Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness.We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.

Possibilistic Information Fusion Using Maximal Coherent Subsets

When multiple sources provide information about the same unknown quantity, their fusion into a synthetic interpretable message is often a tedious problem, especially when sources are conicting. In this paper, we propose to use possibility theory and the notion of maximal coherent subsets, often used in logic-based representations, to build a fuzzy belief structure that will be instrumental both for extracting useful information about various features of the information conveyed by the sources and for compressing this information into a unique possibility distribution. Extensions and properties of the basic fusion rule are also studied.

Hierarchical Bayesian models in ecology: Reconstructing species interaction networks from non-homogeneous species abundance data

The relationships among organisms and their surroundings can be of immense complexity. To describe and understand an ecosystem as a tangled bank, multiple ways of interaction and their effects have to be considered, such as predation, competition, mutualism and facilitation. Understanding the resulting interaction networks is a challenge in changing environments, e.g. to predict knock-on effects of invasive species and to understand how climate change impacts biodiversity. The elucidation of complex ecological systems with their interactions will benefit enormously from the development of new machine learning tools that aim to infer the structure of interaction networks from field data. In the present study, we propose a novel Bayesian regression and multiple changepoint model (BRAM) for reconstructing species interaction networks from observed species distributions. The model has been devised to allow robust inference in the presence of spatial autocorrelation and distributional heterogeneity. We have evaluated the model on simulated data that combines a trophic niche model with a stochastic population model on a 2-dimensional lattice, and we have compared the performance of our model with L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. In addition, we have applied our method to plant ground coverage data from the western shore of the Outer Hebrides with the objective to infer the ecological interactions. (C) 2012 Elsevier B.V. All rights reserved.

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T' has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on $\omega$, $T\oplus T$ is also hypercyclic.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Using temporal analysis of products and flux response technology to determine diffusion coefficients in catalytic monoliths

The importance of accurately measuring gas diffusivity in porous materials has led to a number of methods being developed. In this study the Temporal Analysis of Products (TAP) reactor and Flux Response Technology (FRT) have been used to examine the diffusivity in the washcoat supported on cordierite monoliths. Herein, the molecular diffusion of propane within four monoliths with differently prepared alumina/CeZrOx washcoats was investigated as a function of temperature. Moment-based analysis of the observed TAP responses led to the calculation of the apparent intermediate gas constant, Kp, that characterises adsorption into the mesoporous network and apparent time delay, tapp, that characterises residence time in the mesoporous network. Additionally, FRT has been successfully adapted as an extensive in situ perturbation technique in measuring intraphase diffusion coefficients in the washcoats of the same four monolith samples. The diffusion coefficients obtained by moment-based analysis of TAP responses are larger than the coefficients determined by zero length column (ZLC) analysis of flux response profiles with measured values of the same monolith samples between 20 and 100 °C ranging from 2–5×10^-9 m² s^-1 to 4–8×10^-10 m² s^-1, respectively. The TAP and FRT data, therefore, provide a range of the lower and upper limits of diffusivity, respectively. The reported activation energies and diffusivities clearly correlate with the difference in the washcoat structure of different monolith samples.

On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator
semigroup $\{T_t\}_{t\geq 0}$ acting on a complex $\F$-space, every
$T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic
vectors of $T_t$ does not depend on the choice of $t>0$.

Cyclic behaviour of Volterra composition operators

We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,
where $?$ is a measurable self-map of [0, 1]. The cyclic behaviour of $V_\phi$ is essentially determined by the behaviour of the inducing symbol $\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.

Equidiscrimination contours around an achromatic colour are convex but not balanced

A model based on the postreceptor channels followed by a Minkowski norm (Minkowski model) is widely used to fit experimental data on colour discrimination. This model predicts that contours of equal discrimination in colour space are convex and balanced (symmetrical). We have tested these predictions in an experiment. Two new statistical tests have been developed to analyse convexity and balancedness of experimental curves. Using these tests we have found that while they are in line with the convexity prediction, our experimental contours strongly testify against balancedness. It follows that the Minkowski model is, generally, inappropriate to model colour discrimination data. © 2002 Elsevier Science (USA).

Parimutuel betting under asymmetric information

This paper examines simple parimutuel betting games under asymmetric information, with particular attention to differences between markets in which bets are submitted simultaneously versus sequentially. In the simultaneous parimutuel betting market, all (symmetric and asymmetric) Bayesian-Nash equilibria are generically characterized as a function of the number of bettors and the quality of their private information. There always exists a separating equilibrium, in which all bettors follow their private signals. This equilibrium is unique if the number of bettors is sufficiently large. In the sequential framework, earlier bets have information externalities, because they may reveal private information of bettors. They also have payoff externalities, because they affect the betting odds. One effect of these externalities is that the separating equilibrium disappears if the number of betting periods is sufficiently large. (C) 2006 Elsevier B.V. All rights reserved.

Differential power analysis resistance of Camellia and countermeasure strategy on FPGAs

Security devices are vulnerable to Differential Power Analysis (DPA) that reveals the key by monitoring the power consumption of the circuits. In this paper, we present the first DPA attack against an FPGA implementation of the Camellia encryption algorithm with all key sizes and evaluate the DPA resistance of the algorithm. The Camellia cryptographic algorithm involves several different key-dependent intermediate operations including S-Box operations. In previous research, it was believed that the Camellia is stronger than AES due to the additional Whitening phase protecting the S-Box operation. However, we propose an attack that bypasses the Whitening phase and targets the S-Box. In this paper, we also discuss a lowcost countermeasure strategy to protect the Pre-whitening / Post-whitening and FL function of Camellia using Dual-rail Precharged Logic and to protect against attacks of the S-Box using Random Delay Insertion. © 2009 IEEE.

Ixaru's Extended Frequency Dependent Quadrature Rules for Slater Integrals: Parallel Computation Issues

We describe recent progress of an ongoing research programme aimed at producing computational science software that can exploit high performance architectures in the atomic physics application domain. We examine the computational bottleneck of matrix construction in a suite of two-dimensional R-matrix propagation programs, 2DRMP, that are aimed at creating virtual electron collision experiments on HPC architectures. We build on Ixaru's extended frequency dependent quadrature rules (EFDQR) for Slater integrals and examine the challenge of constructing Hamiltonian matrices in parallel across an m-processor compute node in a block cyclic distribution for subsequent diagonalization by ScaLAPACK.