Stein's method for dependent random variables occurring in Statistical Mechanics

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the Curie-Weiss models. Under appropriate assumptions there exists a real number $\alpha$, a positive real number $\mu$, and a positive integer $k$ such that $(S_n- n \alpha)/n^{1 - 1/2k}$ converges weakly to a random variable with density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. We develop Stein's method for exchangeable pairs for a rich class of distributional approximations including the Gaussian distributions as well as the non-Gaussian limit distributions with density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. Our results include the optimal Berry-Esseen rate in the Central Limit Theorem for the total magnetization in the classical Curie-Weiss model, for high temperatures as well as at the critical temperature $\beta_c=1$, where the Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the temperature $1/ \beta_n$ converges to one and obtain a threshold for the speed of this convergence. Single spin distributions satisfying the Griffiths-Hurst-Sherman (GHS) inequality like models of liquid helium or continuous Curie-Weiss models are considered

Aperture Multipole Moments from Weak Gravitational Lensing

The projected mass of a gravitational lens inside (circular) apertures can be derived from the measured shear inside an annulus which is caused by the tidal field of the deflecting mass distribution. Here we show that also the multipoles of the two-dimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the shear, which allow large flexibility in the choice of a radial weight function. In contrast to determining multipole moments from weak-lensing mass reconstructions, this approach allows to quantify the signal-to-noise ratio of the multipole moments directly from the observed galaxy ellipticities, and thus to estimate the significance of the multipole detection. Radial weight functions can therefore be chosen such as to optimize the significance of the detection given an assumed radial mass profile. Application of our formulae to numerically simulated clusters demonstrates that the quadrupole moment of realistic cluster models can be detected with high signal-to-noise ratio S/N; in about 85 per cent of the simulated cluster fields S/N >~ 3. We also show that the shear inside a circular annulus determines multipole moments inside and outside the annulus. This is relevant for clusters whose central region is too bright to allow the observation of the shear of background galaxies, or which extend beyond the CCD. We also generalize the aperture mass equation to the case of `radial' weight functions which are constant on arbitrarily-shaped curves which are not necessarily self-similar.Comment: 14 pages including 3 figures; submitted to MNRAS; replaced to improve printing on non-A4 pape

TreatJS: Higher-Order Contracts for JavaScript

TreatJS is a language embedded, higher-order contract system for JavaScript which enforces contracts by run-time monitoring. Beyond providing the standard abstractions for building higher-order contracts (base, function, and object contracts), TreatJS's novel contributions are its guarantee of non-interfering contract execution, its systematic approach to blame assignment, its support for contracts in the style of union and intersection types, and its notion of a parameterized contract scope, which is the building block for composable run-time generated contracts that generalize dependent function contracts. TreatJS is implemented as a library so that all aspects of a contract can be specified using the full JavaScript language. The library relies on JavaScript proxies to guarantee full interposition for contracts. It further exploits JavaScript's reflective features to run contracts in a sandbox environment, which guarantees that the execution of contract code does not modify the application state. No source code transformation or change in the JavaScript run-time system is required. The impact of contracts on execution speed is evaluated using the Google Octane benchmark.Comment: Technical Repor

Asymptotic entanglement transformation between W and GHZ states

We investigate entanglement transformations with stochastic local operations and classical communication (SLOCC) in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory. Results well-known in that field imply that GHZ states can be transformed into W states at rate 1 for any number of parties. As a generalization, we find that the asymptotic conversion rate from GHZ states to Dicke states is bounded as the number of subsystems increase and the number of excitations is fixed. By generalizing constructions of Coppersmith and Winograd and by using monotones introduced by Strassen we also compute the conversion rate from W to GHZ states.Comment: 11 page

Type-based Dependency Analysis for JavaScript

Dependency analysis is a program analysis that determines potential data flow between program points. While it is not a security analysis per se, it is a viable basis for investigating data integrity, for ensuring confidentiality, and for guaranteeing sanitization. A noninterference property can be stated and proved for the dependency analysis. We have designed and implemented a dependency analysis for JavaScript. We formalize this analysis as an abstraction of a tainting semantics. We prove the correctness of the tainting semantics, the soundness of the abstraction, a noninterference property, and the termination of the analysis.Comment: Technical Repor