Convergence of U-statistics for interacting particle systems

The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated -although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework

On particle Gibbs Markov chain Monte Carlo models

This article analyses a new class of advanced particle Markov chain Monte Carlo algorithms recently introduced by Andrieu, Doucet, and Holenstein (2010). We present a natural interpretation of these methods in terms of well known unbiasedness properties of Feynman-Kac particle measures, and a new duality with many-body Feynman-Kac models. This perspective sheds a new light on the foundations and the mathematical analysis of this class of methods. A key consequence is the equivalence between the backward and ancestral particle Markov chain Monte Carlo methods, and Gibbs sampling of a many-body Feynman-Kac target distribution. Our approach also presents a new stochastic differential calculus based on geometric combinatorial techniques to derive explicit non-asymptotic Taylor type series of the semigroup of a class of particle Markov chain Monte Carlo models around their invariant measures with respect to the population size of the auxiliary particle sampler. These results provide sharp quan- titative estimates of the convergence properties of conditional particle Markov chain models with respect to the time horizon and the size of the systems. We illustrate the implication of these results with sharp estimates of the contraction coefficient and the Lyapunov exponent of conditional particle samplers, and explicit and non-asymptotic Lp-mean error decompositions of the law of the random states around the limiting invariant measure. The abstract framework developed in the article also allows the design of natural extensions to island (also called SMC2) type particle methodologies

Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Renormalization: a quasi-shuffle approach

In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process

LTE/Wi-Fi Co-existence under Scrutiny: An Empirical Study

Mobile operators are seeking to increase network capacity by extending Long Term Evolution (LTE) cellular operation into unlicensed frequency bands. While these efforts may respond to the projected exponential growth in mobile data traffic, significant concerns exist about the harmonious co-existence of LTE with incumbent Wi-Fi deployments. In this paper we characterise experimentally the LTE and Wi-Fi behaviour when sharing the same spectrum while operating under a broad range of network conditions. Specifically, we deploy a test bed with commodity Wi-Fi hardware and low-cost software-defined radio equipment running an open-source LTE stack. We investigate the user-level performance attainable over these technologies when employing different settings, including LTE duty cycling patterns, Wi-Fi offered loads, transmit power levels, modulation and coding schemes, and packet sizes. We show that co-existence is feasible without modifications to the Wi-Fi stack, if LTE periodically employs "silent" sub-frames; however, optimising the performance of both requires non-trivial tuning of multiple parameters in conjunction with close monitoring of Wi-Fi operation and detection of application-specific requirements. Our findings lay the foundations for coherent design of practical LTE/Wi-Fi co-existence mechanisms

Cycle-Consistent Adversarial Networks and Fast Adaptive Bi-Dimensional Empirical Mode Decomposition for Style Transfer

Recently, research endeavors have shown the potentiality of Cycle-Consistent Adversarial Networks (CycleGAN) in style transfer. In Cycle-Consistent Adversarial Networks, the consistency loss is introduced to measure the difference between the original images and the reconstructed in both directions, forward and backward. In this work, the combination of Cycle-Consistent Adversarial Networks with Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD) is proposed to perform style transfer on images. In the proposed approach the cycle-consistency loss is modified to include the differences between the extracted Intrinsic Mode Functions (BIMFs) images. Instead of an estimation of pixel-to-pixel difference between the produced and input images, the FABEMD is applied and the extracted BIMFs are involved in the computation of the total cycle loss. This method enriches the computation of the total loss in a content-to-content and style-to-style comparison by connecting the spatial information to the frequency components. The experimental results reveal that the proposed method is efficient and produces qualitative results comparable to state-of-the-art methods