On effective sigma-boundedness and sigma-compactness

We prove several theorems on sigma-bounded and sigma-compact pointsets. We start with a known theorem by Kechris, saying that any lightface \Sigma^1_1 set of the Baire space either is effectively sigma-bounded (that is, covered by a countable union of compact lightface \Delta^1_1 sets), or contains a superperfect subset (and then the set is not sigma-bounded, of course). We add different generalizations of this result, in particular, 1) such that the boundedness property involved includes covering by compact sets and equivalence classes of a given finite collection of lightface \Delta^1_1 equivalence relations, 2) generalizations to lightface \Sigma^1_2 sets, 3) generalizations true in the Solovay model. As for effective sigma-compactness, we start with a theorem by Louveau, saying that any lightface \Delta^1_1 set of the Baire space either is effectively sigma-compact (that is, is equal to a countable union of compact lightface \Delta^1_1 sets), or it contains a relatively closed superperfect subset. Then we prove a generalization of this result to lightface \Sigma^1_1 sets.Comment: arXiv admin note: substantial text overlap with arXiv:1103.106

Hidden-Markov Program Algebra with iteration

We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an "implementation" program leaks no more than its "specification" program. This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack

Spartan Daily, October 4, 1961

Volume 49, Issue 6https://scholarworks.sjsu.edu/spartandaily/4193/thumbnail.jp

Brane transport in anomalous (2,2) models and localization

We study B-branes in two-dimensional N=(2,2) anomalous models, and their behaviour as we vary bulk parameters in the quantum K\"ahler moduli space. We focus on the case of (2,2) theories defined by abelian gauged linear sigma models (GLSM). We use the hemisphere partition function as a guide to find how B-branes split in the IR into components supported on Higgs, mixed and Coulomb branches: this generalizes the band restriction rule of Herbst-Hori-Page to anomalous models. As a central example, we work out in detail the case of GLSMs for Hirzebruch-Jung resolutions of cyclic surface singularities. In these non-compact models we explain how to compute and regularize the hemisphere partition function for a brane with compact support, and check that its Higgs branch component explicitly matches with the geometric central charge of an object in the derived category.Comment: 67 page

Higher-order perturbation solutions to dynamic, discrete-time rational expectations models

We present an algorithm and software routines for computing nth order Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to first- or second-order) approximations is that they are valid not just locally, but often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We apply our routines to compute first- through seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions.Macroeconomics - Econometric models ; Business cycles ; Monetary policy

The Cosmic Microwave Background and the Ionization History of the Universe

Details of how the primordial plasma recombined and how the universe later reionized are currently somewhat uncertain. This uncertainty can restrict the accuracy of cosmological parameter measurements from the Cosmic Microwave Background (CMB). More positively, future CMB data can be used to constrain the ionization history using observations. We first discuss how current uncertainties in the recombination history impact parameter constraints, and show how suitable parameterizations can be used to obtain unbiased parameter estimates from future data. Some parameters can be constrained robustly, however there is clear motivation to model recombination more accurately with quantified errors. We then discuss constraints on the ionization fraction binned in redshift during reionization. Perfect CMB polarization data could in principle distinguish different histories that have the same optical depth. We discuss how well the Planck satellite may be able to constrain the ionization history, and show the currently very weak constraints from WMAP three-year data.Comment: Changes to match MNRAS accepted versio