In this work, we study and analyze the aggregate death counts of COVID-19 reported by the United States Centers for Disease Control and Prevention (CDC) for the fifty states in the United States. To do this, we derive a stochastic model describing the cumulative number of deaths reported daily by CDC from the first time Covid-19 death is recorded to June 20, 2021 in the United States, and provide a forecast for the death cases. The stochastic model derived in this (...) work performs better than existing deterministic logistic models because it is able to capture irregularities in the sample path of the aggregate death counts. The probability distribution of the aggregate death counts is derived, analyzed, and used to estimate the count’s per capita initial growth rate, carrying capacity, and the expected value for each given day as at the time this research is conducted. Using this distribution, we estimate the expected first passage time when the aggregate death count is slowing down. Our result shows that the expected aggregate death count is slowing down in all states as at the time this analysis is conducted (June 2021). A formula for predicting the end of Covid-19 deaths is derived. The daily expected death count for each states is plotted as a function of time. The probability density function for the current day, together with the forecast and its confidence interval for the next four days, and the root mean square error for our simulation results are estimated. (shrink)

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation (...) in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM). (shrink)

Hidden Markov models (HMMs) have been successful for modelling the dynamics of carefully dictated speech, but their performance degrades severely when used to model conversational speech. Since speech is produced by a system of loosely coupled articulators, stochastic models explicitly representing this parallelism may have advantages for automatic speech recognition (ASR), particularly when trying to model the phonological effects inherent in casual spontaneous speech. This paper presents a preliminary feasibility study of one such model class: loosely coupled HMMs. Exact model (...) estimation and decoding is potentially expensive, so possible approximate algorithms are also discussed. Comparison of one particular loosely coupled model on an isolated word task suggests loosely coupled HMMs merit further investigation. An approximate algorithm giving performance which is almost always statistically indistinguishable from the exact algorithm is also identified, making more extensive research computationally feasible. (shrink)

A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss asymptotic stability of interior equilibrium. For a stochastic (...) system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis. (shrink)

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. The models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad class (...) of games, demonstrates a novel domain of agreement between the dynamics, and indicates a broader moral for evolutionary modeling. (shrink)

In this paper, I reflect on the puzzle that machine learning presents to social theory to develop an account of its distinct impact on social reality. I start by presenting how machine learning has presented a challenge to social theory as a research subject comprising both familiar and alien characteristics (1.). Taking this as an occasion for theoretical inquiry, I then propose a conceptual framework to investigate how algorithmic models of social phenomena relate to social reality and what their stochastic (...) mode of operation entails in terms of their sociality (2.). Analyzed through a theoretical lens that relies on central tenets of sociological systems theory, I find that machine learning implies a distinct epistemic transformation, based on how algorithmic modeling techniques process meaning as represented in data embedded in vector space. Building on this characterization, I introduce my conceptualization of stochastic technology as distinct from mechanistic technologies that rely on causal fixation (3.). Based on this understanding, I suggest that real-world applications of machine learning are often characterized by a constitutive tension between the stochastic properties of their outputs and the ways in which they are put to use in practice. Focussing on the large language models LaMDA and ChatGPT, I examine the epistemological implications of LLMs to account for the confusion of correlation and causality as the root of this tension. Next, I illustrate my theoretical conception by way of discussing an essay on image models by German media artist Hito Steyerl (4.). Following a critical reflection on Steyerl's characterization of Stable Diffusion as a “white box ”, I finally propose to conceive ofmachine learning-based technologies as stochastic contingency machines that transform social indeterminacy into contingent observations of social phenomena (5.) In this perspective, machine learning constitutes an epistemic technology that operates on meaning as extractable from data by means of algorithmic data modeling techniques to produce stochastic accounts of social reality. (shrink)

The aim of this paper is to establish that free agency, which is a capacity of many animals including human beings, is compatible with indeterminism: an indeterministic world allows for the existence of free agency. The question of the compatibility of free agency and indeterminism is less discussed than its mirror image, the question of the compatibility of free agency and determinism. It is, however, of great importance for our self-conception as free agents in our (arguably) indeterministic world. We begin (...) by explicating the notions of indeterminism and free agency and by clarifying the interrelation of free agency and the human-specific notion of free will. We then situate our claim of the compatibility of free agency and indeterminism precisely in the landscape of the current debate on freedom and determinism, exposing an unhappy asymmetry in that debate. Then we proceed to make our case by describing the mathematically precise, physically motivated model of projective simulation, which employs indeterminism as a central resource for agency modeling. We argue that an indeterministic process of deliberation modeled by the dynamics of projective simulation can exemplify free agency under indeterminism, thereby establishing our compatibility claim: Free agency can develop and thrive in an indeterministic world. (shrink)

Standard models in quantitative linguistics assume that word usage follows a fixed frequency distribution, often Zipf's law or a close relative. This view, however, does not capture the near daily variations in topics of conversation, nor the short-term dynamics of language change. In order to understand the dynamics of human language use, we present a corpus of daily word frequency variation scraped from online news sources every 20 min for more than 2 years. We construct a simple time-varying model with (...) a latent state, which is observed via word frequency counts. We use Bayesian techniques to infer the parameters of this model for 20,000 words, allowing us to convert complex word-frequency trajectories into low-dimensional parameters in word usage. By analyzing the inferred parameters of this model, we quantify the relative mobility and drift of words on a day-to-day basis, while accounting for sampling error. We quantify this variation and show evidence against “rich-get-richer” models of word use, which have been previously hypothesized to explain statistical patterns in language. (shrink)

Recent advances in genomic and imaging techniques have revealed the complex manner of organizing billions of base pairs of DNA necessary for maintaining their functionality and ensuring the proper expression of genetic information. The SMC proteins and cohesin complex primarily contribute to forming higher‐order chromatin structures, such as chromosomal territories, compartments, topologically associating domains (TADs) and chromatin loops anchored by CCCTC‐binding factor (CTCF) protein or other genome organizers. Cohesin plays a fundamental role in chromatin organization, gene expression and regulation. This (...) review aims to describe the current understanding of the dynamic nature of the cohesin‐DNA complex and its dependence on cohesin for genome maintenance. We discuss the current 3C technique and numerous bioinformatics pipelines used to comprehend structural genomics and epigenetics focusing on the analysis of Cohesin‐centred interactions. We also incorporate our present comprehension of Loop Extrusion (LE) and insights from stochastic modelling. (shrink)

HSimulator is a multithread simulator for mass-action biochemical reaction systems placed in a well-mixed environment. HSimulator provides optimized implementation of a set of widespread state-of-the-art stochastic, deterministic, and hybrid simulation strategies including the first publicly available implementation of the Hybrid Rejection-based Stochastic Simulation Algorithm. HRSSA, the fastest hybrid algorithm to date, allows for an efficient simulation of the models while ensuring the exact simulation of a subset of the reaction network modeling slow reactions. Benchmarks show that HSimulator is often (...) considerably faster than the other considered simulators. The software, running on Java v6.0 or higher, offers a simulation GUI for modeling and visually exploring biological processes and a Javadoc-documented Java library to support the development of custom applications. HSimulator is released under the COSBI Shared Source license agreement. (shrink)

The state-of-art research in the field of life’s organization confronts the need to investigate a number of interacting components, their properties and conditions of sustainable behaviour within a natural system. In biology, ecology and life sciences, the performance of such stable system is usually related to homeostasis, a property of the system to actively regulate its state within a certain allowable limits. In our previous work, we proposed a deterministic model for systems’ homeostasis. The model was based on dynamical system’s (...) theory and pairwise relationships of competition, amensalism and antagonism taken from theoretical biology and ecology. However, the present paper proposes a different dimension to our previous results based on the same model. In this paper, we introduce the influence of inter-component relationships in a system, wherein the impact is characterized by direction (neutral, positive, or negative) as well as its (absolute) value, or strength. This makes the model stochastic which, in our opinion, is more consistent with real-world elements affected by various random factors. The case study includes two examples from areas of hydrobiology and medicine. The models acquired for these cases enabled us to propose a convincing explanation for corresponding phenomena identified by different types of natural systems. (shrink)

In recent years, the world knew many challenges concerning the propagation of infectious diseases such as avian influenza, Ebola, SARS-CoV-2, etc. These epidemics caused a change in the healthy balance of humanity. Also, the epidemics disrupt the economies and social activities of countries around the world. Mathematical modeling is a vital means to represent and control the propagation of infectious diseases. In this paper, we consider a stochastic epidemic model with a Markov process and delay, which generalizes many models (...) existing in the literature. In addition, we show the stochastic threshold for the extinction of the disease. Furthermore, numerical examples are discussed to confirm the theoretical result. (shrink)

Model validation in computational cognitive psychology often relies on methods drawn from the testing of theories in experimental physics. However, applications of these methods to computational models in typical cognitive experiments can hide multiple, plausible sources of variation arising from human participants and from stochastic cognitive theories, encouraging a “model fixed, data variable” paradigm that makes it difficult to interpret model predictions and to account for individual differences. This article proposes a likelihood‐based, “data fixed, model variable” paradigm in which models (...) are treated as stochastic processes in experiments with participant‐to‐participant variation that can be applied to a broad range of mechanistic cognitive architectures. This article discusses the implementation and implications of this view in model validation, with a concrete focus on a simple class of ACT‐R models of cognition. This article is not intended as a recipe for broad application of these preliminary, proof‐of‐concept methods, but as a framework for communication between statisticians searching for interesting problems in the cognitive modeling sphere, and cognitive modelers interested in generalizing from deterministic to stochastic model validation, in the face of random variation in human experimental data. (shrink)

Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how (...) their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms. (shrink)

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity (...) theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis. (shrink)

Some contemporary theorists such as Mazzocchi, Theise and Kafatos are convinced that the reformed complementarity may redefine how we might exploit the complexity theory in 21st-century life sciences research. However, the motives behind the profound re-invention of “biological complementarity” need to be substantiated with concrete shreds of evidence about this principle’s applicability in real-life science experimentation, which we found missing in the literature. This paper discusses such pieces of evidence by confronting Bohr’s complementarity and ion channel modeling practice. We (...) examine whether and to what extent this principle might assist in developing ion channel models incorporating both deterministic and stochastic solutions. According to the “mutual exclusiveness of experimental setups” version of Bohr’s complementarity, this principle is needed when two mutually exclusive perspectives or approaches are right, necessary in a particular context, and are not contradictory as they arise in mutually exclusive conditions (mutually exclusive experimental or modeling setups). A detailed examination of the modeling practice reveals that both solutions are often used simultaneously in a single ion channel model, suggesting that the opposite conceptual frameworks can coexist in the same modeling setup. We concluded that Bohr’s complementarity might find applications in these complex modeling setups but only through its realistic phenomenological interpretation that allows applying different modes of description regardless of the nature of the underlying ion channel opening process. Also, we propose the combined use of complementarity and Complex thinking in building the multifaceted ion channel models. Overall, this paper’s results support the efforts to establish a more general form of complementarity to meet today’s complexity theory-inspired life sciences modeling demands. (shrink)

. Fuzzy systems and artificial neural networks, as important components of soft-computation, can be applied together to model uncertainty. A composite block of the fuzzy system and the ANN shares a mutually beneficial association resulting in enhanced performance with smaller networks. It makes them suitable for application with time-varying multi-input multi-output channel modeling enabling such a system to track minute variations in propagation conditions. Here we propose a fuzzy neural system using a fuzzy time delay fully recurrent neural network (...) that has the capability to tackle time-varying inputs in fuzzified form and is used to model MIMO channels. The inference engine is constituted by novel FTDFRNN blocks which determine the decision boundaries and tracks in-phase and quadrature components of input signals encompassing stochastic behavior of the MIMO channel. The system shows significant improvement in performance compared to statistical and ANN approaches in terms of faster processing time, lower bit error rate margins and better precision while carrying out symbol recovery of transmitted data through severely faded MIMO channels. (shrink)

We present a population density and moment-based description of the stochastic dynamics of domain $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type $${\text{Ca}}^{2+}$$ channels. Our approach accounts for the effect of heterogeneity of local $${\text{Ca}}^{2+}$$ signals on whole cell $${\text{Ca}}^{2+}$$ currents; however, in contrast with prior work, e.g., Sherman et al. :985–995, 1990), we do not assume that $${\text{Ca}}^{2+}$$ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain (...) model of an L-type $${\text{Ca}}^{2+}$$ channel introduced by Greenstein and Winslow :2918–2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell $${\text{Ca}}^{2+}$$ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of $${\text{Ca}}^{2+}$$ inactivation that may occur via slow heterogeneous domain [ $${\text{Ca}}^{2+}$$ ]. Next, we find that when channel permeability is held constant, $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [ $${\text{Ca}}^{2+}$$ ] near open channels; conversely, when the maximum domain [ $${\text{Ca}}^{2+}$$ ] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations. (shrink)

Making proper decisions in today’s complex world is a challenging task for decision makers. A promising approach that can support decision makers to have a better understanding of complex systems is agent-based modeling. ABM has been developing during the last few decades as a methodology with many different applications and has enabled a better description of the dynamics of complex systems. However, the prescriptive facet of these applications is rarely portrayed. Adding a prescriptive decision-making aspect to ABM can support (...) the decision makers in making better or, in some cases, optimized decisions for the complex problems as well as explaining the investigated phenomena. In this paper, first, the literature of DM with ABM is inquired and classified based on the methods of integration. Performing a scientometric analysis on the relevant literature lets us conclude that the number of publications attempting to integrate DM and ABM has not grown during the last two decades, while analysis of the current methodologies for integrating DM and ABM indicates that they have serious drawbacks. In this regard, a novel nature-inspired model articulation called optimal agent framework has been proposed to ameliorate the disadvantages and enhance the realization of proper decisions in ABM at a relatively low computational cost. The framework is examined with the Bass diffusion model. The results of the simulation for the customized model developed by OAF have verified the feasibility of the framework. Moreover, sensitivity analyses on different agent populations, network structures, and marketing strategies have depicted the great potential of OAF to find the optimal strategies in various stochastic and unconventional conditions which have not been addressed prior to the implementation of the framework. (shrink)

Residual useful lifetime prediction plays a key role of failure prediction and health management in equipment. Aiming at the problems of residual life prediction without comprehensively considering multistage and individual differences in equipment performance degradation at present, we explore a prediction model that can fit the multistage random performance degradation. Degradation modeling is based on the random Wiener process. Moreover, according to the degradation monitoring data of the same batch of equipment, we apply the expectation maximization algorithm to estimate (...) the prior distribution of the model. The real-time remaining life distribution of the equipment is acquired by merging prior information of real-time degradation data and historical degradation monitoring data. The accuracy of the proposed model is demonstrated by analyzing a practical case of metalized film capacitors, and the result shows that a better RUL estimation accuracy can be provided by our model compared with existing models. (shrink)

This valuable text provides a comprehensive introduction to VAR modelling and how it can be applied. In particular, the author focuses on the properties of the Cointegrated VAR model and its implications for macroeconomic inference when data are non-stationary. The text provides a number of insights into the links between statistical econometric modelling and economic theory and gives a thorough treatment of identification of the long-run and short-run structure as well as of the common stochastic trends and the impulse response (...) functions, providing in each case illustrations of applicability.This book presents the main ingredients of the Copenhagen School of Time-Series Econometrics in a transparent and coherent framework. The distinguishing feature of this school is that econometric theory and applications have been developed in close cooperation. The guiding principle is that good econometric work should take econometrics, institutions, and economics seriously. The author uses a single data set throughout most of the book to guide the reader through the econometric theory while also revealing the full implications for the underlying economic model. To test ensure full understanding the book concludes with the introduction of two new data sets to combine readers understanding of econometric theory and economic models, with economic reality. (shrink)

We present a general framework for analyzing the contribution to reproductive success of a behavioural action. An action may make a direct contribution to reproductive success, but even in the absence of a direct contribution it may make an indirect contribution by changing the animal's state. We consider actions over a period of time, and define a reward function that characterizes the relationship between the animal's state at the end of the period and its future reproductive success. Working back from (...) the end of the period using dynamic programming, the optimal action as a function of state and time can be found. The procedure also yields a measure of the cost, in terms of future reproductive success, of a suboptimal action. These costs provide us with a common currency for comparing activities such as eating and drinking, or eating and hiding from predators. The costs also give an indication of the robustness of the conclusions that can be drawn from a model. We review how our framework can be used to analyze optimal foraging decisions in a stochastic environment. We also discuss the modelling of optimal daily routines and provide an illustration based on singing to attract a mate. We use the model to investigate the features that can produce a dawn song burst in birds. State is defined very broadly so that it includes the information an animal has about its environment. Thus, exploration and learning can be included within the framework. (shrink)

Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data. These challenges are incomplete in two respects: they do not show that chaotic regimes are unpredictable in principle and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this (...) paper we appeal to an asymptotic analysis of state space trajectories and their numerical approximations to show that chaotic regimes are deterministically unpredictable even with unbounded resources. Additionally, we explain why stochastic models of chaotic systems, while predictively successful in some cases, are in general predictively as limited as deterministic ones. We conclude by suggesting that the way in which scientists deal with such principled obstructions to predictability calls for a more comprehensive approach to theory validation, on which experimental testing is augmented by a multifaceted mathematical analysis of theoretical models, capable of identifying chaos-related predictive failures as due to principled limitations which the world itself imposes on any less-than-omniscient epistemic access to some natural systems. (shrink)

After the financial crisis of 2008, many economists expressed dissatisfaction with the state of macroeconomics. They criticised deficiencies in the dominant dynamic stochastic general equilibrium modelling approach and conceptions of good macroeconomic research behind that dominance. This paper argues that there is a deeper problem in macroeconomics, which remains unaddressed. I connect existing literature critical of the institutions of macroeconomics and of economics in general to the institutional preconditions of effective criticism outlined by the philosopher Helen Longino. I find that (...) as an epistemic community, macroeconomics does not function in a way that adequately supports critical evaluation of established beliefs, norms and practices. This failure may partly explain why many views on macroeconomic modelling, the tenability of which economists questioned after the crisis, were able to persist for so long. My analysis gives additional support to several recent proposals for institutional reforms in economics. (shrink)

The paper offers a partial vindication of Sterelny’s view on the role of error rates and reliability in his theory of decoupled representation based on modelling techniques borrowed from the biological literature on evolution in stochastic environments. In the case of a tight link between tracking states and behaviour, I argue that in its full generality Sterelny’s account instantiates the base-rate fallacy. With regard to non-tightly linked behaviour, I show that Sterelny’s account can be vindicated subject to an adequate evolutionary (...) model and a suitable notion of reliability. (shrink)

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on (...) to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. (shrink)

Over the last 40 years or so, there has been an explosion of cultural evolution research in anthropology and archaeology. In each discipline, cultural evolutionists investigate how interactions between individuals translate into group level patterns, with the aim of explaining the diachronic dynamics and diversity of cultural traits. However, while much attention has been given to deterministic processes, we contend that current evolutionary accounts of cultural change are limited because they do not adopt a systematic stochastic approach. First, we show (...) that, in contrast with the intense debates in ecology and population genetics, the importance of stochasticity in evolutionary processes has generated little discussion in the sciences of cultural evolution to date. Second, we speculate on the reasons, both ideological and methodological, why that should be so. Third, we highlight the inadequacy of genetically-inspired stochastic models in the context of cultural evolution modelling, and ask which fundamental stochastic processes might be more relevant to take up. We conclude that the field of cultural evolution would benefit from a stochastic revolution. For that to occur, stochastic models ought to be developed specifically for cultural data and not through a copy-pasting of neutral models from population genetics or ecology. (shrink)

Biological processes span several scales in space, from the single molecules to organisms and ecosystems. Multiscale modelling approaches in biology are useful to take into account the complex interactions between different organisation levels in those systems. We review several single- and multiscale models, from the most simple to the complex ones, and discuss their properties from a multiscale point of view. Approaches based on master equations for stochastic processes, individual-based models, hybrid continuous-discrete models and structured PDE models are presented.

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine, a stochastic recurrent neural network that extracts high-order structure from sensory data through unsupervised generative learning and can encode (...) contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high-quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non-connectionist probabilistic models. We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain. (shrink)

The distribution of the flap allophone [ɾ] of American English, along with the other allophones of /t/,[t h,t =, ʔ, t] has been accounted for in various formal frameworks by assuming a number of different abstract mechanisms and entities. The desirability or usefulness of these formalisms is not at issue in the present paper. Instead, a computationally explicit model of categorization is used (Skousen 1989, 1992) in order to account for the distribution of the allophones of /t/ without recourse to (...) such formalisms. The simulations that were carried out suggest that they are not needed because analogy to surface apparent variables such as phones and word boundaries is sufficient to predict allophony. In analogy, the particular allophone of /t/ (i.e. [ɾ, t h, t =, ʔ, t]) that appears in a given context is determined on the basis of similarity to stored exemplars in the mental lexicon. From an acquisitional standpoint, categorization by analogy to stored exemplars dispenses with the need for rule induction although it does suggest that speakers group functionally related sounds into mental categories, a process that is influenced to a great deal by orthography. Analogy also explains the stochastic nature of linguistic performance. In the present study, 3,719 tokens of the allophones of the phoneme /t/ were extracted from the TIMIT corpus and constitute the database from which analogs were chosen. The variables used included the three phones or boundaries on either side of /t/, and the stress of the syllables preceding and following /t/. The model proves quite successful in predicting the correct allophone, and the errors made are generally possible alternative pronunciations (e.g. moun[ʔ]ain, moun[t h ]ain). The success rate changes little when only small sub-samples of the database are incorporated. In addition, exemplar-modeling is found to be quite robust because even when a feature such as stress is eliminated, (a feature which is critical in most rule approaches), allophony is still highly predictable. (shrink)

Some dichotomies related to modeling electrocortical activities are analyzed. Attractor neural networks versus biologically motivated models, near-equilibrium versus nonequilibrium processes, linear and nonlinear dynamics, stochastic and chaotic patterns, local and global scale simulation of cortical activities are discussed.

We propose a general framework for integrating theory and empiricism in human evolutionary ecology. We specifically emphasize the joint use of stochastic nonlinear dynamics and information theory. To illustrate critical ideas associated with historical contingency and complex dynamics, we review recent research on social preferences and social learning from behavioral economics. We additionally examine recent work on ecological approaches in history, the modeling of chaotic populations, and statistical application of information theory.

The neutral theory of biodiversity assumes that coexisting organisms are equally able to survive, reproduce and disperse, but predicts that stochastic fluctuations of these abilities drive diversity dynamics. It predicts remarkably well many biodiversity patterns, although substantial evidence for the role of niche variation across organisms seems contradictory. Here, we discuss this apparent paradox by exploring the meaning and implications of ecological equivalence. We address the question whether neutral theory provides an explanation for biodiversity patterns and acknowledges causal processes. We (...) underline that ecological equivalence, although central to neutral theory, can emerge at local and regional scales from niche-based processes through equalizing and stabilizing mechanisms. Such emerging equivalence corresponds to a weak conception of neutral theory, as opposed to the assumption of strict equivalence at individual level in the strong conception. We show that this duality is related to diverging views on hypothesis-testing and modeling in ecology. In addition, the stochastic dynamics exposed in neutral theory are pervasive in ecological systems and, rather than a null hypothesis, ecological equivalence is best understood as a parsimonious baseline to address biodiversity dynamics at multiple scales. (shrink)

Sex‐determining factors are usually assumed to be either genetic or environmental. The present paper aims at drawing attention to the potential contribution of developmental noise, an important but often‐neglected component of phenotypic variance. Mutual inhibitions between male and female pathways make sex a bistable equilibrium, such that random fluctuations in the expression of genes at the top of the cascade are sufficient to drive individual development toward one or the other stable state. Evolutionary modeling shows that stochastic sex determinants (...) should resist elimination by genetic or environmental sex determinants under ecologically meaningful settings. On the empirical side, many sex‐determination systems traditionally considered as environmental or polygenic actually provide evidence for large components of stochasticity. In reviewing the field, I argue that sex‐determination systems should be considered within a three‐ends continuum, rather than the classical two‐ends continuum. (shrink)

The objective of the paper is threefold. First, to argue that some of Haavelmo's methodological ideas and insights have been neglected because they are largely at odds with the traditional perspective that views empirical modeling in economics as an exercise in curve-fitting. Second, to make a case that this neglect has contributed to the unreliability of empirical evidence in economics that is largely due to statistical misspecification. The latter affects the reliability of inference by inducing discrepancies between the actual (...) and nominal error probabilities. Third, to argue that the ‘bridge pier’ between theory and data, as envisaged by Haavelmo, T [The Probability Approach to Econometrics, Econometrica, 12, 1–115], can be completed by blending some of his key methodological ideas and insights into a refined/extended version of the frequentist approach to inference. This new perspective is used to revisit dynamic stochastic general equilibrium modeling in an attempt to bring.. (shrink)

This paper is concerned with the multivariate stochastic volatility modeling of the stock market. We investigate a DGC-t-MSV model to find the historical volatility spillovers between nine markets, including S&P, Nasdaq, SSE, SZSE, HSI, FTSE, CAC, DAX, and Nikkei indices. We use the Bayesian network to analyze the spreading of herd behavior between nine markets. The main results are as follows: the DGC-t-MSV model we considered is a useful way to estimate the parameter and fit the data well in (...) the stock market; our computational analysis shows that the S&P and Nasdaq have higher volatility spillovers to the Shanghai and Shenzhen stock markets; the results also show that there is a strong correlation between stock markets in the same region. (shrink)

How do we come to like the things that we do? Each one of us starts from a relatively similar state at birth, yet we end up with vastly different sets of aesthetic preferences. These preferences go on to define us both as individuals and as members of our cultures. Therefore, it is important to understand how aesthetic preferences form over our lifetimes. This poses a challenging problem: to understand this process, one must account for the many factors at play (...) in the formation of aesthetic values and how these factors influence each other over time. A general framework based on basic neuroscientific principles that can also account for this process is needed. Here, we present such a framework and illustrate it through a model that accounts for the trajectories of aesthetic values over time. Our framework is inspired by meta-analytic data of neuroimaging studies of aesthetic appraisal. This framework incorporates effects of sensory inputs, rewards, and motivational states. Crucially, each one of these effects is probabilistic. We model their interactions under a reinforcement-learning circuitry. Simulations of this model and mathematical analysis of the framework lead to three main findings. First, different people may develop distinct weighing of aesthetic variables because of individual variability in motivation. Second, individuals from different cultures and environments may develop different aesthetic values because of unique sensory inputs and social rewards. Third, because learning is stochastic stemming from probabilistic sensory inputs, motivations, and rewards, aesthetic values vary in time. These three theoretical findings account for different lines of empirical research. Through our study, we hope to provide a general and unifying framework for understanding the various aspects involved in the formation of aesthetic values over time. (shrink)

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters. The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size (...) and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c. We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results. (shrink)

Chaos, once considered antithetical to scientific law and order, is presently the subject of a vigorous and progressive scientific research program. "Chaos" as it is used in current scientific literature is a technical term: it refers to stochastic behavior generated by deterministic systems. This behavior has appeared in models of a wide range of phenomena including atmospheric patterns, population dynamics, celestial motion, heartbeat rhythms, turbulent fluids, chemical reactions and social structures. In general, chaos arises in the nonlinear dynamics of complex (...) systems. Grebogi, Ott and Yorke reflect the sentiment of the scientific community when they state that chaotic nonlinear dynamics has "fundamental implications." This dissertation explores these results in a philosophic context. ;The research is organized as follows: The Context of Science. Scientific results are achieved in and make sense in the practical context of research which includes both experiment and theory. Drawing on the work of Dyke, Galison, Garfinkel and Hacking, a philosophic context is described which more accurately reflects the significance of scientific results than do the contexts of discovery and justification. Models. Chaos theory is constituted by a family of numerical models. In this chapter, Giere's account of modeling is extended to both bio-medical and numerical models. Chaos in Scientific Models. This is a rather lengthy primer of chaos theory that is, although technically accurate, accessible to nonspecialists. It constitutes a road map for the primary literature on chaos. Chaos and Prediction. Chaos theory shows a limit of our science, namely, chaotic systems are deterministic yet unpredictable in the long run. The chapter includes a discussion of scientific determinism following Popper and, it concludes by providing evidence against the laplacian claim that deterministic systems are predictable. Chaos and Complexity. This shows what contribution chaos theory makes toward answering the challenge of organized complexity articulated by Weaver. It discusses attempts to characterize complexity and shows how the results of chaos theory can help. I draw on the work of Abraham, Arecchi, Atlan, Chaitin, Eckmann, Peacocke, Rosen, Ruelle, and others. Chaos theory provides a thoroughly nonvitalistic framework for understanding dynamical complexity in organic, as well as inorganic, systems. (shrink)

We describe reversible adaptive trees, a class of stochastic algorithms modified from the formerly described adaptive trees. They evolve in time a finite subset of an ambient Euclidean space of any dimension, starting from a seed point and, accreting points to the evolving set, they grow branches towards a target set which can depend on time. In contrast with plain adaptive trees, which were formerly proven to have strong convergence properties to a static target, the points of reversible adaptive trees (...) are removed from the tree when they have not been used recently enough in a path from the root to an accreted point. This, together with a straightening process performed on the branches, permits the tree to follow some moving targets and still remain adapted to it. We then discuss in what way one can see such reversible trees as a model for a qualitative property of resilience, which leads us to discuss qualitative modeling. (shrink)

We describe a software system for the analysis of defined benefit actuarial plans. The system uses a recursive formulation of the actuarial stochastic processes to implement precise and efficient computations of individual and group cash flows.

The risk of cigarette smoking plays a pivotal role in increasing the incidence rates of lung cancer. This paper sheds new light on modeling the impact of cigarette smoking on lung cancer evolution, especially genetic instability and the number of gene mutations in the genome of stem cells. To handle this issue, we have set up stochastic multi-stage models to fit the data set of the probabilities of current and former smokers from the Nurses’ Health Study cohort of females (...) and the Health Professionals Follow up Study cohort of men. Throughout this paper, we consider both mutation rates and clonal expansion rates as parameters in each compartment. For current and former smokers, three-driver mutations are most likely to take place in the progression of lung cancer under smoking risk. For current smokers, our findings reveal that two to sixteen gene mutations are required to obtain a cancerous cell among men and women in US. Moreover, two to six cancer-mutations are available in the pathway to lung cancer among former smokers who have quit smoking for more than ten years for both male and female patients. This highlights that cigarette smoking stimulates the number of driver mutations during lung tumorigenesis in both sexes. It is very crucial to examine the role of cigarette smoking in determining whether genomic instability is an early stage or late stage in the process of lung carcinogenesis. (shrink)

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate how learners handle such situations. We focus on the setting where a learner receives and processes a sequence of utterances to master associations between objects and their labels, (...) where the source is inconsistent by design: It uses both “correct” and “incorrect” object‐label pairings. We hypothesize that depending on the order of presentation, the result of the learning may be different. To this end, we consider two types of symbolic learning procedures: the Object‐Label (OL) and the Label‐Object (LO) process. In the OL process, the learner is first exposed to the object, and then the label. In the LO process, this order is reversed. We perform experiments with human subjects, and also construct a computational model that is based on a nonlinear stochastic reinforcement learning algorithm. It is observed experimentally that OL learners are generally better at processing inconsistent input compared to LO learners. We show that the patterns observed in the learning experiments can be reproduced in the simulations if the model includes (a) an ability to regularize the input (and also to do the opposite, i.e., undermatch) and (b) an ability to take account of implicit negative evidence (i.e., interactions among different objects/labels). The model suggests that while both types of learners utilize implicit negative evidence in a similar way, there is a difference in regularization patterns: OL learners regularize the input, whereas LO learners undermatch. As a result, OL learners are able to form a more consistent system of image‐utterance associations, despite the ambiguous learning task. (shrink)

Cognitive models that represent individuals provide many benefits for understanding the full range of human behavior. One way in which individual differences emerge is through differences in knowledge. In dynamic situations, where decisions are made from experience, models built upon a theory of experiential choice (instance-based learning theory; IBLT) can provide accurate predictions of individual human learning and adaptivity to changing environments. Here, we demonstrate how an instance-based learning (IBL) cognitive model, implemented in a cognitive architecture (Adaptive Control of Thought–Rational), (...) can be used to model an individual's decisions in a cybersecurity defense task, accounting for both population average and individual variances. The same IBL model structure with identical architectural parameters generates the full range of human behavior through stochastic memory retrieval processes operating over and contributing to unique experiences. Recurrence quantification analyses allow us to look beyond average behavior between and within individuals to sequential patterns of trial-to-trial behavior. We show how model-tracing and knowledge-tracing techniques can be used to align the model to an individual in real time to drive adaptive and personalized signaling algorithms for a cybersecurity defense system. We also present a method for introspecting into the cognitive model to gain further insight into the cognitive salience of features factored into individual decisions. The combination of techniques provides a blueprint for personalized modeling of individuals. We discuss the results and implications of this adaptive and personalized method for cybersecurity defense and more generally for intelligent artifacts tailored to individual differences in domains such as human–machine teaming. (shrink)

Fluorescence microscopy is the primary tool for studying complex processes inside individual living cells. Technical advances in both molecular biology and microscopy have made it possible to image cells from many genetic and environmental backgrounds. These images contain a vast amount of information, which is often hidden behind various sources of noise, convoluted with other information and stochastic in nature. Accessing the desired biological information therefore requires new tools of computational image analysis and modeling. Here, we review some of (...) the recent advances in computational analysis of images obtained from fluorescence microscopy, focusing on bacterial systems. We emphasize techniques that are readily available to molecular and cell biologists but also point out examples where problem‐specific image analyses are necessary. Thus, image analysis is not only a toolkit to be applied to new images but also an integral part of the design and implementation of a microscopy experiment. (shrink)

Acquiring perceptual expertise is slow and effortful. However, untrained novices can accurately make difficult classification decisions by reformulating the task as similarity judgment. Given a query image and a set of reference images, individuals are asked to select the best matching reference. When references are suitably chosen, the procedure yields an implicit classification of the query image. To optimize reference selection, we develop and evaluate a predictive model of similarity-based choice. The model builds on existing psychological literature and accommodates stochastic, (...) dynamic shifts of attention among visual feature dimensions. We perform a series of human experiments with two stimulus types and nine classification tasks to validate the model and to demonstrate the model's potential to boost performance. Our system achieves high accuracy for participants who are naive as to the classification task, even when the classification task switches from trial to trial. (shrink)

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.