Sample records for 2-stage stochastic cancer

  1. Mode-of-Action Uncertainty for Dual-Mode Carcinogens:Lower Bounds for Naphthalene-Induced Nasal Tumors in Rats Implied byPBPK and 2-Stage Stochastic Cancer Risk Models

    Bogen, K T


    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

  2. Mode-of-Action Uncertainty for Dual-Mode Carcinogens: A Bounding Approach for Naphthalene-Induced Nasal Tumors in Rats Based on PBPK and 2-Stage Stochastic Cancer Risk Models

    Bogen, K T


    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.

  3. 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)


    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.

  4. Gompertzian stochastic model with delay effect to cervical cancer growth

    Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah


    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.

  5. Contributions of stochastic events to biological evolution and cancer

    Anderson KM


    Full Text Available Stochastic genetic and epigenetic events have been fundamental in contributing to the development of manifold life-forms, past and present. The development of malignant cell clones and the role of stochasticity as a driving force in cancer cell evolution complements, in a perverse way evidence for the role of chance in normal cellular development and evolution. Stochastic events at multiple levels of cellular control and implementation represent a primary driving force and an ultimate filter through which evolutionary innovation occurs. Stochasticity provides the opportunity for a random assortment of disparate genetic and epigenetic events, in some instances resulting in altered metabolic and developmental capabilities of sufficient stability and uniqueness to contribute to deterministic sequelae that promote the viability and procreation of cells under stress. Cellular evolution has so far resulted in a “survival of a (sic fittest”, often dependent mechanistically on and determined by stochastic events. The implications of this are mirrored in the evolution of malignant change, to some extent as a variant of “reverse engineering” of dedifferentiation. Efforts to reduce the incidence of malignant change will have to take in to account its random nature and further the understanding of this feature.


    M. Stehlík


    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.

  7. Sentinel lymph node biopsy in clinically N0 T1-T2 staged oral cancer: the Dutch multicenter trial

    Flach, G.B.; Bloemena, E.; Klop, W.M.C.; van Es, R.J.J.; Schepman, K.P.; Hoekstra, O.S.; Castelijns, J.A.; Leemans, C.R.; de Bree, R.


    Objectives Results of the Dutch multi-institutional trial on sentinel lymph node (SLN) biopsy in oral cancer. Patients and methods Patients were consecutively enrolled from 4 institutions, with T1/T2 oral cancer and cN0 neck based on palpation and ultrasound guided fine needle aspiration cytology. L

  8. A Stochastic Model for Cancer Stem Cell Origin in Metastatic Colon Cancer

    Odoux, Christine; Fohrer, Helene; Hoppo, Toshitaka; Guzik, Lynda; Stolz, Donna Beer; Lewis, Dale W.; Gollin, Susanne M.; Gamblin, T. Clark; Geller, David A.; Lagasse, Eric


    Human cancers have been found to include transformed stem cells that may drive cancer progression to metastasis. Here we report that metastatic colon cancer contains clonally derived tumor cells with all of the critical properties expected of stem cells, including self-renewal and to the ability to differentiate into mature colon cells. Additionally, when injected into mice, these cells initiated tumors that closely resemble human cancer. Karyotype analyses of parental and clonally-derived tumor cells expressed many consistent (clonal), along with unique chromosomal aberrations, suggesting the presence of chromosomal instability in the cancer stem cells. Thus, this new model for cancer origin and metastatic progression includes features of both the hierarchical model for cancerous stem cells and the stochastic model, driven by the observation of chromosomal instability. PMID:18757407

  9. A 2-Stage Genome-Wide Association Study to Identify Single Nucleotide Polymorphisms Associated With Development of Erectile Dysfunction Following Radiation Therapy for Prostate Cancer

    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: [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)


    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.

  10. Dynamics between cancer cell subpopulations reveals a model coordinating with both hierarchical and stochastic concepts.

    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.

  11. Stochastic model for computer simulation of the number of cancer cells and lymphocytes in homogeneous sections of cancer tumors

    Castellanos-Moreno, Arnulfo; Corella-Madueño, Adalberto; Gutiérrez-López, Sergio; Rosas-Burgos, Rodrigo


    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 ...

  12. Discovery Radiomics via StochasticNet Sequencers for Cancer Detection

    Shafiee, Mohammad Javad; Chung, Audrey G.; Kumar, Devinder; Khalvati, Farzad; Haider, Masoom; Wong, Alexander


    Radiomics has proven to be a powerful prognostic tool for cancer detection, and has previously been applied in lung, breast, prostate, and head-and-neck cancer studies with great success. However, these radiomics-driven methods rely on pre-defined, hand-crafted radiomic feature sets that can limit their ability to characterize unique cancer traits. In this study, we introduce a novel discovery radiomics framework where we directly discover custom radiomic features from the wealth of available...

  13. A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis

    Newton, Paul K.; Jeremy Mason; Kelly Bethel; Bazhenova, Lyudmila A.; Jorge Nieva; Peter Kuhn


    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 d...

  14. Stochastic Effects in Computational Biology of Space Radiation Cancer Risk

    Cucinotta, Francis A.; Pluth, Janis; Harper, Jane; O'Neill, Peter


    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.

  15. Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model

    Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe


    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.

  16. A stochastic model for identifying differential gene pair co-expression patterns in prostate cancer progression

    Mao Yu


    Full Text Available Abstract Background The identification of gene differential co-expression patterns between cancer stages is a newly developing method to reveal the underlying molecular mechanisms of carcinogenesis. Most researches of this subject lack an algorithm useful for performing a statistical significance assessment involving cancer progression. Lacking this specific algorithm is apparently absent in identifying precise gene pairs correlating to cancer progression. Results In this investigation we studied gene pair co-expression change by using a stochastic process model for approximating the underlying dynamic procedure of the co-expression change during cancer progression. Also, we presented a novel analytical method named 'Stochastic process model for Identifying differentially co-expressed Gene pair' (SIG method. This method has been applied to two well known prostate cancer data sets: hormone sensitive versus hormone resistant, and healthy versus cancerous. From these data sets, 428,582 gene pairs and 303,992 gene pairs were identified respectively. Afterwards, we used two different current statistical methods to the same data sets, which were developed to identify gene pair differential co-expression and did not consider cancer progression in algorithm. We then compared these results from three different perspectives: progression analysis, gene pair identification effectiveness analysis, and pathway enrichment analysis. Statistical methods were used to quantify the quality and performance of these different perspectives. They included: Re-identification Scale (RS and Progression Score (PS in progression analysis, True Positive Rate (TPR in gene pair analysis, and Pathway Enrichment Score (PES in pathway analysis. Our results show small values of RS and large values of PS, TPR, and PES; thus, suggesting that gene pairs identified by the SIG method are highly correlated with cancer progression, and highly enriched in disease-specific pathways. From

  17. Stochastic modeling and experimental analysis of phenotypic switching and survival of cancer cells under stress

    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.

  18. Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer.

    Grazziela P Figueredo

    Full Text Available There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1 Does this new stochastic formulation produce similar results to the agent-based version? (2 Can these methods be used interchangeably? (3 Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.

  19. Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer.

    Figueredo, Grazziela P; Siebers, Peer-Olaf; Owen, Markus R; Reps, Jenna; Aickelin, Uwe


    There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.

  20. Identification of Potential Drug Targets in Cancer Signaling Pathways using Stochastic Logical Models.

    Zhu, Peican; Aliabadi, Hamidreza Montazeri; Uludağ, Hasan; Han, Jie


    The investigation of vulnerable components in a signaling pathway can contribute to development of drug therapy addressing aberrations in that pathway. Here, an original signaling pathway is derived from the published literature on breast cancer models. New stochastic logical models are then developed to analyze the vulnerability of the components in multiple signalling sub-pathways involved in this signaling cascade. The computational results are consistent with the experimental results, where the selected proteins were silenced using specific siRNAs and the viability of the cells were analyzed 72 hours after silencing. The genes elF4E and NFkB are found to have nearly no effect on the relative cell viability and the genes JAK2, Stat3, S6K, JUN, FOS, Myc, and Mcl1 are effective candidates to influence the relative cell growth. The vulnerabilities of some targets such as Myc and S6K are found to vary significantly depending on the weights of the sub-pathways; this will be indicative of the chosen target to require customization for therapy. When these targets are utilized, the response of breast cancers from different patients will be highly variable because of the known heterogeneities in signaling pathways among the patients. The targets whose vulnerabilities are invariably high might be more universally acceptable targets.

  1. Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

    L. G. Hanin


    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.

  2. Fractal and stochastic geometry inference for breast cancer: a case study with random fractal models and Quermass-interaction process.

    Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan


    Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.

  3. 开塞露在直肠癌MRI术前T1和T2分期中的应用%The value of Enema Glycerine applying in preoperative MRI T1 staging and T2 staging of rectal cancer

    李兆祥; 薛华丹; 秦明伟; 潘卫东


    目的:探讨使用开塞露进行肠道准备对直肠癌磁共振术前T1和T2分期的意义。材料与方法回顾经手术病理证实为T1或T2分期的直肠癌患者81例,男51例,女30例,平均年龄(64.2±12.2)岁。其中,45例(男30例,女15例)使用开塞露,36例(男21例,女15例)未使用开塞露。分别分析两组MRI术前分期与手术病理分期结果的一致性,计算并比较两组MRI T1、T2分期的敏感度、特异度、准确度、阳性预测值、阴性预测值和T1+T2分期的敏感度。结果 Kappa检验证实两组MRI术前分期与手术病理分期结果的一致性均为中等,K值分别为使用开塞露组0.693,未使用开塞露组0.537。使用开塞露组直肠癌磁共振T分期的敏感度、特异度、准确度、阳性预测值、阴性预测值分别为T1分期:76.5%、92.9%、86.7%、86.7%、86.7%;T2分期:78.6%、76.5%、86.7%、84.5%、68.4%;T1+T2分期的敏感度为:77.8%。未使用开塞露组直肠癌磁共振T分期的敏感度、特异度、准确度、阳性预测值、阴性预测值分别为T1分期:57.1%、95.5%、80.6%、88.9%、77.8%;T2分期:77.3%、57.1%、69.4%、73.9%、61.5%;T1+T2分期的敏感度为:69.4%。统计分析证实使用开塞露组T1分期的敏感度及T2分期的特异度、准确度高于未使用开塞露组(P<0.05,单侧)。结论使用开塞露进行肠道准备能够明显提高直肠癌磁共振T1分期的敏感度、T2分期特异度及准确度,同时在一定程度上提高T1和T1+T2分期的诊断准确性,建议作为直肠癌磁共振检查的肠道准备常规应用。%Objective: To evaluate the value of Enema Glycerine applied in preoperative MRI T1 staging and T2 staging of rectal cancer. Materials and Methods:The MRI datum of 81 cases of pathologically conifrmed T1 staging or T2 staging of rectal cancer suffers after operation (50 males and 31 females whose ages, 64.2±12.2 on average, range from 31 to 88

  4. Stochastic volatility and stochastic leverage

    Veraart, Almut; Veraart, Luitgard A. M.

    This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

  5. A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer

    Liu, Yifang; Lee, Chi-Guhn [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S 3G8 (Canada); Chan, Timothy C. Y., E-mail: [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S 3G8, Canada and Techna Institute for the Advancement of Technology for Health, 124-100 College Street Toronto, Ontario M5G 1P5 (Canada); Cho, Young-Bin [Department of Radiation Physics, Radiation Medicine Program, Princess Margaret Cancer Centre, University Health Network, 610 University of Avenue, Toronto, Ontario M5T 2M9, Canada and Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2 (Canada); Islam, Mohammad K. [Department of Radiation Physics, Radiation Medicine Program, Princess Margaret Cancer Centre, University Health Network, 610 University of Avenue, Toronto, Ontario M5T 2M9 (Canada); Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2 (Canada); Techna Institute for the Advancement of Technology for Health, 124-100 College Street, Toronto, Ontario M5G 1P5 (Canada)


    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.

  6. Stochastic Shadowing and Stochastic Stability

    Todorov, Dmitry


    The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.

  7. 术中肠系膜下动脉注射亚甲蓝溶液对T2期直肠癌淋巴结检出数目的影响%Change of T2 stage rectal cancer's lymph nodes by injecting methylene blue into the inferior mesenteric artery of intraoperative

    胡丰良; 金鑫; 孙锋; 陈丹; 赵文韬


    目的 探讨直肠癌根治术中使用亚甲蓝溶液注入肠系膜下动脉对T2期的直肠癌标本淋巴结的检出情况.方法 对2004年12月至2011年6月间43例T2期直肠癌患者术后标本进行研究分析,其中2004年12月至2008年8月间,采取常规方法即肉眼加触摸对标本获取淋巴结(常规方法组,23例);2008年9月至2011年6月采取术中肠系膜下动脉注射亚甲蓝溶液配合常规方法获取淋巴结(亚甲蓝注射组,20例).比较2组的淋巴结检出情况及阳性淋巴结检出情况.结果 亚甲蓝注射组共检出淋巴结484枚,平均淋巴结检出数为(24±14)枚;常规方法组检出淋巴结总数为214枚,平均淋巴结检出数为(9±5)枚,2组差异有统计学意义(P<0.05).亚甲蓝注射组共检出直径<5 mm的淋巴结228枚,平均淋巴结检出数为(1l.4±6.4)枚;常规方法共检出直径<5 mm淋巴结60枚,平均淋巴结检出数为(3.0±1.4)枚,2组差异有统计学意义(P<0.01).亚甲蓝注射组共检出22枚阳性淋巴结,平均检出数为(1.1±1.0)枚;常规方法组共检出16枚阳性淋巴结,平均检出数为(0.7±0.6)枚,2组差异无统计学意义(P>0.05).结论 对于T2期直肠癌患者实施根治术时采用肠系膜下动脉注射亚甲蓝溶液可以明显提高淋巴结检出数目,从而可能提高术后分期的准确性,为术后的辅助治疗提供依据.%Objective To study whether injecting methylene blue into the inferior mesenteric artery(IMA)in the redical operation of T2 stage rectal cancer can harvest more lymph nodes than the conventional method.Methods From December 2004 to June 2011,43 specimens of T2 stage colorectal cancer were studied,including 23 cases of conventional method group(using the naked eye and douching specimens to get lymph nodes)in December 2004 to August 2008,and 20 cases of methylene blue injection group(injecting methylene blue into the interior mesenteric artery combined with the conventional method

  8. The clinical efficacy of TME combined with different ISR surgery in the treatment of T1 and T2 stage ultra-low rectal cancer%TME联合ISR不同术式治疗T1和T2期超低位直肠癌的临床疗效观察



    Objective To evaluate the clinical effect and postoperative anal function of total mesorectum excision (TME) combined with different intersphincteric resection (ISR) surgery in the treatment of T1 and T2 stage ultra-low rectal cancer patients. Methods The clinical data of 68 cases of T1 and T2 stage ultra-low colorectal cancer patients who received the TME combined with different ISR surgeries from January 2010 - January 2014 were retrospectively analyzed, in which there were 22 cases of complete internal anal sphincter excision (complete ISR), and 26 cases of partial internal anal sphincter excision, and the remaining 20 cases were administered with ISR + dentate line preser-vation. Results 1) The operation time, intraoperative blood loss, length of removed intestinal canal, distance of surgi-cal margin, the number of resected lymph nodes, negativity of surgical margin, and postoperative complications of the three groups were compared, and no statistically significant differences were observed (P > 0.05); 2) In 3, 6, 12 months after surgery, there were more patients with normal anal function in the partial ISR group and the dentate line preservation group than in the completely ISR group (χ2 = 4.384, 4.227, 4.654, P = 0.026, 0.018, 0.015, respective-ly). Conclusion TME combined with ISR surgery is safe and effective in the treatment of T1 and T2 stage ultra-low rectal cancer, and it is clinically important to improve postoperative anal function that the radical resection is guaran-teed while partial internal anal sphincter and dentate line are preserved as much as possible.%目的:探讨全直肠系膜切除术(TME)联合经肛门括约肌间切除术(ISR)不同术式治疗T1和T2期超低位直肠癌的肿瘤根治效果及术后肛门功能观察。方法回顾性分析68例实施TME联合ISR手术的T1和T2期超低位直肠癌患者的临床资料,其中实施切除全部内括约肌的ISR者22例作为完全ISR组,

  9. 经肛门括约肌间切除术治疗超低位直肠癌根治效果及术后肛门功能观察%Radical effect and postoperative anal function of total mesorectum excision combined with different intersphincter resection in treatment of T1 and T2 stage ultra-low rectal cancer

    马磊; 丁克; 刘广余; 张丹丹


    Objective To evaluate the radical effect and postoperative anal function of total mesorectum excision (TME) combined with different intersphincter resection (ISR) in treatment of T1 and T2 stage ultra-low rectal cancer. Methods Clinical data of 102 T1 and T2 stage ultra-low colorectal cancer patients who received TME combined with different ISR from January 2004 to December 2013 in our department, including 33 cases of complete internal anal sphincter excision ISR (complete ISR group), 39 cases of partial internal anal sphincter excision ISR(partial ISR), 30 cases of partial dentate line reservation ISR (dentate line group). All the operation procedures followed the principles of TME. Radical conditions were compared and similarly, postoperative anal function was evaluated by Williams classification standard among 3 groups. Results The general information, such as gender, age, BMI, maximum diameter of tumor, distance of tumor edge to dentate line, TNM staging, degree of differentiation among 3 groups had no statistically significant differences (all P>0.05). The operation time, intraoperative blood loss, length of removed intestinal canal, resection margin, the harvested number of lymph nodes, and postoperative complications among 3 groups also had no statistically significant differences (all P>0.05). Twelve months after surgery, good anal function rate in part ISR group and dentate line group was 100%, significantly better than that incomplete ISR group (75.8%) with significant difference (x2=4.654, P=0.015). Conclusion TME combined with ISR surgery in treatment of T1 and T2 stage ultra-low rectal cancer is safe and effective, which, as far as possible to preserve partial internal sphincter and dentate line on the premise of the guarantee of radical condition, can help to improve the postoperative anal function.%目的:探讨经肛门括约肌间切除术(ISR)治疗T1和T2期超低位直肠癌的肿瘤根治效果及术后肛门

  10. Stochastic processes

    Parzen, Emanuel


    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

  11. Stochastic optimization

    Schneider, Johannes J


    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.

  12. 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)


    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.

  13. Application of biomarkers in cancer risk management: evaluation from stochastic clonal evolutionary and dynamic system optimization points of view.

    Xiaohong Li


    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.

  14. Quantum stochastics

    Chang, Mou-Hsiung


    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...

  15. Stochastic partial differential equations

    Chow, Pao-Liu


    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  16. Stochastic Constraint Programming

    Walsh, Toby


    To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number...

  17. Stochastic thermodynamics

    Eichhorn, Ralf; Aurell, Erik


    '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

  18. Stochastic Analysis 2010

    Crisan, Dan


    "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

  19. 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


    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.

  20. Stochastic Jeux

    Romanu Ekaterini


    Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.

  1. Stochastic modeling

    Lanchier, Nicolas


    Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...

  2. Stochastic Cooling

    Blaskiewicz, M.


    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.



    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.

  4. Stochastic Averaging and Stochastic Extremum Seeking

    Liu, Shu-Jun


    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...

  5. Stochastic homothetically revealed preference for tight stochastic demand functions

    Jan Heufer


    This paper strengthens the framework of stochastic revealed preferences introduced by Bandyopadhyay et al. (1999, 2004) for stochastic homothetically revealed preferences for tight stochastic demand functions.

  6. Cancer

    ... cancer Non-Hodgkin lymphoma Ovarian cancer Pancreatic cancer Testicular cancer Thyroid cancer Uterine cancer Symptoms Symptoms of cancer ... tumor Obesity Pancreatic cancer Prostate cancer Stomach cancer Testicular cancer Throat or larynx cancer Thyroid cancer Patient Instructions ...

  7. The stochastic integrable AKNS hierarchy

    Arnaudon, Alexis


    We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose som...

  8. New stochastic calculus

    Moawia Alghalith


    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.

  9. Stochastic processes - quantum physics

    Streit, L. (Bielefeld Univ. (Germany, F.R.))


    The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.

  10. Stochastic tools in turbulence

    Lumey, John L


    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


    Qi-Ming HE; Eldon GUNN


    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.

  12. Stochastic Lie group integrators

    Malham, Simon J A


    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...

  13. Fundamentals of Stochastic Networks

    Ibe, Oliver C


    An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physi

  14. Singular stochastic differential equations

    Cherny, Alexander S


    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  15. Fluctuations as stochastic deformation

    Kazinski, P. O.


    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.

  16. Stochastic longshore current dynamics

    Restrepo, Juan M.; Venkataramani, Shankar


    We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.

  17. 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...

  18. Instantaneous stochastic perturbation theory

    Lüscher, Martin


    A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

  19. A Stochastic Employment Problem

    Wu, Teng


    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…

  20. Stochastic Convection Parameterizations

    Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios


    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

  1. Stochastic Flutter Analysis

    Verhoosel, C.V.; Gutiérrez, M.A.; Hulshoff, S.J.


    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 con

  2. Stochastic volatility selected readings

    Shephard, Neil


    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...

  3. Stochastic neuron models

    Greenwood, Priscilla E


    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...

  4. Stochastic Skellam model

    Kraenkel, R. A.; da Silva, D. J. Pamplona


    We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.

  5. Sequential stochastic optimization

    Cairoli, Renzo


    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

  6. Stochastic differential equations and applications

    Friedman, Avner


    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

  7. Stochastic processes inference theory

    Rao, Malempati M


    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.

  8. Stochastic modelling of turbulence

    Sørensen, Emil Hedevang Lohse

    This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... 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...... is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has...

  9. Stochastic calculus with infinitesimals

    Herzberg, Frederik


    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.

  10. Stochastic Gauss Equations

    Frédéric, Pierret


    The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.

  11. Notes on the Stochastic Exponential and Logarithm

    Larsson, Martin; Ruf, Johannes


    Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.

  12. Geometric Stochastic Resonance

    Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco


    A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.

  13. Quantum Spontaneous Stochasticity

    Eyink, Gregory L


    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...

  14. Stochastic dynamics and irreversibility

    Tomé, Tânia


    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 ...

  15. Stochastic models, estimation, and control

    Maybeck, Peter S


    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.




    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.

  17. Stochastic Electrochemical Kinetics

    Beruski, O


    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.

  18. Foundations of stochastic analysis

    Rao, M M; Lukacs, E


    Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea

  19. Stochastic Gauss equations

    Pierret, Frédéric


    We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.

  20. Stochastic dynamics and control

    Sun, Jian-Qiao; Zaslavsky, George


    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

  1. Markov stochasticity coordinates

    Eliazar, Iddo


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

  2. Stochastic integrals: a combinatorial approach

    Rota, Gian-Carlo; Wallstrom, Timothy C.


    A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...

  3. Hamiltonian mechanics of stochastic acceleration.

    Burby, J W; Zhmoginov, A I; Qin, H


    We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

  4. Design of 12-phase, 2-stage Harmonic Rejection Mixer for TV Tuners

    D. Lee


    Full Text Available A two-stage 12-phase harmonic rejection mixer (HRM for TV tuners is proposed in order to reject the local oscillator (LO harmonics up to the ninth order. The proposed weighing scheme for 12-phase, 2-stage harmonic mixing can reduce the harmonic rejection (HR sensitivity to the amplitude error caused by irrational numbers such as . To verify this HR, the 2-stage HR circuit is designed with baseband gm weighting in order to save power and improve the HR ratios without calibration. The proposed HRM achieves the third to ninth worst HR ratios, more than 55 dB, according to Monte Carlo simulations. It consumes 6.5 mA under a 2.5 V supply voltage.

  5. Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor

    Songtao WANG; Xin DU; Zhongqi WANG


    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.

  6. Stochastic integral equations without probability

    Mikosch, T; Norvaisa, R


    A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0

    stochastic process. Typical examples of such

  7. Analysis of bilinear stochastic systems

    Willsky, A. S.; Martin, D. N.; Marcus, S. I.


    Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

  8. Multistage quadratic stochastic programming

    Lau, Karen K.; Womersley, Robert S.


    Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.

  9. Understanding Stochastic Subspace Identification

    Brincker, Rune; Andersen, Palle


    The data driven Stochastic Subspace Identification techniques is considered to be the most powerful class of the known identification techniques for natural input modal analysis in the time domain. However, the techniques involves several steps of "mysterious mathematics" that is difficult...

  10. Stochastic Control - External Models

    Poulsen, Niels Kjølstad


    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...

  11. Affine stochastic mortality

    D.F. Schrager


    We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing m

  12. Stochastic biophysical modeling of irradiated cells

    Fornalski, Krzysztof Wojciech


    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 ...

  13. Estimation of Large-Scale Implicit Models Using 2-Stage Methods

    Rolf Henriksen


    Full Text Available The problem of estimating large scale implicit (non-recursive models by two- stage methods is considered. The first stage of the methods is used to construct or estimate an explicit form of the total model, by constructing a minimal stochastic realization of the system. This model is then subsequently used in the second stage to generate instrumental variables for the purpose of estimating each sub-model separately. This latter stage can be carried out by utilizing a generalized least squares method, but most emphasis is put on utilizing decentralized filtering algorithms and a prediction error formulation. A note about the connection between the original TSLS-method (two-stage least squares method and stochastic realization is also made.

  14. Stochastic processes in cell biology

    Bressloff, Paul C


    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...

  15. Limits for Stochastic Reaction Networks

    Cappelletti, Daniele

    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 a path...... of the stochastic reaction systems. Specically, we build a theory for stochastic reaction systems that is parallel to the deciency zero theory for deterministic systems, which dates back to the 70s. A deciency theory for stochastic reaction systems was missing, and few results connecting deciency and stochastic....... Such species, in the deterministic modelling regime, assume always the same value at any positive steady state. In the stochastic setting, we prove that, if the initial condition is a point in the basin of attraction of a positive steady state of the corresponding deterministic model and tends to innity...

  16. Stochastic response surface methodology: A study in the human health area

    Oliveira, Teresa A., E-mail:; Oliveira, Amílcar, E-mail: [Departamento de Ciências e Tecnologia, Universidade Aberta (Portugal); Centro de Estatística e Aplicações, Universidade de Lisboa (Portugal); Leal, Conceição, E-mail: [Departamento de Ciências e Tecnologia, Universidade Aberta (Portugal)


    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.

  17. Dimensional accuracy of 2-stage putty-wash impressions: influence of impression trays and viscosity.

    Balkenhol, Markus; Ferger, Paul; Wöstmann, Bernd


    The aim of this in vitro study was to evaluate the influence of the impression tray and viscosity of the wash material on the dimensional accuracy of impressions taken using a 2-stage putty-wash technique. Identically shaped metal stock trays (MeTs) and disposable plastic stock trays (DiTs) were used for taking impressions (n = 10) of a mandibular cast (4 abutments) with 2 different impression materials. Dies were poured and the relative diameter deviation was calculated after measurement. Zero viscosity of the materials was determined. Dimensional accuracy was significantly affected when DiTs were used. Lower-viscosity wash materials led to more precise impressions.

  18. 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)


    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.

  19. Stochastic porous media equations

    Barbu, Viorel; Röckner, Michael


    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  20. Dynamic stochastic optimization

    Ermoliev, Yuri; Pflug, Georg


    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...

  1. Stochastic calculus and applications

    Cohen, Samuel N


    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...

  2. Essentials of stochastic processes

    Durrett, Richard


    Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...

  3. A stochastic control problem

    William Margulies


    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.

  4. Multistage stochastic optimization

    Pflug, Georg Ch


    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

  5. Dynamics of stochastic systems

    Klyatskin, Valery I


    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 ...

  6. Stochastic power system operation

    Power, Michael


    This paper outlines how to economically and reliably operate a power system with high levels of renewable generation which are stochastic in nature. It outlines the challenges for system operators, and suggests tools and methods for meeting this challenge, which is one of the most fundamental since large scale power networks were instituted. The Ireland power system, due to its nature and level of renewable generation, is considered as an example in this paper.

  7. Stochastic Games. I. Foundations,


    stimulate discussion and critical coment. Requests for single copies of a Paper will be filled by the Cowles Foundation within the limits of the supply...underpinning for the theory of stochastic games. Section 2 is a reworking of the Bevley- Kohlberg result integrated with Shapley’s; the "black magic" of... Kohlberg : The values of the r-discount game, and the stationary optimal strategies, have Puiseaux expansions. L.. 11" 6 3. More generally, consider an

  8. Stochastic Thermodynamics of Learning

    Goldt, Sebastian; Seifert, Udo


    Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.

  9. Stochastic disks that roll

    Holmes-Cerfon, Miranda


    We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.

  10. Stochastic gravitoelectromagnetic inflation

    Madriz Aguilar, José Edgar; Bellini, Mauricio


    Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this Letter, we study a stochastic treatment for the gravitoelectromagnetic components A=(A,φ), on cosmological scales. We focus our study on the seed magnetic fields on super-Hubble scales, which could play an important role in large scale structure formation of the universe.

  11. Stochastic gravitoelectromagnetic inflation

    Aguilar, J E M; Bellini, Mauricio


    Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this paper, we study a stochastic treatment for the gravitoelectromagnetic components $A_B=(A_{\\mu},\\phi)$, on cosmological scales. We focus our study on the seed magnetic fields on super Hubble scales, which could play an important role in large scale structure formation of the universe.

  12. Identifiability in stochastic models


    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.

  13. Stochastic Thermodynamics of Learning

    Goldt, Sebastian


    Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\\eta\\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit.

  14. Stochastic Nonlinear Aeroelasticity


    STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right

  15. Stochasticity Modeling in Memristors

    Naous, Rawan


    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.

  16. Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours

    Lang, Annika


    This thesis discusses several aspects of the simulation of stochastic partial differential equations. First, two fast algorithms for the approximation of infinite dimensional Gaussian random fields with given covariance are introduced. Later Hilbert space-valued Wiener processes are constructed out of these random fields. A short introduction to infinite-dimensional stochastic analysis and stochastic differential equations is given. Furthermore different definitions of numerical stability for...

  17. Some stochastic aspects of quantization

    Ichiro Ohba


    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.

  18. Verification of Stochastic Process Calculi

    Skrypnyuk, Nataliya

    Stochastic process calculi represent widely accepted formalisms within Computer Science for modelling nondeterministic stochastic systems in a compositional way. Similar to process calculi in general, they are suited for modelling systems in a hierarchical manner, by explicitly specifying...... subsystems as well as their interdependences and communication channels. Stochastic process calculi incorporate both the quantified uncertainty on probabilities or durations of events and nondeterministic choices between several possible continuations of the system behaviour. Modelling of a system is often...

  19. Stochastic Analysis of Cylindrical Shell

    Grzywiński Maksym


    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.

  20. Stochastic Nature in Cellular Processes

    刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa


    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.

  1. A recurrent stochastic binary network



    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.

  2. Mesoscopic Fluctuations in Stochastic Spacetime

    Shiokawa, K


    Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.

  3. Hydrogen production by Anabaena sp. CH1 with 2-stage process

    Chiang, C.L.; Lee, C.M. [National Chung Hsing Univ., Taiwan (China). Dept. of Environmental Engineering; Chen, P.C. [Hungkuang Univ., Taiwan (China). Dept. of Biomedical Nutrition


    While hydrogen can be produced by cyanobacteria under anoxic conditions, chlorophylls can break down and provide the nitrogen needed for cell material synthesis. The breakdown of chlorophylls is unfavorable for the long-term production of hydrogen. This study provided details of a 2-stage operation designed to prevent chlorophyll breakdown. Anabaena sp. CH1 was used in both the hydrogen production and recovery stages. Nitrogenase activity, chlorophyll concentrations, and hydrogen production rates decreased to 54 per cent after argon gases were used for a 3-day period. Growth conditions than shifted to normal conditions after 3 to 5 days. Cells recovered their nitrogenase activities, biomass, and chlorophyll concentrations within 4 days. The recovery stage then shifted to the hydrogen production stage, where hydrogen production rates were as high as previous observed rates. It was concluded that the effects of nitrogen deprivation on photosynthetic mechanisms are reversible.

  4. Stochastic Physicochemical Dynamics

    Tsekov, R.


    Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic

  5. Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

    Varga, Katherine Yvonne


    We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

  6. 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 the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...

  7. Deduction as Stochastic Simulation


    Eab Oa b Eab Ob a Iab Aab Iab Aba Iab Eab Iab EbaIab Iab Iab Iba Iab Oa b Iab Ob a Oa bAa b Oa bAb a Oa bEa b Oa bEb a Oa bIa b Oa bIb a Oa bO ab Oa bO...Oa bIa b Oa bIb a Oa bO ab Oa bO ba % C or re ct A. B. stochastic system’s parameters could be tweaked for individual reasoners. For example, the λ

  8. Stochastic conditional intensity processes

    Bauwens, Luc; Hautsch, Nikolaus


    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...... 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...

  9. Stochastic ontogenetic growth model

    West, B. J.; West, D.


    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.

  10. Stochastic multi-stage optimization at the crossroads between discrete time stochastic control and stochastic programming

    Carpentier, Pierre; Cohen, Guy; De Lara, Michel


    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.

  11. Stochastic Runge-Kutta Software Package for Stochastic Differential Equations

    Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A


    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...

  12. Mixed effects in stochastic differential equation models

    Ditlevsen, Susanne; De Gaetano, Andrea


    maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...

  13. Discretization error of Stochastic Integrals

    Fukasawa, Masaaki


    Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.

  14. 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...

  15. Stochastic ferromagnetism analysis and numerics

    Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas


    This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.

  16. Stochastic Pi-calculus Revisited

    Cardelli, Luca; Mardare, Radu Iulian


    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...

  17. Recursive Concurrent Stochastic Games

    Etessami, Kousha


    We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [16,17] to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \\epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \\epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy r...

  18. Stochastic power flow modeling


    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.

  19. AA, stochastic precooling pickup


    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...

  20. Stochastic Blind Motion Deblurring

    Xiao, Lei


    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.

  1. Simple stochastic simulation.

    Schilstra, Maria J; Martin, Stephen R


    Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.

  2. Variance decomposition in stochastic simulators

    Le Maître, O. P.


    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.

  3. Variance decomposition in stochastic simulators

    Le Maître, O. P.; Knio, O. M.; Moraes, A.


    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.

  4. Variance decomposition in stochastic simulators.

    Le Maître, O P; Knio, O M; Moraes, A


    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.

  5. Brownian motion and stochastic calculus

    Karatzas, Ioannis


    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...

  6. Classical and spatial stochastic processes with applications to biology

    Schinazi, Rinaldo B


    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...

  7. 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


    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.

  8. Technical note: a 2-stage cecal cannulation technique in standing horses.

    Beard, W L; Slough, T L; Gunkel, C D


    Cecal cannulation is necessary for sampling of intestinal contents for a variety of nutritional or digestive physiology studies. This report describes a 2-stage technique for permanent cecal cannulation in standing horses. For the first procedure, a right flank laparotomy is performed and a small pouch of the cecal base exteriorized and sutured to the body wall. The second procedure is performed approximately 1 wk later. During the second procedure, the exposed cecal pouch is removed and the cannula inserted. Ten horses were cannulated using this technique. After the first procedure, 1 horse developed a cecal impaction unresponsive to medical therapy and ruptured its cecum, whereas 2 other horses developed mild transient colic that responded to medical management. Insertion of the cecal cannula after creation of the stoma in the second procedure resulted in transient colic in 4 of 9 horses, but they responded to analgesic therapy in less than 24 h in all instances. The time to complete healing of the cannula site was approximately 30 d. The technique described in this report decreases the risk of peritonitis due to intestinal leakage and is technically easier to perform than previously described techniques.

  9. Stochastic population theories

    Ludwig, Donald


    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...

  10. Stochastic Engine Convergence Diagnostics

    Glaser, R


    The stochastic engine uses a Markov Chain Monte Carlo (MCMC) sampling device to allow an analyst to construct a reasonable estimate of the state of nature that is consistent with observed data and modeling assumptions. The key engine output is a sample from the posterior distribution, which is the conditional probability distribution of the state of nature, given the data. In applications the state of nature may refer to a complicated, multi-attributed feature like the lithology map of a volume of earth, or to a particular related parameter of interest, say the centroid of the largest contiguous sub-region of specified lithology type. The posterior distribution, which we will call f, can be thought of as the best stochastic description of the state of nature that incorporates all pertinent physical and theoretical models as well as observed data. Characterization of the posterior distribution is the primary goal in the Bayesian statistical paradigm. In applications of the stochastic engine, however, analytical calculation of the posterior distribution is precluded, and only a sample drawn from the distribution is feasible. The engine's MCMC technique, which employs the Metropolis-Hastings algorithm, provides a sample in the form of a sequence (chain) of possible states of nature, x{sup (1)}, x{sup (2)}, ..., x{sup (T)}, .... The sequencing is motivated by consideration of comparative likelihoods of the data. Asymptotic results ensure that the sample ultimately spans the entire posterior distribution and reveals the actual state frequencies that characterize the posterior. In mathematical jargon, the sample is an ergodic Markov chain with stationary distribution f. What this means is that once the chain has gone a sufficient number of steps, T{sub 0}, the (unconditional) distribution of the state, x{sup (T)}, at any step T {ge} T{sub 0} is the same (i.e., is ''stationary''), and is the posterior distribution, f. We call T{sub 0} the &apos

  11. Stochastic reconstruction of sandstones

    Manwart; Torquato; Hilfer


    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.

  12. Crystallization by stochastic flips

    Bodini, Olivier; Fernique, Thomas; Regnault, Damien


    Tilings are often used as a toy model for quasicrystals, with the ground states corresponding to the tilings satisfying some local properties (matching rules). In this context, a challenging problem is to provide a theory for quasicrystals growth. One of the proposed theories is the relaxation process. One assumes that the entropy of a tiling increases with the number of tilings which can be formed with the same tiles, while its energy is proportional to the ratio of satisfied matching rules. Then, by starting from an entropically stabilized tiling at high temperature and by decreasing the temperature, the phason flips which decrease (resp. increase) the energy would become more and more favoured (resp. inhibited). Ideally, the tiling eventually satisfies all the matching rules, and thus shows a quasicrystalline structure. This paper describes a stochastic process inspired by this and discusses its convergence rate.

  13. Stochastic dynamic equations on general time scales

    Martin Bohner


    Full Text Available 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.

  14. Overview of Stochastic Vehicle Routing Problems

    郭耀煌; 谢秉磊; 郭强


    Stochastic vehicle routing problems (VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.

  15. An introduction to probability and stochastic processes

    Melsa, James L


    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.

  16. Introduction to stochastic dynamic programming

    Ross, Sheldon M; Lukacs, E


    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

  17. Frequency Resonance in Stochastic Systems

    钱敏; 张雪娟


    The phenomenon of frequency resonance, which is usually related to deterministic systems, is investigated in stochastic systems. We show that for those autonomous systems driven only by white noise, if the output power spectrum exhibits a nonzero peak frequency, then applying a periodic signel just on this noise-induced central frequency can also induce a resonance phenomenon, which we call the frequency stochastic resonance. The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.

  18. Uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes

    Wei, Jinlong; Liu, Bin


    In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the It\\^{o} formula and the regularization techniques. Furthermore, as an application, we derive the uniqueness of stochastic entropy solutions for stochastic porous media type equations.

  19. Stochastic analysis of laminated composite plate considering stochastic homogenization problem



    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.

  20. A Note on Almost Stochastic Dominance

    Guo, Xu; Zhu, Xuehu; Wong, Wing-Keung; Zhu, Lixing


    To satisfy the property of expected-utility maximization, Tzeng et al. (2012) modify the almost second-degree stochastic dominance proposed by Leshno and Levy (2002) and define almost higher-degree stochastic dominance. In this note, we further investigate the relevant properties. We define an almost third-degree stochastic dominance in the same way that Leshno and Levy (2002) define second-degree stochastic dominance and show that Leshno and Levy's (2002) almost stochastic dominance has t...

  1. Computer Auxiliary Analysis for Stochasticity of Chaos

    ZHAOGeng; FANGJin-qing


    In this work, we propose a mathematics-physical statistic analytical method for stochastic process of chaos, based on stochastic test via combination measurement of Monobit and Runs. Computer auxiliary analysis shows that it is of stochasticity for stochastic number produced from the chaotic circuit. Our software is written by VB and C++, the later can be tested by the former, and at the same time it is verified by stochastic number produced by the computer. So the data treatment results are reliable.

  2. Predicting population extinction or disease outbreaks with stochastic models

    Linda J. S. Allen


    Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.

  3. Stochastic Climate Theory and Modelling

    Franzke, Christian L E; Berner, Judith; Williams, Paul D; Lucarini, Valerio


    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...

  4. Stochastic Modelling of Hydrologic Systems

    Jonsdottir, Harpa


    In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains an introduct......In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...

  5. Stochastic Still Water Response Model

    Friis-Hansen, Peter; Ditlevsen, Ove Dalager


    In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...... the stochastic cargo container load field is based on a queuing and loading policy that assumes containers are handled by a first-come-first-serve policy. The load field is assumed to be Gaussian. The ballast system is imposed to counteract the angle of heel and to regulate both the draft and the trim caused...

  6. Detecting Stochastic Information of Electrocardiograms

    Gutíerrez, R M; Guti'errez, Rafael M.; Sandoval, Luis A.


    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.

  7. Stochastic superparameterization in quasigeostrophic turbulence

    Grooms, Ian, E-mail: [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Majda, Andrew J., E-mail: [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Center for Prototype Climate Modelling, NYU-Abu Dhabi (United Arab Emirates)


    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

  8. Stochastic roots of growth phenomena

    De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.


    We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.

  9. Stochastic Analysis and Related Topics

    Ustunel, Ali


    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.

  10. Foliated stochastic calculus: Harmonic measures

    Catuogno, Pedro J; Ruffino, Paulo R


    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.

  11. Cancer

    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 ...

  12. Steganalysis of stochastic modulation steganography

    HE Junhui; HUANG Jiwu


    Stochastic modulation steganography embeds secret message within the cover image by adding stego-noise with a specific probabilistic distribution. No method is known to be applicable to the estimation of stochastic modulation steganography. By analyzing the distributions of the horizontal pixel difference of images before and after stochastic modulation embedding, we present a new steganalytic approach to accurately estimate the length of secret message in stochastic modulation steganography. The proposed method first establishes a model describing the statistical relationship among the differences of the cover image, stego-image and stego-noise. In the case of stego- image-only steganalysis, rough estimate of the distributional parameters of the cover image's pixel difference is obtained with the use of the provided stego-image. And grid search and Chi-square goodness of fit test are exploited to estimate the length of the secret message embedded with stochastic modulation steganography. The experimental results demonstrate that our new approach is effective for steganalyzing stochastic modulation steganography and accurately estimating the length of the secret message.

  13. Stochastic Methods in Biology

    Kallianpur, Gopinath; Hida, Takeyuki


    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...

  14. AA, stochastic precooling kicker


    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...

  15. Stochastic cooling in RHIC

    Brennan J. M.; Blaskiewicz, M.; Mernick, K.


    The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.

  16. Adaptation in stochastic environments

    Clark, Colib


    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...

  17. Stacking with Stochastic Cooling

    Caspers, Friedhelm


    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)....

  18. Turbulence and Stochastic Processes

    Celani, Antonio; Mazzino, Andrea; Pumir, Alain

    sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.

  19. Segmentation of stochastic images with a stochastic random walker method.

    Pätz, Torben; Preusser, Tobias


    We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.

  20. A Stochastic Collocation Algorithm for Uncertainty Analysis

    Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)


    This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.

  1. Stability Analysis for Stochastic Optimization Problems


    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.

  2. General N-th Degree Stochastic Dominance



    This paper examines N-th degree stochastic dominance which isused to compare the risk factor of risky assets after summarizing the definitions of first degree stochastic dominance and second degree stochastic dominance. The paper defines general N-th degree stochastic dominance, presents a sufficient and necessary condition which is the equivalent theorem of general N-th degree stochastic dominance. The feasible utility form is constructed to explain the economic meaning of N-th degree stochastic dominance in the field of financial economics. The equivalent condition is described by the probability distribution functions of risky assets, which are not related to utility functions (preference relations).

  3. Stochastic models: theory and simulation.

    Field, Richard V., Jr.


    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.

  4. Stochastic simulation in systems biology.

    Székely, Tamás; Burrage, Kevin


    Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.

  5. Stochastic models of cell motility

    Gradinaru, Cristian


    Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...

  6. Mechanical autonomous stochastic heat engines

    Serra-Garcia, Marc; Foehr, Andre; Moleron, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara; . Team

    Stochastic heat engines extract work from the Brownian motion of a set of particles out of equilibrium. So far, experimental demonstrations of stochastic heat engines have required extreme operating conditions or nonautonomous external control systems. In this talk, we will present a simple, purely classical, autonomous stochastic heat engine that uses the well-known tension induced nonlinearity in a string. Our engine operates between two heat baths out of equilibrium, and transfers energy from the hot bath to a work reservoir. This energy transfer occurs even if the work reservoir is at a higher temperature than the hot reservoir. The talk will cover a theoretical investigation and experimental results on a macroscopic setup subject to external noise excitations. This system presents an opportunity for the study of non equilibrium thermodynamics and is an interesting candidate for innovative energy conversion devices.

  7. Principal axes for stochastic dynamics.

    Vasconcelos, V V; Raischel, F; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D


    We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.

  8. Principal axes for stochastic dynamics

    Vasconcelos, V V; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D


    We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.

  9. Correlation functions in stochastic inflation

    Vennin, Vincent [University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth (United Kingdom); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow (Russian Federation); Utrecht University, Department of Physics and Astronomy, Institute for Theoretical Physics, Utrecht (Netherlands)


    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.)

  10. Stochastic models for atmospheric dispersion

    Ditlevsen, Ove Dalager


    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...... 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...... dependent particle velocity into a position independent Gaussian velocity. Boundary conditions are obtained from Itos rule of stochastic differentiation. The model directly point at a canonical rule of reflection for the approximating random walk with finite time step. This reflection rule is different from...

  11. Applied probability and stochastic processes

    Sumita, Ushio


    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...

  12. Intrinsic optimization using stochastic nanomagnets

    Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo


    This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053

  13. Stochastic superparameterization in quasigeostrophic turbulence

    Grooms, Ian


    In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) 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 SP 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 SP 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 th...

  14. Stochastic decision analysis

    Lacksonen, Thomas A.


    Small space flight project design at NASA Langley Research Center goes through a multi-phase process from preliminary analysis to flight operations. The process insures that each system achieves its technical objectives with demonstrated quality and within planned budgets and schedules. A key technical component of early phases is decision analysis, which is a structure procedure for determining the best of a number of feasible concepts based upon project objectives. Feasible system concepts are generated by the designers and analyzed for schedule, cost, risk, and technical measures. Each performance measure value is normalized between the best and worst values and a weighted average score of all measures is calculated for each concept. The concept(s) with the highest scores are retained, while others are eliminated from further analysis. This project automated and enhanced the decision analysis process. Automation of the decision analysis process was done by creating a user-friendly, menu-driven, spreadsheet macro based decision analysis software program. The program contains data entry dialog boxes, automated data and output report generation, and automated output chart generation. The enhancements to the decision analysis process permit stochastic data entry and analysis. Rather than enter single measure values, the designers enter the range and most likely value for each measure and concept. The data can be entered at the system or subsystem level. System level data can be calculated as either sum, maximum, or product functions of the subsystem data. For each concept, the probability distributions are approximated for each measure and the total score for each concept as either constant, triangular, normal, or log-normal distributions. Based on these distributions, formulas are derived for the probability that the concept meets any given constraint, the probability that the concept meets all constraints, and the probability that the concept is within a given

  15. Stacking with stochastic cooling

    Caspers, Fritz E-mail:; Moehl, Dieter


    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

  16. When greediness fails: examples from stochastic scheduling

    Uetz, Marc


    The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.

  17. Transport properties of stochastic Lorentz models

    Beijeren, H. van


    Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed waiti

  18. Stochastic geometry and its applications

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph


    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

  19. Schwinger Mechanism with Stochastic Quantization

    Fukushima, Kenji


    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.

  20. Algebraic and stochastic coding theory

    Kythe, Dave K


    Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.

  1. Stochastic and infinite dimensional analysis

    Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José


    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.

  2. Stochastic geometry for image analysis

    Descombes, Xavier


    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.

  3. 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...

  4. Stochastic methods in quantum mechanics

    Gudder, Stanley P


    Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

  5. QB1 - Stochastic Gene Regulation

    Munsky, Brian [Los Alamos National Laboratory


    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.

  6. Stochastic Kinetics of Nascent RNA

    Xu, Heng; Skinner, Samuel O.; Sokac, Anna Marie; Golding, Ido


    The stochastic kinetics of transcription is typically inferred from the distribution of RNA numbers in individual cells. However, cellular RNA reflects additional processes downstream of transcription, hampering this analysis. In contrast, nascent (actively transcribed) RNA closely reflects the kinetics of transcription. We present a theoretical model for the stochastic kinetics of nascent RNA, which we solve to obtain the probability distribution of nascent RNA per gene. The model allows us to evaluate the kinetic parameters of transcription from single-cell measurements of nascent RNA. The model also predicts surprising discontinuities in the distribution of nascent RNA, a feature which we verify experimentally.

  7. Stochastic epidemic models: a survey

    Britton, Tom


    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.

  8. 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


    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.

  9. 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)


    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.

  10. Exact Algorithms for Solving Stochastic Games

    Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels;


    Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

  11. Stochastic modeling and analysis of telecoms networks

    Decreusefond, Laurent


    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

  12. Observability Estimate for Stochastic Schroedinger Equations


    In this paper, we establish a boundary observability estimate for stochastic Schr\\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr\\"{o}dinger-like operator. Applications to the state observation problem for semilinear stochastic Schr\\"{o}dinger equations and the unique continuation problem for stochastic Schr\\"{o}dinger equations are also addressed.

  13. Stochastic Model Checking of the Stochastic Quality Calculus

    Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin


    The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input...

  14. On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales

    Michta, Mariusz


    In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.

  15. Radiation-induced chromosomal hot spots at G 1 and G 2 stages of human lymphocytes in culture

    Murugesan R


    Full Text Available Radiation-induced chromosomal break points in cultured lymphocytes of normal healthy individuals as well as of those with certain genetic disorders are reported to be localized at certain specific loci (hot spots. These reports are based on studies carried out in lymphocytes irradiated at G 1 stage. The present study examines whether the location of hot spots and the frequency seen in cells irradiated at G 1 are similar to those irradiated at G 2 stage of the cell cycle and also tests whether cells of patients exhibit hot spots on irradiation.The results showed that the radiation induced chromosomal break points to be similar in those irradiated are G 1 and G 2 stages of the cell cycle and also that cells of patients exhibited chromosomal hot spots.

  16. Symmetry reduction for stochastic hybrid systems

    Bujorianu, L.M.; Katoen, J.P.


    This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we genera

  17. Symmetry Reduction For Stochastic Hybrid Systems

    Bujorianu, L.M.; Katoen, J.P.


    This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Th

  18. Stochastic Programming with Simple Integer Recourse

    Louveaux, François V.; van der Vlerk, Maarten H.


    Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic c

  19. Symmetrized solutions for nonlinear stochastic differential equations

    G. Adomian


    Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.

  20. Variational principles for stochastic soliton dynamics.

    Holm, Darryl D; Tyranowski, Tomasz M


    We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.

  1. Immunopathological patterns from EAE and Theiler's virus infection: Is multiple sclerosis a homogenous 1-stage or heterogenous 2-stage disease?

    Martinez, Nicholas E; Sato, Fumitaka; Omura, Seiichi; Minagar, Alireza; Alexander, J Steven; Tsunoda, Ikuo


    Multiple sclerosis (MS) is a disease which can presents in different clinical courses. The most common form of MS is the relapsing-remitting (RR) course, which in many cases evolves into secondary progressive (SP) disease. Autoimmune models such as experimental autoimmune encephalomyelitis (EAE) have been developed to represent the various clinical forms of MS. These models along with clinico-pathological evidence obtained from MS patients have allowed us to propose '1-stage' and '2-stage' disease theories to explain the transition in the clinical course of MS from RR to SP. Relapses in MS are associated with pro-inflammatory T helper (Th) 1/Th17 immune responses, while remissions are associated with anti-inflammatory Th2/regulatory T (Treg) immune responses. Based on the '1-stage disease' theory, the transition from RR to SP disease occurs when the inflammatory immune response overwhelms the anti-inflammatory immune response. The '2-stage disease' theory proposes that the transition from RR to SP-MS occurs when the Th2 response or some other responses overwhelm the inflammatory response resulting in the sustained production of anti-myelin antibodies, which cause continuing demyelination, neurodegeneration, and axonal loss. The Theiler's virus model is also a 2-stage disease, where axonal degeneration precedes demyelination during the first stage, followed by inflammatory demyelination during the second stage.

  2. Network Analysis with Stochastic Grammars


    hypotheses. In practice, association rarely identifies the specific offending element, but focuses the investigation by reducing the suspect pool [73...J. Young , “The estimation of stochastic context-free grammars using the Inside-Outside algorithm,” Comput. Speech Lang., vol. 4, no. 1, pp. 35– 56

  3. Stochastic Processes in Epidemic Theory

    Lefèvre, Claude; Picard, Philippe


    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.

  4. Model checking mobile stochastic logic.

    De Nicola, Rocco; Katoen, Joost-Pieter; Latella, Diego; Loreti, Michele; Massink, Mieke


    The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution awarenes

  5. 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...

  6. Stochastic-field cavitation model

    Dumond, J., E-mail: [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen (Germany); Magagnato, F. [Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstrasse 12, D-76131 Karlsruhe (Germany); Class, A. [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)


    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

  7. Stochastic-field cavitation model

    Dumond, J.; Magagnato, F.; Class, A.


    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

  8. Stochastic Modelling of Energy Systems

    Andersen, Klaus Kaae


    equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate...

  9. Stochastic Modelling of River Geometry

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.


    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...

  10. 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...

  11. Stochastic Volatility and DSGE Models

    Andreasen, Martin Møller

    This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...

  12. Stochastic resin transfer molding process

    Park, M


    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.

  13. Stochastic nonlinear differential equations. I

    Heilmann, O.J.; Kampen, N.G. van


    A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these co

  14. Etiology and treatment of hematological neoplasms: stochastic mathematical models.

    Radivoyevitch, Tomas; Li, Huamin; Sachs, Rainer K


    Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.

  15. Cancer

    ... uses a surgical tool to remove the tumor.Mohs' surgery. Layers of cancer cells are removed one ... usually have not been approved by the U.S. Food and Drug Administration (FDA). The medicine may have ...

  16. Research on nonlinear stochastic dynamical price model

    Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail:; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)


    In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.

  17. Stochastic averaging of quasi-Hamiltonian systems



    A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.

  18. Stochastic Reachability Analysis of Hybrid Systems

    Bujorianu, Luminita Manuela


    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...

  19. Stochastic Analysis : A Series of Lectures

    Dozzi, Marco; Flandoli, Franco; Russo, Francesco


    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...

  20. Ruin problems with stochastic premium stochastic return on investments

    WANG Rongming; XU Lin; YAO Dingjun


    In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro- differential equations for the expected discounted penalty function are ob- tained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper.

  1. Fourier analysis and stochastic processes

    Brémaud, Pierre


    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...

  2. Stochastic Vehicle Routing with Recourse

    Goertz, Inge Li; Saket, Rishi


    We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization 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 lambda. We present an O(log^2 n log(n lambda))-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 orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.

  3. Optical stochastic cooling in Tevatron

    Lebedev, V


    Intrabeam scattering is the major mechanism resulting in a growth of beam emittances and fast luminosity degradation in the Tevatron. As a result in the case of optimal collider operation only about 40% of antiprotons are used to the store end and the rest are discarded. Beam cooling is the only effective remedy to increase the particle burn rate and, consequently, the luminosity. Unfortunately neither electron nor stochastic cooling can be effective at the Tevatron energy and bunch density. Thus the optical stochastic cooling (OSC) is the only promising technology capable to cool the Tevatron beam. Possible ways of such cooling implementation in the Tevatron and advances in the OSC cooling theory are discussed in this paper. The technique looks promising and potentially can double the average Tevatron luminosity without increasing its peak value and the antiproton production.

  4. Stochastic Modeling of Soil Salinity

    Suweis, S; Van der Zee, S E A T M; Daly, E; Maritan, A; Porporato, A; 10.1029/2010GL042495


    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...

  5. Stochastic integration and differential equations

    Protter, Philip E


    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...

  6. Stochastic problems in population genetics

    Maruyama, Takeo


    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...

  7. Self-Organising Stochastic Encoders

    Luttrell, Stephen


    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...

  8. Stochastic control of traffic patterns

    Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer


    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....

  9. Foundations of infinitesimal stochastic analysis

    Stroyan, KD


    This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

  10. Stochastic processes and filtering theory

    Jazwinski, Andrew H


    This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab

  11. Stochastic Gravity: Theory and Applications

    Hu Bei Lok


    Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out

  12. Stochastic cooling technology at Fermilab

    Pasquinelli, R.J. E-mail:


    The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.

  13. Information Anatomy of Stochastic Equilibria

    Sarah Marzen


    Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.

  14. Nonlinear and Stochastic Morphological Segregation

    Blanton, M R


    I perform a joint counts-in-cells analysis of galaxies of different spectral types using the Las Campanas Redshift Survey (LCRS). Using a maximum-likelihood technique to fit for the relationship between the density fields of early- and late-type galaxies, I find a relative linear bias of $b=0.76\\pm 0.02$. This technique can probe the nonlinearity and stochasticity of the relationship as well. However, the degree to which nonlinear and stochastic fits improve upon the linear fit turns out to depend on the redshift range in question. In particular, there seems to be a systematic difference between the high- and low-redshift halves of the data (respectively, further than and closer than $cz\\approx 36,000$ km/s); all of the signal of stochasticity and nonlinearity comes from the low-redshift portion. Analysis of mock catalogs shows that the peculiar geometry and variable flux limits of the LCRS do not cause this effect. I speculate that the central surface brightness selection criteria of the LCRS may be responsi...

  15. Stochastic analysis of biochemical systems

    Anderson, David F


    This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology.  The book should serve well as a supplement for courses in probability and stochastic processes.  While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest.    David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...

  16. Stochastic gravity: beyond semiclassical gravity

    Verdaguer, E [Departament de Fisica Fonamental and CER en Astrofisica, Fisica de Particules i Cosmologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)


    The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by these quantum fluctuations. The correlation functions of the metric fluctuations obtained in stochastic gravity reproduce the correlation functions in the quantum theory to leading order in an 1/N expansion. Two main applications of stochastic gravity are discussed. The first, in cosmology, to obtain the spectrum of primordial metric perturbations induced by the inflaton fluctuations, even beyond the linear approximation. The second, in black hole physics, to study the fluctuations of the horizon of an evaporating black hole.

  17. Mechanical Autonomous Stochastic Heat Engine

    Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara


    Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

  18. AESS: Accelerated Exact Stochastic Simulation

    Jenkins, David D.; Peterson, Gregory D.


    The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution

  19. Strategy for stochastic dose-rate induced enhanced elimination of malignant tumour without dose escalation.

    Paul, Subhadip; Roy, Prasun Kumar


    The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition-increasing the elimination of prostate tumour cells and enhancing the relative sparing of normal tissue in fractionated radiation therapy, within a prescribed limit of total radiation dose. Our study predicts that stochastic temporal modulation in radiation dose-rate appreciably enhances prostate tumour cell elimination, without needing dose escalation in radiation therapy. However, constant higher dose-rate can also enhance the elimination of tumour cells. In this context, we have shown that the sparing of normal tissue with stochastic dose-rate is considerably more than the sparing of normal tissue with the equivalent constant higher dose-rate. Further, by contrasting the stochastic dose-rate effects under LQL and linear-quadratic (LQ) models, we have also shown that the LQ model over-estimates stochastic dose-rate effect in tumour and under-estimates the stochastic dose-rate effect in normal tissue. Our study indicates the possibility of utilizing stochastic modulation of radiation dose-rate for designing enhanced radiation therapy protocol for cancer.

  20. Brownian motion, martingales, and stochastic calculus

    Le Gall, Jean-François


    This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

  1. Intrinsic Simulations between Stochastic Cellular Automata

    Pablo Arrighi


    Full Text Available The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the non-deterministic and stochastic settings. We then provide explicit tools to prove or disprove the existence of such a simulation between two stochastic cellular automata, even though the intrinsic simulation relation is shown to be undecidable in dimension two and higher. The key result behind this is the caracterization of equality of stochastic global maps by the existence of a coupling between the random sources. We then prove that there is a universal non-deterministic cellular automaton, but no universal stochastic cellular automaton. Yet we provide stochastic cellular automata achieving optimal partial universality.

  2. Consistent Stochastic Modelling of Meteocean Design Parameters

    Sørensen, John Dalsgaard; Sterndorff, M. J.


    Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...... velocity, and water level is presented. The stochastic model includes statistical uncertainty and dependency between the four stochastic variables. Further, a new stochastic model for annual maximum directional significant wave heights is presented. The model includes dependency between the maximum wave...... height from neighboring directional sectors. Numerical examples are presented where the models are calibrated using the Maximum Likelihood method to data from the central part of the North Sea. The calibration of the directional distributions is made such that the stochastic model for the omnidirectional...

  3. Trajectory averaging for stochastic approximation MCMC algorithms

    Liang, Faming


    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305--320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE al...

  4. Stochastic synaptic plasticity with memristor crossbar arrays

    Naous, Rawan


    Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.

  5. Quadratic stabilization for uncertain stochastic systems

    Jun'e FENG; Weihai ZHANG


    This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.

  6. Stochastic Descent Analysis of Representation Learning Algorithms

    Golden, Richard M.


    Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate and verify. This paper presents a new stochastic approximation theorem for state-dependent noise with easily verifiable assumptions applicable to the analysis and design of import...

  7. Impulsive control of stochastic system under the sense of stochastic asymptotical stability

    Niu Yu-Jun; Ma Ge


    This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.

  8. A minicourse on stochastic partial differential equations

    Rassoul-Agha, Firas


    In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Particular emphasis is paid to showcasing central ideas and displaying some of the many deep connections between the mentioned disciplines, all the time keeping a realistic pace for the student of the subject.

  9. Stochastic versus deterministic systems of differential equations

    Ladde, G S


    This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/flu

  10. Introduction to stochastic models in biology

    Ditlevsen, Susanne; Samson, Adeline


    be exposed to influences that are not completely understood or not feasible to model explicitly. Ignoring these phenomena in the modeling may affect the analysis of the studied biological systems. Therefore there is an increasing need to extend the deterministic models to models that embrace more complex...... variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise. A natural extension of a deterministic differential equations model is a system of stochastic differential equations (SDEs), where relevant parameters are modeled as suitable stochastic processes......, or stochastic processes are added to the driving system equations. This approach assumes that the dynamics are partly driven by noise....


    SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin


    Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.

  12. Efficient numerical integrators for stochastic models

    De Fabritiis, G; Español, P; Coveney, P V


    The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.

  13. Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

    van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.


    We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Sc

  14. CANCER

    N. Kavoussi


    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.

  15. A note on maximal estimates for stochastic convolutions

    Veraar, M.; Weis, L.


    In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.

  16. Controllability of quasilinear stochastic evolution equations in Hilbert spaces

    P. Balasubramaniam


    Full Text Available Controllability of the quasilinear stochastic evolution equation is studied using semigroup theory and a stochastic version of the well known fixed point theorem. An application to stochastic partial differential equations is given.

  17. Treatment of Renal Cell Carcinoma with 2-Stage Total en bloc Spondylectomy after Marked Response to Molecular Target Drugs

    Yasuhiro Inoue


    Full Text Available Metastatic renal cell carcinoma of the bone occurs at a high rate, and the prognosis is poor. In general, total en bloc spondylectomy is considered when there is only one vertebral metastasis and the primary disease is treated. However, palliative surgery is selected when the primary disease is not being treated or metastasis occurs to an important organ. We encountered a patient in whom lung and vertebra metastases were already present at the time of the first examination at our department and the prognosis was considered poor. However, molecular targeted therapy was markedly effective and enabled 2-stage total en bloc spondylectomy. As of one year after total en bloc spondylectomy, the condition has improved to cane gait, and surgery for lung metastasis is planned. Molecular target drugs might markedly change the current therapeutic strategy for renal cell carcinoma.

  18. Mathematical statistics and stochastic processes

    Bosq, Denis


    Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob

  19. Probability, Statistics, and Stochastic Processes

    Olofsson, Peter


    This book provides a unique and 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.  The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and

  20. Stochastic Calculus of Wrapped Compartments

    Coppo, Mario; Drocco, Maurizio; Grassi, Elena; Troina, Angelo; 10.4204/EPTCS.28.6


    The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term (whose complexity in CLS is strongly affected by the variables matching in the sequences). We define a stochastic semantics for this new calculus. As an application we model the interaction between macrophages and apoptotic neutrophils and a mechanism of gene regulation in E.Coli.

  1. Stochastic Gravity: Theory and Applications

    Hu Bei Lok


    Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction

  2. Boundary layers in stochastic thermodynamics.

    Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo


    We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

  3. Stochastic noise in splicing machinery

    Melamud, Eugene; Moult, John


    The number of known alternative human isoforms has been increasing steadily with the amount of available transcription data. To date, over 100 000 isoforms have been detected in EST libraries, and at least 75% of human genes have at least one alternative isoform. In this paper, we propose that most alternative splicing events are the result of noise in the splicing process. We show that the number of isoforms and their abundance can be predicted by a simple stochastic noise model that takes i...

  4. Stochastic modeling analysis and simulation

    Nelson, Barry L


    A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se

  5. Stochastic Forcing for Ocean Uncertainty Prediction


    shallow water waves governed by Korteweg-de Vries ( KdV ) dynamics with stochastic forcing. Uncertain Boundary Conditions and DO Equations: A...schemes to time-integrate shallow water surface waves governed by KdV equations with external stochastic forcing. We find that the DO scheme is

  6. Safety Analysis of Stochastic Dynamical Systems

    Sloth, Christoffer; Wisniewski, Rafael


    This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...

  7. Parallel transports associated to stochastic holonomies

    CHEN; Shiping(陈世平); XIANG; Kainan(向开南)


    A stochastic holonomy along a loop obtained from the OU process on the path space over acompact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives theparallel transport with respect to the Markov connection along the OU process on the path space.

  8. From Complex to Simple: Interdisciplinary Stochastic Models

    Mazilu, D. A.; Zamora, G.; Mazilu, I.


    We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

  9. A stochastic indicator for sovereign debt sustainability

    Lukkezen, J.H.J.; Rojas-Romagosa, Hugo


    We propose a stochastic indicator to assess government debt sustainability. This indicator combines the effect of economic uncertainty –represented by stochastic simulations of interest and growth rates– with the expected fiscal response that provides information on the long-term country specific at

  10. Stochastic Modelling and Analysis of Warehouse Operations

    Y. Gong (Yeming)


    textabstractThis thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a

  11. Integration of stochastic generation in power systems

    Papaefthymiou, G.


    Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation uncerta

  12. Some Recent Developments in Ambit Stochastics

    Barndorff-Nielsen, Ole E.; Hedevang, Emil; Schmiegel, Jürgen

    Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws...

  13. Stochastic stabilization analysis of networked control systems

    Ma Changlin; Fang Huajing


    Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.

  14. Stochastic models for uncertain flexible systems

    Curtain, R.F.; Kotelenez, P.


    If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexib

  15. Statistical Model Checking for Stochastic Hybrid Systems

    David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand


    This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...

  16. Variational principles for stochastic fluid dynamics.

    Holm, Darryl D


    This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.

  17. Stochastic Methods for Aircraft Design

    Pelz, Richard B.; Ogot, Madara


    The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.

  18. Multiple Fields in Stochastic Inflation

    Assadullahi, Hooshyar; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David


    Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary $e$-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of $e$-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the...

  19. Stochastic noise in splicing machinery.

    Melamud, Eugene; Moult, John


    The number of known alternative human isoforms has been increasing steadily with the amount of available transcription data. To date, over 100 000 isoforms have been detected in EST libraries, and at least 75% of human genes have at least one alternative isoform. In this paper, we propose that most alternative splicing events are the result of noise in the splicing process. We show that the number of isoforms and their abundance can be predicted by a simple stochastic noise model that takes into account two factors: the number of introns in a gene and the expression level of a gene. The results strongly support the hypothesis that most alternative splicing is a consequence of stochastic noise in the splicing machinery, and has no functional significance. The results are also consistent with error rates tuned to ensure that an adequate level of functional product is produced and to reduce the toxic effect of accumulation of misfolding proteins. Based on simulation of sampling of virtual cDNA libraries, we estimate that error rates range from 1 to 10% depending on the number of introns and the expression level of a gene.

  20. Single-molecule stochastic resonance

    Hayashi, K; Manosas, M; Huguet, J M; Ritort, F; 10.1103/PhysRevX.2.031012


    Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively folding/unfolding transitions under the action of an applied oscillating mechanical force with optical tweezers. By varying the frequency of the force oscillation, we investigated the folding/unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measured several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins is a good quantifier of the SR. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance match...


    Laslett, L. Jackson.


    Detailed examination of computed particle trajectories has revealed a complexity and disorder that is of increasing interest to accelerator specialists. To introduce this topic, the author would like you to consider for a moment the analysis of synchrotron oscillations for a particle in a coasting beam, regarded as a problem in one degree of freedom. A simple analysis replaces the electric field of the RF-v cavity system by a traveling wave, having the speed of a synchronous reference particle, and leads to a pair of differential equations of the form dy/dn = -K sin {pi}x, (1A) where y measures the fractional departure of energy from the reference value {pi}x measures the electrical phase angle at which the particle traverses the cavity, and K is proportional to the cavity voltage; and dx/dn = {lambda}{prime}y, (1b) in which {lambda}{prime} is proportional to the change of revolution period with respect to particle energy. It will be recognized that these equations can be derived from a Hamiltonian function H = (1/2){lambda}{prime}y{sup 2}-(K/{pi})cos {pi}x. (2) Because this Hamiltonian function does not contain the independent variable explicitly, it will constitute a constant of the motion and possible trajectories in the x,y phase space will be just the curves defined by H = Constant, namely the familiar simple curves in phase space that are characteristic of a physical (non-linear) pendulum.

  2. Modelling and application of stochastic processes


    The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

  3. Ambit processes and stochastic partial differential equations

    Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut

    Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.......Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between...

  4. A Temporal Approach to Stochastic Network Calculus

    Xie, Jing; Xie, Min


    Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of traffic or cumulative amount of service. However, there are network scenarios where direct application of such models is difficult. This paper presents a temporal approach to stochastic network calculus. The key idea is to develop models and derive results from the time perspective. Particularly, we define traffic models and service models based on the cumulative packet inter-arrival time and the cumulative packet service time, respectively. Relations among these models as well as with the existing models in the literature are established. In addition, we prove the basic properties of the proposed models, such as delay bound and backlog bound, output characterization, concatenation property and superposition property. These results form a temporal stochastic network calculus an...

  5. Improved bounds for stochastic matching

    Li, Jian


    In this paper we study stochastic matching problems that are motivated by applications in online dating and kidney exchange programs. We consider two probing models: edge probing and matching probing. Our main result is an algorithm that finds a matching-probing strategy attaining a small constant approximation ratio. An interesting aspect of our approach is that we compare the cost our solution to the best edge-probing strategy. Thus, we indirectly show that the best matching-probing strategy is only a constant factor away from the best edge-probing strategy. Even though our algorithm has a slightly worse approximation ratio than a greedy algorithm for edge-probing strategies, we show that the two algorithms can be combined to get improved approximations.

  6. Efficient Discretization of Stochastic Integrals

    Fukasawa, Masaaki


    Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

  7. Stochastic sensing through covalent interactions

    Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen


    A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.

  8. Parameterization of stochastic multiscale triads

    Wouters, Jeroen; Iankov Dolaptchiev, Stamen; Lucarini, Valerio; Achatz, Ulrich


    We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system; we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.

  9. A Stochastic Cobweb Dynamical Model

    Serena Brianzoni


    _,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.

  10. Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method

    Voyant, Cyril; Tamas, Wani; Paoli, Christophe; Balu, Aurélia; Muselli, Marc; Nivet, Marie-Laure; Notton, Gilles


    A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its "black box" aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where "all" configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA.

  11. Mixed culture polyhydroxyalkanoates production from sugar molasses: the use of a 2-stage CSTR system for culture selection.

    Albuquerque, M G E; Concas, S; Bengtsson, S; Reis, M A M


    Polyhydroxyalkanoates (PHAs) are promising biodegradable polymers. The use of mixed microbial cultures (MMC) and low cost feedstocks have a positive impact on the cost-effectiveness of the process. It has typically been carried out in Sequencing Batch Reactors (SBR). In this study, a 2-stage CSTR system (under Feast and Famine conditions) was used to effectively select for PHA-storing organisms using fermented molasses as feedstock. The effect of influent substrate concentration (60-120 Cmmol VFA/L) and HRT ratio between the reactors (0.2-0.5h/h) on the system's selection efficiency was assessed. It was shown that Feast reactor residual substrate concentration impacted on the selective pressure for PHA storage (due to substrate-dependent kinetic limitation). Moreover, a residual substrate concentration coming from the Feast to the Famine reactor did not jeopardize the physiological adaptation required for enhanced PHA storage. The culture reached a maximum PHA content of 61%. This success opens new perspectives to the use of wastewater treatment infrastructure for PHA production, thus valorizing either excess sludge or wastewaters.

  12. On stochastic fractional Volterra equations in Hilbert space

    Karczewska, Anna; Lizama, Carlos


    In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra equation.

  13. Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations

    Ren, Jiagang; Zhang, Xicheng


    We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.

  14. Observability estimate and state observation problems for stochastic hyperbolic equations


    In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations.

  15. An Internal Observability Estimate for Stochastic Hyperbolic Equations


    This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting.

  16. Statistical Methods for Stochastic Differential Equations

    Kessler, Mathieu; Sorensen, Michael


    The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

  17. Modeling and analysis of stochastic systems

    Kulkarni, Vidyadhar G


    Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi

  18. Stochastic Control Model on Rent Seeking


    A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modern risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.

  19. Selected papers on noise and stochastic processes

    Wax, Nelson


    Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre

  20. Stochastic system identification in structural dynamics

    Safak, Erdal


    Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.

  1. Stochastic Modeling Of Wind Turbine Drivetrain Components

    Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard


    reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...... are needed for initial defects and damage accumulation. In this paper, stochastic models are formulated considering some of the failure modes observed in these components. The models are based on theoretical considerations, manufacturing uncertainties, size effects of different scales. It is illustrated how...... the stochastic models can be used to obtain estimates of failure rates for wind turbine components....

  2. CAM Stochastic Volatility Model for Option Pricing

    Wanwan Huang


    Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.

  3. Asymptotic analysis for functional stochastic differential equations

    Bao, Jianhai; Yuan, Chenggui


    This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

  4. Stochastic Einstein equations with fluctuating volume

    Dzhunushaliev, Vladimir


    We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a stochastic Friedmann-Lema\\^itre-Robertson-Walker cosmology, and show that the resulting field equations can lead to solutions which avoid the initial big bang singularity. By interpreting the fluctuations as the result of the presence of a quantum spacetime, we conclude that classical singularities can be avoided even within a stochastic model that include quantum effects in a very simple manner.

  5. Quantum Stochastic Resonance in Electron Shelving

    Huelga, S F


    Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems, there is complete lack of experimental evidence within the purely quantum mechanical domain. Here we demonstrate that stochastic resonance can be exhibited in a single ion and would be experimentally observable using well mastered experimental techniques. We discuss the use of this scheme for the detection of the frequency difference of two lasers to demonstrate that stochastic resonance may have applications in precision measurements at the quantum limit.

  6. Stochastic deformation of a thermodynamic symplectic structure

    Kazinski, P. O.


    A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.

  7. Stochastic transition model for pedestrian dynamics

    Schultz, Michael


    The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.

  8. The astrophysical gravitational wave stochastic background

    Tania Regimbau


    A stochastic background of gravitational waves with astrophysical origins may have resulted from the superposition of a large number of unresolved sources since the beginning of stellar activity.Its detection would put very strong constraints on the physical properties of compact objects, the initial mass function and star formarion history.On the other hand, it could be a ‘noise' that would mask the stochastic background of its cosmological origin.We review the main astrophysical processes which are able to produce a stochastic background and discuss how they may differ from the primordial contribution in terms of statistical properties.Current detection methods are also presented.

  9. Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

    Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut

    Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general...... properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures...... and to probability and L\\'{e}vy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given....

  10. Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty

    Fei Long


    Full Text Available For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.

  11. Stochastic pump effect and geometric phases in dissipative and stochastic systems

    Sinitsyn, Nikolai [Los Alamos National Laboratory


    The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

  12. Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain

    Li, Juan


    In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by Pardoux and Zhang [17]. The value function is shown to be the viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. The method of stochastic "backward semigroups" introduced by Peng [18] is adapted to our context.

  13. Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle.

    Liu, Meng; Wang, Ke; Wu, Qiong


    Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.

  14. New results in global stabilization for stochastic nonlinear systems

    Tao BIAN; Zhong-Ping JIANG


    This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

  15. Dimension Reduction and Discretization in Stochastic Problems by Regression Method

    Ditlevsen, Ove Dalager


    The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ......, Slepian models, Stochastic finite elements.......The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation...

  16. Modular and Stochastic Approaches to Molecular Pathway Models of ATM, TGF beta, and WNT Signaling

    Cucinotta, Francis A.; O'Neill, Peter; Ponomarev, Artem; Carra, Claudio; Whalen, Mary; Pluth, Janice M.


    Deterministic pathway models that describe the biochemical interactions of a group of related proteins, their complexes, activation through kinase, etc. are often the basis for many systems biology models. Low dose radiation effects present a unique set of challenges to these models including the importance of stochastic effects due to the nature of radiation tracks and small number of molecules activated, and the search for infrequent events that contribute to cancer risks. We have been studying models of the ATM, TGF -Smad and WNT signaling pathways with the goal of applying pathway models to the investigation of low dose radiation cancer risks. Modeling challenges include introduction of stochastic models of radiation tracks, their relationships to more than one substrate species that perturb pathways, and the identification of a representative set of enzymes that act on the dominant substrates. Because several pathways are activated concurrently by radiation the development of modular pathway approach is of interest.

  17. Numerical Investigation of the Interaction between Mainstream and Tip Shroud Leakage Flow in a 2-Stage Low Pressure Turbine

    Jia, Wei; Liu, Huoxing


    The pressing demand for future advanced gas turbine requires to identify the losses in a turbine and to understand the physical mechanisms producing them. In low pressure turbines with shrouded blades, a large portion of these losses is generated by tip shroud leakage flow and associated interaction. For this reason, shroud leakage losses are generally grouped into the losses of leakage flow itself and the losses caused by the interaction between leakage flow and mainstream. In order to evaluate the influence of shroud leakage flow and related losses on turbine performance, computational investigations for a 2-stage low pressure turbine is presented and discussed in this paper. Three dimensional steady multistage calculations using mixing plane approach were performed including detailed tip shroud geometry. Results showed that turbines with shrouded blades have an obvious advantage over unshrouded ones in terms of aerodynamic performance. A loss mechanism breakdown analysis demonstrated that the leakage loss is the main contributor in the first stage while mixing loss dominates in the second stage. Due to the blade-to-blade pressure gradient, both inlet and exit cavity present non-uniform leakage injection and extraction. The flow in the exit cavity is filled with cavity vortex, leakage jet attached to the cavity wall and recirculation zone induced by main flow ingestion. Furthermore, radial gap and exit cavity size of tip shroud have a major effect on the yaw angle near the tip region in the main flow. Therefore, a full calculation of shroud leakage flow is necessary in turbine performance analysis and the shroud geometric features need to be considered during turbine design process.

  18. Synchronization of noisy systems by stochastic signals

    Neiman, A.; Schimansky-Geier, L.; Moss, F. [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Schimansky-Geier, L. [Institute of Physics, Humboldt University at Berlin, Invalidenstrasse 110, D-10115 Berlin (Germany); Shulgin, B.; Collins, J.J. [Center for BioDynamics and Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215 (United States)


    We study, in terms of synchronization, the {ital nonlinear response} of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level{emdash}this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train. {copyright} {ital 1999} {ital The American Physical Society}

  19. Quantum Fields, Stochastic PDE, and Reflection Positivity

    Jaffe, Arthur


    We outline some known relations between classical random fields and quantum fields. In the scalar case, the existence of a quantum field is equivalent to the existence of a Euclidean-invariant, reflection-positive (RP) measure on the Schwartz space tempered distributions. Martin Hairer recently investigated random fields in a series of interesting papers, by studying non-linear stochastic partial differential equations, with a white noise driving term. To understand such stochastic quantization, we consider a linear example. We ask: does the measure on the solution induced by the stochastic driving term yield a quantum field? The RP property yields a general method to implement quantization. We show that the RP property fails for finite stochastic parameter $\\lambda$, although it holds in the limiting case $\\lambda=\\infty$.

  20. Stochastic differential equation model to Prendiville processes

    Granita, E-mail: [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)


    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  1. Stochastic multireference Epstein-Nesbet perturbation theory

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali; Umrigar, C J


    We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a stochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed stochastic algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, stochastic-HCI (s-HCI) is faster than the deterministic variant for most systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the s-HCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly par...

  2. Modelling Cow Behaviour Using Stochastic Automata

    Jónsson, Ragnar Ingi

    of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last......This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...

  3. Extending Stochastic Network Calculus to Loss Analysis

    Chao Luo


    Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.

  4. Stochastic structure formation in random media

    Klyatskin, V. I.


    Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.

  5. Extending stochastic network calculus to loss analysis.

    Luo, Chao; Yu, Li; Zheng, Jun


    Loss is an important parameter of Quality of Service (QoS). Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.

  6. Perspective: Stochastic algorithms for chemical kinetics

    Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.


    We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.

  7. Asynchronous stochastic approximation with differential inclusions

    David S. Leslie


    Full Text Available The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.

  8. Transient Growth in Stochastic Burgers Flows

    Poças, Diogo


    This study considers the problem of the extreme behavior exhibited by solutions to Burgers equation subject to stochastic forcing. More specifically, we are interested in the maximum growth achieved by the "enstrophy" (the Sobolev $H^1$ seminorm of the solution) as a function of the initial enstrophy $\\mathcal{E}_0$, in particular, whether in the stochastic setting this growth is different than in the deterministic case considered by Ayala & Protas (2011). This problem is motivated by questions about the effect of noise on the possible singularity formation in hydrodynamic models. The main quantities of interest in the stochastic problem are the expected value of the enstrophy and the enstrophy of the expected value of the solution. The stochastic Burgers equation is solved numerically with a Monte Carlo sampling approach. By studying solutions obtained for a range of optimal initial data and different noise magnitudes, we reveal different solution behaviors and it is demonstrated that the two quantities ...

  9. Perspective: Stochastic algorithms for chemical kinetics.

    Gillespie, Daniel T; Hellander, Andreas; Petzold, Linda R


    We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.

  10. Fractional Smoothness of Some Stochastic Integrals

    Peng XIE; Xi Cheng ZHANG


    We study the fractional smoothness in the sense of Malliavin calculus of stochastic integralsof the form ∫10 φ(Xs)d Xs,where Xs is a semimartingale and φ belongs to some fractional Sobolev spaceover R.

  11. Assessing the quality of stochastic oscillations

    Guillermo Abramson; Sebastián Risau-Gusman


    We analyze the relationship between the macroscopic and microscopic descriptions of two-state systems, in particular the regime in which the microscopic one shows sustained `stochastic oscillations' while the macroscopic tends to a fixed point. We propose a quantification of the oscillatory appearance of the fluctuating populations, and show that good stochastic oscillations are present if a parameter of the macroscopic model is small, and that no microscopic model will show oscillations if that parameter is large. The transition between these two regimes is smooth. In other words, given a macroscopic deterministic model, one can know whether any microscopic stochastic model that has it as a limit, will display good sustained stochastic oscillations.

  12. Testing for Stochastic Dominance with Diversification Possibilities

    G.T. Post (Thierry)


    textabstractWe derive empirical tests for stochastic dominance that allow for diversification between choice alternatives. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the te


    Martin Albertyn


    Full Text Available The key objective is to develop a method which can be utilized to model a stochastic continuous system. A system from the "real world" is used as the basis for the simulation modelling technique that is presented. The conceptualization phase indicates that the model has to incorporate stochastic and deterministic elements. A method is developed that utilizes the discrete simulation ability of a stochastic package (ARENA, in conjunction with a deterministic package (FORTRAN, to model the continuous system. (Software packages tend to specialize in either stochastic, or deterministic modelling. The length of the iteration time interval and adequate sample size are investigated. The method is authenticated by the verification and validation ofthe defined model. Two scenarios are modelled and the results are discussed . Conclusions are presented and strengths and weaknesses of this method are considered and discussed .

  14. Discretizing a backward stochastic differential equation

    Yinnan Zhang; Weian Zheng


    We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.

  15. ECE6010 - Stochastic Processes, Spring 2006

    Moon, Todd K.


    This course provides an introduction to stochastic processes in communications, signal processing, digital and computer systems, and control. Topics include continuous and discrete random processes, correlation and power spectral density, optimal filtering, Markov chains, and queuing theory. Technical Requirements: MATLAB

  16. Stochastic description of quantum Brownian dynamics

    Yan, Yun-An; Shao, Jiushu


    Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems

  17. Second Quantization Approach to Stochastic Epidemic Models

    Mondaini, Leonardo


    We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic models. In order to do that, we introduce an SIR-inspired stochastic model for hepatitis C virus epidemic, from which we obtain the time evolution of the mean number of susceptible, infected, recovered and chronically infected individuals in a population whose total size is allowed to change.

  18. On the stochastic dynamics of molecular conformation


    An important functioning mechanism of biological macromolecules is the transition between different conformed states due to thermal fluctuation. In the present paper, a biological macromolecule is modeled as two strands with side chains facing each other, and its stochastic dynamics including the statistics of stationary motion and the statistics of conformational transition is studied by using the stochastic averaging method for quasi Hamiltonian systems. The theoretical results are confirmed with the results from Monte Carlo simulation.

  19. Monostable array-enhanced stochastic resonance.

    Lindner, J F; Breen, B J; Wills, M E; Bulsara, A R; Ditto, W L


    We present a simple nonlinear system that exhibits multiple distinct stochastic resonances. By adjusting the noise and coupling of an array of underdamped, monostable oscillators, we modify the array's natural frequencies so that the spectral response of a typical oscillator in an array of N oscillators exhibits N-1 different stochastic resonances. Such families of resonances may elucidate and facilitate a variety of noise-mediated cooperative phenomena, such as noise-enhanced propagation, in a broad class of similar nonlinear systems.

  20. Desynchronization of stochastically synchronized chemical oscillators

    Snari, Razan; Tinsley, Mark R., E-mail:, E-mail:; Faramarzi, Sadegh; Showalter, Kenneth, E-mail:, E-mail: [C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045 (United States); Wilson, Dan; Moehlis, Jeff [Department of Mechanical Engineering, University of California, Santa Barbara, California 93106 (United States); Netoff, Theoden Ivan [Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455 (United States)


    Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

  1. Stochastic relations foundations for Markov transition systems

    Doberkat, Ernst-Erich


    Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general

  2. Crossing Statistics of Anisotropic Stochastic Surface

    Nezhadhaghighi, M Ghasemi; Yasseri, T; Allaei, S M Vaez


    We use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields in $(2+1)$Dimension. This approach enables us to examine not only the rotational invariance of morphology but also we can determine the Gaussianity of underlying stochastic field in various dimensions. Theoretical prediction of up-crossing statistics (crossing with positive slope at a given threshold $\\alpha$ of height fluctuation), $\

  3. A Note on Indefinite Stochastic Riccati Equations

    Qian, Zhongmin


    An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BSDEs (without involving any algebraic constraint) whose existence of solutions automatically enforces the original algebraic constraint to be satisfied.

  4. Complexity and synchronization in stochastic chaotic systems

    Son Dang, Thai; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo


    We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.

  5. Stochastic Physics, Complex Systems and Biology

    Qian, Hong


    In complex systems, the interplay between nonlinear and stochastic dynamics gives rise to an evolution process in Darwinian sense with punctuated equilibrium, random "mutations" and "adaptations". The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Epigenetic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a framework.

  6. Stochastic synchronization in finite size spiking networks

    Doiron, Brent; Rinzel, John; Reyes, Alex


    We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.

  7. Sequential decision analysis for nonstationary stochastic processes

    Schaefer, B.


    A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.

  8. Stochastic differential games with inside information

    Draouil, Olfa; Øksendal, Bernt


    We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.

  9. Algebraic polynomials and moments of stochastic integrals

    Langovoy, Mikhail A


    We propose an algebraic method for proving estimates on moments of stochastic integrals. The method uses qualitative properties of roots of algebraic polynomials from certain general classes. As an application, we give a new proof of a variation of the Burkholder-Davis-Gundy inequality for the case of stochastic integrals with respect to real locally square integrable martingales. Further possible applications and extensions of the method are outlined.

  10. Trajectory averaging for stochastic approximation MCMC algorithms

    Liang, Faming


    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

  11. Stochastic flux freezing and magnetic dynamo.

    Eyink, Gregory L


    Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.

  12. Stochastic learning via optimizing the variational inequalities.

    Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei


    A wide variety of learning problems can be posed in the framework of convex optimization. Many efficient algorithms have been developed based on solving the induced optimization problems. However, there exists a gap between the theoretically unbeatable convergence rate and the practically efficient learning speed. In this paper, we use the variational inequality (VI) convergence to describe the learning speed. To this end, we avoid the hard concept of regret in online learning and directly discuss the stochastic learning algorithms. We first cast the regularized learning problem as a VI. Then, we present a stochastic version of alternating direction method of multipliers (ADMMs) to solve the induced VI. We define a new VI-criterion to measure the convergence of stochastic algorithms. While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems cannot be better than O(1/√t), the proposed stochastic ADMM (SADMM) is proved to have an O(1/t) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness. The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly. The experiments demonstrate that SADMM has almost the same performance as the state-of-the-art stochastic learning algorithms but its O(1/t) VI-convergence rate is capable of tightly characterizing the real learning speed.

  13. Stochastic resonance during a polymer translocation process.

    Mondal, Debasish; Muthukumar, M


    We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

  14. Stochastic Systems Uncertainty Quantification and Propagation

    Grigoriu, Mircea


    Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables an...

  15. Spatial stochastic dynamics enable robust cell polarization.

    Michael J Lawson

    Full Text Available Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function.

  16. Automated Flight Routing Using Stochastic Dynamic Programming

    Ng, Hok K.; Morando, Alex; Grabbe, Shon


    Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

  17. Stochastic phase-change neurons

    Tuma, Tomas; Pantazi, Angeliki; Le Gallo, Manuel; Sebastian, Abu; Eleftheriou, Evangelos


    Artificial neuromorphic systems based on populations of spiking neurons are an indispensable tool in understanding the human brain and in constructing neuromimetic computational systems. To reach areal and power efficiencies comparable to those seen in biological systems, electroionics-based and phase-change-based memristive devices have been explored as nanoscale counterparts of synapses. However, progress on scalable realizations of neurons has so far been limited. Here, we show that chalcogenide-based phase-change materials can be used to create an artificial neuron in which the membrane potential is represented by the phase configuration of the nanoscale phase-change device. By exploiting the physics of reversible amorphous-to-crystal phase transitions, we show that the temporal integration of postsynaptic potentials can be achieved on a nanosecond timescale. Moreover, we show that this is inherently stochastic because of the melt-quench-induced reconfiguration of the atomic structure occurring when the neuron is reset. We demonstrate the use of these phase-change neurons, and their populations, in the detection of temporal correlations in parallel data streams and in sub-Nyquist representation of high-bandwidth signals.

  18. Stochastic models of intracellular transport

    Bressloff, Paul C.


    The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures. © 2013 American Physical Society.

  19. Fractal Geometry and Stochastics V

    Falconer, Kenneth; Zähle, Martina


    This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Te...

  20. Postmodern string theory stochastic formulation

    Aurilia, A


    In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carath\\'eodory formulation of the Nambu-Goto action, supplemented by an averaging procedure over the family of classical string world-sheets which are solutions of the equation of motion. In this new framework, the string geodesic field is reinterpreted as the Gibbs current density associated with the string statistical ensemble. Next, we show that the classical field equations derived from the string gauge action, can be obtained as the semi-classical limit of the string functional wave equation. For closed strings, the wave equation itself is completely analogous to the Wheeler-DeWitt equation used in quantum cosmology. Thus, in the string case, the wave function has support on the space of all possible spatial loop configurations. Finally, we show that the string distribution induces a multi-phase, or ...

  1. Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer-van der Pol system

    Zhang Ying; Xu Wei; Fang Tong; Xu Xu-Lin


    In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol (BVP for short) system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter.The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.

  2. Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem



    In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.

  3. Stochastic Chaos with Its Control and Synchronization

    Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong


    The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior, called chaos, could happen even in a deterministic nonlinear system under barely deterministic disturbance. After a series of serious studies, people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones, featuring a sensitive dependence on initial conditions, resulting from the intrinsic randomness of a nonlinear system itself. In fact, chaos is a collective phenomenon consisting of massive individual chaotic responses, corresponding to different initial conditions in phase space. Any two adjacent individual chaotic responses repel each other, thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent (TLE) for chaos. Meanwhile, all the sample responses share one common invariant set on the Poincaré map, called chaotic attractor,which every sample response visits from time to time ergodically. So far, the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos. We know that there are various forms of uncertainties in the real world. In theoretical studies, people often use stochastic models to describe these uncertainties, such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems. No doubt, chaotic phenomena also exist in stochastic systems, which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system. Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence, stochastic chaos is also a collective massive phenomenon, corresponding not only to different initial

  4. Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power

    Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte;


    . The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation......This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...

  5. Prospective Randomized Trial Comparing the 1-Stage with the 2-Stage Implantation of a Pulse Generator in Patients with Pelvic Floor Dysfunction Selected for Sacral Nerve Stimulation.

    Everaert, Karel; Kerckhaert, Wim; Caluwaerts, Hilde; Audenaert, M; Vereecke, Hugo Eric Marc; De Cuypere, G; Boelaert, A; Van den Hombergh, U; Oosterlinck, Wim A


    Abstract Objective: The aim of this study was to evaluate in a prospective, randomized setting if the 2-stage implant, compared to a 1-stage implant, leads to a superior subjective or objective outcome of sacral nerve stimulation after implantation of the pulse generator in patients with lower urina

  6. Clinical and radiologic evaluation of 2-stage IMZ implants placed in a single-stage procedure : 2-year results of a prospective comparative study

    Heydenrijk, K; Raghoebar, GM; Meijer, HJA; Stegenga, B


    Purpose: The aim of this study was to evaluate the feasibility of using a 2-stage implant system in a single-stage procedure and to study the impact of the microgap between the implant and the abutment. Materials and Methods: Sixty edentulous patients (Cawood class V or VI) participated in this stud

  7. Memristors Empower Spiking Neurons With Stochasticity

    Al-Shedivat, Maruan


    Recent theoretical studies have shown that probabilistic spiking can be interpreted as learning and inference in cortical microcircuits. This interpretation creates new opportunities for building neuromorphic systems driven by probabilistic learning algorithms. However, such systems must have two crucial features: 1) the neurons should follow a specific behavioral model, and 2) stochastic spiking should be implemented efficiently for it to be scalable. This paper proposes a memristor-based stochastically spiking neuron that fulfills these requirements. First, the analytical model of the memristor is enhanced so it can capture the behavioral stochasticity consistent with experimentally observed phenomena. The switching behavior of the memristor model is demonstrated to be akin to the firing of the stochastic spike response neuron model, the primary building block for probabilistic algorithms in spiking neural networks. Furthermore, the paper proposes a neural soma circuit that utilizes the intrinsic nondeterminism of memristive switching for efficient spike generation. The simulations and analysis of the behavior of a single stochastic neuron and a winner-take-all network built of such neurons and trained on handwritten digits confirm that the circuit can be used for building probabilistic sampling and pattern adaptation machinery in spiking networks. The findings constitute an important step towards scalable and efficient probabilistic neuromorphic platforms. © 2011 IEEE.

  8. Seismic Waveform Inversion by Stochastic Optimization

    Tristan van Leeuwen


    Full Text Available We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.

  9. Robustness analysis of stochastic biochemical systems.

    Ceska, Milan; Safránek, David; Dražan, Sven; Brim, Luboš


    We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.

  10. Models and Algorithm for Stochastic Network Designs

    Anthony Chen; Juyoung Kim; Seungjae Lee; Jaisung Choi


    The network design problem (NDP) is one of the most difficult and challenging problems in trans-portation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all rele-vant inputs are known with certainty. This paper presents three stochastic models for designing transporta-tion networks with demand uncertainty. These three stochastic NDP models were formulated as the ex-pected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Cado simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.

  11. Stochastic Reservoir Characterization Constrained by Seismic Data

    Eide, Alfhild Lien


    In order to predict future production of oil and gas from a petroleum reservoir, it is important to have a good description of the reservoir in terms of geometry and physical parameters. This description is used as input to large numerical models for the fluid flow in the reservoir. With increased quality of seismic data, it is becoming possible to extend their use from the study of large geologic structures such as seismic horizons to characterization of the properties of the reservoir between the horizons. Uncertainties because of the low resolution of seismic data can be successfully handled by means of stochastic modeling, and spatial statistics can provide tools for interpolation and simulation of reservoir properties not completely resolved by seismic data. This thesis deals with stochastic reservoir modeling conditioned to seismic data and well data. Part I presents a new model for stochastic reservoir characterization conditioned to seismic traces. Part II deals with stochastic simulation of high resolution impedance conditioned to measured impedance. Part III develops a new stochastic model for calcite cemented objects in a sandstone background; it is a superposition of a marked point model for the calcites and a continuous model for the background.

  12. Lectures on Topics in Spatial Stochastic Processes

    Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S


    The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

  13. Stochastic analysis for finance with simulations

    Choe, Geon Ho


    This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoret...

  14. Computational stochastic model of ions implantation

    Zmievskaya, Galina I., E-mail:; Bondareva, Anna L., E-mail: [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)


    Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

  15. Algorithm refinement for stochastic partial differential equations.

    Alexander, F. J. (Francis J.); Garcia, Alejandro L.,; Tartakovsky, D. M. (Daniel M.)


    A hybrid particle/continuum algorithm is formulated for Fickian diffusion in the fluctuating hydrodynamic limit. The particles are taken as independent random walkers; the fluctuating diffusion equation is solved by finite differences with deterministic and white-noise fluxes. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass conservation. This methodology is an extension of Adaptive Mesh and Algorithm Refinement to stochastic partial differential equations. A variety of numerical experiments were performed for both steady and time-dependent scenarios. In all cases the mean and variance of density are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the mean density is correct, but the variance is reduced except within the particle region, far from the interface. Extensions of the methodology to fluid mechanics applications are discussed.

  16. Online Stochastic Ad Allocation: Efficiency and Fairness

    Feldman, Jon; Korula, Nitish; Mirrokni, Vahab S; Stein, Cliff


    We study the efficiency and fairness of online stochastic display ad allocation algorithms from a theoretical and practical standpoint. In particular, we study the problem of maximizing efficiency in the presence of stochastic information. In this setting, each advertiser has a maximum demand for impressions of display ads that will arrive online. In our model, inspired by the concept of free disposal in economics, we assume that impressions that are given to an advertiser above her demand are given to her for free. Our main theoretical result is to present a training-based algorithm that achieves a (1-\\epsilon)-approximation guarantee in the random order stochastic model. In the corresponding online matching problem, we learn a dual variable for each advertiser, based on data obtained from a sample of impressions. We also discuss different fairness measures in online ad allocation, based on comparison to an ideal offline fair solution, and develop algorithms to compute "fair" allocations. We then discuss sev...

  17. Stochastic simulation of supercritical fluid extraction processes

    Mizutani F. T.


    Full Text Available Process simulation involves the evaluation of output variables by the specification of input variables and process parameters. However, in a real process, input data and parameters cannot be known without uncertainty. This fact may limit the utilization of simulation results to predict plant behavior. In order to achieve a more realistic analysis, the procedure of stochastic simulation can be conducted. This technique is based on a large set of simulation runs where input variables and parameters are randomly selected according to adequate probability density functions. The objective of this work is to illustrate the application of a stochastic simulation procedure to the process of fractionation of orange essential oil, using supercritical carbon dioxide in a multistage extraction column. Analysis of the proposed example demonstrates the importance of the stochastic simulation to develop more reliable designs and operating conditions for a supercritical fluid extraction process.

  18. Stochastic approach to scientific development and innovations

    Eto, H. (The University of Tokyo, Tokyo (Japan))


    Scientific development and technological innovations were studied by stochastic methods, in particular, scientometric method. The Bradford law was discussed which describes the behavior of scientific and engineering documents in the view point of their development and innovations. It was found that scientific development and innovations were governed more strongly by cumulative advantage effect and selfmultiplicative or self-reproductive effect than natural development and economic innovations. The elite characteristics were also pointed out by which a relatively small number of eminent scientific resources was selected in order to go ahead the others. These stochastic efforts could not fully explain peculiar characteristics of the Bradford law, and this inability probably indicated the essential gap between natural or economic science and bibliometrics. In addition, several attempts in stochastic theories and several possible trends of scientific activities in various scientific fields and in developing countries were discussed which might dissolve above gap. 23 refs., 8 figs., 24 tabs.

  19. Modeling stochasticity in biochemical reaction networks

    Constantino, P. H.; Vlysidis, M.; Smadbeck, P.; Kaznessis, Y. N.


    Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts.

  20. Online Advertisement, Optimization and Stochastic Networks

    Bo,; Srikant, R


    In this paper, we propose a stochastic model to describe how modern search service providers charge client companies based on users' queries for their related "adwords" by using certain advertisement assignment strategies. We formulate an optimization problem to maximize the long-term average revenue for the service provider under each client's long-term average budget constraint, and design an online algorithm which captures the stochastic properties of users' queries and click-through behaviors. We solve the optimization problem by making connections to scheduling problems in wireless networks, queueing theory and stochastic networks. With a small customizable parameter $\\epsilon$ which is the step size used in each iteration of the online algorithm, we have shown that our online algorithm achieves a long-term average revenue which is within $O(\\epsilon)$ of the optimal revenue and the overdraft level of this algorithm is upper-bounded by $O(1/\\epsilon)$.

  1. [Deterministic and stochastic identification of neurophysiologic systems].

    Piatigorskiĭ, B Ia; Kostiukov, A I; Chinarov, V A; Cherkasskiĭ, V L


    The paper deals with deterministic and stochastic identification methods applied to the concrete neurophysiological systems. The deterministic identification was carried out for the system: efferent fibres-muscle. The obtained transition characteristics demonstrated dynamic nonlinearity of the system. Identification of the neuronal model and the "afferent fibres-synapses-neuron" system in mollusc Planorbis corneus was carried out using the stochastic methods. For these purpose the Wiener method of stochastic identification was expanded for the case of pulse trains as input and output signals. The weight of the nonlinear component in the Wiener model and accuracy of the model prediction were quantitatively estimated. The results obtained proves the possibility of using these identification methods for various neurophysiological systems.

  2. Stochastic description for open quantum systems

    Calzetta, E A; Verdaguer, E; Calzetta, Esteban; Roura, Albert; Verdaguer, Enric


    A linear open quantum system consisting of a harmonic oscillator coupled linearly to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in thermal equilibrium. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stochastic source of the formal Langevin equation. The master equation for the reduced density matrix is then obtained in the same way a Fokker-Planck equation can always be derived from a Langevin equation characterizing a stochastic process. We also show that the quantum correlation functions for the system can be deduced within the stochastic description provided by the Langevin equation. It is emphasized that when the s...

  3. Stochastic Dominance under the Nonlinear Expected Utilities

    Xinling Xiao


    Full Text Available In 1947, von Neumann and Morgenstern introduced the well-known expected utility and the related axiomatic system (see von Neumann and Morgenstern (1953. It is widely used in economics, for example, financial economics. But the well-known Allais paradox (see Allais (1979 shows that the linear expected utility has some limitations sometimes. Because of this, Peng proposed a concept of nonlinear expected utility (see Peng (2005. In this paper we propose a concept of stochastic dominance under the nonlinear expected utilities. We give sufficient conditions on which a random choice X stochastically dominates a random choice Y under the nonlinear expected utilities. We also provide sufficient conditions on which a random choice X strictly stochastically dominates a random choice Y under the sublinear expected utilities.

  4. Stochastic Power Grid Analysis Considering Process Variations

    Ghanta, Praveen; Panda, Rajendran; Wang, Janet


    In this paper, we investigate the impact of interconnect and device process variations on voltage fluctuations in power grids. We consider random variations in the power grid's electrical parameters as spatial stochastic processes and propose a new and efficient method to compute the stochastic voltage response of the power grid. Our approach provides an explicit analytical representation of the stochastic voltage response using orthogonal polynomials in a Hilbert space. The approach has been implemented in a prototype software called OPERA (Orthogonal Polynomial Expansions for Response Analysis). Use of OPERA on industrial power grids demonstrated speed-ups of up to two orders of magnitude. The results also show a significant variation of about $\\pm$ 35% in the nominal voltage drops at various nodes of the power grids and demonstrate the need for variation-aware power grid analysis.

  5. Stochastic phenomena in a fiber Raman amplifier

    Kalashnikov, Vladimir; Ania-Castanón, Juan Diego; Jacobsen, Gunnar; Popov, Sergei


    The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering-based nonlinearity, the random birefringence of a fiber, and the pump-to-signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence-induced resonance-like enhancement of the gain fluctuations (stochastic anti-resonance) accompanied by pulse broadening and rare events in the form of low power outpu...

  6. Astrophysical disks Collective and Stochastic Phenomena

    Fridman, Alexei M; Kovalenko, Ilya G


    The book deals with collective and stochastic processes in astrophysical discs involving theory, observations, and the results of modelling. Among others, it examines the spiral-vortex structure in galactic and accretion disks , stochastic and ordered structures in the developed turbulence. It also describes sources of turbulence in the accretion disks, internal structure of disk in the vicinity of a black hole, numerical modelling of Be envelopes in binaries, gaseous disks in spiral galaxies with shock waves formation, observation of accretion disks in a binary system and mass distribution of luminous matter in disk galaxies. The editors adaptly brought together collective and stochastic phenomena in the modern field of astrophysical discs, their formation, structure, and evolution involving the methodology to deal with, the results of observation and modelling, thereby advancing the study in this important branch of astrophysics and benefiting Professional Researchers, Lecturers, and Graduate Students.

  7. Stochastic Differential Equation of Earthquakes Series

    Mariani, Maria C.; Tweneboah, Osei K.; Gonzalez-Huizar, Hector; Serpa, Laura


    This work is devoted to modeling earthquake time series. We propose a stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ (α, β ) process. Superposition of independent Γ (α, β ) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to the study of earthquakes by fitting the superposed Γ (α, β ) Ornstein-Uhlenbeck model to earthquake sequences in South America containing very large events (Mw ≥ 8). We obtained very good fit of the observed magnitudes of the earthquakes with the stochastic differential equations, which supports the use of this methodology for the study of earthquakes sequence.

  8. A Compositional Semantics for Stochastic Reo Connectors

    Moon, Young-Joo; Krause, Christian; Arbab, Farhad; 10.4204/EPTCS.30.7


    In this paper we present a compositional semantics for the channel-based coordination language Reo which enables the analysis of quality of service (QoS) properties of service compositions. For this purpose, we annotate Reo channels with stochastic delay rates and explicitly model data-arrival rates at the boundary of a connector, to capture its interaction with the services that comprise its environment. We propose Stochastic Reo automata as an extension of Reo automata, in order to compositionally derive a QoS-aware semantics for Reo. We further present a translation of Stochastic Reo automata to Continuous-Time Markov Chains (CTMCs). This translation enables us to use third-party CTMC verification tools to do an end-to-end performance analysis of service compositions.

  9. Stochastic partial differential equations an introduction

    Liu, Wei


    This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...

  10. Stochastic approach to equilibrium and nonequilibrium thermodynamics.

    Tomé, Tânia; de Oliveira, Mário J


    We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.

  11. Stochastic Modelling Of The Repairable System

    Andrzejczak Karol


    Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

  12. Asymptotic problems for stochastic partial differential equations

    Salins, Michael

    Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

  13. Stochastic biomathematical models with applications to neuronal modeling

    Batzel, Jerry; Ditlevsen, Susanne


    Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

  14. Pesin’s entropy formula for stochastic flows of diffeomorphisms



    Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.

  15. Doubly stochastic Poisson processes in artificial neural learning.

    Card, H C


    This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

  16. Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

    Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe


    We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

  17. A Note on the Stochastic Nature of Feynman Quantum Paths

    L. Botelho, Luiz C.


    We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.


    朱位秋; 蔡国强


    This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested.

  19. A Note on the Stochastic Nature of Feynman Quantum Paths

    Botelho, Luiz C. L.


    We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.

  20. Master-equation approach to stochastic neurodynamics

    Ohira, Toru; Cowan, Jack D.


    A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.

  1. An introduction to stochastic differential equations

    Evans, Lawrence C


    These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. -Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. -George Papa

  2. Level Crossing Methods in Stochastic Models

    Brill, Percy H


    Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems fa

  3. Predicting Footbridge Response using Stochastic Load Models

    Pedersen, Lars; Frier, Christian


    Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing s...... as it pinpoints which decisions to be concerned about when the goal is to predict footbridge response. The studies involve estimating footbridge responses using Monte-Carlo simulations and focus is on estimating vertical structural response to single person loading....

  4. Stochasticity in cell biology: Modeling across levels

    Pedraza, Juan Manuel


    Effective modeling of biological processes requires focusing on a particular level of description, and this requires summarizing de details of lower levels into effective variables and properly accounting for the constrains that other levels impose. In the context of stochasticity in gene expression, I will show how the details of the stochastic process can be characterized by a few effective parameters, which facilitates modeling but complicates interpretation of current experiments. I will show how the resulting noise can provide advantageous or deleterious phenotypic fluctuation and how noise control in the copy number control system of plasmids can change the selective pressures. This system illustrates the direct connection between molecular dynamics and evolutionary dynamics.

  5. Communication nets stochastic message flow and delay

    Kleinrock, Leonard


    Considerable research has been devoted to the formulation and solution of problems involving flow within connected networks. Independent of these surveys, an extensive body of knowledge has accumulated on the subject of queues, particularly in regard to stochastic flow through single-node servicing facilities. This text combines studies of connected networks with those of stochastic flow, providing a basis for understanding the general behavior and operation of communication networks in realistic situations.Author Leonard Kleinrock of the Computer Science Department at UCLA created the basic p

  6. An introduction to quantum stochastic calculus

    Parthasarathy, KR


    An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle.Quantum stochastic integration

  7. Analysing Social Epidemics by Delayed Stochastic Models

    Francisco-José Santonja


    Full Text Available We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.

  8. On orthogonality preserving quadratic stochastic operators

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)


    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  9. Stochastic resonance in an intracellular genetic perceptron

    Bates, Russell; Blyuss, Oleg; Zaikin, Alexey


    Intracellular genetic networks are more intelligent than was first assumed due to their ability to learn. One of the manifestations of this intelligence is the ability to learn associations of two stimuli within gene-regulating circuitry: Hebbian-type learning within the cellular life. However, gene expression is an intrinsically noisy process; hence, we investigate the effect of intrinsic and extrinsic noise on this kind of intracellular intelligence. We report a stochastic resonance in an intracellular associative genetic perceptron, a noise-induced phenomenon, which manifests itself in noise-induced increase of response in efficiency after the learning event under the conditions of optimal stochasticity.

  10. Identification methods for nonlinear stochastic systems.

    Fullana, Jose-Maria; Rossi, Maurice


    Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.

  11. Operation of Distributed Generation Under Stochastic Prices

    Siddiqui, Afzal S.; Marnay, Chris


    We model the operating decisions of a commercial enterprisethatneeds to satisfy its periodic electricity demand with either on-sitedistributed generation (DG) or purchases from the wholesale market. Whilethe former option involves electricity generation at relatively high andpossibly stochastic costs from a set of capacity-constrained DGtechnologies, the latter implies unlimited open-market transactions atstochastic prices. A stochastic dynamic programme (SDP) is used to solvethe resulting optimisation problem. By solving the SDP with and withoutthe availability of DG units, the implied option values of the DG unitsare obtained.

  12. Statistical mechanics of stochastic growth phenomena

    Alekseev, Oleg


    We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasi-static) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with planar domains. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with the free-particle propagator on the infinite dimensional complex manifold with the K\\"ahler metric.

  13. Reserves and cash flows under stochastic retirement

    Gad, Kamille Sofie Tågholt; Nielsen, Jeppe Woetmann


    Uncertain time of retirement and uncertain structure of retirement benefits are risk factors for life insurance companies. Nevertheless, classical life insurance models assume these are deterministic. In this paper, we include the risk from stochastic time of retirement and stochastic benefit...... structure in a classical finite-state Markov model for a life insurance contract. We include discontinuities in the distribution of the retirement time. First, we derive formulas for appropriate scaling of the benefits according to the time of retirement and discuss the link between the scaling...

  14. ada: An R Package for Stochastic Boosting

    Mark Culp


    Full Text Available Boosting is an iterative algorithm that combines simple classification rules with ‘mediocre’ performance in terms of misclassification error rate to produce a highly accurate classification rule. Stochastic gradient boosting provides an enhancement which incorporates a random mechanism at each boosting step showing an improvement in performance and speed in generating the ensemble. ada is an R package that implements three popular variants of boosting, together with a version of stochastic gradient boosting. In addition, useful plots for data analytic purposes are provided along with an extension to the multi-class case. The algorithms are illustrated with synthetic and real data sets.

  15. ada: An R Package for Stochastic Boosting

    Mark Culp


    Full Text Available Boosting is an iterative algorithm that combines simple classification rules with "mediocre" performance in terms of misclassification error rate to produce a highly accurate classification rule. Stochastic gradient boosting provides an enhancement which incorporates a random mechanism at each boosting step showing an improvement in performance and speed in generating the ensemble. ada is an R package that implements three popular variants of boosting, together with a version of stochastic gradient boosting. In addition, useful plots for data analytic purposes are provided along with an extension to the multi-class case. The algorithms are illustrated with synthetic and real data sets.

  16. High-speed Stochastic Fatigue Testing

    Brincker, Rune; Sørensen, John Dalsgaard


    Good stochastic fatigue tests are difficult to perform. One of the major reasons is that ordinary servohydraulic loading systems realize the prescribed load history accurately at very low testing speeds only. If the speeds used for constant amplitude testing are applied to stochastic fatigue...... the analog control device remain as the basic control mechanism in the system, but distorting the input signal by computer in order to minimize the errors of the load history extremes. The principle proves to be very efficient to reduce all kinds of system errors and has shown to be able to increase...

  17. Stochastics introduction to probability and statistics

    Georgii, Hans-Otto


    This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and methods are motivated by examples and developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems offer applications and supplements to the text.

  18. Scattering theory of stochastic electromagnetic light waves.

    Wang, Tao; Zhao, Daomu


    We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.

  19. A theory of stochastic choice under uncertainty

    Karni, Edi; Safra, Zvi


    In this paper we propose a characterization of stochastic choice\\ud under risk and under uncertainty. We presume that decision makers'\\ud actual choices are governed by randomly selected states of mind, and\\ud study the representation of decision makers' perceptions of the stochastic process underlying the selection of their state of mind. The\\ud connections of this work to the literatures on random choice, choice\\ud behavior when preference are incomplete; choice of menus; and grades of inde...

  20. Observability of stochastic resonance in neutron scattering.

    Condat, C A; Lamberti, P W


    The observability of the stochastic resonance phenomenon in a neutron scattering experiment is investigated, considering that the scatterer can hop between two sites. Under stochastic resonance conditions scattered intensity is transferred from the quasielastic region to two inelastic peaks. The magnitude of the signal-to-noise ratio is shown to be similar to that arising in the corresponding power spectrum. Effects of potential asymmetry are discussed in detail. Asymmetry leads to a reduction of the signal-to-noise ratio by a factor of 1-xi(2), where xi is an asymmetry parameter which is zero for symmetric problems and equal to unity in a completely asymmetric case.

  1. Stochastic Modeling of Traffic Air Pollution

    Thoft-Christensen, Palle


    In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...

  2. Towards sub-optimal stochastic control of partially observable stochastic systems

    Ruzicka, G. J.


    The paper deals with a class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in n dimensions is proved.

  3. New travelling wave solutions for nonlinear stochastic evolution equations

    Hyunsoo Kim; Rathinasamy Sakthivel


    The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.


    Haijun WANG; Shigeng HU


    This paper employs a stochastic endogenous growth model with productive government expenditure in a small open economy to analyze the optimal fiscal policy.First,a stochastic model of a small open economy is constructed.Second.the equilibrium solutions of the representative agent's stochastic optimization problem are derived.Third,we obtain the equilibrium solutions of the central planner's stochastic optimization problem and the optimal government expenditure policy.Finally,the optimal tax policy is characterized.

  5. Verification and Planning for Stochastic Processes with Asynchronous Events


    IEEE Transactions on Automatic Control 38, no. 7: 1040–1059. Bartlett, M. S. 1966. An Introduction to Stochastic Processes with Special Reference to...Artificial Intelligence, 875–881, Madison, Wisconsin. AAAI Press. Çinlar, Erhan. 1975. Introduction to Stochastic Processes . Englewood Cliffs, New... to Stochastic Processes . Boston: Houghton Mifflin Company. Hoey, Jesse, Robert St-Aubin, Alan Hu, and Craig Boutilier. 1999. SPUDD: Stochastic

  6. Stochastic population growth in spatially heterogeneous environments.

    Evans, Steven N; Ralph, Peter L; Schreiber, Sebastian J; Sen, Arnab


    Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZ(t) = μZ(t)dt + σZ(t)dW(t), t ≥ 0, where the conditional law of Z(t+Δt)-Z(t) given Z(t) = z has mean and variance approximately z μΔt and z²σ²Δt when the time increment Δt is small. The long-term stochastic growth rate lim(t→∞) t⁻¹ log Z(t) for such a population equals μ − σ²/2 . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model X(t) = (X¹(t) , . . . , X(n)(t)), t ≥ 0, for the population abundances in n patches: the conditional law of X(t+Δt) given X(t) = x is such that the conditional mean of X(i)(t+Δt) − X(i)(t) is approximately [x(i)μ(i) + Σ(j) (x(j) D(ji) − x(i) D(i j) )]Δt where μ(i) is the per capita growth rate in the ith patch and D(ij) is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of X(i)(t+Δt)− X(i)(t) and X(j)(t+Δt) − X(j)(t) is approximately x(i)x(j)σ(ij)Δt for some covariance matrix Σ = (σ(ij)). We show for such a spatially extended population that if S(t) = X¹(t)+· · ·+ X(n)(t) denotes the total population abundance, then Y(t) = X(t)/S(t), the vector of patch proportions, converges in law to a random vector Y(∞) as t → ∞, and the stochastic growth rate lim(t→∞) t⁻¹ log S(t) equals the space-time average per-capita growth rate Σ(i)μ(i)E[Y(i)(∞)] experienced by the population minus half of the space-time average temporal variation E[Σ(i,j) σ(i j)Y(i)(∞) Y(j)(∞)] experienced by the population. Using this characterization of the

  7. Analysis of stochastic bifurcation and chaos in stochastic Duffing-van der Pol system via Chebyshev polynomial approximation

    Ma Shao-Juan; Xu Wei; Li Wei; Fang Tong


    The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter.Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.

  8. Second Workshop on Stochastic Analysis and Related Topics

    Ustunel, Ali


    The Second Silivri Workshop functioned as a short summer school and a working conference, producing lecture notes and research papers on recent developments of Stochastic Analysis on Wiener space. The topics of the lectures concern short time asymptotic problems and anticipative stochastic differential equations. Research papers are mostly extensions and applications of the techniques of anticipative stochastic calculus.

  9. Analysis of bilinear stochastic systems. [involving multiplicative noise processes

    Willsky, A. S.; Marcus, S. I.; Martin, D. N.


    Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

  10. Stochastic Finite Elements in Reliability-Based Structural Optimization

    Sørensen, John Dalsgaard; Engelund, S.

    Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

  11. Stochastic Finite Elements in Reliability-Based Structural Optimization

    Sørensen, John Dalsgaard; Engelund, S.


    Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

  12. Intermittent stochastic fields and space-time symmetry

    Barndorff-Nielsen, Ole E.; Schmiegel, Jürgen

    We present a spatio-temporal modelling framework for stochastic fields that obey exact symmetry in space and time, i.e. the field amplitude considered as a stochastic process in time at a fixed position in space is identical, as a stochastic process, to the field amplitude considered...

  13. Solving Simple Stochastic Games with Few Random Vertices

    Gimbert, H.; Horn, F.


    Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a cla

  14. Adaptive and Optimal Control of Stochastic Dynamical Systems


    games that does not require finding solutions to nonlinear partial differential equations or solv- ing backward stochastic differential equations ...for stochastic partial differential equations with fractional Brownian motions having the Hurst parameter in the interval (1/2,1), which includes the...Linear exponential-quadratic control problems for stochastic partial differential equations are explicitly solved. Discrete time linear quadratic

  15. Teaching Tip: When a Matrix and Its Inverse Are Stochastic

    Ding, J.; Rhee, N. H.


    A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

  16. Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions


    motions and other stochastic processes. For the control of both continuous time and discrete time finite dimensional linear systems with quadratic...problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...2010 30-Jun-2014 Approved for Public Release; Distribution Unlimited Final Report: Optimal Control of Stochastic Systems Driven by Fractional Brownian

  17. Strong Limit Theorems for Arbitrary Fuzzy Stochastic Sequences

    FEI Wei-yin


    Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are extended. In order to prove results of this paper, the notion of fuzzy martingale difference sequences is also introduced.

  18. Robust stability of uncertain neutral linear stochastic differential delay system

    JIANG Ming-hui; SHEN Yi; LIAO Xiao-xin


    The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.

  19. Vaccination Control in a Stochastic SVIR Epidemic Model.

    Witbooi, Peter J; Muller, Grant E; Van Schalkwyk, Garth J


    For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium for ℛ(0) stochastic model as well as for the underlying deterministic model. In order to solve the stochastic problem numerically, we use an approximation based on the solution of the deterministic model.

  20. Numerical solution of stochastic SIR model by Bernstein polynomials

    N. Rahmani


    Full Text Available In this paper, we present numerical method based on Bernstein polynomials for solving the stochastic SIR model. By use of Bernstein operational matrix and its stochastic operational matrix we convert stochastic SIR model to a nonlinear system that can be solved by Newton method. Finally, a test problem of SIR model is presented to illustrate our mathematical findings.

  1. Stochastic Analysis and Applied Probability(3.3.1): Topics in the Theory and Applications of Stochastic Analysis


    Stochastic Analysis and Applied Probability(3.3.1): Topics in the Theory and Applications of Stochastic Analysis . The views, opinions and/or findings...of Papers published in non peer-reviewed journals: Final Report: Stochastic Analysis and Applied Probability(3.3.1): Topics in the Theory and...Applications of Stochastic Analysis . Report Title Research partially supported by this grant culminated in the submission of twenty eight new research papers

  2. S-2 stage 1/25 scale model base region thermal environment test. Volume 1: Test results, comparison with theory and flight data

    Sadunas, J. A.; French, E. P.; Sexton, H.


    A 1/25 scale model S-2 stage base region thermal environment test is presented. Analytical results are included which reflect the effect of engine operating conditions, model scale, turbo-pump exhaust gas injection on base region thermal environment. Comparisons are made between full scale flight data, model test data, and analytical results. The report is prepared in two volumes. The description of analytical predictions and comparisons with flight data are presented. Tabulation of the test data is provided.

  3. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)


    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  4. White Noise Path Integrals in Stochastic Neurodynamics

    Carpio-Bernido, M. Victoria; Bernido, Christopher C.


    The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.

  5. Bayesian Vector Autoregressions with Stochastic Volatility

    Uhlig, H.F.H.V.S.


    This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate.Exact updating formulas are given to the nonlinear filtering of the precision matrix.Estimation of the au

  6. Maximal stochastic transport in the Lorenz equations

    Agarwal, Sahil, E-mail: [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)


    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  7. Investigation of the stochastic properties of wind

    Dimitriadis, Panayiotis; Koutsoyiannis, Demetris; Papanicolaou, Panos


    Understanding atmospheric motion in the form of wind is essential to many fields in hydroclimatics. The wind is considered one of the most important processes in hydrometeorology since, along with temperature, it generates and drives climate dynamics. Currently, the interest has increased due to its involvement to renewable energy resources through wind power production and forecasting. However, there seems to be a puzzle about which stochastic model best describes the wind process. In this analysis, we attempt to explain the reason around this confusion regarding the stochastic properties of the wind process using statistical as well as hydrometeorological reasoning, starting from the microscale of turbulence and extending the analysis to the macroscale of climatic processes. Particularly, some models seem to exhibit good agreement with data mostly due to instrumental errors. Moreover, we show that extending the theory of turbulence to the atmospheric motion can reveal stochastic properties that are not only accompanied with physical interference but also exhibit excellent agreement with wind measurements. Finally, we apply the theoretical analysis to multiple stations around the globe and we derive conclusions on the variation of stochastic parameters of wind regarding dominant climatic conditions.

  8. A Nucleolus for Stochastic Cooperative Games

    Suijs, J.P.M.


    This paper extends the definition of the nucleolus to stochastic cooperative games, that is, to cooperative games with random payoffs to the coalitions. It is shown that the nucleolus is nonempty and that it belongs to the core whenever the core is nonempty. Furthermore, it is shown for a particular

  9. Stochastic energy balancing in substation energy management

    Hassan Shirzeh


    Full Text Available In the current research, a smart grid is considered as a network of distributed interacting nodes represented by renewable energy sources, storage and loads. The source nodes become active or inactive in a stochastic manner due to the intermittent nature of natural resources such as wind and solar irradiance. Prediction and stochastic modelling of electrical energy flow is a critical task in such a network in order to achieve load levelling and/or peak shaving in order to minimise the fluctuation between off-peak and peak energy demand. An effective approach is proposed to model and administer the behaviour of source nodes in this grid through a scheduling strategy control algorithm using the historical data collected from the system. The stochastic model predicts future power consumption/injection to determine the power required for storage components. The stochastic models developed based on the Box-Jenkins method predict the most efficient state of the electrical energy flow between a distribution network and nodes and minimises the peak demand and off-peak consumption of acquiring electrical energy from the main grid. The performance of the models is validated against the autoregressive moving average (ARIMA and the Markov chain models used in previous work. The results demonstrate that the proposed method outperforms both the ARIMA and the Markov chain model in terms of forecast accuracy. Results are presented, the strengths and limitations of the approach are discussed, and possible future work is described.

  10. A Stochastic Dynamic Model of Computer Viruses

    Chunming Zhang


    Full Text Available A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.

  11. A Note on Boolean Stochastic Processes

    Fidaleo, Francesco


    For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.

  12. Micro-level stochastic loss reserving

    Antonio, K.; Plat, R.


    To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insu

  13. Nonlinear stochastic inflation modelling using SEASETARs

    de Gooijer, J.G.; Vidiella-i-Anguera, A.


    The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynam

  14. Magnetohydrodynamic stability of stochastically driven accretion flows.

    Nath, Sujit Kumar; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K


    We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.

  15. Comparing Several Robust Tests of Stochastic Equality.

    Vargha, Andras; Delaney, Harold D.

    In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or…

  16. On the Adaptivity Gap of Stochastic Orienteering

    Bansal, N.; Nagarajan, V.


    The input to the stochastic orienteering problem consists of a budget B and metric (V,d) where each vertex v has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a non-anticipator

  17. AA, vacuum tank for stochastic precooling


    The vaccum tank in which the fast stochastic precooling kicker was installed. It is clad with heating jackets for bake-out to 200 deg C, indispensable for reaching the operational vacuum of 7E-11 Torr. Alain Poncet, responsible for AA vacuum, is looking on. See also 7910268, 8002234.

  18. Stochastic models of intracellular calcium signals

    Rüdiger, Sten, E-mail:


    Cellular signaling operates in a noisy environment shaped by low molecular concentrations and cellular heterogeneity. For calcium release through intracellular channels–one of the most important cellular signaling mechanisms–feedback by liberated calcium endows fluctuations with critical functions in signal generation and formation. In this review it is first described, under which general conditions the environment makes stochasticity relevant, and which conditions allow approximating or deterministic equations. This analysis provides a framework, in which one can deduce an efficient hybrid description combining stochastic and deterministic evolution laws. Within the hybrid approach, Markov chains model gating of channels, while the concentrations of calcium and calcium binding molecules (buffers) are described by reaction–diffusion equations. The article further focuses on the spatial representation of subcellular calcium domains related to intracellular calcium channels. It presents analysis for single channels and clusters of channels and reviews the effects of buffers on the calcium release. For clustered channels, we discuss the application and validity of coarse-graining as well as approaches based on continuous gating variables (Fokker–Planck and chemical Langevin equations). Comparison with recent experiments substantiates the stochastic and spatial approach, identifies minimal requirements for a realistic modeling, and facilitates an understanding of collective channel behavior. At the end of the review, implications of stochastic and local modeling for the generation and properties of cell-wide release and the integration of calcium dynamics into cellular signaling models are discussed.

  19. Stochastic Resonance in Protein Folding Dynamics.

    Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A


    Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.

  20. Importance Sampling for Stochastic Timed Automata

    Jegourel, Cyrille; Larsen, Kim Guldstrand; Legay, Axel


    We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state...

  1. Stochastic analysis/synthesis using sinusoidal atoms

    Jensen, Kristoffer


    This work proposes a method for re-synthesizing music for use in perceptual experiments regarding structural changes and in music creation. Atoms are estimated from music audio, modelled in a stochastic model, and re-synthesized from the model pa- rameters. The atoms are found by splitting...

  2. Stochastic Simulation Tool for Aerospace Structural Analysis

    Knight, Norman F.; Moore, David F.


    Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.

  3. Stochastic model updating using distance discrimination analysis

    Deng Zhongmin; Bi Sifeng; Sez Atamturktur


    This manuscript presents a stochastic model updating method, taking both uncertainties in models and variability in testing into account. The updated finite element (FE) models obtained through the proposed technique can aid in the analysis and design of structural systems. The authors developed a stochastic model updating method integrating distance discrimination analysis (DDA) and advanced Monte Carlo (MC) technique to (1) enable more efficient MC by using a response surface model, (2) calibrate parameters with an iterative test-analysis correlation based upon DDA, and (3) utilize and compare different distance functions as correlation metrics. Using DDA, the influence of distance functions on model updating results is analyzed. The proposed sto-chastic method makes it possible to obtain a precise model updating outcome with acceptable cal-culation cost. The stochastic method is demonstrated on a helicopter case study updated using both Euclidian and Mahalanobis distance metrics. It is observed that the selected distance function influ-ences the iterative calibration process and thus, the calibration outcome, indicating that an integra-tion of different metrics might yield improved results.

  4. Stochastic analysis of self-induced vibrations

    Rüdinger, Finn; Krenk, Steen


    Vortex-induced vibrations of a structurl element are modelled as a non-linear stochastic single-degree-of-freedom system. The deterministic part of the governing equation represents laminar flow conditions with a stationary non-zero solution corresponding to lock-in. Across-wind turbulence...

  5. Stochastic dominance and medical decision making.

    Leshno, Moshe; Levy, Haim


    Stochastic Dominance (SD) criteria are decision making tools which allow us to choose among various strategies with only partial information on the decision makers' preferences. The notion of Stochastic Dominance has been extensively employed and developed in the area of economics, finance, agriculture, statistics, marketing and operation research since the late 1960s. For example, it may tell us which of two medical treatments with uncertain outcomes is preferred in the absence of full information on the patients' preferences. This paper presents a short review of the SD paradigm and demonstrates how the SD criteria may be employed in medical decision making, using the case of small abdominal aortic aneurysms as an illustration. Thus, for instance by assuming risk aversion one can employ second-degree stochastic dominance to divide the set of all possible treatments into the efficient set, from which the decision makers should always choose, and the inefficient (inferior) set. By employing Prospect Stochastic Dominance (PSD) a similar division can be conducted corresponding to all S-shaped utility functions.

  6. Stochastic electromagnetic radiation of complex sources

    Naus, H.W.L.


    The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a prior

  7. A stochastic model for bacteriophage therapies

    Bardina, Xavier; Rovira, Carles; Tindel, Samy


    In this article, we analyze a system modeling bacteriophage treatments for infections in a noisy context. In the small noise regime, we show that after a reasonable amount of time the system is close to a sane equilibrium (which is a relevant biologic information) with high probability. Mathematically speaking, our study hinges on concentration techniques for delayed stochastic differential equations.

  8. Stochastic nonhomogeneous incompressible Navier-Stokes equations

    Cutland, Nigel J.; Enright, Brendan

    We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.

  9. Stochastic models in reliability and maintenance


    Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main­ tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which cla...

  10. Computer Aided Continuous Time Stochastic Process Modelling

    Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay


    A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...

  11. Stochastic beamforming for cochlear implant coding

    Morse, Robert P.; Holmes, Stephen D.; Shulgin, Boris; Nikitin, Alexander; Stocks, Nigel G.


    Cochlear implants are prosthetic devices used to provide hearing to people who would otherwise be profoundly deaf. The deliberate addition of noise to the electrode signals could increase the amount of information transmitted, but standard cochlear implants do not replicate the noise characteristic of normal hearing because if noise is added in an uncontrolled manner with a limited number of electrodes then it will almost certainly lead to worse performance. Only if partially independent stochastic activity can be achieved in each nerve fibre can mechanisms like suprathreshold stochastic resonance be effective. We are investigating the use of stochastic beamforming to achieve greater independence. The strategy involves presenting each electrode with a linear combination of independent Gaussian noise sources. Because the cochlea is filled with conductive salt solutions, the noise currents from the electrodes interact and the effective stimulus for each nerve fibre will therefore be a different weighted sum of the noise sources. To some extent therefore, the effective stimulus for a nerve fibre will be independent of the effective stimulus of neighbouring fibres. For a particular patient, the electrode position and the amount of current spread are fixed. The objective is therefore to find the linear combination of noise sources that leads to the greatest independence between nerve discharges. In this theoretical study we show that it is possible to get one independent point of excitation (one null) for each electrode and that stochastic beamforming can greatly decrease the correlation between the noise exciting different regions of the cochlea.

  12. Stochastic wind turbine control in multiblade coordinates

    Thomsen, Sven Creutz; Niemann, Hans Henrik; Poulsen, Niels Kjølstad


    In this paper we consider wind turbine load attenuation through model based control. Asymmetric loads caused by the wind field can be reduced by pitching the blades individually. To this end we investigate the use of stochastic models of the wind which can be included in a model based individual ...

  13. Stochastic optimization in the power grid

    Leenman, T.S.


    In this thesis steps are described to determine the locations of new wind mills which minimize energy loss on the Dutch High Voltage power grid. A vindication of the used power grid model is provided; the simulation procedure for stochastic wind power is described; and the required mathematical opti

  14. Some recent developments in stochastic volatility modelling

    Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.


    This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...

  15. Stochastic models for turbulent reacting flows

    Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)


    The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.

  16. Efficient Estimating Functions for Stochastic Differential Equations

    Jakobsen, Nina Munkholt

    The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...

  17. Jensen's Inequality for Backward Stochastic Differential Equations

    Long JIANG


    Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations ith generator g if and only ifg is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for gexpectation in [4, 7-9].

  18. Long term dynamics of stochastic evolution equations

    Bierkens, Gregorius Nicolaas Johannes Cornelis


    Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often

  19. Stochastic resonance in Gaussian quantum channels

    Lupo, Cosmo; Mancini, Stefano; Wilde, Mark M.


    We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a ‘forbidden interval’. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the ‘forbidden interval’ may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.

  20. Stochastic Cooperative Games in Insurance and Reinsurance

    Suijs, J.P.M.; De Waegenaere, A.M.B.; Borm, P.E.M.


    This paper shows how problems in `non life'-insurance and `non life'-reinsurance can be modelled simultaneously as cooperative games with stochastic payoffs.Pareto optimal allocations of the risks faced by the insurers and the insureds are determined.It is shown that the core of the corresponding in