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Books on the topic 'First order Markov model'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Jacobs, Patricia A. Estimation of the probability of a long time to the first entrance to a state in a semi-Markov model. Naval Postgraduate School, 1987.

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2

Reinhardt, Elizabeth D. First Order Fire Effects Model: FOFEM 4.0, user's guide. U.S. Dept. of Agriculture, Forest Sevice, Intermountain Research Station, 1997.

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3

Nguyen, Van O. Analysis of the U.S. Marine Corps' steady state Markov model for forecasting annual first-term enlisted classification requirements. Naval Postgraduate School, 1997.

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4

Hoque, Asraul. The exact multiperiod mean-square forecast error for the first-order autoregressive model. London School of Economics, 1986.

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5

Weaver, George. Henkin-Keisler models. Kluwer Academic Publishers, 1997.

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6

Weaver, George. Henkin-Keisler Models {Mathematics and Its Applications (Kluwer Academic Publishers) ; V. 392}. Springer, 1997.

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7

Simple theories and hyperimaginaries. Cambridge University Press, 2011.

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8

Magnus, Jan R. The exact multiperiod mean-square forecast error for the first-order autoregressive model with an intercept. International Centre for Economics and Related Disciplines, 1988.

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9

Abou-Taleb, A. A. A microwave model for investigating first and second order electromagnetic scattering from gravity water waves on the surface. University of Birmingham, 1985.

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10

Poletaeva, Vladislava. Economics of sustainable industrial growth: concept, problems and possible mechanisms of formation. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1086387.

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The monograph examines the issues of transformation of the Russian economy from raw materials export model to a model of sustainable industrial growth. In the first Chapter of the work the author formulates the definition of sustainable economy growth and the expediency of its formation, analyzes the problems that hinder the transformation of national economic system into a model for sustainable industrial growth, and identified possible mechanisms of such transformation. In the second Chapter, in order to determine the sources of the implementation of the financial mechanism of forming of eco

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11

Maugeri, Giuseppe, and Graziano Serragiotto. L’insegnamento della lingua italiana in Giappone Uno studio di caso sul Kansai. Fondazione Università Ca’ Foscari, 2021. http://dx.doi.org/10.30687/978-88-6969-525-4.

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This research stems from the need of the Italian Cultural Institute to map the institutions involved in teaching Italian in the area considered and to analyse the quality of the teaching and learning process of the Italian language. The objectives are multiple and linked to the importance of finding the causes that slow the growth of the study of Italian in Japanese Kansai. Therefore, the first part of this action research will outline the cultural and linguistic education coordinates that characterize the Japanese context; in the second part, the research data will be interpreted in order to

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12

Bao, Yun, Carl Chiarella, and Boda Kang. Particle Filters for Markov-Switching Stochastic Volatility Models. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.9.

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This chapter proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. It proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method that demonstrates the ability to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is implemen

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13

Schütze, Robert. The Rise of the Federal Model I. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803379.003.0005.

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What philosophy governs the European common market today? This chapter examines this question by exploring the doctrinal structure of Article 34 since Cassis de Dijon. It will be argued that after Cassis, the substantive structure of the European market could no longer be presented as a ‘new legal order of international law’. For the principle of mutual recognition ‘breaks’ the backbone of the international model, as each State loses a part of its (internal) sovereignty over its own (internal) market. This loss of sovereignty was first established for national rules relating to product require

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14

Richard, Kaye, and Macpherson Dugald, eds. Automorphisms of first-order structures. Clarendon Press, 1994.

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15

El Karoui, Noureddine. Algebraic geometry and matrix models. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.29.

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This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first desc

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16

Westerhoff, Frank, and Reiner Franke. Agent-Based Models for Economic Policy Design. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.40.

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With the help of two examples, this chapter illustrates the usefulness of agent-based models as tools for economic policy design. The first example applies a financial market model in which the order flow of speculators, relying on technical and fundamental analysis, generates intricate price dynamics. The second example applies a Keynesian-type goods market model in which the investment behavior of firms, relying on extrapolative and regressive predictors, generates complex business cycles. It adds a central authority to these two setups and explores the impact of simple intervention strategi

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17

Analysis of the U.S. Marine Corps' Steady State Markov Model for Forecasting Annual First-Term Enlisted Classification Requirements. Storming Media, 1997.

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18

First Order Fire Effects Model: FOFEM 4.0, User Guide, General Technical Report INT-GTR-344, U.S. Department of Agriculture (Microfiche). Agriculture Department - Forest Service, 1997.

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19

Service, United States Forest, ed. First Order Fire Effects Model: FOFEM 4.0, User Guide... General Technical Report INT-GTR-344... U.S. Department Of Agriculture... January 1997. s.n., 1997.

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20

Back, Kerry E. Dynamic Portfolio Choice. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0009.

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The first‐order condition for optimal portfolio choice is called the Euler equation. Optimal consumption can be computed by a static approach in a dynamic complete market and by orthogonal projection for a quadratic utility investor. Dynamic programming and the Bellman equation are explained. The envelope condition and hedging demands are explained. Investors with CRRA utility have CRRA value functions. Whether the marginal value of wealth is higher for a CRRA investor in good states or in bad states depends on whether risk aversion is less than or greater than 1. With IID returns, the optimal

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21

Henderson, Daniel A., R. J. Boys, Carole J. Proctor, and Darren J. Wilkinson. Linking systems biology models to data: A stochastic kinetic model of p53 oscillations. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.7.

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This article discusses the use of a stochastic kinetic model to study protein level oscillations in single living cancer cells, using the p53 and Mdm2 proteins as examples. It describes the refinement of a dynamic stochastic process model of the cellular response to DNA damage and compares this model to time course data on the levels of p53 and Mdm2. The article first provides a biological background on p53 and Mdm2 before explaining how the stochastic kinetic model is constructed. It then introduces the stochastic kinetic model and links it to the data and goes on to apply sophisticated MCMC

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22

Shapiro, Stewart. Higher‐order Logic. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0025.

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The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.

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23

Jean-Bernard, Auby. 17 The Transformation of the Administrative State and Administrative Law. Oxford University Press, 2017. http://dx.doi.org/10.1093/law/9780198726401.003.0017.

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This chapter investigates four lines of transformation and the impact they have had — and still have — on European administrative laws. These are the evolutionary trends regarding the relationship between the public sphere and society, between public spaces and private ones, between the state and the market, and, finally, between the international and the domestic sphere. The chapter first considers how the administrative state and related orders of administrative law came into being in Europe. It then questions the factors and the main lines of transformation in contemporary evolutions, befor

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24

Alter, Karen J., and Laurence R. Helfer. Transplanting International Courts. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199680788.001.0001.

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The Andean Pact was founded in 1969 to build a common market in South America. Andean leaders copied the institutional and treaty design of the European Community, and in the 1970s, member states decided to add a tribunal, again turning to the European Community as its model. Since its first ruling in 1987, the Andean Tribunal of Justice (ATJ) has exercised authority over the countries which are members of the Andean Community: Bolivia, Colombia, Ecuador, and Peru (formerly also Venezuela). It is now the third most active international court in the world, used by governments and private actors

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25

Linarelli, John, Margot E. Salomon, and Muthucumaraswamy Sornarajah. International Trade. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198753957.003.0004.

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Despite significant attention in recent times, the law of international trade has been remarkably resilient in steering clear of compliance with the demands of justice. The history of the law governing international trade is rooted in forms of coercion and violence designed to promote the interests of powerful states and their multinational enterprises. The first norm of international trade law for the modern state, the principle of freedom to trade, was a rationalization to commit atrocities, including genocide, to promote the interests of European powers and their commercial interests. This

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26

Bell, John L. Categorical Logic and Model Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0007.

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The chapter begins with an introduction describing the development of categorical logic from the 1960s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation. In the section `Local Set Theories and Toposes’ the categorical counterparts—toposes—to higher-order logic are introduced, along with their associated theories—local set theories. In the section `Models of First-Order

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27

Ash, Susan. Funding Philanthropy. Liverpool University Press, 2016. http://dx.doi.org/10.5949/liverpool/9781781381397.001.0001.

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This book investigates how Dr. Barnardo, the Victorian children’s philanthropist, operated as both story teller and showman, using mass media to create a globalised support network. His philanthropic ‘empire’ operated as an exceptional Victorian manifestation of promotional and branding mechanisms that are perceived as commonplace in the twentieth century. Metaphor and narrative modes normally associated with fiction such as Charles Dickens’s novels, as well as public spectacles associated with showmen such as P. T. Barnum, provide the organising principle for the book. Ultimately, however, th

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28

Manseau, Marc W., and Jay Crosby. First Episode Psychosis. Edited by Hunter L. McQuistion. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190610999.003.0012.

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Engaging people experiencing a first episode of psychosis (FEP) in treatment is a priority. The duration of untreated psychosis (DUP) is the period of time between the onset of the FEP and the initiation of adequate treatment; longer DUP is associated with negative outcomes. Coordinated specialty care (CSC) is an evidence-based model that uses a team-based, multidisciplinary approach to engage people early in their psychotic illness in order to improve long-term psychosocial functioning and treatment outcomes. Best practices within CSC include assertive outreach, prescribing of low-dose antips

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29

Hedman, Shawn. A First Course in Logic. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198529804.001.0001.

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The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is

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30

Jäger, Agnes, Gisella Ferraresi, and Helmut Weiß, eds. Clause Structure and Word Order in the History of German. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198813545.001.0001.

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Over roughly the last decade, there has been a notable rise in new research on historical German syntax in a generative perspective. This volume presents a state-of-the-art survey of this thriving new line of research by leading scholars in the field, combining it with new insights into the syntax of historical German. It is the first comprehensive and concise generative historical syntax of German covering numerous central aspects of clause structure and word order, tracing them throughout various historical stages. Each chapter combines a solid empirical basis and valid descriptive generaliz

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31

Crawford, Matthew R. The Eusebian Canon Tables. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198802600.001.0001.

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A central book in late antique religious life was the four-gospel codex—a manuscript containing the Gospels of Matthew, Mark, Luke, and John—and one of the most common features of such manuscripts is a marginal cross-referencing system known as the Canon Tables. This reading aid, invented in the early fourth century by Eusebius of Caesarea, represented a milestone achievement both in the history of the book and in the scholarly study of the fourfold gospel. The present monograph is the first ever book-length treatment of the origins and use of the Canon Tables apparatus in any language. Part o

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32

Fischer, Conan. Remaking Europe after the First World War. Edited by Nicholas Doumanis. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199695669.013.10.

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Victorious Allied governments legitimized wartime sacrifice with promises of domestic prosperity and a peaceful international order. An American-sponsored League of Nations would mediate relations between liberal-democratic nation states. However, although parliamentary government was consolidated across north-western Europe, the peace fell short, failing to accommodate Bolshevik Russia or reach a legitimate settlement with a new and fragile German democracy. Paris deemed the settlement inadequate; the US Congress refused to ratify the German treaty and remained outwith the League; China and J

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33

van Moerbeke, Pierre. Determinantal point processes. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.11.

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This article presents a list of algebraic, combinatorial, and analytic mechanisms that give rise to determinantal point processes. Determinantal point processes have been used in random matrix theory (RMT) since the early 1960s. As a separate class, determinantal processes were first used to model fermions in thermal equilibrium and the term ‘fermion’ point processes were adopted. The article first provides an overview of the generalities associated with determinantal point processes before discussing loop-free Markov chains, that is, the trajectories of the Markov chain do not pass through th

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34

Chiaburu, Dan S., In-Sue Oh, and Sophia V. Marinova. Five-Factor Model of Personality Traits and Organizational Citizenship Behavior: Current Research and Future Directions. Edited by Philip M. Podsakoff, Scott B. Mackenzie, and Nathan P. Podsakoff. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780190219000.013.13.

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For over a quarter of a century, organizational scholars have sought to understand the ways in which employees contribute to organizational success through their organizational citizenship behavior (OCB). Concurrently, personality traits have provided an important lens for illuminating what motivates such discretionary efforts. Our first purpose is to provide a state-of-the art, theoretically grounded review of the literature linking five-factor model (FFM) of personality traits to OCB. Second, we strive to clarify both our criterion construct (OCB) and our predictor space in order to facilita

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35

Quintana, José Mario, Carlos Carvalho, James Scott, and Thomas Costigliola. Extracting S&P500 and NASDAQ Volatility: The Credit Crisis of 2007–2008. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.13.

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This article demonstrates the utility of Bayesian modelling and inference in financial market volatility analysis, using the 2007-2008 credit crisis as a case study. It first describes the applied problem and goal of the Bayesian analysis before introducing the sequential estimation models. It then discusses the simulation-based methodology for inference, including Markov chain Monte Carlo (MCMC) and particle filtering methods for filtering and parameter learning. In the study, Bayesian sequential model choice techniques are used to estimate volatility and volatility dynamics for daily data fo

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36

Cheng, Russell. Finite Mixture Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0017.

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Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampli

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37

Rubin, Donald, Xiaoqin Wang, Li Yin, and Elizabeth Zell. Bayesian causal inference: Approaches to estimating the effect of treating hospital type on cancer survival in Sweden using principal stratification. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.24.

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This article discusses the use of Bayesian causal inference, and more specifically the posterior predictive approach of Rubin’s causal model (RCM) and methods of principal stratification, in estimating the effects of ‘treating hospital type’ on cancer survival. Using the Karolinska Institute in Stockholm, Sweden, as a case study, the article investigates which type of hospital (large patient volume vs. small volume) is superior for treating certain serious conditions. The study examines which factors may reasonably be considered ignorable in the context of covariates available, as well as non-

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38

Busemeyer, Jerome R., Zheng Wang, and Emmanuel Pothos. Quantum Models of Cognition and Decision. Edited by Jerome R. Busemeyer, Zheng Wang, James T. Townsend, and Ami Eidels. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199957996.013.17.

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Quantum probability theory provides a new formalism for constructing probabilistic and dynamic systems of cognition and decision. The purpose of this chapter is to introduce psychologists to this fascinating theory. This chapter is organized into six sections. First, some of the basic psychological principles supporting a quantum approach to cognition and decision are summarized; second, some notations and definitions needed to understand quantum probability theory are presented; third, a comparison of quantum and classical probability theories is presented; fourth, quantum probability theory

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39

Laver, Michael, and Ernest Sergenti. Systematically Interrogating Agent-Based Models. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691139036.003.0004.

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This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the different methods of experimental design, such as grid sweeping and Monte Carlo parameterization. Next, it demonstrates how to calculate mean estimates of output variables of interest. It does so by first discussing stochastic processes, Markov Chain representations, and model burn-in. It focuses on three stochastic process representations: nonergodic deterministic processes that converge on a single state

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40

Delsol, Laurent. Nonparametric Methods for α-Mixing Functional Random Variables. Редактори Frédéric Ferraty та Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.5.

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This article considers how functional kernel methods can be used to study α-mixing datasets. It first provides an overview of how prediction problems involving dependent functional datasets may arise from the study of time series, focusing on the standard discretized model and modelization that takes into account the functional nature of the evolution of the quantity to be studied over time. It then considers strong mixing conditions, with emphasis on the notion of α-mixing coefficients and α-mixing variables introduced by Rosenblatt (1956). It also describes some conditions for a Markov chain

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41

Oaksford, Mike, and Nick Chater. Causal Models and Conditional Reasoning. Edited by Michael R. Waldmann. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199399550.013.5.

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There are deep intuitions that the meaning of conditional statements relate to probabilistic law-like dependencies. In this chapter it is argued that these intuitions can be captured by representing conditionals in causal Bayes nets (CBNs) and that this conjecture is theoretically productive. This proposal is borne out in a variety of results. First, causal considerations can provide a unified account of abstract and causal conditional reasoning. Second, a recent model (Fernbach & Erb, 2013) can be extended to the explicit causal conditional reasoning paradigm (Byrne, 1989), making some no

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42

Johansen, Bruce, and Adebowale Akande, eds. Nationalism: Past as Prologue. Nova Science Publishers, Inc., 2021. http://dx.doi.org/10.52305/aief3847.

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Nationalism: Past as Prologue began as a single volume being compiled by Ad Akande, a scholar from South Africa, who proposed it to me as co-author about two years ago. The original idea was to examine how the damaging roots of nationalism have been corroding political systems around the world, and creating dangerous obstacles for necessary international cooperation. Since I (Bruce E. Johansen) has written profusely about climate change (global warming, a.k.a. infrared forcing), I suggested a concerted effort in that direction. This is a worldwide existential threat that affects every living t

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Sarotte, Mary Elise. Restoring Four-Power Rights, Reviving a Confederation in 1989. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691163710.003.0003.

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This chapter examines the Soviet restoration model and former German Chancellor Helmut Kohl's revivalist model. The Union of Soviet Socialist Republics (USSR) hoped to use its weight as a victor in the Second World War to restore the old quadripartite mechanism of four-power control exactly as it used to be in 1945, before subsequent layers of Cold War modifications created room for German contributions. This restoration model, which called for the reuse of the old Allied Control Commission to dominate all further proceedings in divided Germany, represented a realist vision of politics run by

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Laver, Michael, and Ernest Sergenti. Using Theoretical Models to Analyze Real Party Systems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691139036.003.0011.

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Having specified theoretical models of multiparty competition in the first ten chapters of the book, this chapter analyzes recent party competition in postwar democracies in order to verify whether the empirical implications of the party competition model can indeed be systematically observed in real party competition. This is easy to say but hard to do in a rigorous way. Fundamental difficulties arise from two distinct sources. The first concerns calibration of key parameters of the model to the real political environments it is used to analyze. The second concerns data, specifically the need

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45

Moore, Robin D., Juan Agudelo, Katie Chapman, et al. Sample Curricular Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190658397.003.0014.

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By examining degree plans and conducting interviews with faculty and students at various national and international institutions, the authors of this chapter have generated four curricular models that suggest how existing degree plans and/or core music courses might be productively modified. The enhanced core model (1) aims to broaden the scope of existing curricula by emphasizing more diverse, cross-disciplinary content. The pluralist model (2) requires students to diversify their focus during their first two years of study in order to incorporate a greater degree of critical thinking, creati

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46

Buchler, Justin. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190865580.003.0001.

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Spatial theory is divided between models of elections and models of roll call voting, neither of which alone can explain congressional polarization. This chapter discusses the history of spatial theory, why it is important to link the two strands of spatial models, and the value of reversing the order of conventional models. Conventional models place an election before policy decisions are made. This chapter proposes a unified spatial model of Congress in which the conventional order is reversed. First, there is a legislative session, then an election in which voters respond retrospectively, n

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47

Button, Tim, and Sean Walsh. Boolean-valued structures. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0013.

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Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or

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48

Rau, Jochen. Phase Transitions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0008.

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At a phase transition two or more different phases may coexist, such as vapour and liquid. Phase transitions can be classified according to their order. A phase transition is of first order if going from one phase to the other involves a discontinuous change in entropy, and, thus, a finite amount of latent heat; higher-order phase transitions do not involve latent heat but exhibit other types of discontinuities. This chapter investigates the necessary conditions for the coexistence of phases, and how phases are represented in a phase diagram. The order of a phase transition is defined with the

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49

Back, Kerry E. Portfolio Choice. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0002.

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The portfolio choice model is introduced, and the first‐order condition is derived. Properties of the demand for a single risky asset are derived from second‐order risk aversion and decreasing absolute risk aversion. Optimal investments are independent of initial wealth for investors with constant absolute risk aversion. Optimal investments are affine functions of initial wealth for investors iwth linear risk tolerance. The optimal portfolio for an investor with constant absolute risk aversion is derived when asset returns are normally distributed. Investors with quadratic utility have mean‐va

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Verbaarschot, Jac. Quantum chaos and quantum graphs. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.33.

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Abstract:

This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’

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