Abstract:
In a previous work (S. Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs). The aim of the present manuscript is to improve the above-mentioned random number generation method by changing the learning principle, while retaining the efficient LUT-based implementation. The new method proposed here proves easier to implement and relaxes some previous limitations.

Abstract:
Bivariate statistical modeling from incomplete data is a useful statistical tool that allows to discover the model underlying two data sets when the data in the two sets do not correspond in size nor in ordering. Such situation may occur when the sizes of the two data sets do not match (i.e., there are holes in the data) or when the data sets have been acquired independently. Also, statistical modeling is useful when the amount of available data is enough to show relevant statistical features of the phenomenon underlying the data. We propose to tackle the problem of statistical modeling via a neural (nonlinear) system that is able to match its input-output statistic to the statistic of the available data sets. A key point of the new implementation proposed here is that it is based on look-up-table (LUT) neural systems, which guarantee a computationally advantageous way of implementing neural systems. A number of numerical experiments, performed on both synthetic and real-world data sets, illustrate the features of the proposed modeling procedure.

Abstract:
We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of the branch and ramification locus have simple normal crossings.

Abstract:
We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type G2, focusing on the case of number fields and p-adic fields. In the same context we characterize the rational conjugacy classes of A2 subgroups of G2. Having obtained the concrete characterization, we then relate it to the more abstract characterization which can be given in terms of Galois cohomology. We note that these results on A2 subgroups were simultaneously and independently developed in the work of Hooda whereas the results on tori were simultaneously and independently developed in the work of Beli-Gille-Lee.

Abstract:
We characterize the possible reductions of $j$-invariants of elliptic curves which admit complex multiplication by an order $\mathcal{O}$ where the curve itself is defined over $\mathbb{Z}_p$. In particular, we show that the distribution of these $j$-invariants depends on which primes divide the discriminant and conductor of the order.

Abstract:
The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R)$. The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradient steepest descent on manifold may be implemented through a geodesic-based stepping method. As the space Sp(2n,R) is a non-compact Lie group, it is convenient to endow it with a pseudo-Riemannian geometry. Indeed, a pseudo-Riemannian metric allows the computation of geodesic arcs and geodesic distances in closed form on Sp(2n,R).

Abstract:
The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever learning/adaptation algorithms insist on high-dimensional parameter manifolds.

Abstract:
contemporary architecture is dangerously enmeshed with the entertainment industry and the field of advertising. this meshing has pushed architectural form to the limits of materiality. architecture today searches for maximum informational rent, a process typical of global product branding; through this process, established building and production principles are subverted by a play of volumes and effects beyond any rule or limitation. relying on digital design technologies and the reorganization of the building site, this new fetishism of form, analogous to the autonomization of power and abstract wealth in contemporary capitalism, defines the new condition of cutting-edge architecture.

Abstract:
the article discusses the possibilities of "global governance". taking the notions of global "hegemony" and "governance" as a guideline, the author examines the constitution and expansion of hegemonic powers since the 17th century. further on, he puts into question the notion of "cosmopolitanism" proposed by kant and discusses the actual possibility of a global government.