Bogen, K T
2007-05-11
pharmacokinetic and 2 harmacokinetic 2-stage stochastic carcinogenesis modeling results all clearly indicate that naphthalene is a DMOA carcinogen. Plausibility bounds on rat rat-tumor tumor-type specific DMOA DMOA-related uncertainty were obtained using a 2-stage model adapted to reflec reflect the empirical link between genotoxic and cytotoxic effects of t the most potent identified genotoxic naphthalene metabolites, 1,2 1,2- and 1,4 1,4-naphthoquinone. Bound Bound-specific 'adjustment' factors were then used to reduce naphthalene risk estimated by linear ex extrapolation (under the default genotoxic MOA assumption), to account for the DMOA trapolation exhibited by this compound.
Bogen, K T
2007-01-30
As reflected in the 2005 USEPA Guidelines for Cancer Risk Assessment, some chemical carcinogens may have a site-specific mode of action (MOA) that is dual, involving mutation in addition to cell-killing induced hyperplasia. Although genotoxicity may contribute to increased risk at all doses, the Guidelines imply that for dual MOA (DMOA) carcinogens, judgment be used to compare and assess results obtained using separate ''linear'' (genotoxic) vs. ''nonlinear'' (nongenotoxic) approaches to low-level risk extrapolation. However, the Guidelines allow the latter approach to be used only when evidence is sufficient to parameterize a biologically based model that reliably extrapolates risk to low levels of concern. The Guidelines thus effectively prevent MOA uncertainty from being characterized and addressed when data are insufficient to parameterize such a model, but otherwise clearly support a DMOA. A bounding factor approach--similar to that used in reference dose procedures for classic toxicity endpoints--can address MOA uncertainty in a way that avoids explicit modeling of low-dose risk as a function of administered or internal dose. Even when a ''nonlinear'' toxicokinetic model cannot be fully validated, implications of DMOA uncertainty on low-dose risk may be bounded with reasonable confidence when target tumor types happen to be extremely rare. This concept was illustrated for the rodent carcinogen naphthalene. Bioassay data, supplemental toxicokinetic data, and related physiologically based pharmacokinetic and 2-stage stochastic carcinogenesis modeling results all clearly indicate that naphthalene is a DMOA carcinogen. Plausibility bounds on rat-tumor-type specific DMOA-related uncertainty were obtained using a 2-stage model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Resulting
Stochastic dynamics of cancer initiation
Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population
A stochastic model for immunotherapy of cancer.
Baar, Martina; Coquille, Loren; Mayer, Hannah; Hölzel, Michael; Rogava, Meri; Tüting, Thomas; Bovier, Anton
2016-01-01
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations. PMID:27063839
Gompertzian stochastic model with delay effect to cervical cancer growth
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits
Gompertzian stochastic model with delay effect to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
RECENT DEVELOPMENTS ON TESTING IN CANCER RISK: A FRACTAL AND STOCHASTIC GEOMETRY
M. Stehlík
2012-01-01
Full Text Available The aim of this paper is to discuss recent development on testing in cancer risk. Weconsider both area of fractal and stochastic geometry based cancer. We introduce the exactdistributions of the likelihood ratio tests of several recently used tests and discuss their properties.We also show possibility of testing for cancer using some stochastic geometry descriptors. Testsfor some new stochastic models in cancer risk are also given.
STOCHASTIC MODELS FOR OPTIMAL DRUG ADMINISTRATION IN CANCER CHEMOTHERAPY
Tirupathi Rao. P
2010-05-01
Full Text Available Stochastic models play a prominent role in analysis and designing of processes at various places like, biological, physical, medical and other areas. One of the important areas of concentration in medical sciences is developing optimal operating strategies for drug administration in chronic diseases like, Cancer, TB, Leprosy etc. In this paper, we develop a suitable stochastic model for optimal drug administration in cancer chemotherapy problem. The analysis for drug administration period is discussed. The sensitivity of the model with respect to the parameters is also studied with numerical llustrations. Average time for mutant cell duration in the tumor during the drug administration and absence of drug spells are derived. This study is very much useful for health care takers.Developing software and automation of these models will make this work more user friendly.
Kerns, Sarah L. [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); Departments of Pathology and Genetics, Albert Einstein College of Medicine, Bronx, New York (United States); Stock, Richard [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); Stone, Nelson [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); Department of Urology, Mount Sinai School of Medicine, New York, New York (United States); Buckstein, Michael [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); Shao, Yongzhao [Division of Biostatistics, New York University School of Medicine, New York, New York (United States); Campbell, Christopher [Departments of Pathology and Genetics, Albert Einstein College of Medicine, Bronx, New York (United States); Rath, Lynda [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); De Ruysscher, Dirk; Lammering, Guido [Department of Radiation Oncology, Maastricht University Medical Center, Maastricht (Netherlands); Hixson, Rosetta; Cesaretti, Jamie; Terk, Mitchell [Florida Radiation Oncology Group, Jacksonville, Florida (United States); Ostrer, Harry [Departments of Pathology and Genetics, Albert Einstein College of Medicine, Bronx, New York (United States); Rosenstein, Barry S., E-mail: barry.rosenstein@mssm.edu [Department of Radiation Oncology, Mount Sinai School of Medicine, New York, New York (United States); Department of Radiation Oncology, New York University School of Medicine, New York, New York (United States); Departments of Dermatology and Preventive Medicine, Mount Sinai School of Medicine, New York, New York (United States)
2013-01-01
Purpose: To identify single nucleotide polymorphisms (SNPs) associated with development of erectile dysfunction (ED) among prostate cancer patients treated with radiation therapy. Methods and Materials: A 2-stage genome-wide association study was performed. Patients were split randomly into a stage I discovery cohort (132 cases, 103 controls) and a stage II replication cohort (128 cases, 102 controls). The discovery cohort was genotyped using Affymetrix 6.0 genome-wide arrays. The 940 top ranking SNPs selected from the discovery cohort were genotyped in the replication cohort using Illumina iSelect custom SNP arrays. Results: Twelve SNPs identified in the discovery cohort and validated in the replication cohort were associated with development of ED following radiation therapy (Fisher combined P values 2.1 Multiplication-Sign 10{sup -5} to 6.2 Multiplication-Sign 10{sup -4}). Notably, these 12 SNPs lie in or near genes involved in erectile function or other normal cellular functions (adhesion and signaling) rather than DNA damage repair. In a multivariable model including nongenetic risk factors, the odds ratios for these SNPs ranged from 1.6 to 5.6 in the pooled cohort. There was a striking relationship between the cumulative number of SNP risk alleles an individual possessed and ED status (Sommers' D P value = 1.7 Multiplication-Sign 10{sup -29}). A 1-allele increase in cumulative SNP score increased the odds for developing ED by a factor of 2.2 (P value = 2.1 Multiplication-Sign 10{sup -19}). The cumulative SNP score model had a sensitivity of 84% and specificity of 75% for prediction of developing ED at the radiation therapy planning stage. Conclusions: This genome-wide association study identified a set of SNPs that are associated with development of ED following radiation therapy. These candidate genetic predictors warrant more definitive validation in an independent cohort.
Purpose: To identify single nucleotide polymorphisms (SNPs) associated with development of erectile dysfunction (ED) among prostate cancer patients treated with radiation therapy. Methods and Materials: A 2-stage genome-wide association study was performed. Patients were split randomly into a stage I discovery cohort (132 cases, 103 controls) and a stage II replication cohort (128 cases, 102 controls). The discovery cohort was genotyped using Affymetrix 6.0 genome-wide arrays. The 940 top ranking SNPs selected from the discovery cohort were genotyped in the replication cohort using Illumina iSelect custom SNP arrays. Results: Twelve SNPs identified in the discovery cohort and validated in the replication cohort were associated with development of ED following radiation therapy (Fisher combined P values 2.1 × 10−5 to 6.2 × 10−4). Notably, these 12 SNPs lie in or near genes involved in erectile function or other normal cellular functions (adhesion and signaling) rather than DNA damage repair. In a multivariable model including nongenetic risk factors, the odds ratios for these SNPs ranged from 1.6 to 5.6 in the pooled cohort. There was a striking relationship between the cumulative number of SNP risk alleles an individual possessed and ED status (Sommers’ D P value = 1.7 × 10−29). A 1-allele increase in cumulative SNP score increased the odds for developing ED by a factor of 2.2 (P value = 2.1 × 10−19). The cumulative SNP score model had a sensitivity of 84% and specificity of 75% for prediction of developing ED at the radiation therapy planning stage. Conclusions: This genome-wide association study identified a set of SNPs that are associated with development of ED following radiation therapy. These candidate genetic predictors warrant more definitive validation in an independent cohort.
Wang, Weikang; Quan, Yi; Fu, Qibin; Liu, Yu; Liang, Ying; Wu, Jingwen; Yang, Gen; Luo, Chunxiong; Ouyang, Qi; Wang, Yugang
2014-01-01
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy. PMID:24416258
Weikang Wang
Full Text Available Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy.
Castellanos-Moreno, Arnulfo; Corella-Madueño, Adalberto; Gutiérrez-López, Sergio; Rosas-Burgos, Rodrigo
2014-01-01
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into account natural birth and death rates. Other rates are also introduced to consider medical treatment: natural birth rate of lymphocytes and cancer cells; induced death rate of cancer cells due to self-competition, and other ones caused by the activated lymphocytes acting on cancer cells. Additionally, a death rate of cancer cells due to induced apoptosis is considered. Weakness due to the advance of sickness is considered by introducing a lymphocytes death rate proportional to proliferation of cancer cells. Simulation is developed considering different combinations of the parameters and its values, so that several strategies are taken into account to study the effect of anti-angiogenic drugs as well the self-competition between cancer cells. Immune response, with the presence ...
Figueredo, Grazziela P.; Peer-Olaf Siebers; Owen, Markus R.; Jenna Reps; Uwe Aickelin
2014-01-01
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation w...
Wang, Weikang; Quan, Yi; Fu, Qibin; Liu, Yu; Liang, Ying; Wu, Jingwen; Yang, Gen; Luo, Chunxiong; Ouyang, Qi; Wang, Yugang
2014-01-01
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities ...
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.
Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model
Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe
2013-10-01
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest—a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.
Zamani Dahaj, Seyed Alireza; Kumar, Niraj; Sundaram, Bala; Celli, Jonathan; Kulkarni, Rahul
The phenotypic heterogeneity of cancer cells is critical to their survival under stress. A significant contribution to heterogeneity of cancer calls derives from the epithelial-mesenchymal transition (EMT), a conserved cellular program that is crucial for embryonic development. Several studies have investigated the role of EMT in growth of early stage tumors into invasive malignancies. Also, EMT has been closely associated with the acquisition of chemoresistance properties in cancer cells. Motivated by these studies, we analyze multi-phenotype stochastic models of the evolution of cancers cell populations under stress. We derive analytical results for time-dependent probability distributions that provide insights into the competing rates underlying phenotypic switching (e.g. during EMT) and the corresponding survival of cancer cells. Experimentally, we evaluate these model-based predictions by imaging human pancreatic cancer cell lines grown with and without cytotoxic agents and measure growth kinetics, survival, morphological changes and (terminal evaluation of) biomarkers with associated epithelial and mesenchymal phenotypes. The results derived suggest approaches for distinguishing between adaptation and selection scenarios for survival in the presence of external stresses.
Stochasticity in Physiologically Based Kinetics Models : implications for cancer risk assessment
Pery, Alexandre; Bois, Frédéric Y.
2009-01-01
International audience In case of low-dose exposure to a substance, its concentration in cells is likely to be stochastic. Assessing the consequences of this stochasticity in toxicological risk assessment requires the coupling of macroscopic dynamics models describing whole-body kinetics with microscopic tools designed to simulate stochasticity. In this article, we propose an approach to approximate stochastic cell concentration of butadiene in the cells of diverse organs. We adapted the d...
A stochastic Markov chain model to describe lung cancer growth and metastasis.
Paul K Newton
Full Text Available A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold. Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.
L. G. Hanin
2002-01-01
Full Text Available A general framework for solving identification problem for a broad class of deterministic and stochastic models is discussed. This methodology allows for a unified approach to studying identifiability of various stochastic models arising in biology and medicine including models of spontaneous and induced Carcinogenesis, tumor progression and detection, and randomized hit and target models of irradiated cell survival. A variety of known results on parameter identification for stochastic models is reviewed and several new results are presented with an emphasis on rigorous mathematical development.
Mattfeldt, T; Gottfried, H; Schmidt, V; Kestler, H A
2000-05-01
Stereology and stochastic geometry can be used as auxiliary tools for diagnostic purposes in tumour pathology. Whether first-order parameters or stochastic-geometric functions are more important for the classification of the texture of biological tissues is not known. In the present study, volume and surface area per unit reference volume, the pair correlation function and the centred quadratic contact density function of epithelium were estimated in three case series of benign and malignant lesions of glandular tissues. The information provided by the latter functions was summarized by the total absolute areas between the estimated curves and their horizontal reference lines. These areas are considered as indicators of deviation of the tissue texture from a completely uncorrelated volume process and from the Boolean model with convex grains, respectively. We used both areas and the first-order parameters for the classification of cases using artificial neural networks (ANNs). Learning vector quantization and multilayer feedforward networks with backpropagation were applied as neural paradigms. Applications included distinction between mastopathy and mammary cancer (40 cases), between benign prostatic hyperplasia and prostatic cancer (70 cases) and between chronic pancreatitis and pancreatic cancer (60 cases). The same data sets were also classified with linear discriminant analysis. The stereological estimates in combination with ANNs or discriminant analysis provided high accuracy in the classification of individual cases. The question of which category of estimator is the most informative cannot be answered globally, but must be explored empirically for each specific data set. Using learning vector quantization, better results could often be obtained than by multilayer feedforward networks with backpropagation. PMID:10810010
Stochastic volatility and stochastic leverage
Veraart, Almut; Veraart, Luitgard A. M.
2009-01-01
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 correlationparameter between the asset return and the stochastic volatility process. We provide a systematictreatment 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 analyticallytractable and allo...
Stochastic volatility and stochastic leverage
Veraart, Almut; Veraart, Luitgard A. M.
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......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...
This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio RSNR is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength λ and the delay time τ on RSNR are respectively discussed. The existence of a peak in the curves of RSNR as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that λ and τ play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing λ whereas it is enhanced with the increase of τ, which is different from the case where the periodic signal is additive. (general)
A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer
Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxels on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer
Ohira, Toru
2006-01-01
We present a simple dynamical model to address the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the "space" variable, which is opposite to the normal description of stochastic dynamics. The notable feature is that these models can induce a "resonance" with varying noise strength in the time variable. Thus, they provide a different mechanism for stochastic resonance, which has been discussed within the normal context ...
Parzen, Emanuel
2015-01-01
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
Evaluation of 2-Stage Injection Technique in Children.
Sandeep, Valasingam; Kumar, Manikya; Jyostna, P; Duggi, Vijay
2016-01-01
Effective pain control during local anesthetic injection is the cornerstone of behavior guidance in pediatric dentistry. The aim of this study was to evaluate the practical efficacy of a 2-stage injection technique in reducing injection pain in children. This was a split-mouth, randomized controlled crossover trial. One hundred cooperative children aged 7 to 13 years in need of bilateral local anesthetic injections (inferior alveolar nerve block, posterior superior alveolar nerve block, or maxillary and mandibular buccal infiltrations) for restorative, endodontic, and extraction treatments were recruited for the study. Children were randomly allocated to receive either the 2-stage injection technique or conventional technique at the first appointment. The other technique was used at the successive visit after 1 week. Subjective and objective evaluation of pain was done using the Wong-Baker FACES Pain Rating Scale (FPS) and Sound Eye Motor (SEM) scale, respectively. The comparison of pain scores was done by Wilcoxon sign-rank test. Both FPS and SEM scores were significantly lower when the 2-stage injection technique of local anesthetic nerve block/infiltration was used compared with the conventional technique. The 2-stage injection technique is a simple and effective means of reducing injection pain in children. PMID:26866405
Hu, B. L. (Bei-Lok)
1999-01-01
We give a summary of the status of current research in stochastic semiclassical gravity and suggest directions for further investigations. This theory generalizes the semiclassical Einstein equation to an Einstein-Langevin equation with a stochastic source term arising from the fluctuations of the energy-momentum tensor of quantum fields. We mention recent efforts in applying this theory to the study of black hole fluctuations and backreaction problems, linear response of hot flat space, and ...
Schneider, Johannes J
2007-01-01
This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.
Xiaohong Li
2011-02-01
Full Text Available Aside from primary prevention, early detection remains the most effective way to decrease mortality associated with the majority of solid cancers. Previous cancer screening models are largely based on classification of at-risk populations into three conceptually defined groups (normal, cancer without symptoms, and cancer with symptoms. Unfortunately, this approach has achieved limited successes in reducing cancer mortality. With advances in molecular biology and genomic technologies, many candidate somatic genetic and epigenetic "biomarkers" have been identified as potential predictors of cancer risk. However, none have yet been validated as robust predictors of progression to cancer or shown to reduce cancer mortality. In this Perspective, we first define the necessary and sufficient conditions for precise prediction of future cancer development and early cancer detection within a simple physical model framework. We then evaluate cancer risk prediction and early detection from a dynamic clonal evolution point of view, examining the implications of dynamic clonal evolution of biomarkers and the application of clonal evolution for cancer risk management in clinical practice. Finally, we propose a framework to guide future collaborative research between mathematical modelers and biomarker researchers to design studies to investigate and model dynamic clonal evolution. This approach will allow optimization of available resources for cancer control and intervention timing based on molecular biomarkers in predicting cancer among various risk subsets that dynamically evolve over time.
2–stage stochastic Runge–Kutta for stochastic delay differential equations
Rosli, Norhayati; Jusoh Awang, Rahimah [Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia); Bahar, Arifah; Yeak, S. H. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-05-15
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.
2–stage stochastic Runge–Kutta for stochastic delay differential equations
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron
Recent biological data from man and pig on the non-stochastic effects following exposure with a range of β-emitters are combined with recent epidemiological analyses of skin cancer risks in man to form a basis for suggested improved protection criteria following whole- or partial-body skin exposures. Specific consideration is given to the choice of an organ weighting factor for evaluation of effective dose-equivalent. Since stochastic and non-stochastic end-points involve different cell types at different depths in the skin, the design of an ideal physical dosemeter may depend on the proportion of the body skin exposed and the radiation penetrating power. Possible choices of design parameters for skin dosemeters are discussed. Limitation of skin exposure from small radioactive sources ('hot particles') is addressed using animal data. (author)
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
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
Shephard, Neil
2005-01-01
Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) ...
The 2-stage liver transplant: 3 clinical scenarios.
Gedik, Ender; Bıçakçıoğlu, Murat; Otan, Emrah; İlksen Toprak, Hüseyin; Işık, Burak; Aydın, Cemalettin; Kayaalp, Cüneyt; Yılmaz, Sezai
2015-04-01
The main goal of 2-stage liver transplant is to provide time to obtain a new liver source. We describe our experience of 3 patients with 3 different clinical conditions. A 57-year-old man was retransplanted successfully with this technique due to hepatic artery thrombosis. However, a 38-year-old woman with fulminant toxic hepatitis and a 5-year-old-boy with abdominal trauma had poor outcome. This technique could serve as a rescue therapy for liver transplant patients who have toxic liver syndrome or abdominal trauma. These patients required intensive support during long anhepatic states. The transplant team should decide early whether to use this technique before irreversible conditions develop. PMID:25894175
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.
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
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...
Moawia Alghalith
2012-01-01
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Stochastic approximation: invited paper
Lai, Tze Leung
2003-01-01
Stochastic approximation, introduced by Robbins and Monro in 1951, has become an important and vibrant subject in optimization, control and signal processing. This paper reviews Robbins' contributions to stochastic approximation and gives an overview of several related developments.
Stochastic component mode synthesis
Bah, Mamadou T.; Nair, Prasanth B.; Bhaskar, Atul; Keane, Andy J.
2003-01-01
In this paper, a stochastic component mode synthesis method is developed for the dynamic analysis of large-scale structures with parameter uncertainties. The main idea is to represent each component displacement using a subspace spanned by a set of stochastic basis vectors in the same fashion as in stochastic reduced basis methods [1, 2]. These vectors represent however stochastic modes in contrast to the deterministic modes used in conventional substructuring methods [3]. The Craig-Bampton r...
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
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
Ramsey Stochastic Model via Multistage Stochastic Programming
Kaňková, Vlasta
Vol. Part II. České Budějovice: University of South Bohemia in České Budějovice, Faculty of Economy , 2010 - (Houda, M.; Friebelová, J.), s. 328-333 ISBN 978-80-7394-218-2. [28th International Conference on Mathematical Methods in Economics 2010. České Budějovice (CZ), 08.09.2010-10.09.2010] R&D Projects: GA ČR GAP402/10/0956; GA ČR(CZ) GA402/08/0107; GA ČR GAP402/10/1610 Institutional research plan: CEZ:AV0Z10750506 Keywords : Ramsey stochastic model * Multistage stochastic programming * Confidence intervals * Autoregressive sequences * Stability * Empirical estimates Subject RIV: AH - Economics http://library.utia.cas.cz/separaty/2010/E/kankova-ramsey stochastic model via multistage stochastic programming.pdf
A High-Payload Fraction, Pump-Fed, 2-Stage Nano Launch Vehicle Project
National Aeronautics and Space Administration — Ventions proposes the development of a pump-fed, 2-stage nano launch vehicle for low-cost on-demand placement of cube and nano-satellites into LEO. The proposed...
Verhoosel, C.V.; Gutiérrez, M. A.; Hulshoff, S.J.
2006-01-01
The field of fluid-structure interaction is combined with the field of stochastics to perform a stochastic flutter analysis. Various methods to directly incorporate the effects of uncertainties in the flutter analysis are investigated. The panel problem with a supersonic fluid flowing over it is considered as a testcase. The stochastic moments (mean, standard deviation, etc.) of the flutter point are computed by an uncertainty analysis. Sensitivity-based methods are used to determine the stoc...
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
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…
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
Ole Peters; Alexander Adamou
2011-01-01
It is argued that the simple trading strategy of leveraging or deleveraging an investment in the market portfolio cannot outperform the market. Such stochastic market efficiency places strong constraints on the possible stochastic properties of the market. Historical data confirm the hypothesis.
Stochastic and non-stochastic radiation effects
Both the carcinogenic and the mutagenic effects of ionizing radiation are thought to be induced by 'stochastic' mechanisms of action. It is generally accepted that the number of carcinogenic injury is proportional to the radiation dose applied, and that there is no direct relationship between radiation dose and severity of induced injury, so that no threshold dose can be defined. However, the severity of mutagenic effects, resulting for example from cell death or leading to functional disorders or malformations, has been observed to be a function of the radiation dose, so that in principle threshold doses can be defined. These latter effects are called non-stochastic radiation effects. (orig./DG)
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...
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...
Stochastic quantization and gravity
We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)
Stochastic Schroedinger equations
A derivation of Belavkin's stochastic Schroedinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system's quantum state given the observations made. This estimate satisfies a stochastic Schroedinger equation, which can be derived from the quantum stochastic differential equation for the interaction picture evolution of system and field together. Throughout the paper we focus on the basic example of resonance fluorescence
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. PMID:27120701
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
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 Physicochemical Dynamics
Tsekov, Roumen
2001-01-01
The monograph considers thermodynamic relaxation in quantum systems, stochastic dynamics of gas molecules, fluctuation stability of thin liquid films, resonant diffusion in modulated solid structures and catalytic kinetics of chemical dissociation.
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.
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
Dynamics of Double Stochastic Operators
Saburov, Mansoor
2016-03-01
A double stochastic operator is a generalization of a double stochastic matrix. In this paper, we study the dynamics of double stochastic operators. We give a criterion for a regularity of a double stochastic operator in terms of absences of its periodic points. We provide some examples to insure that, in general, a trajectory of a double stochastic operator may converge to any interior point of the simplex.
After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)
What is Stochastic Independence?
Franz, Uwe
2002-01-01
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with inclusions or projections. In this context, the classifications of quantum stochastic independence by Muraki, Ben Ghorbal, and Sch\\"urmann become classifications of the tensor products with inclusions for the categories of algebraic probabilit...
Stochastic Processes in Finance
Madan, Dilip B.
2010-01-01
Stochastic processes arising in the description of the risk-neutral evolution of equity prices are reviewed. Starting with Brownian motion, I review extensions to Lévy and Sato processes. These processes have independent increments; the former are homogeneous in time, whereas the latter are inhomogeneous. One-dimensional Markov processes such as local volatility and local Lévy are discussed next. Finally, I take up two forms of stochastic volatility that are due to either space scaling or tim...
Quantum Spontaneous Stochasticity
Eyink, Gregory L
2015-01-01
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions for given initial data are unique. In fluid turbulence non-uniqueness due to "roughness" of the advecting velocity field is known to lead to stochastic motion of classical particles. Vanishingly small random perturbations are magnified by Richardson diffusion in a "nearly rough" velocity field so that motion remains stochastic as the noise disappears, or classical spontaneous stochasticity, . Analogies between stochastic particle motion in turbulence and quantum evolution suggest that there should be quantum spontaneous stochasticity (QSS). We show this for 1D models of a particle in a repulsive potential that is "nearly rough" with $V(x) \\sim C|x|^{1+\\alpha}$ at distances $|x|\\gg \\ell$ , for some UV cut-off $\\ell$, and for initial Gaussian wave-packet centered at 0. We consi...
Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption
Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor
Songtao WANG; Xin DU; Zhongqi WANG
2009-01-01
Leading edge recambering is applied to the cantilevered stator vanes in a 2-stage compressor in this paper. Dif-ferent curving effects are produced when the end-bend stator vanes are stacked in different ways. Stacking on the leading edge induces a positive curving effect near the casing.When it is stacked on the centre of gravity, a nega-tive curving effect takes place. The numerical investigation shows that the flow field is redistributed when the end-bend stators with leading edge stacking are applied. The variations in the stage matching for the mainstream and near the hub have an impact on the performance of the 2-stage compressor. The isentropic efficiency and the total pressure ratio of the compressor are increased near the design condition. The compressor total pressure ratio is decreased near choke and near stall. The maximum flow rate is reduced and the stall margin is decreased.
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 modelling of turbulence
Sørensen, Emil Hedevang Lohse
stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating......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...
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
Stochastic Electrochemical Kinetics
Beruski, O
2016-01-01
A model enabling the extension of the Stochastic Simulation Algorithm to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a chemical master equation are provided and discussed. The electrochemical driving forces are included in the mathematical framework, and equations are provided for the associated electric responses. The implementation for potentiostatic and galvanostatic systems is presented, with results pointing out the stochastic nature of the algorithm. The electric responses presented are in line with the expected results from the theory, providing a new tool for the modeling of electrochemical kinetics.
Stochastic Geometric Wave Equations
Brzezniak, Z.; Ondreját, Martin
Cham: Springer, 2015, s. 157-188. (Progress in Probability. 68). ISBN 978-3-0348-0908-5. ISSN 1050-6977. [Stochastic analysis and applications at the Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne. Lausanne (CH), 09.01.2012-29.6.2012] R&D Projects: GA ČR GAP201/10/0752 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Stochastic wave equation * Riemannian manifold * homogeneous space Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2015/SI/ondrejat-0447803.pdf
Decentralized stochastic control
Speyer, J. L.
1980-01-01
Decentralized stochastic control is characterized by being decentralized in that the information to one controller is not the same as information to another controller. The system including the information has a stochastic or uncertain component. This complicates the development of decision rules which one determines under the assumption that the system is deterministic. The system is dynamic which means the present decisions affect future system responses and the information in the system. This circumstance presents a complex problem where tools like dynamic programming are no longer applicable. These difficulties are discussed from an intuitive viewpoint. Particular assumptions are introduced which allow a limited theory which produces mechanizable affine decision rules.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
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.
Stochastic entrainment of a stochastic oscillator.
Wang, Guanyu; Peskin, Charles S
2015-11-01
In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs. PMID:26651734
Stochastic Contraction in Riemannian Metrics
Pham, Quang-Cuong; Slotine, Jean-Jacques
2013-01-01
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic contraction results and sharp associated performance bounds have been established only in the specialized context of state-independent metrics, which restricts their applicability. This paper extends stochastic contraction analysis to the case of general time- and...
Stochastic quantization: Stabilizing quantum models
Osterwalder-Schrader positivity is shown to be fulfilled for stochastically quantized lattice gauge theories, spin models and P(phi) interactions bounded from below. Problems arising are discussed. A stochastic equation is derived to stabilize the quantum Einstein gravity. It is shown that the stochastic quantization of the Yang-Mills theory leads to a well-defined semiclassical expansion. (orig.)
Stochastic quantization of Proca field
We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)
The stochastic quality calculus
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
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...
Stochastic Control - External Models
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 and...
Stochastic nonlinear beam equations
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149. ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
The stochastic quality calculus
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...
Focus on stochastic thermodynamics
Van den Broeck, Christian; Sasa, Shin-ichi; Seifert, Udo
2016-02-01
We introduce the thirty papers collected in this ‘focus on’ issue. The contributions explore conceptual issues within and around stochastic thermodynamics, use this framework for the theoretical modeling and experimental investigation of specific systems, and provide further perspectives on and for this active field.
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
Jiang, Yuming
2009-01-01
Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. This title presents a comprehensive treatment for the stochastic service-guarantee analysis research and provides basic introductory material on the subject, as well as discusses the various researches in the area.
Stochastic biophysical modeling of irradiated cells
Fornalski, Krzysztof Wojciech
2014-01-01
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the entire colony. Biophysics of the cells is described by probabilities and probability distributions provided as the input. The adaptation of nucleation and catastrophe theories, well known in physics, yields sigmoidal relationships for carcinogenic risk as a function of the irradiation. Adaptive response and bystander effect, incorporated into the model, improves its application. The results show that behavior of virtual cells can be successfully modeled, e.g. cancer transformation, creation of mutations, radioadaptation or radiotherapy. The used methodology makes the model universal and practical for simulations of general processes. Potential biophysical curves and relationships are also widely discussed in the paper. However, the presented theoretical model does not describe ...
Adaptive stochastic cellular automata: Applications
Qian, S.; Lee, Y. C.; Jones, R. D.; Barnes, C. W.; Flake, G. W.; O'Rourke, M. K.; Lee, K.; Chen, H. H.; Sun, G. Z.; Zhang, Y. Q.; Chen, D.; Giles, C. L.
1990-09-01
The stochastic learning cellular automata model has been applied to the problem of controlling unstable systems. Two example unstable systems studied are controlled by an adaptive stochastic cellular automata algorithm with an adaptive critic. The reinforcement learning algorithm and the architecture of the stochastic CA controller are presented. Learning to balance a single pole is discussed in detail. Balancing an inverted double pendulum highlights the power of the stochastic CA approach. The stochastic CA model is compared to conventional adaptive control and artificial neural network approaches.
New 2-stage ion microprobes and a move to higher energies
Legge, G.J.F.; Dymnikov, A.; Moloney, G.; Saint, A. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Cohen, D. [Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW (Australia)
1996-12-31
Recent moves in Ion Beam Microanalysis towards the use of a rapidly growing number of very high resolution, low current and single ion techniques has led to the need for high demagnification and greatly improved beam quality. There is also a move to apply Microbeams at higher energies and with heavier ions. This also puts demands on the focusing system and beam control. This paper describes the recent development of 2-stage lens systems to be applied here and overseas, both at very high resolution and at high energies with heavy ions. It looks at new ion beam analysis applications of such ion microprobes. 8 refs., 1 tab., 1 fig.
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 response surface methodology: A study in the human health area
Oliveira, Teresa A., E-mail: teresa.oliveira@uab.pt; Oliveira, Amílcar, E-mail: amilcar.oliveira@uab.pt [Departamento de Ciências e Tecnologia, Universidade Aberta (Portugal); Centro de Estatística e Aplicações, Universidade de Lisboa (Portugal); Leal, Conceição, E-mail: conceicao.leal2010@gmail.com [Departamento de Ciências e Tecnologia, Universidade Aberta (Portugal)
2015-03-10
In this paper we review Stochastic Response Surface Methodology as a tool for modeling uncertainty in the context of Risk Analysis. An application in the survival analysis in the breast cancer context is implemented with R software.
Stochastic flights of propellers
Pan, Margaret; Chiang, Eugene; Evans, Steven N
2012-01-01
Kilometer-sized moonlets in Saturn's A ring create S-shaped wakes called "propellers" in surrounding material. The Cassini spacecraft has tracked the motions of propellers for several years and finds that they deviate from Keplerian orbits having constant semimajor axes. The inferred orbital migration is known to switch sign. We show using a statistical test that the time series of orbital longitudes of the propeller Bl\\'eriot is consistent with that of a time-integrated Gaussian random walk. That is, Bl\\'eriot's observed migration pattern is consistent with being stochastic. We further show, using a combination of analytic estimates and collisional N-body simulations, that stochastic migration of the right magnitude to explain the Cassini observations can be driven by encounters with ring particles 10-20 m in radius. That the local ring mass is concentrated in decameter-sized particles is supported on independent grounds by occultation analyses.
Samuelson, P A
1971-02-01
Because a commodity like wheat can be carried forward from one period to the next, speculative arbitrage serves to link its prices at different points of time. Since, however, the size of the harvest depends on complicated probability processes impossible to forecast with certainty, the minimal model for understanding market behavior must involve stochastic processes. The present study, on the basis of the axiom that it is the expected rather than the known-for-certain prices which enter into all arbitrage relations and carryover decisions, determines the behavior of price as the solution to a stochastic-dynamic-programming problem. The resulting stationary time series possesses an ergodic state and normative properties like those often observed for real-world bourses. PMID:16591903
William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
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 ...
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...
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 resonance and computation
Torres, José-Leonel; Trainor, Lynn
1997-09-01
Stochastic resonance (SR) occurs in bistable nonlinear systems subject to noise, as the entrainment of their output by a weak periodic modulation added to the input. Electronic computation involves switching of memory elements between two states that correspond to 1 and 0, respectively. The possibility of switching errors due to SR in memory elements is considered, showing that it represents a negligible danger to reliable computation.
Stochastic reconstruction of sandstones
Manwart, C.; Torquato, S.; Hilfer, R.
2000-01-01
A simulated annealing algorithm is employed to generate a stochastic model for a Berea and a Fontainebleau sandstone with prescribed two-point probability function, lineal path function, and ``pore size'' distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandston...
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 Volatility Demand Systems
Apostolos Serletis; Maksim Isakin
2014-01-01
We address the estimation of stochastic volatility demand systems. In particular, we relax the homoscedasticity assumption and instead assume that the covariance matrix of the errors of demand systems is time-varying. Since most economic and fiÂ…nancial time series are nonlinear, we achieve superior modeling using parametric nonlinear demand systems in which the unconditional variance is constant but the conditional variance, like the conditional mean, is also a random variable depending on c...
Stochastic Overall Equipment Effectiveness
Zammori, Francesco Aldo; Braglia, Marcello; Frosolini, Marco
2011-01-01
Abstract This paper focuses on the Overall Equipment Effectiveness (OEE), a key performance indicator typically adopted to support Lean Manufacturing and Total Productive Maintenance. Unfortunately, being a deterministic metric, the OEE only provides a static representation of a process, but fails to capture the real variability of manufacturing performances. To take into account the stochastic nature of the OEE, an approximated procedure based on the application of the Central Lim...
Decentralized stochastic control
Mahajan, Aditya; Mannan, Mehnaz
2013-01-01
Decentralized stochastic control refers to the multi-stage optimization of a dynamical system by multiple controllers that have access to different information. Decentralization of information gives rise to new conceptual challenges that require new solution approaches. In this expository paper, we use the notion of an \\emph{information-state} to explain the two commonly used solution approaches to decentralized control: the person-by-person approach and the common-information approach.
Stochastic Weighted Fractal Networks
Carletti, Timoteo
2010-01-01
In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both classes can be completely analytically characterized in terms of the involved parameters. The proposed algorithms improve and extend the framework of weighted fractal networks recently proposed in (T. Carletti & S. Righi, in press Physica A, 2010)
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.
Evolution of waves subject to a randomly varying growth rate is considered and the statistical properties of the waves are calculated in terms of the mean, variance, and correlation time of the growth rate. This enables stochastic growth to be studied without needing full knowledge of the microphysics. However, where the microphysics is understood, this approach also allows it to be easily incorporated into studies of larger-scale phenomena involving stochastic growth. Stochastic differential equations and Fokker--Planck equations are obtained, which describe the wave evolution in the presence of a variety of linear and nonlinear processes and boundary conditions, and it is shown that these phenomena can be diagnosed observationally through their effects on the statistical distribution of the wave field strengths. The results are particularly useful for waves with small dispersion, where they explain the strong wave clumping often observed in nature and emphasize the role of marginal stability in setting the level about which fluctuations occur and in determining their magnitude. Application to type III solar radio bursts illustrates many of the main results and verifies and generalizes earlier conclusions reached using a less rigorous approach. In particular, a new condition for marginally stable propagation of type III solar electron beams is found. copyright 1995 American Institute of Physics
Boelter, Fred W; Xia, Yulin; Dell, Linda
2015-05-01
Sanding joint compounds is a dusty activity and exposures are not well characterized. Until the mid 1970s, asbestos-containing joint compounds were used by some people such that sanding could emit dust and asbestos fibers. We estimated the distribution of 8-h TWA concentrations and cumulative exposures to respirable dusts and chrysotile asbestos fibers for four worker groups: (1) drywall specialists, (2) generalists, (3) tradespersons who are bystanders to drywall finishing, and (4) do-it-yourselfers (DIYers). Data collected through a survey of experienced contractors, direct field observations, and literature were used to develop prototypical exposure scenarios for each worker group. To these exposure scenarios, we applied a previously developed semi-empirical mathematical model that predicts area as well as personal breathing zone respirable dust concentrations. An empirical factor was used to estimate chrysotile fiber concentrations from respirable dust concentrations. On a task basis, we found mean 8-h TWA concentrations of respirable dust and chrysotile fibers are numerically highest for specialists, followed by generalists, DIYers, and bystander tradespersons; these concentrations are estimated to be in excess of the respective current but not historical Threshold Limit Values. Due to differences in frequency of activities, annual cumulative exposures are highest for specialists, followed by generalists, bystander tradespersons, and DIYers. Cumulative exposure estimates for chrysotile fibers from drywall finishing are expected to result in few, if any, mesothelioma or excess lung cancer deaths according to recently published risk assessments. Given the dustiness of drywall finishing, we recommend diligence in the use of readily available source controls. PMID:25428276
Stochastic and non-stochastic effects - a conceptual analysis
The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)
Radiotracer study on the efficiency of a cylindrical 2-stage anaerobic sludge digester
Radiotracer experiments were carried out on a cylindrical 2-stage anaerobic sludge digester in order to investigate the improvement of their efficiency by means of RTD (residence time distribution) measurements before and after cleaning up the inside of the digester. The tracer was scandium in an EDTA solution which forms such a stable complex compound to keep the isotope form being adsorbed onto the surface of the pipelines or the wall. It was injected into the digester by pressurized nitrogen gas and its movement was monitored by NaI(Tl) scintillation detectors installed around the digester and recorded for a month by a 24-channel data acquisition system specially developed for radiotracer experiments by the Korea Tracer Group of KAERI. The experimental data was analysed for the MRT (mean residence time) and other parameters characterizing the flow behaviour. (author)
Qualitatively stability of nonstandard 2-stage explicit Runge-Kutta methods of order two
Khalsaraei, M. M.; Khodadosti, F.
2016-02-01
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, a class of nonstandard 2-stage Runge-Kutta methods of order two (we call it nonstandard RK2) is considered. The preservation of some qualitative properties by this class of methods are discussed. In order to illustrate our results, we provide some numerical examples.
Stochastic Analysis of Cylindrical Shell
Grzywiński Maksym
2014-06-01
Full Text Available The paper deals with some chosen aspects of stochastic structural analysis and its application in the engineering practice. The main aim of the study is to apply the generalized stochastic perturbation techniques based on classical Taylor expansion with a single random variable for solution of stochastic problems in structural mechanics. The study is illustrated by numerical results concerning an industrial thin shell structure modeled as a 3-D structure.
Stochastic Nature in Cellular Processes
刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa
2011-01-01
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.
Some stochastic aspects of quantization
Ichiro Ohba
2002-08-01
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 quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.
Stochastic Analysis with Financial Applications
Kohatsu-Higa, Arturo; Sheu, Shuenn-Jyi
2011-01-01
Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. This book also covers the areas of backward stochastic differential equations via the (non-li
A recurrent stochastic binary network
赵杰煜
2001-01-01
Stochastic neural networks are usually built by introducing random fluctuations into the network. A natural method is to use stochastic connections rather than stochastic activation functions. We propose a new model in which each neuron has very simple functionality but all the connections are stochastic. It is shown that the stationary distribution of the network uniquely exists and it is approximately a Boltzmann-Gibbs distribution. The relationship between the model and the Markov random field is discussed. New techniques to implement simulated annealing and Boltzmann learning are proposed. Simulation results on the graph bisection problem and image recognition show that the network is powerful enough to solve real world problems.
Stochastic thermodynamics of resetting
Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo
2016-03-01
Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
Stochastic cooling for beginners
These two lectures have been prepared to give a simple introduction to the principles. In Part I we try to explain stochastic cooling using the time-domain picture which starts from the pulse response of the system. In Part II the discussion is repeated, looking more closely at the frequency-domain response. An attempt is made to familiarize the beginners with some of the elementary cooling equations, from the 'single particle case' up to equations which describe the evolution of the particle distribution. (orig.)
Stochastic conditional intensity processes
Bauwens, Luc; Hautsch, Nikolaus
2006-01-01
model allows for a wide range of (cross-)autocorrelation structures in multivariate point processes. The model is estimated by simulated maximum likelihood (SML) using the efficient importance sampling (EIS) technique. By modeling price intensities based on NYSE trading, we provide significant evidence......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 proposed...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...
Structured Stochastic Linear Bandits
Johnson, Nicholas; Sivakumar, Vidyashankar; Banerjee, Arindam
2016-01-01
The stochastic linear bandit problem proceeds in rounds where at each round the algorithm selects a vector from a decision set after which it receives a noisy linear loss parameterized by an unknown vector. The goal in such a problem is to minimize the (pseudo) regret which is the difference between the total expected loss of the algorithm and the total expected loss of the best fixed vector in hindsight. In this paper, we consider settings where the unknown parameter has structure, e.g., spa...
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
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...
Stochastic power flow modeling
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
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
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...
Non Monotone Stochastic Evolution Equations
Kenneth L. Kuttler; Li, Ji
2013-01-01
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the existence of strong solutions to a stochastic Navier Stokes problem in dimension less than four.
On stochastic finite difference schemes
Gyongy, Istvan
2013-01-01
Finite difference schemes in the spatial variable for degenerate stochastic parabolic PDEs are investigated. Sharp results on the rate of $L_p$ and almost sure convergence of the finite difference approximations are presented and results on Richardson extrapolation are established for stochastic parabolic schemes under smoothness assumptions.
Evolutionary computation in stochastic environments
Schmidt, Christian
2007-01-01
This book develops efficient methods for the application of Evolutionary Algorithms on stochastic problems. To achieve this, procedures for statistical selection are systematically analyzed with respect to different measures and significantly improved. It is shown how to adapt one of the best procedures for the needs of Evolutionary Algorithms and Evolutionary operators for efficient implementation in stochastic environments are identified.
Alternative Asymmetric Stochastic Volatility Models
M. Asai (Manabu); M.J. McAleer (Michael)
2010-01-01
textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is
Stochastic Pi-calculus Revisited
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 of...
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2009-01-01
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
Variance decomposition in stochastic simulators
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...
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.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
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.
A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game
Fang Xiang-Sheng; Zhu Ping; Liu Run-Ran; Liu En-Yu; Wei Gui-Yi
2012-01-01
In this study,we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule. The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases; but a high cooperation level can be obtained in the intermediate region of -3 ＜ β ＜ -1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.
A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game
Fang, Xiang-Sheng; Zhu, Ping; Liu, Run-Ran; Liu, En-Yu; Wei, Gui-Yi
2012-10-01
In this study, we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule, and focus on the cooperation behavior of the system. In the first stage, i.e., the pre-learning stage, a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors. If the player makes up his mind to update, he enters into the second stage, i.e., the learning stage, and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule. The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor. Generally, the cooperation frequency decreases as the pre-learning factor increases; but a high cooperation level can be obtained in the intermediate region of -3 learning and learning. Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.
Unsteady Aero Computation of a 1 1/2 Stage Large Scale Rotating Turbine
To, Wai-Ming
2012-01-01
This report is the documentation of the work performed for the Subsonic Rotary Wing Project under the NASA s Fundamental Aeronautics Program. It was funded through Task Number NNC10E420T under GESS-2 Contract NNC06BA07B in the period of 10/1/2010 to 8/31/2011. The objective of the task is to provide support for the development of variable speed power turbine technology through application of computational fluid dynamics analyses. This includes work elements in mesh generation, multistage URANS simulations, and post-processing of the simulation results for comparison with the experimental data. The unsteady CFD calculations were performed with the TURBO code running in multistage single passage (phase lag) mode. Meshes for the blade rows were generated with the NASA developed TCGRID code. The CFD performance is assessed and improvements are recommended for future research in this area. For that, the United Technologies Research Center's 1 1/2 stage Large Scale Rotating Turbine was selected to be the candidate engine configuration for this computational effort because of the completeness and availability of the data.
Classical and spatial stochastic processes with applications to biology
Schinazi, Rinaldo B
2014-01-01
The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a f...
Cancer begins in your cells, which are the building blocks of your body. Normally, your body forms ... be benign or malignant. Benign tumors aren't cancer while malignant ones are. Cells from malignant tumors ...
... Blood tests (which look for chemicals such as tumor markers) Bone marrow biopsy (for lymphoma or leukemia) Chest ... the case with skin cancers , as well as cancers of the lung, breast, and colon. If the tumor has spread ...
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...
Stochastic reconstruction of sandstones
Manwart; Torquato; Hilfer
2000-07-01
A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and "pore size" distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples. PMID:11088546
Bunched beam stochastic cooling
Wei, Jie
1992-09-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Bunched beam stochastic cooling
Wei, Jie.
1992-01-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Stochastic Programming with Probability
Andrieu, Laetitia; Vázquez-Abad, Felisa
2007-01-01
In this work we study optimization problems subject to a failure constraint. This constraint is expressed in terms of a condition that causes failure, representing a physical or technical breakdown. We formulate the problem in terms of a probability constraint, where the level of "confidence" is a modelling parameter and has the interpretation that the probability of failure should not exceed that level. Application of the stochastic Arrow-Hurwicz algorithm poses two difficulties: one is structural and arises from the lack of convexity of the probability constraint, and the other is the estimation of the gradient of the probability constraint. We develop two gradient estimators with decreasing bias via a convolution method and a finite difference technique, respectively, and we provide a full analysis of convergence of the algorithms. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of ...
Stochastic reconstruction of sandstones
A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and ''pore size'' distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples. (c) 2000 The American Physical Society
Backward stochastic differential equations and its application to stochastic control
Veverka, Petr
Praha : Nakladatelství ČVUT - výroba, 2010 - (Hobza, T.), s. 181-189 ISBN 978-80-01-04641-8. [Stochastic and Physical Monitoring Systems 2010. Děčín (CZ), 27.06.2010-03.07.2010] R&D Projects: GA ČR GD402/09/H045; GA ČR GAP402/10/1610 Institutional research plan: CEZ:AV0Z10750506 Keywords : BSDE * Stochastic control Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2010/E/veverka-backward%20stochastic%20differential%20equations%20and%20its%20application%20to%20stochastic%20control.pdf
Stochasticity in the Josephson map
The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)
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
Linear stochastic neutron transport theory
A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)
Stochastic dynamic equations on general time scales
Martin Bohner; Olexandr M. Stanzhytskyi; Anastasiia O. Bratochkina
2013-01-01
In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense.
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.
Stochastic analysis of laminated composite plate considering stochastic homogenization problem
S. SAKATA; K. OKUDA; K. IKEDA
2015-01-01
This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.
de la Peña-López, Roberto; Remolina-Bonilla, Yuly Andrea
2016-09-01
Cancer is a group of diseases which represents a significant public health problem in Mexico and worldwide. In Mexico neoplasms are the second leading cause of death. An increased morbidity and mortality are expected in the next decades. Several preventable risk factors for cancer development have been identified, the most relevant including tobacco use, which accounts for 30% of the cancer cases; and obesity, associated to another 30%. These factors, in turn, are related to sedentarism, alcohol abuse and imbalanced diets. Some agents are well knokn to cause cancer such as ionizing radiation, viruses such as the papilloma virus (HPV) and hepatitis virus (B and C), and more recently environmental pollution exposure and red meat consumption have been pointed out as carcinogens by the International Agency for Research in Cancer (IARC). The scientific evidence currently available is insufficient to consider milk either as a risk factor or protective factor against different types of cancer. PMID:27603890
Nucleon structure from stochastic estimators
Bali, Gunnar S; Gläßle, Benjamin; Göckeler, Meinulf; Najjar, Johannes; Rödl, Rudolf; Schäfer, Andreas; Sternbeck, André; Söldner, Wolfgang
2013-01-01
Using stochastic estimators for connected meson and baryon three-point functions has successfully been tried in the past years. Compared to the standard sequential source method we trade the freedom to compute the current-to-sink propagator independently of the hadron sink for additional stochastic noise in our observables. In the case of the nucleon we can use this freedom to compute many different sink-momentum/polarization combinations, which grants access to more virtualities. We will present preliminary results on the scalar, electro-magnetic and axial form factors of the nucleon in $N_f=2+1$ lattice QCD and contrast the performance of the stochastic method to the sequential source method. We find the stochastic method to be competitive in terms of errors at fixed cost.
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...
Detecting Stochastic Information of Electrocardiograms
Gutíerrez, R M; Guti'errez, Rafael M.; Sandoval, Luis A.
2003-01-01
In this work we present a method to detect, identify and characterize stochastic information contained in an electrocardiogram (ECG). We assume, as it is well known, that the ECG has information corresponding to many different processes related to the cardiac activity. We analyze scaling and Markov processes properties of the detected stochastic information using the power spectrum of the ECG and the Fokker-Planck equation respectively. The detected stochastic information is then characterized by three measures. First, the slope of the power spectrum in a particular range of frequencies as a scaling parameter. Second, an empirical estimation of the drift and diffusion coefficients of the Fokker-Planck equation through the Kramers-Moyal coefficients which define the evolution of the probability distribution of the detected stochastic information.
Markovian Projection of Stochastic Processes
Bentata, Amel
2012-01-01
This PhD thesis studies various mathematical aspects of problems related to the Markovian projection of stochastic processes, and explores some ap- plications of the results obtained to mathematical finance, in the context of semimartingale models. Given a stochastic process ξ, modeled as a semimartingale, our aim is to build a Markov process X whose marginal laws are the same as ξ. This construction allows us to use analytical tools such as integro-differential equa- tions to explore or comp...
Abstractions of stochastic hybrid systems
Bujorianu, L.M.; Lygeros, J.; Bujorianu, M.C.
2005-01-01
Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is in...
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 Geometric Partial Differential Equations
Brzezniak, Z.; Goldys, B.; Ondreját, Martin
1. Singapore : World Scientific Publishing Company, 2011 - (Zhao, H.; Truman, A.), s. 1-32 ISBN 978-981-4360-91-3. - (Interdisciplinary Mathematical Sciences. 12) R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic geometric * partial differential equations Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2012/SI/ondrejat-stochastic geometric partial differential equations. pdf
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.
Optimization of stochastic database cracking
Bhardwaj, Meenesh
2013-01-01
Variant Stochastic cracking is a significantly more resilient approach to adaptive indexing. It showed [1]that Stochastic cracking uses each query as a hint on how to reorganize data, but not blindly so; it gains resilience and avoids performance bottlenecks by deliberately applying certain arbitrary choices in its decision making. Therefore bring, adaptive indexing forward to a mature formulation that confers the workload-robustness that previous approaches lacked. Original cracking relies o...
Pathwise construction of stochastic integrals
Nutz, Marcel
2012-01-01
We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale. This method applies to any predictable integrand.
On solving stochastic MADM problems
Văduva Ion; Resteanu Cornel
2009-01-01
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 di...
Stochastic superparameterization in quasigeostrophic turbulence
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
The dynamics of stochastic processes
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...... result is obtained and applied. Moreover, martingales indexed by the whole real line is studied and characterized and the thesis is concluded with a study of stationary solutions of the Langevin equation....
Stochastic comparisons of nonhomogeneous processes
Belzunce, Félix; Lillo, Rosa E.; Ruiz, José M.; Shaked, Moshe
2000-01-01
The purpose of this paper is to describe various conditions on the parameters of pairs of nonhomogeneous Poisson or birth processes under which the corresponding epoch or inter-epoch times are stochastically ordered in various senses. We derive results involving the usual stochastic order, the multivariate hazard rate order, the multivariate likelihood ratio order, and the multivariate mean residual life order. A sample of applications involving generalized Yule processes, load-sharing models...
Stochastic quantization and gauge theories
Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author)
Foliated stochastic calculus: Harmonic measures
Catuogno, Pedro J.; Ledesma, Diego S.; Ruffino, Paulo R
2010-01-01
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
Stochastic quantization and gauge invariance
A survey of the fundamental ideas about Parisi-Wu's Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories, is done. In particular, the Analytic Stochastic Regularization Scheme is used to calculate the polarization tensor for Quantum Electrodynamics with Dirac bosons or Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested. (author)
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...
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...
AA, stochastic precooling kicker
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
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105 the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some considerations to the 'azimuthal' schemes
Stability Analysis for Stochastic Optimization Problems
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
Stochastic quantization and topological theories
In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Transcriptional stochasticity in gene expression.
Lipniacki, Tomasz; Paszek, Pawel; Marciniak-Czochra, Anna; Brasier, Allan R; Kimmel, Marek
2006-01-21
Due to the small number of copies of molecular species involved, such as DNA, mRNA and regulatory proteins, gene expression is a stochastic phenomenon. In eukaryotic cells, the stochastic effects primarily originate in regulation of gene activity. Transcription can be initiated by a single transcription factor binding to a specific regulatory site in the target gene. Stochasticity of transcription factor binding and dissociation is then amplified by transcription and translation, since target gene activation results in a burst of mRNA molecules, and each mRNA copy serves as a template for translating numerous protein molecules. In the present paper, we explore a mathematical approach to stochastic modeling. In this approach, the ordinary differential equations with a stochastic component for mRNA and protein levels in a single cells yield a system of first-order partial differential equations (PDEs) for two-dimensional probability density functions (pdf). We consider the following examples: Regulation of a single auto-repressing gene, and regulation of a system of two mutual repressors and of an activator-repressor system. The resulting PDEs are approximated by a system of many ordinary equations, which are then numerically solved. PMID:16039671
The El Nino Stochastic Oscillator
Burgers, G
1997-01-01
Anomalies during an El Nino are dominated by a single, irregularly oscillating, mode. Equatorial dynamics has been linked to delayed-oscillator models of this mode. Usually, the El Nino mode is regarded as an unstable mode of the coupled atmosphere system and the irregularity is attributed to noise and possibly chaos. Here a variation on the delayed oscillator is explored. In this stochastic-oscillator view, El Nino is a stable mode excited by noise. It is shown that the autocorrelation function of the observed NINO3.4 index is that of a stochastic oscillator, within the measurement uncertainty. Decadal variations as would occur in a stochastic oscillator are shown to be comparable to those observed, only the increase in the long-term mean around 1980 is rather large. The observed dependence of the seasonal cycle on the variance and the correlation is so large that it can not be attributed to the natural variability of a stationary stochastic oscillator. So the El Niño stochastic-oscillator parameters must d...
Stochastic Model Checking of the Stochastic Quality Calculus
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 inp...... based on stochastic model checking and we compute closed form solutions for a number of interesting scenarios. The analyses are applied to the design of an intelligent smart electrical meter of the kind to be installed in European households by 2020....
Stacking with stochastic cooling
Caspers, Fritz E-mail: Fritz.Caspers@cern.ch; Moehl, Dieter
2004-10-11
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 10{sup 5} the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some
A stochastic approach to microphysics
The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e+e- collisions, or pp → π0 + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...)
Correlation functions in stochastic inflation
Combining the stochastic and δ N formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and we comment on the physical implications of this effect. (orig.)
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...
Stochastic approach to quantum mechanics
A critical review of the Copenhagen interpretation of quantum mechanics, both in its early and later versions, shows that, as a model for the individual system, it suffers from severe conceptual difficulties, particularly with regard to the problem of measurement. Nor are the most common hidden variable interpretations free from complications in providing a physical explanation for the properties of the quantum system. A promising alternative interpretation is the stochastic approach, which presumes that every physical system is continually interacting with a hidden thermostat. This thermostat has a randomizing effect on the position variable and necessitates a probabilistic description of the path of the system. If the concepts of both backward and forward diffusion are utilized, it is possible to construct a straightforward stochastic rule for computing the mean value of any observable which has a classical operational definition. Estimates based upon this rule agree with standard quantum predictions up to second order in momentum but disagree in higher order terms. The rule also predicts the average measurement results for observables which cannot, in general, be estimated by the usual operator formalism. The Schroedinger equation is derivable by the stochastic approach if Newton's Second Law is assumed. Also, quantization of energy and the Heisenberg uncertainty principle are readily explained through the stochastic model, but spatial quantization is not predicted by this method. If the magnitude of the free velocity of the relativistic stochastic particle is assumed to be the speed of light, as in Dirac's relativistic theory of the electron, it is possible to provide a relativistic extension of the stochastic approach and to derive (from this extension) the Klein-Gordon equation
Stochastic Optimization of Complex Systems
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.
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.
QB1 - Stochastic Gene Regulation
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 Modelling of Hydrologic Systems
Jonsdottir, Harpa
2007-01-01
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 modeling of Lagrangian accelerations
Reynolds, Andy
2002-11-01
It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.
Stochastic cooling of bunched beams
Numerical simulation studies are presented for transverse and longitudinal stochastic cooling of bunched particle beams. Radio frequency buckets of various shapes (e.g. rectangular, parabolic well, single sinusoidal waveform) are used to investigate the enhancement of phase space cooling by nonlinearities of synchrotron motion. The connection between the notions of Landau damping for instabilities and mixing for stochastic cooling are discussed. In particular, the need for synchrotron frequency spread for both Landau damping and good mixing is seen to be comparable for bunched beams
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 vehicle routing with recourse
Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi
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...... instantiations, a recourse route is computed - but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular...
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 epidemic models: a survey
Britton, Tom
2009-01-01
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
Schwinger Mechanism with Stochastic Quantization
Fukushima, Kenji
2014-01-01
We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive the Schwinger mechanism under a time-dependent electric field. We also discuss a physical interpretation with help of numerical simulations and develop an analogue to the one-dimensional scattering with the non-relativistic Schroedinger equation. We can then reformulate the Schwinger mechanism as the high-energy quantum reflection problem rather than tunneling.
Stochastic heating of cooling flows
Pavlovski, Georgi
2009-01-01
It is generally accepted that the heating of gas in clusters of galaxies by active galactic nuclei (AGN) is a form of feedback. Feedback is required to ensure a long term, sustainable balance between heating and cooling. This work investigates the impact of proportional stochastic feedback on the energy balance in the intracluster medium. Using a generalised analytical model for a cluster atmosphere, it is shown that an energy equilibrium can be reached exponentially quickly. Applying the tools of stochastic calculus it is demonstrated that the result is robust with regard to the model parameters, even though they affect the amount of variability in the system.
Stochastic Simulation of Turing Patterns
FU Zheng-Ping; XU Xin-Hang; WANG Hong-Li; OUYANG Qi
2008-01-01
@@ We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction-diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie's algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion processes are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Stochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.
Stochastic model in microwave propagation
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.
Elimination of stochasticity in stellarators
A method for optimizing stellarator vacuum magnetic fields is introduced. Application of this method shows that the stochasticity of vacuum magnetic fields can be made negligible by proper choice of the coil configuration. This optimization is shown to increase the equilibrium β-limit by factors of two or more over that of the simple, straight coil winding law. This method is general and ought to be applicable to other systems in which stochasticity: (1) is a problem, yet (2) is affected by the design parameters
Work fluctuations and stochastic resonance
We study Brownian particle motion in a double-well potential driven by an ac force. This system exhibits the phenomenon of stochastic resonance. Distribution of work done on the system over a drive period in the time asymptotic regime has been calculated. We show that fluctuations in the input energy or work done dominate the mean value. The mean value of work done over a period as a function of noise strength can also be used to characterize stochastic resonance in the system. We also discuss the validity of steady state fluctuation theorems in this particular system
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.
Exact Algorithms for Solving Stochastic Games
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....
Theory, technology, and technique of stochastic cooling
The theory and technological implementation of stochastic cooling is described. Theoretical and technological limitations are discussed. Data from existing stochastic cooling systems are shown to illustrate some useful techniques
When greediness fails: Examples from stochastic scheduling
Uetz, Marc
2002-01-01
The purpose of this paper is to present examples which show that deterministic and stochastic scheduling problems often have a surprisingly different behavior. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.
Enhancing stochastic kriging metamodels with gradient estimators
Chen, X.; Ankenman, B. E.; Nelson, B. L.
2013-01-01
Stochastic kriging is a new metamodeling technique for effectively representing the mean response surface implied by a stochastic simulation; it takes into account both stochastic simulation noise and uncertainty about the underlying response surface of interest. We show theoretically, through some simplified models, that incorporating gradient estimators into stochastic kriging tends to significantly improve surface prediction. To address the issue of which type of gradient estimator to use,...
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
Transport in a stochastic magnetic field
White, R.B.; Wu, Yanlin [Princeton Univ., NJ (United States). Plasma Physics Lab.; Rax, J.M. [Association Euratom-CEA, Centre d`Etudes Nucleaires de Cadarache, 13 -Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
1992-09-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
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...
Stability of stochastic switched SIRS models
Meng, Xiaoying; Liu, Xinzhi; Deng, Feiqi
2011-11-01
Stochastic stability problems of a stochastic switched SIRS model with or without distributed time delay are considered. By utilizing the Lyapunov methods, sufficient stability conditions of the disease-free equilibrium are established. Stability conditions about the subsystem of the stochastic switched SIRS systems are also obtained.
Models and algorithms for stochastic online scheduling
Megow, N.; Uetz, M.J.; Vredeveld, T.
2006-01-01
We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that job
On physical diffusion and stochastic diffusion
Narasimhan, T.N.
2010-01-01
Although the same mathematical expression is used to describe physical diffusion and stochastic diffusion, there are intrinsic similarities and differences in their nature. A comparative study shows that characteristic terms of physical and stochastic diffusion cannot be placed exactly in one-to-one correspondence. Therefore, judgment needs to be exercised in transferring ideas between physical and stochastic diffusion.
Information theory in stochastic process
Methods for calculating the Kolmogorov-Sinai disorder from Gaussian Probability density functions and by using information theory for chaotic dynamical systems are suggested. The autoregressive models may prove stochastic deterministic both for chaotic and non-chaotic dynamical systems. (author)
The bicriterion stochastic knapsack problem
Andersen, Kim Allan
We discuss the bicriterion stochastic knapsack problem. It is described as follows. We have a known capacity of some resource, and a finite set of projects. Each project requires some units of the resource which is not known in advance, but given by a discrete probability distribution with a finite...
Stochastic Subspace Modelling of Turbulence
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
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...
Stochastic Modelling of River Geometry
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...... river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
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 resin transfer molding process
Park, M
2016-01-01
We consider one-dimensional and two-dimensional models of stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field.
Algorithmic advances in stochastic programming
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
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...
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...
N. Kavoussi
1973-09-01
Full Text Available There are many carcinogenetic elements in industry and it is for this reason that study and research concerning the effect of these materials is carried out on a national and international level. The establishment and growth of cancer are affected by different factors in two main areas:-1 The nature of the human or animal including sex, age, point and method of entry, fat metabolism, place of agglomeration of carcinogenetic material, amount of material absorbed by the body and the immunity of the body.2 The different nature of the carcinogenetic material e.g. physical, chemical quality, degree of solvency in fat and purity of impurity of the element. As the development of cancer is dependent upon so many factors, it is extremely difficult to determine whether a causative element is principle or contributory. Some materials are not carcinogenetic when they are pure but become so when they combine with other elements. All of this creates an industrial health problem in that it is almost impossible to plan an adequate prevention and safety program. The body through its system of immunity protects itself against small amounts of carcinogens but when this amount increases and reaches a certain level the body is not longer able to defend itself. ILO advises an effective protection campaign against cancer based on the Well –equipped laboratories, Well-educated personnel, the establishment of industrial hygiene within factories, the regular control of safety systems, and the implementation of industrial health principles and research programs.
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 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...
Stochastic models of cell motility
Gradinaru, Cristian
2012-01-01
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...... coefficient. By adding a persistence component to simple random motion I introduce the standard Ornstein-Uhlenbeck process. I build on this commonly used cell motility model to address the challenges of working with real-life data: positional (centroid coordinate measuring) error and time discretization (due...... generalizing the Orstein-Uhlenbeck process to study cell motility on anisotropic substrates. I apply the general model to analyze cell motility on a series of anisotropic substrates and discuss the implications of our observations. This work is potentially useful to cell biologists by addressing their need for...
Limits for Stochastic Reaction Networks
Cappelletti, Daniele
Reaction systems have been introduced in the 70s to model biochemical systems. Nowadays their range of applications has increased and they are fruitfully used in dierent elds. The concept is simple: some chemical species react, the set of chemical reactions form a graph and a rate function is...... associated with each reaction. Such functions describe the speed of the dierent reactions, or their propensities. Two modelling regimes are then available: the evolution of the dierent species concentrations can be deterministically modelled through a system of ODE, while the counts of the dierent species at...... a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along...
Self-Organising Stochastic Encoders
Luttrell, Stephen
2010-01-01
The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing windows. A stochastic encoder that is an extension of the standard Linde-Buzo-Gray vector quantiser, called a stochastic vector quantiser (SVQ), includes this required behaviour amongst its emergent properties, because it automatically splits the input space into statistically independent subspaces, which it then separately encodes. Various optimal SVQs have been obtained, both analytically and numerically. Analytic solutions which demonstrate how the input space is split into independent subspaces may be obtained when an SVQ is used to encode data that lives on a 2-torus (e.g. the superposition of a pair of uncorrelated sinusoids). Many numerical solutions have also been obtained, using both SVQs and chains of linked SVQs: (1) images of multiple independent targets (encod...
Stochastic stability of traffic maps
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. (paper)
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 models for atmospheric dispersion
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...... variation by height is adopted. A particular problem for simulation studies with finite time steps is the construction of a reflection rule different from the rule of perfect reflection at the boundaries such that the rule complies with the imposed skewness of the velocity distribution for particle...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...
Concentration Bounds for Stochastic Approximations
Frikha, Noufel
2012-01-01
We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. For the first case, as opposed to the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any systematic bias in our estimates. Also, no specific non-degeneracy conditions are assumed.
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...
Stochastic quantization in general relativity
The stochastic quantization method of Parisi and Wu is briefly reviewed stressing its formal resemblance to the Einstein-Smoluchowski theory of Brownian motion. In order to make it applicable in the context of General Relativity, we present a generalization of the method to the case of Lorentzian signature of the space-time metric. It is shown that this approach has non-trivial implications even for linear quantum fields in curved space-time, where it introduces preferred quantum states characterized by the analyticity of the Feynman propagator in the mass parameter. Finally we propose a stochastic quantization scheme for the full nonlinear Einstein theory of gravitation. It employs the concept of a metric in field configuration space and is based mathematically on Ito's calculus. Non-trivial implications for the gravitational path integral measure and for perturbation theory are pointed out. (Author)
The analysis of stochastic stability of stochastic models that describe tumor-immune systems
Chis, O; Opris, D
2009-01-01
In this paper we investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved by constructing a Lyapunov function. We have studied and and analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model for tumor-immune systems. These stochastic models are studied from stability point of view and they were represented using the second Euler scheme and Maple 12 software.
Lower Hybrid Wavepacket Stochasticity Revisited
Fuchs, Vladimír; Laqua, H.P.; Krlín, Ladislav; Pánek, Radomír; Preinhaelter, Josef; Seidl, Jakub; Urban, Jakub
Vol. 1580. Melville : American Institute of Physics, 2014, s. 442-445. ISBN 978-0-7354-1210-1. ISSN 0094-243X. - (AIP Publishing. 1580). [Topical conference on radio frequency power in plasmas/20./. Sorrento (IT), 25.06.2013-28.06.2013] Institutional support: RVO:61389021 Keywords : stellarator * lower hybrid * current drive * Hamiltonian * electron * stochastic Subject RIV: BL - Plasma and Gas Discharge Physics http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4864583
Optimal Advertising with Stochastic Demand
George E. Monahan
1983-01-01
A stochastic, sequential model is developed to determine optimal advertising expenditures as a function of product maturity and past advertising. Random demand for the product depends upon an aggregate measure of current and past advertising called "goodwill," and the position of the product in its life cycle measured by sales-to-date. Conditions on the parameters of the model are established that insure that it is optimal to advertise less as the product matures. Additional characteristics o...
Verification of Stochastic Process Calculi
Skrypnyuk, Nataliya
performed with the purpose to verify the system. In this dissertation it is argued that the verification techniques that have their origin in the analysis of programming code with the purpose to deduce the properties of the code's execution, i.e. Static Analysis techniques, are transferable to stochastic...... description of a system. The presented methods have a clear application in the areas of embedded systems, (randomised) protocols run between a fixed number of parties etc....
Stochastic control of traffic patterns
Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer; Christiansen, Peter L.; Kawamoto, Atsushi; Sørensen, Mads Peter; Starke, Jens
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 of heterogeneous performance of the drivers in time as well as individually. This opens the possibility for the construction of technical tools to control traffic jam formation.