460 research outputs found

    Deriving GENERIC from a generalized fluctuation symmetry

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    Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of the Lagrangian for the path-space action leads to gradient zero-cost flow. We find a new such fluctuation symmetry that implies GENERIC, an extension of gradient flow where a Hamiltonian part is added to the dissipative term in such a way as to retain the free energy as Lyapunov function

    Mean-Variance and Expected Utility: The Borch Paradox

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    The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation (ÎŒ,σ)(\mu,\sigma) of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside.Comment: Published in at http://dx.doi.org/10.1214/12-STS408 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    The incidence of some voting paradoxes under domain restrictions

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    Voting paradoxes have played an important role in the theory of voting. They typically say very little about the circumstances in which they are particularly likely or unlikely to occur. They are basically existence findings. In this article we study some well known voting paradoxes under the assumption that the underlying profiles are drawn from the Condorcet domain, i.e. a set of preference profiles where a Condorcet winner exists. The motivation for this restriction is the often stated assumption that profiles with a Condorcet winner are more likely than those without it. We further restrict the profiles by assuming that the starting point of our analysis is that the Condorcet winner coincides with the choice of the voting rule under scrutiny. The reason for making this additional restriction is that - intuitively - the outcomes that coincide with the Condorcet winner make those outcomes stable and, thus, presumably less vulnerable to various voting paradoxes. It will be seen that this is, indeed, the case for some voting rules and some voting paradoxes, but not for all of them.</p

    Revisiting the dynamic of Q-deformed logistic maps

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    We consider the logistic family and apply the qq-deformation ϕq(x)=1−qx1−q\phi_q(x)=\frac{1-q^x}{1-q}. We study the stability regions of the fixed points of the qq-deformed logistic map and the regions where the dynamic is complex through topological entropy and Lyapunov exponents. Our results show that the dynamic of this deformed family is richer than that of the qq-deformed family studied in [8].Comment: 23 pages, 52 figur

    Boundary Effects on Ideal Fluid Forces and Kelvin's Minimum Energy Theorem

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    The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson 2011), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (1849), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. We present a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb 1975, {\S}137). We also present a model of a Bernoulli suction gripper, for which the steady force is typically attractive. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem

    Discrete Methods in Statistics: Feature Selection and Fairness-Aware Data Mining

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    This dissertation is a detailed investigation of issues that arise in models that change discretely. Models are often constructed by either including or excluding features based on some criteria. These discrete changes are challenging to analyze due to correlation between features. Feature selection is the problem of identifying an appropriate set of features to include in a model, while fairness-aware data mining is the problem of needing to remove the \emph{influence} of protected features from a model. This dissertation provides frameworks for understanding each problem and algorithms for accomplishing the desired goal. The feature selection problem is addressed through the framework of sequential hypothesis testing. We elucidate the statistical challenges in repeatedly using inference in this domain and demonstrate how current methods fail to address them. Our algorithms build on classically motivated, multiple testing procedures to control measures of false rejections when using hypothesis testing during forward stepwise regression. Furthermore, these methods have much higher power than recent proposals from the conditional inference literature. The fairness-aware data mining community is grappling with fundamental questions concerning fairness in statistical modeling. Tension exists between identifying explainable differences between groups and discriminatory ones. We provide a framework for understanding the connections between fairness and the use of protected information in modeling. With this discussion in hand, generating fair estimates is straight-forward

    Compensation and responsibility

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    This a chapter for the Handbook of Social Choice and Welfare. It deals with the theory of fairness applied to situations when individuals are partly responsible for their characteristics.fairness, responsibility, equal opportunity, compensation, handicap, talent, effort
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