In this article, we introduce a new family of polar codes from evaluation codes, called decreasing monomial-Cartesian and prove that families with multiple kernels over certain symmetric channels can be viewed as codes. This offers unified treatment for such any finite field. We define obtained set monomials closed under divisibility Cartesian product determine their parameters (length, dimensi...

We consider a new family of regularizers, termed weighted sorted `1 norms (WSL1), which generalizes the recently introduced octagonal shrinkage and clustering algorithm for regression (OSCAR) and also contains the `1 and `∞ norms as particular instances. We focus on a special case of the WSL1, the decreasing WSL1 (DWSL1), where the elements of the argument vector are sorted in non-increasing or...

The classical method for program analysis by abstract interpretation consists in computing a increasing sequence with widening, which converges towards a correct solution, then computing a decreasing sequence of correct solutions without widening. It is generally admitted that, when the decreasing sequence reaches a fixpoint, it cannot be improved further. As a consequence, all efforts for impr...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract A new nonparametric estimation procedure is introduced for a class of deconvolution problems where the convolution kernel is decreasing on 0; 1). The estimator is shown to be consistent and its cube root asymptotic distribution theory is established.

Forest fires are a serious environmental hazard in southern Europe. Quantitative assessment of recent trends in fire statistics is important for assessing the possible shifts induced by climate and other environmental/socioeconomic changes in this area. Here we analyse recent fire trends in Portugal, Spain, southern France, Italy and Greece, building on a homogenized fire database integrating o...

We present and compare some well-founded proof orders for decreasing diagrams. These proof orders order a conversion above another conversion if the latter is obtained by filling any peak in the former by a (locally) decreasing diagram. Therefore each such proof order entails the decreasing diagrams technique for proving confluence. The proof orders differ with respect to monotonicity and compl...

We study strictly level-decreasing logic programs (sld-programs) as defined earlier by the present authors. It will be seen that sld-programs, unlike most other classes of logic programs, have both a highly intuitive declarative semantics, given as a unique supported model, and are computationally adequate in the sense that every partial recursive function can be represented by some sld-program...

Alon, Gyárfás and Ruszinkó [1] established a bound for the minimum number of edges that have to be added to a graph of n ≥ n0 vertices in order to obtain a graph of diameter 2. Alon et al. approximated n0 by a polynomial function of the maximum degree of the initial graph. They conjectured that the minimum value for n0 is 12 for the case of Cn, as opposed to n0 = 274 obtained by calculations fo...

Living organisms are constrained by both resource quantity and quality. Ecological stoichiometry offers important insights into how the elemental composition of resources affects their consumers. If resource quality decreases, consumers can respond by shifting their body stoichiometry, avoiding low-quality resources, or up-regulating feeding rates to maintain the supply of required elements whi...