A General Update Rule for Convex Capacities

A characterization of a general update rule for convex capacities, the G-updating rule, is investigated. We introduce a consistency property which bridges between unconditional and conditional preferences, and deduce an update rule for unconditional capacities. The axiomatic basis for the G-updating rule is established through consistent counterfactual acts, which take the form of trinary acts expressed in terms of G, an ordered tripartition of global states.ambiguous belief, Bayes' rule, update rule, convex capacity, Choquet ex- pected utility, conditional preference

Propagation of singularities for Schr\"odinger equations with modestly long range type potentials

In a previous paper by the second author, we discussed a characterization of the microlocal singularities for solutions to Schr\"odinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this paper we show that we may use Dollard type approximate solutions to the Hamilton-Jacobi equation if the perturbation satisfies somewhat stronger conditions. As applications, we describe the propagation of microlocal singularities for $e^{itH_0}e^{-itH}$ when the potential is asymptotically homogeneous as $|x|\to\infty$, where $H$ is our Schr\"odinger operator, and $H_0$ is the free Schr\"odinger operator, i.e., $H_0=-\frac12 \triangle$. We show $e^{itH_0}e^{-itH}$ shifts the wave front set if the potential $V$ is asymptotically homogeneous of order 1, whereas $e^{itH}e^{-itH_0}$ is smoothing if $V$ is asymptotically homogenous of order $\beta\in (1,3/2)$

A unified representation of conditioning rules for convex capacities

This paper proposes a unified representation, called the G-updating rule, which includes three conditioning rules as special cases, the naïve Bayes rule, the Dempster-Shafer rule (Shafer(1976)), and the generalized Bayes' updating rule introduced by Dempster(1967) or Fagin and Halpern(1991). It is shown that the G-updating rule constitutes a three-step conditioning, where one of the three rules is applied in each step.

Superfield description of (4+2n)-dimensional SYM theories and their mixtures on magnetized tori

We provide a systematic way of dimensional reduction for $(4+2n)$-dimensional $U(N)$ supersymmetric Yang-Mills (SYM) theories ($n=0,1,2,3$) and their mixtures compactified on two-dimensional tori with background magnetic fluxes, which preserve a partial ${\mathcal N}=1$ supersymmetry out of full ${\mathcal N}=2,3$ or $4$ in the original SYM theories. It is formulated in an $\mathcal N=1$ superspace respecting the unbroken supersymmetry, and the four-dimensional effective action is written in terms of superfields representing $\mathcal N=1$ vector and chiral multiplets, those arise from the higher-dimensional SYM theories. We also identify the dilaton and geometric moduli dependence of matter K\"ahler metrics and superpotential couplings as well as of gauge kinetic functions in the effective action. The results would be useful for various phenomenological/cosmological model buildings with SYM theories or D-branes wrapping magnetized tori, especially, with mixture configurations of them with different dimensionalities from each other.Comment: 37page

Optimal Detection Strategies for an Established Invasive Forest Pest

When it comes to invasive species management, economists have focused on the trade-off between prevention of potential invasions and management of established populations. The intermediate step-detection of established populations on the landscape so that management can commence-has only recently received attention in the economics literature. A recent paper (Mehta et al., 2007) explores how biological and economic parameters affect optimal detection spending, recognizing that greater expenditures on detection can lead to smaller and more manageable population sizes upon detection because populations are discovered early. We build upon this framework by considering the optimal spatial allocation of detection effort when it is impossible to stop the advance of the main front of an invasive species, yet it is beneficial to detect and control sub-populations of the species that erupt ahead of the front. Our approach recognizes that the duration of management of sub-populations is constrained by the amount of time remaining before the main front arrives. Locations close to the front have less time remaining than locations that are more distant. These differences imply different levels of potential benefit from early detection; in particular, shorter management horizons translate into lower benefits from intervention. The optimal intensity of detection effort varies over space along with this variation in the benefits from management.Resource /Energy Economics and Policy,

Quantum Caustics for Systems with Quadratic Lagrangians in Multi-Dimensions

We study quantum caustics in $d$-dimensional systems with quadratic Lagrangians. Based on Schulman's procedure in the path-integral we derive the transition amplitude on caustics in a closed form for generic multiplicity $f$, and thereby complete the previous analysis carried out for the maximal multiplicity case $f=d$. Multiplicity dependence of the caustics phenomena is illusrated by examples of a particle interacting with external electromagnetic fields.Comment: TeX file, 27 pages, 2 figure