Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.Comment: 6 pages, 3 figure

A Pilot Trial of the Effectiveness of Acceptance and Commitment Therapy Self-Help for Problematic Pornography Viewing

Although problematic pornography viewing (PV) is quite prevalent (Carroll et al., 2008), very few studies have been done to test treatments addressing this issue. Preliminary research indicates Acceptance and Commitment Therapy (ACT) is a promising potential treatment for problematic pornography viewing, but this has only been evaluated in face-to-face therapy trials to-date. This study sought to determine the effectiveness of a general ACT self-help book on PV. A sample of 19 participants were recruited and given a copy of the book with directions to read and apply its principles over the course of 8 weeks. Assessments were completed at baseline, post, and 8--week follow up. Results indicate that participants made significant improvements in PV, scrupulosity, and cognitive fusion at post and follow up, but not in overall psychological flexibility and quality of life. Furthermore, those who were highly engaged in the intervention or not in a relationship showed stronger improvements in psychological flexibility and psychosocial functioning than those who were less engaged or in a relationship. Overall results indicate that a general ACT self-help approach is both feasible and reasonably effective in addressing PV and related outcomes. Findings also suggest that a more tailored and engaging intervention may increase retention and be even more effective in reducing PV. Feedback given by participants also served to provide recommendations for improving self-help interventions for PV

Approximate common divisors via lattices

We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^(n^epsilon) approximation algorithm with epsilon<2/3 for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of multivariate polynomial reconstruction, and we develop a corresponding lattice-based algorithm for the latter problem. In particular, it specializes to a lattice-based list decoding algorithm for Parvaresh-Vardy and Guruswami-Rudra codes, which are multivariate extensions of Reed-Solomon codes. This yields a new proof of the list decoding radii for these codes.Comment: 17 page

Real-time quantitative analysis of volatile products generated during solid-state polypropylene thermal oxidation

Analysis of volatile organic compounds (VOCs) during PP thermal oxidation under three oxygen partial pressures (0%, 21% and 100% of atmospheric pressure) at 140 C was performed by proton transfer reaction coupled with Fourier transform ion cyclotron resonance mass spectrometry. Six main VOCs were identified: acetone, acetic acid, 2,4- pentanedione, acetaldehyde, formaldehyde and methyl acrolein. Their formation was shown to obey two main reaction pathways, both involving methyne units as driving oxidation sites: (i) the widely accepted chain scission mechanism of tertiary alkoxy radicals, which generates primary radicals undergoing secondary reactions leading to the oxidation of methylene units; (ii) the chain scission mechanism occurring on tertiary alkyl radical, which is proposed here as a realistic path leading to methyl acrolein. The relative proportions of the six main VOCs depend on the oxygen partial pressure, which mostly impacts the oxidation of methylene units rather than the competition between the two previous paths

Verified Correctness and Security of mbedTLS HMAC-DRBG

We have formalized the functional specification of HMAC-DRBG (NIST 800-90A), and we have proved its cryptographic security--that its output is pseudorandom--using a hybrid game-based proof. We have also proved that the mbedTLS implementation (C program) correctly implements this functional specification. That proof composes with an existing C compiler correctness proof to guarantee, end-to-end, that the machine language program gives strong pseudorandomness. All proofs (hybrid games, C program verification, compiler, and their composition) are machine-checked in the Coq proof assistant. Our proofs are modular: the hybrid game proof holds on any implementation of HMAC-DRBG that satisfies our functional specification. Therefore, our functional specification can serve as a high-assurance reference.Comment: Appearing in CCS '1

RSA, DH, and DSA in the Wild

This book chapter outlines techniques for breaking cryptography by taking advantage of implementation mistakes made in practice, with a focus on those that exploit the mathematical structure of the most widely used public-key primitives