460 research outputs found
Deriving GENERIC from a generalized fluctuation symmetry
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
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
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
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
We consider the logistic family and apply the -deformation
. We study the stability regions of the fixed
points of the -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
-deformed family studied in [8].Comment: 23 pages, 52 figur
Boundary Effects on Ideal Fluid Forces and Kelvin's Minimum Energy Theorem
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
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
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
- âŠ