-01
A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part...... of the model illustrates that hysteresis effect and regime shifts can be obtained for a limited range of parameter values only. The effect of multiplicative noise components entering at different levels of the model is presented and discussed. Including noise leads to very different results on the stability...... of regimes, depending on how the noise propagates through the system. The dynamical properties of a system should therefore be described through propagation of the state distributions rather than the state means and consequently, stochastic models should be compared in a probabilistic framework....
The Stochastic Field Transport associated with the Slab ITG Modes
Connor, J W; Zocco, A
2013-01-01
Many models for anomalous transport consider the turbulent ExB transport arising from electrostatic micro-instabilities. In this paper we investigate whether the perturbed magnetic field that is associated with such instabilities at small but finite values of {beta} can lead to significant stochastic magnetic field transport. Using the tearing parity, long wave-length ion temperature gradient (ITG) modes in a plasma slab with magnetic shear as an example, we calculate the amplitude of the perturbed magnetic field that results at the resonant surface for the case when the plasma dissipation is given by the semi-collisional electron model. The resulting stochastic field transport is estimated and also compared with an estimate for the ExB transport due to the ITG mode.
Stochastic dynamics and combinatorial optimization
Ovchinnikov, Igor V.; Wang, Kang L.
2017-11-01
Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.
A Stochastic Description of Precipitation
1961-01-01
modification of a theorem of Bochner ([6], theorem 5.44), gives the following result. PROPOSITION 1. Let p be a complex function defined on the real linear...limit in probability in V. Let F1 be the subset of F formed by the limits of Cauchy sequences of F (this is the first Baire hull of STOCHASTIC THEORY...0 or E ac,f(y,) 2 0. According to Kolmogorov’s theorem there exists on TD a probability measure PD defined on the Borel sets of 5YD and having on B
Adaptive Stochastic Disturbance Accommodating Control
2010-05-01
obtained from the Stratonovich integral equation converges a.s. and uniformly to that obtained from the Itô integral equation . For more details please...edition. Appleby, J. A. D., 2002: Almost sure stability of linear itô- volterra equations with damped stochastic perturbations. Electronic Communications...the linear operator L(·) and the covariance of the white noise process V(t), are unknown. The measurement equation is given as Y(t) = CX(t) +V(t) (3
Stochastic modeling analysis and simulation
Nelson, Barry L
1995-01-01
A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...
Stochastic Model of Microtubule Dynamics
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... water bending moment is compared to statistics from available regression formulas. It is found that the suggested model predicts a coefficient of variation of the maximum still water bending moment that is a factor of two to three times lower than that obtained by use of the regression formula. It turns...
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2004-01-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction
... blue-gray metal that is mined from the earth’s crust. • Lead has been used for many industrial ... including the kidneys, heart, and reproductive system, • Pregnant women should know that the developing fetus is very ...
... has also been associated with juvenile delinquency and criminal behavior. In adults, lead can increase blood pressure ... and-forth manner, but rather from left to right (or vise-versa), or from the top of ...
... poison you. Most lead is present as an inorganic compound and does not move well through the ... D. R., Editors (© 2006). Contemporary Practice in Clinical Chemistry: AACC Press, Washington, DC. Pp 474. Wu, A. (© ...
Zhang, Yan; Chen, Shihua; Gao, Shujing; Wei, Xiang
2017-11-01
In this paper, stochastic non-autonomous predator-prey models with and without impulses are investigated. The effects of generalized nonlinear harvesting for prey and predator populations are considered. For the stochastic system without impulses, the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved. We show the existence of a nontrivial positive periodic solution by constructing appropriate Lyapunov functions and using Khasminskii's theory. Moreover, the global attractiveness and stochastic persistence in probability of the stochastic model are discussed. Results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population. Additionally, for the stochastic predator-prey system with impulsive effect, we prove that there exists a positive periodic solution. Numerical simulations are conducted to show the effectiveness and feasibility of the obtained results.
Temporal Processing Dysfunction in Schizophrenia
Carroll, Christine A.; Boggs, Jennifer; O'Donnell, Brian F.; Shekhar, Anantha; Hetrick, William P.
2008-01-01
Schizophrenia may be associated with a fundamental disturbance in the temporal coordination of information processing in the brain, leading to classic symptoms of schizophrenia such as thought disorder and disorganized and contextually inappropriate behavior. Despite the growing interest and centrality of time-dependent conceptualizations of the…
Directory of Open Access Journals (Sweden)
YouHua Chen
2014-06-01
Full Text Available In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability. The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc. As such, when WT (WTm and/or WTc is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40] and colonization (WTc-[0.1,40] was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3, extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic
Vector Integration and Stochastic Integration in Banach Spaces
Dinculeanu, Nicolae
2000-01-01
A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinc
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Spatio-temporal dynamics of security investments in an interdependent risk environment
Shafi, Kamran; Bender, Axel; Zhong, Weicai; Abbass, Hussein A.
2012-10-01
In a globalised world where risks spread through contagion, the decision of an entity to invest in securing its premises from stochastic risks no longer depends solely on its own actions but also on the actions of other interacting entities in the system. This phenomenon is commonly seen in many domains including airline, logistics and computer security and is referred to as Interdependent Security (IDS). An IDS game models this decision problem from a game-theoretic perspective and deals with the behavioural dynamics of risk-reduction investments in such settings. This paper enhances this model and investigates the spatio-temporal aspects of the IDS games. The spatio-temporal dynamics are studied using simple replicator dynamics on a variety of network structures and for various security cost tradeoffs that lead to different Nash equilibria in an IDS game. The simulation results show that the neighbourhood configuration has a greater effect on the IDS game dynamics than network structure. An in-depth empirical analysis of game dynamics is carried out on regular graphs, which leads to the articulation of necessary and sufficient conditions for dominance in IDS games under spatial constraints.
Effects of time delay on the stochastic resonance in small-world neuronal networks.
Yu, Haitao; Wang, Jiang; Du, Jiwei; Deng, Bin; Wei, Xile; Liu, Chen
2013-03-01
The effects of time delay on stochastic resonance in small-world neuronal networks are investigated. Without delay, an intermediate intensity of additive noise is able to optimize the temporal response of the neural system to the subthreshold periodic signal imposed on all neurons constituting the network. The time delay in the coupling process can either enhance or destroy stochastic resonance of neuronal activity in the small-world network. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of weak external forcing. It is found that the delay-induced multiple stochastic resonances are most efficient when the forcing frequency is close to the global-resonance frequency of each individual neuron. Furthermore, the impact of time delay on stochastic resonance is largely independent of the small-world topology, except for resonance peaks. Considering that information transmission delays are inevitable in intra- and inter-neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.
Single-Molecule Stochastic Resonance
Directory of Open Access Journals (Sweden)
K. Hayashi
2012-08-01
Full Text Available Stochastic resonance (SR is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR.
Adaptive stochastic disturbance accommodating control
George, Jemin; Singla, Puneet; Crassidis, John L.
2011-02-01
This article presents a Kalman filter based adaptive disturbance accommodating stochastic control scheme for linear uncertain systems to minimise the adverse effects of both model uncertainties and external disturbances. Instead of dealing with system uncertainties and external disturbances separately, the disturbance accommodating control scheme lumps the overall effects of these errors in a to-be-determined model-error vector and then utilises a Kalman filter in the feedback loop for simultaneously estimating the system states and the model-error vector from noisy measurements. Since the model-error dynamics is unknown, the process noise covariance associated with the model-error dynamics is used to empirically tune the Kalman filter to yield accurate estimates. A rigorous stochastic stability analysis reveals a lower bound requirement on the assumed system process noise covariance to ensure the stability of the controlled system when the nominal control action on the true plant is unstable. An adaptive law is synthesised for the selection of stabilising system process noise covariance. Simulation results are presented where the proposed control scheme is implemented on a two degree-of-freedom helicopter.
Stochastic Time-Series Spectroscopy
Scoville, John
2015-01-01
Spectroscopically measuring low levels of non-equilibrium phenomena (e.g. emission in the presence of a large thermal background) can be problematic due to an unfavorable signal-to-noise ratio. An approach is presented to use time-series spectroscopy to separate non-equilibrium quantities from slowly varying equilibria. A stochastic process associated with the non-equilibrium part of the spectrum is characterized in terms of its central moments or cumulants, which may vary over time. This parameterization encodes information about the non-equilibrium behavior of the system. Stochastic time-series spectroscopy (STSS) can be implemented at very little expense in many settings since a series of scans are typically recorded in order to generate a low-noise averaged spectrum. Higher moments or cumulants may be readily calculated from this series, enabling the observation of quantities that would be difficult or impossible to determine from an average spectrum or from prinicipal components analysis (PCA). This meth...
Stochastic clustered-dot dithering
Ostromoukhov, Victor; Hersch, Roger D.
1999-10-01
A new technique for building stochastic clustered-dot screens is being proposed. A large dither matrix comprising thousands of stochastically laid out screen dots is constructed by first laying out the screen dot centers. Screen dot centers are obtained by placing discrete disks of a chosen radius at free cell locations when traversing the dither array cells according to either a discretely rotated Hilbert space-filling curve or a random space-filling curve. After Delauney triangulation of the screen dot centers, the maximal surface of each screen dot is computed and isointensity regions are created. This isointensity map is converted into an antialiased gray scale image, i.e., into an array of preliminary threshold values. These threshold values are renumbered to obtain the threshold values of the final dither threshold array. By changing the disk radius, the screen dot size can be adapted to the characteristics of particular printing devices. Larger screen dots may improve the one reproduction of printers having important dot gain.
Stochastic online scheduling on parallel machines
Persiano, G; Megow, N.; Uetz, Marc Jochen; Solis-Oba, R; Vredeveld, T.
We consider a non-preemptive, stochastic parallel machine scheduling model with the goal to minimize the weighted completion times of jobs. In contrast to the classical stochastic model where jobs with their processing time distributions are known beforehand, we assume that jobs appear one by one,
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...
Causal random geometry from stochastic quantization
DEFF Research Database (Denmark)
Ambjørn, Jan; Loll, R.; Westra, W.
2010-01-01
in this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including...... the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries...
A stochastic indicator for sovereign debt sustainability
Lukkezen, J.H.J.|info:eu-repo/dai/nl/358211875; Rojas-Romagosa, Hugo
2016-01-01
We propose a stochastic indicator to assess government debt sustainability. This indicator combines the effect of economic uncertainty –represented by stochastic simulations of interest and growth rates– with the expected fiscal response that provides information on the long-term country specific
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Stochastic Modelling and Analysis of Warehouse Operations
Y. Gong (Yeming)
2009-01-01
textabstractThis thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a
Stochastic integral representations of quantum martingales on ...
Indian Academy of Sciences (India)
Introduction. The stochastic integral representations of quantum martingales have been studied by many authors (see [2,6,7,10,11,14,15,18,19], etc). In [18], Parthasarathy and Sinha established a stochastic integral representation of a regular bounded quantum martingale on Fock space with respect to the basic ...
Variational principles for stochastic fluid dynamics
Holm, Darryl D.
2015-01-01
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083
Assessing the quality of stochastic oscillations
Indian Academy of Sciences (India)
Population dynamics; stochastic oscillations. ... We propose a quantification of the oscillatory appearance of the fluctuating populations, and show that good stochastic oscillations are present if a parameter of the macroscopic model is small, and that no microscopic model will show oscillations if that parameter is large.
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...
Derivation of Stochastic Equations for Computational Uncertainties ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: This paper presents a simple mathematical algorithm or procedure for computing the uncertainties at the various percent of data input, using the stochastic approach of simulating the input variables to compute the output variables. A simple algorithm was used to derive stochastic equations for some selected ...
Derivation of Stochastic Equations for Computational Uncertainties ...
African Journals Online (AJOL)
This paper presents a simple mathematical algorithm or procedure for computing the uncertainties at the various percent of data input, using the stochastic approach of simulating the input variables to compute the output variables. A simple algorithm was used to derive stochastic equations for some selected petrophysical ...
Interrupted monitoring of a stochastic process
Palmer, E.
1977-01-01
Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies. The optimum strategy is also compared to the strategies used by subjects in a pilot experiment.
The Measurable Space of Stochastic Processes
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2010-01-01
The Measurable Space of Stochastic Processes. In Proc. of Seventh International Conference on the Quantitative Evaluation of Systems, QEST2010, IEEE Computer Society, pp. 171-180, 2010......The Measurable Space of Stochastic Processes. In Proc. of Seventh International Conference on the Quantitative Evaluation of Systems, QEST2010, IEEE Computer Society, pp. 171-180, 2010...
Cyclic Railway Timetabling: a Stochastic Optimization Approach
L.G. Kroon (Leo); R. Dekker (Rommert); M.J.C.M. Vromans (Michiel)
2005-01-01
textabstractReal-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can absorb the stochastic disturbances as well as possible. To that end, a timetable contains buffer times
Stochastic Current of Bifractional Brownian Motion
Directory of Open Access Journals (Sweden)
Jingjun Guo
2014-01-01
Full Text Available We study the regularity of stochastic current defined as Skorohod integral with respect to bifractional Brownian motion through Malliavin calculus. Moreover, we similarly derive some results in the case of multidimensional multiparameter. Finally, we consider stochastic current of bifractional Brownian motion as a distribution in Watanabe spaces.
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation
Stochastic calculus for symmetric Markov processes
Chen, Z.-Q.; Fitzsimmons, P.J.; Kuwae, K; Zhang, T.-S.
2008-01-01
Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an It\\^{o} formula for Dirichlet processes is obtained.
Temperature stochastic modeling and weather derivatives pricing ...
African Journals Online (AJOL)
... over a sufficient period to apply a stochastic process that describes the evolution of the temperature. A numerical example of a swap contract pricing is presented, using an approximation formula as well as Monte Carlo simulations. Keywords: Weather derivatives, temperature stochastic model, Monte Carlo simulation.
Some Recent Developments in Ambit Stochastics
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Hedevang, Emil; Schmiegel, Jürgen
Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws...
Products of Generalized Stochastic Sarymsakov Matrices
Xia, Weiguo; Liu, Ji; Cao, Ming; Johansson, Karl; Basar, Tamer
2015-01-01
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the inﬁnitely long left-product of the elements from a compact subset converges to a rank-one matrix. In
Dynamics of a stochastically driven running sandpile
Becker, T; Eckhardt, B
1994-01-01
We analyze in detail a one-dimensional stochastically driven running sandpile. The dynamics shows three different phases, depending on the on-site relaxation rate and stochastic driving rate. Two phases are characterized by the presence of travelling waves. The third shows algebraic relaxation.
A stochastic Fubini theorem: BSDE method.
Wang, Yanqing
2017-01-01
In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short) which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.
A stochastic Fubini theorem: BSDE method
Directory of Open Access Journals (Sweden)
Yanqing Wang
2017-04-01
Full Text Available Abstract In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.
Löb, D; Lengert, N; Chagin, V O; Reinhart, M; Casas-Delucchi, C S; Cardoso, M C; Drossel, B
2016-04-07
DNA replication dynamics in cells from higher eukaryotes follows very complex but highly efficient mechanisms. However, the principles behind initiation of potential replication origins and emergence of typical patterns of nuclear replication sites remain unclear. Here, we propose a comprehensive model of DNA replication in human cells that is based on stochastic, proximity-induced replication initiation. Critical model features are: spontaneous stochastic firing of individual origins in euchromatin and facultative heterochromatin, inhibition of firing at distances below the size of chromatin loops and a domino-like effect by which replication forks induce firing of nearby origins. The model reproduces the empirical temporal and chromatin-related properties of DNA replication in human cells. We advance the one-dimensional DNA replication model to a spatial model by taking into account chromatin folding in the nucleus, and we are able to reproduce the spatial and temporal characteristics of the replication foci distribution throughout S-phase.
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
height from neighboring directional sectors. Numerical examples are presented where the models are calibrated using the Maximum Likelihood method to data from the central part of the North Sea. The calibration of the directional distributions is made such that the stochastic model for the omnidirectional...... maximum wave height is statistically consistent with the directional distribution functions. Finally, it is shown how the stochastic models can be used to estimate characteristic values and in reliability assessment of offshore structures....... velocity, and water level is presented. The stochastic model includes statistical uncertainty and dependency between the four stochastic variables. Further, a new stochastic model for annual maximum directional significant wave heights is presented. The model includes dependency between the maximum wave...
Stochastic resonance in noisy threshold neurons.
Kosko, Bart; Mitaim, Sanya
2003-01-01
Stochastic resonance occurs when noise improves how a nonlinear system performs. This paper presents two general stochastic-resonance theorems for threshold neurons that process noisy Bernoulli input sequences. The performance measure is Shannon mutual information. The theorems show that small amounts of independent additive noise can increase the mutual information of threshold neurons if the neurons detect subthreshold signals. The first theorem shows that this stochastic-resonance effect holds for all finite-variance noise probability density functions that obey a simple mean constraint that the user can control. A corollary shows that this stochastic-resonance effect occurs for the important family of (right-sided) gamma noise. The second theorem shows that this effect holds for all infinite-variance noise types in the broad family of stable distributions. Stable bell curves can model extremely impulsive noise environments. So the second theorem shows that this stochastic-resonance effect is robust against violent fluctuations in the additive noise process.
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
Noise-induced temporal dynamics in Turing systems
Schumacher, Linus J.
2013-04-25
We examine the ability of intrinsic noise to produce complex temporal dynamics in Turing pattern formation systems, with particular emphasis on the Schnakenberg kinetics. Using power spectral methods, we characterize the behavior of the system using stochastic simulations at a wide range of points in parameter space and compare with analytical approximations. Specifically, we investigate whether polarity switching of stochastic patterns occurs at a defined frequency. We find that it can do so in individual realizations of a stochastic simulation, but that the frequency is not defined consistently across realizations in our samples of parameter space. Further, we examine the effect of noise on deterministically predicted traveling waves and find them increased in amplitude and decreased in speed. © 2013 American Physical Society.
Scheuhammer, A.M.; Beyer, W.N.; Schmitt, C.J.; Jorgensen, Sven Erik; Fath, Brian D.
2008-01-01
Lead (Pb) is a naturally occurring metallic element; trace concentrations are found in all environmental media and in all living things. However, certain human activities, especially base metal mining and smelting; combustion of leaded gasoline; the use of Pb in hunting, target shooting, and recreational angling; the use of Pb-based paints; and the uncontrolled disposal of Pb-containing products such as old vehicle batteries and electronic devices have resulted in increased environmental levels of Pb, and have created risks for Pb exposure and toxicity in invertebrates, fish, and wildlife in some ecosystems.
FAST TRACK COMMUNICATION: Current fluctuations in stochastic systems with long-range memory
Harris, R. J.; Touchette, H.
2009-08-01
We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem.
Stochastic flow modeling : Quasi-Geostrophy, Taylor state and torsional wave excitation
DEFF Research Database (Denmark)
Gillet, Nicolas; Jault, D.; Finlay, Chris
We reconstruct the core flow evolution over the period 1840-2010 under the quasi-geostrophic assumption, from the stochastic magnetic field model COV-OBS and its full model error covariance matrix. We make use of a prior information on the flow temporal power spectrum compatible with that of obse...... variations from 1950 onward. We propose a triggering mechanism for these waves involving non-zonal motions in the framework of Taylor's state....
Polymyalgia rheumatica and temporal arthritis.
Epperly, T D; Moore, K E; Harrover, J D
2000-08-15
Polymyalgia rheumatica and temporal arteritis are closely related inflammatory conditions that affect different cellular targets in genetically predisposed persons. Compared with temporal arteritis, polymyalgla rheumatica is much more common, affecting one in 200 persons older than 50 years. Temporal arteritis, however, is more dangerous and can lead to sudden blindness. The diagnosis of polymyalgia rheumatica is based on the presence of a clinical syndrome consisting of fever, nonspecific somatic complaints, pain and stiffness in the shoulder and pelvic girdles, and an elevated erythrocyte sedimentation rate. Temporal arteritis typically presents with many of the same findings as polymyalgia rheumatica, but patients also have headaches and tenderness to palpation over the involved artery. Arterial biopsy usually confirms the diagnosis of temporal arteritis. Early diagnosis and treatment of polymyalgia rheumatica or temporal arteritis can dramatically improve patients' lives and return them to previous functional status. Corticosteroid therapy provides rapid and dramatic improvement of the clinical features of both conditions. Therapy is generally continued for six to 24 months. Throughout treatment, clinical condition is assessed periodically. Patients are instructed to see their physician immediately if symptoms recur or they develop new headache, jaw claudication or visual problems.
Effects of stochastic channel gating and distribution on the cardiac action potential.
Lemay, Mathieu; de Lange, Enno; Kucera, Jan P
2011-07-21
Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000ms) was essentially caused by stochastic channel gating of I(Ks), persistent I(Na) and I(Ca,L). In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling. Copyright © 2011 Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Bekker-Nielsen, Tønnes
2016-01-01
Through a systematic comparison of c. 50 careers leading to the koinarchate or high priesthood of Asia, Bithynia, Galatia, Lycia, Macedonia and coastal Pontus, as described in funeral or honorary inscriptions of individual koinarchs, it is possible to identify common denominators but also disting...
Pricing real estate index options under stochastic interest rates
Gong, Pu; Dai, Jun
2017-08-01
Real estate derivatives as new financial instruments are not merely risk management tools but also provide a novel way to gain exposure to real estate assets without buying or selling the physical assets. Although real estate derivatives market has exhibited a rapid development in recent years, the valuation challenge of real estate derivatives remains a great obstacle for further development in this market. In this paper, we derive a partial differential equation contingent on a real estate index in a stochastic interest rate environment and propose a modified finite difference method that adopts the non-uniform grids to solve this problem. Numerical results confirm the efficiency of the method and indicate that constant interest rate models lead to the mispricing of options and the effects of stochastic interest rates on option prices depend on whether the term structure of interest rates is rising or falling. Finally, we have investigated and compared the different effects of stochastic interest rates on European and American option prices.
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.
Bressloff, Paul C
2011-05-03
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.
Multiple-scale stochastic processes: Decimation, averaging and beyond
Bo, Stefano; Celani, Antonio
2017-02-01
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.
Considering inventory distributions in a stochastic periodic inventory routing system
Yadollahi, Ehsan; Aghezzaf, El-Houssaine
2017-07-01
Dealing with the stochasticity of parameters is one of the critical issues in business and industry nowadays. Supply chain planners have difficulties in forecasting stochastic parameters of a distribution system. Demand rates of customers during their lead time are one of these parameters. In addition, holding a huge level of inventory at the retailers is costly and inefficient. To cover the uncertainty of forecasting demand rates, researchers have proposed the usage of safety stock to avoid stock-out. However, finding the precise level of safety stock depends on forecasting the statistical distribution of demand rates and their variations in different settings among the planning horizon. In this paper the demand rate distributions and its parameters are taken into account for each time period in a stochastic periodic IRP. An analysis of the achieved statistical distribution of the inventory and safety stock level is provided to measure the effects of input parameters on the output indicators. Different values for coefficient of variation are applied to the customers' demand rate in the optimization model. The outcome of the deterministic equivalent model of SPIRP is simulated in form of an illustrative case.
Wolff, J.; Jankov, I.; Beck, J.; Carson, L.; Frimel, J.; Harrold, M.; Jiang, H.
2016-12-01
, allowing for a more extensive set of tests over multiple seasons, consequently leading to more robust results. Through the use of these stochastic innovations and powerful supercomputing at NCAR, further insights and advancements in ensemble forecasting at convection-permitting scales will be possible.
A Stochastic-Variational Model for Soft Mumford-Shah Segmentation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented.
Stochastic processes dominate during boreal bryophyte community assembly.
Fenton, Nicole J; Bergeron, Yves
2013-09-01
Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of
Stochastic analysis of complex reaction networks using binomial moment equations
Barzel, Baruch; Biham, Ofer
2012-09-01
The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.150602 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.
Full particle orbit effects in regular and stochastic magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France); Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); Castillo-Negrete, Diego del [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States); Dif-Pradalier, Guilhem; Garbet, Xavier [CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France)
2016-07-15
We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the
Stochastic analysis of complex reaction networks using binomial moment equations.
Barzel, Baruch; Biham, Ofer
2012-09-01
The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.
Stochastic dynamics of genetic broadcasting networks
Potoyan, Davit A.; Wolynes, Peter G.
2017-11-01
The complex genetic programs of eukaryotic cells are often regulated by key transcription factors occupying or clearing out of a large number of genomic locations. Orchestrating the residence times of these factors is therefore important for the well organized functioning of a large network. The classic models of genetic switches sidestep this timing issue by assuming the binding of transcription factors to be governed entirely by thermodynamic protein-DNA affinities. Here we show that relying on passive thermodynamics and random release times can lead to a "time-scale crisis" for master genes that broadcast their signals to a large number of binding sites. We demonstrate that this time-scale crisis for clearance in a large broadcasting network can be resolved by actively regulating residence times through molecular stripping. We illustrate these ideas by studying a model of the stochastic dynamics of the genetic network of the central eukaryotic master regulator NFκ B which broadcasts its signals to many downstream genes that regulate immune response, apoptosis, etc.
Extending Newtonian Dynamics to Include Stochastic Processes
Zak, Michail
2009-01-01
A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.
Minimum Entropy Rate Simplification of Stochastic Processes.
Henter, Gustav Eje; Kleijn, W Bastiaan
2016-12-01
We propose minimum entropy rate simplification (MERS), an information-theoretic, parameterization-independent framework for simplifying generative models of stochastic processes. Applications include improving model quality for sampling tasks by concentrating the probability mass on the most characteristic and accurately described behaviors while de-emphasizing the tails, and obtaining clean models from corrupted data (nonparametric denoising). This is the opposite of the smoothing step commonly applied to classification models. Drawing on rate-distortion theory, MERS seeks the minimum entropy-rate process under a constraint on the dissimilarity between the original and simplified processes. We particularly investigate the Kullback-Leibler divergence rate as a dissimilarity measure, where, compatible with our assumption that the starting model is disturbed or inaccurate, the simplification rather than the starting model is used for the reference distribution of the divergence. This leads to analytic solutions for stationary and ergodic Gaussian processes and Markov chains. The same formulas are also valid for maximum-entropy smoothing under the same divergence constraint. In experiments, MERS successfully simplifies and denoises models from audio, text, speech, and meteorology.
Loizou, Nicolas
2017-12-27
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.
Records in fractal stochastic processes.
Aliakbari, A; Manshour, P; Salehi, M J
2017-03-01
The record statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions, the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes; otherwise, it has no impact on the record statistics.
Nonparametric weighted stochastic block models
Peixoto, Tiago P.
2018-01-01
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...... an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite...... positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order...
Classical and stochastic Laplacian growth
Gustafsson, Björn; Vasil’ev, Alexander
2014-01-01
This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive biblio...
Classical and Quantum Stochastic Resonance
Hänggi, Peter
1996-03-01
The idea that noise can assist the formation of order might sound paradoxical but does indeed occur in nonlinear systems with the phenomenon of Stochastic Resonance (SR)(F. Moss et al., Stochastic Resonance: Tutorial and Update), Int. J. Bif. and Chaos 4, 1383 (1994); K. Wiesenfeld and F. Moss, Nature 373, 33 (1995); P. Jung, Phys. Rep. 234 C, 175 (1993). This term is given to the effect where the detection of weak periodic signals is enhanced in presence of noise activated crossings of barriers or threshold levels. After introducing the audience into the common characterization of SR by use of the power spectrum of the output signal and/or the probability density of correponding residence times, I shall report new features for nonlinear SR where strong driving can give rise to anomalous amplification of higher harmonics, hole-burning in power spectra, or SR-induced, almost complete deletion of higher harmonics(R. Bartussek, P. Jung, P. Hänggi, Phys. Rev. E49), 3930 (1994); V. Shneidman, P. Jung, P. Hänggi, Phys. Rev. Lett. 72, 2682 (1994). These novel effects have recently been confirmed experimentally in a magnetic flux driven sensitive detection device (superconducting quantum-interference device)(R. Rouse, S. Han, J.E. Lukens, Appl. Phys. Lett. 66), 108 (1995). This device constitutes a macroscopic quantum system where with decreasing temperature quantum tunneling transitions begin to modify and blur the classical SR-responce. Recent progress in the quest of SR phenomena in the deep quantum regime(M. Grifoni and P. Hänggi, submitted to PRL) is reviewed together with experimental proposals where Quantum-SR induced manipulation of individual atoms, or whole molecular groups, can be observed.
Space-time-modulated stochastic processes
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Towards General Temporal Aggregation
DEFF Research Database (Denmark)
Boehlen, Michael H.; Gamper, Johann; Jensen, Christian Søndergaard
2008-01-01
Most database applications manage time-referenced, or temporal, data. Temporal data management is difficult when using conventional database technology, and many contributions have been made for how to better model, store, and query temporal data. Temporal aggregation illustrates well the problem...
Who Leads China's Leading Universities?
Huang, Futao
2017-01-01
This study attempts to identify the major characteristics of two different groups of institutional leaders in China's leading universities. The study begins with a review of relevant literature and theory. Then, there is a brief introduction to the selection of party secretaries, deputy secretaries, presidents and vice presidents in leading…
Badenhorst, Werner; Hanekom, Tania; Hanekom, Johan J
2017-12-01
The study presents the application of a purely conductance-based stochastic nerve fibre model to human auditory nerve fibres within finite element volume conduction models of a semi-generic head and user-specific cochleae. The stochastic, threshold and temporal characteristics of the human model are compared and successfully validated against physiological feline results with the application of a mono-polar, bi-phasic, cathodic first stimulus. Stochastic characteristics validated include: (i) the log(Relative Spread) versus log(fibre diameter) distribution for the discharge probability versus stimulus intensity plots and (ii) the required exponential membrane noise versus transmembrane voltage distribution. Intra-user, and to a lesser degree inter-user, comparisons are made with respect to threshold and dynamic range at short and long pulse widths for full versus degenerate single fibres as well as for populations of degenerate fibres of a single user having distributed and aligned somas with varying and equal diameters. Temporal characteristics validated through application of different stimulus pulse rates and different stimulus intensities include: (i) discharge rate, latency and latency standard deviation versus stimulus intensity, (ii) period histograms and (iii) interspike interval histograms. Although the stochastic population model does not reduce the modelled single deterministic fibre threshold, the simulated stochastic and temporal characteristics show that it could be used in future studies to model user-specific temporally encoded information, which influences the speech perception of CI users.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon
2014-07-01
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.
Dynamic analysis of a stochastic rumor propagation model
Jia, Fangju; Lv, Guangying
2018-01-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
Unexpectedly wide distributions in the stochastic synthesis of functionalized nanoparticles.
Waddell, Jack; Mullen, Douglas; Orr, Bradford; Banaszak Holl, Mark; Sander, Leonard
2009-03-01
Functionalized nanoparticles are promising devices with a variety of applications, such as the targeted delivery of chemotherapy drugs to cancer cells. Their properties depend on the specifics of the distribution of functional groups on the nanoparticle. Stochastic ligand conjugation is an efficient strategy for synthesizing large quantities of functionalized nanoparticles. We developed a kinetic model for the study of ligand distribution on a generation 5 poly(amidoamine) dendrimer, as measured by HPLC and SPR. We found a cooperative effect in single species ligation, leading to a broader-than-Poisson distribution of ligands on nanoparticles, and suggesting a high spatial correlation of functional groups.
Effective cosmological constant induced by stochastic fluctuations of Newton's constant
Directory of Open Access Journals (Sweden)
Marco de Cesare
2016-09-01
Full Text Available We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector.
Stochastic Subspace Method for Experimental Modal Analysis
Directory of Open Access Journals (Sweden)
Liu Dazhi
2016-01-01
Full Text Available The formula of stochastic subspace identification method is deduced in details and the program is written out. The two methods are verified by a vibration test on a 5-floor rigid frame model. In this test the gauss white noise generated from a shaker table to simulate the ambient vibration on the model, and the response signals are measured. Next, the response data of experiment are processed by auto-cross spectrum density method and stochastic subspace identification method respectively, the two methods are verified by comparing with the theory result. and bearing out the superiority of stochastic subspace identification method compared to auto-cross spectrum density method.
CAM Stochastic Volatility Model for Option Pricing
Directory of Open Access Journals (Sweden)
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Stochastic processes for line shapes and intensities
Stamm, R.; Hammami, R.; Hannachi, I.; Capes, H.; Godbert-Mouret, L.; Koubiti, M.; Marandet, Y.; Rosato, J.
2014-10-01
Stochastic processes provide flexible and fast calculations for modeling dynamical interactions between an atom and charged particles. We use a stochastic renewal process for the plasma microfield being the cause of Stark broadening. The accuracy and improvement possibilities of Lyman profiles calculations with a renewal process are analyzed by comparing to ab initio simulations for ion broadening only. Stochastic processes may also be applied to out of equilibrium plasmas. We present our first results for the effect of Langmuir waves on a line broadened by electrons only, and for the changes of atomic populations submitted to strong temperature fluctuations.
Stochastic transition model for pedestrian dynamics
Schultz, Michael
2012-01-01
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.
Selected papers on noise and stochastic processes
1954-01-01
Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Permanence of Stochastic Lotka-Volterra Systems
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Asymptotic analysis for functional stochastic differential equations
Bao, Jianhai; Yuan, Chenggui
2016-01-01
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Stochastic differential equations and diffusion processes
Ikeda, N
1989-01-01
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio
Coding of multisensory temporal patterns in human superior temporal sulcus
Directory of Open Access Journals (Sweden)
Toemme eNoesselt
2012-08-01
Full Text Available Philosophers, psychologists, and neuroscientists have long been interested in how the temporal aspects of perception are represented in the brain. In the present study, we investigated the neural basis of the temporal perception of synchrony/asynchrony for audiovisual speech stimuli using functional magnetic imaging (fMRI. Subjects judged the temporal relation of (asynchronous audiovisual speech streams, and indicated any changes in their perception of the stimuli over time. Differential hemodynamic responses for synchronous versus asynchronous stimuli were observed in the multisensory superior temporal sulcus complex (mSTS-c and prefrontal cortex. Within mSTS-c we found adjacent regions expressing an enhanced BOLD-response to the different physical (asynchrony conditions. These regions were further modulated by the subjects’ perceptual state. By calculating the distances between the modulated regions within mSTS-c in single-subjects we demonstrate that the ‘auditory’ and ‘visual leading areas’ lie closer to ‘synchrony areas’ than to each other. Moreover, analysis of interregional connectivity indicates a stronger functional connection between multisensory prefrontal cortex and mSTS-c during the perception of asynchrony. Taken together, these results therefore suggest the presence of distinct sub-regions within the human STS-c for the maintenance of temporal relations for audiovisual speech stimuli plus differential functional connectivity with prefrontal regions. The respective local activity in mSTS-c is dependent both upon the physical properties of the stimuli presented and upon the subjects’ perception of (asynchrony.
Model of an excitatory synapse based on stochastic processes.
L'Espérance, Pierre-Yves; Labib, Richard
2013-09-01
We present a mathematical model of a biological synapse based on stochastic processes to establish the temporal behavior of the postsynaptic potential following a quantal synaptic transmission. This potential form is the basis of the neural code. We suppose that the release of neurotransmitters in the synaptic cleft follows a Poisson process, and that they diffuse according to integrated Ornstein-Uhlenbeck processes in 3-D with random initial positions and velocities. The diffusion occurs in an isotropic environment between two infinite parallel planes representing the pre- and postsynaptic membrane. We state that the presynaptic membrane is perfectly reflecting and that the other is perfectly absorbing. The activation of the receptors polarizes the postsynaptic membrane according to a parallel RC circuit scheme. We present the results obtained by simulations according to a Gillespie algorithm and we show that our model exhibits realistic postsynaptic behaviors from a simple quantal occurrence.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes
García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
The Apriori Stochastic Dependency Detection (ASDD) algorithm for learning Stochastic logic rules
Child, C. H. T.; Stathis, K.
2005-01-01
Apriori Stochastic Dependency Detection (ASDD) is an algorithm for fast induction of stochastic logic rules from a database of observations made by an agent situated in an environment. ASDD is based on features of the Apriori algorithm for mining association rules in large databases of sales transactions [1] and the MSDD algorithm for discovering stochastic dependencies in multiple streams of data [15]. Once these rules have been acquired the Precedence algorithm assigns operator precedence w...
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Sinitsyn, Nikolai [Los Alamos National Laboratory
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut
Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on genera...... and to probability and L\\'{e}vy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given....
Schilde, M.; Doerner, K.F.; Hartl, R.F.
2014-01-01
In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013
An investigation of setup instability in non-stationary stochastic inventory systems
Kilic, Onur A.; Tarim, S. Armagan
In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments,
Approximating stochastic biochemical processes with Wasserstein pseudometrics.
Thorsley, D; Klavins, E
2010-05-01
Modelling stochastic processes inside the cell is difficult due to the size and complexity of the processes being investigated. As a result, new approaches are needed to address the problems of model reduction, parameter estimation, model comparison and model invalidation. Here, the authors propose addressing these problems by using Wasserstein pseudometrics to quantify the differences between processes. The method the authors propose is applicable to any bounded continuous-time stochastic process and pseudometrics between processes are defined only in terms of the available outputs. Algorithms for approximating Wasserstein pseudometrics are developed from experimental or simulation data and demonstrate how to optimise parameter values to minimise the pseudometrics. The approach is illustrated with studies of a stochastic toggle switch and of stochastic gene expression in E. coli.
Synchronization of noisy systems by stochastic signals
Energy Technology Data Exchange (ETDEWEB)
Neiman, A.; Schimansky-Geier, L.; Moss, F. [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Schimansky-Geier, L. [Institute of Physics, Humboldt University at Berlin, Invalidenstrasse 110, D-10115 Berlin (Germany); Shulgin, B.; Collins, J.J. [Center for BioDynamics and Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215 (United States)
1999-07-01
We study, in terms of synchronization, the {ital nonlinear response} of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level{emdash}this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train. {copyright} {ital 1999} {ital The American Physical Society}
Stochastic Thermodynamics: A Dynamical Systems Approach
Directory of Open Access Journals (Sweden)
Tanmay Rajpurohit
2017-12-01
Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.
Perspective: Stochastic algorithms for chemical kinetics.
Gillespie, Daniel T; Hellander, Andreas; Petzold, Linda R
2013-05-07
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
Stochastic integral representations of quantum martingales on ...
Indian Academy of Sciences (India)
Abstract. In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales and those of the author to multidimensions.
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
Moment Closure for the Stochastic Logistic Model
National Research Council Canada - National Science Library
Singh, Abhyudai; Hespanha, Joao P
2006-01-01
..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...
Communication: Embedded fragment stochastic density functional theory
Energy Technology Data Exchange (ETDEWEB)
Neuhauser, Daniel, E-mail: dxn@chem.ucla.edu [Department of Chemistry, University of California at Los Angeles, Los Angeles, California 90095 (United States); Baer, Roi, E-mail: roi.baer@huji.ac.il [Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Rabani, Eran, E-mail: eran.rabani@gmail.com [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Extending Stochastic Network Calculus to Loss Analysis
Directory of Open Access Journals (Sweden)
Chao Luo
2013-01-01
Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Stochastic development regression using method of moments
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
This paper considers the estimation problem arising when inferring parameters in the stochastic development regression model for manifold valued non-linear data. Stochastic development regression captures the relation between manifold-valued response and Euclidean covariate variables using...... the stochastic development construction. It is thereby able to incorporate several covariate variables and random effects. The model is intrinsically defined using the connection of the manifold, and the use of stochastic development avoids linearizing the geometry. We propose to infer parameters using...... the Method of Moments procedure that matches known constraints on moments of the observations conditional on the latent variables. The performance of the model is investigated in a simulation example using data on finite dimensional landmark manifolds....
MODELLING OF A STOCHASTIC CONTINUOUS SYSTEM
Directory of Open Access Journals (Sweden)
Martin Albertyn
2012-01-01
Full Text Available The key objective is to develop a method which can be utilized to model a stochastic continuous system. A system from the "real world" is used as the basis for the simulation modelling technique that is presented. The conceptualization phase indicates that the model has to incorporate stochastic and deterministic elements. A method is developed that utilizes the discrete simulation ability of a stochastic package (ARENA, in conjunction with a deterministic package (FORTRAN, to model the continuous system. (Software packages tend to specialize in either stochastic, or deterministic modelling. The length of the iteration time interval and adequate sample size are investigated. The method is authenticated by the verification and validation ofthe defined model. Two scenarios are modelled and the results are discussed . Conclusions are presented and strengths and weaknesses of this method are considered and discussed .
A Stochastic Approach to Stereo Vision
National Research Council Canada - National Science Library
Barnard, Stephen T
1986-01-01
A stochastic optimization approach to stereo matching is presented. Unlike conventional correlation matching and feature matching, the approach provides a dense array of disparities, eliminating the need for interpolation...
Evolutionary stability concepts in a stochastic environment
Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi
2017-09-01
Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.
Stochastic differential equation model to Prendiville processes
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic population dynamics in spatially extended predator–prey systems
Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.
2018-02-01
Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator–prey competition invalidates the neutral Lotka–Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator–prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi–Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May–Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a
Stochastic Modeling of Soil Salinity
Suweis, Samir; Rinaldo, Andrea; van der Zee, Sjoerd E. A. T. M.; Maritan, Amos; Porporato, Amilcare
2010-05-01
Large areas of cultivated land worldwide are affected by soil salinity. Estimates report that 10% of arable land in over 100 countries, and nine million km2 are salt affected, especially in arid and semi-arid regions. High salinity causes both ion specific and osmotic stress effects, with important consequences for plant production and quality. Salt accumulation in the root zone may be due to natural factors (primary salinization) or due to irrigation (secondary salinization). Simple (e.g., vertically averaged over the soil depth) coupled soil moisture and salt balance equations have been used in the past. Despite their approximations, these models have the advantage of parsimony, thus allowing a direct analysis of the interplay of the main processes. They also provide the ideal starting point to include external, random hydro-climatic fluctuations in the analysis of long-term salinization trends. We propose a minimalist stochastic model of primary soil salinity, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long-term soil salinization. In fact, soil salinity statistics are obtained as a function of climate, soil and vegetation parameters. These, in turn, can be combined with soil moisture statistics to obtain a full characterization of soil salt concentrations and the ensuing risk of primary salinization. In particular, the solutions show the existence of two quite distinct regimes, the first one where the mean salt mass remains nearly constant with increasing rainfall frequency, and the
The stochastic edge in adaptive evolution
Brunet, Éric; Rouzine, Igor M.; Wilke, Claus O
2007-01-01
In a recent article, Desai and Fisher (2007) proposed that the speed of adaptation in an asexual population is determined by the dynamics of the stochastic edge of the population, that is, by the emergence and subsequent establishment of rare mutants that exceed the fitness of all sequences currently present in the population. Desai and Fisher perform an elaborate stochastic calculation of the mean time $\\tau$ until a new class of mutants has been established, and interpret $1/\\tau$ as the sp...