The motive of a smooth Theta divisor

We prove a motivic version of the Lefschetz hyperplane theorem for a smooth ample divisor $\Theta$ on an Abelian variety. We use this to construct a motive $P$ that realizes the primitive cohomology of $\Theta$

The Chow group mod ℓ\ell for a product of elliptic curves

Generalizing work of Schoen, we prove that the Chow group modulo $\ell$ of a product of $3$ or more very general complex elliptic curves is infinite

Some nilpotence theorems for algebraic cycles

Using fundamental results of Deligne, we prove a nilpotence theorem for algebraic cycles and use this to prove a torsion nilpotence result for correspondences on surfaces.Comment: 10 pages, more errors corrected. Some applications have been removed since they cannot be proved using the main result; these applications will be proved independently in a future pape

The standard conjectures for the variety of lines on a cubic hypersurface

The purpose of this note is to prove Grothendieck's standard conjectures for the Fano variety of lines on a smooth cubic hypersurface in projective space

Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies

Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter $\epsilon$. We demonstrate, that within Gaussian noise, the variance of the resulting wealth distribution will significantly decrease, and the equilibrium state is reached faster than in the case of a uniform distributed $\epsilon$ parameter. Also, we show that the system with Gaussian noise strongly resembles a deterministic system which is solved by means of a Z-Transform based technique.Comment: 7 pages, 6 figure

Introducing a Probabilistic Structure on Sequential Dynamical Systems, Simulation and Reduction of Probabilistic Sequential Networks

A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions. It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either an epimorphism or a monomorphism. Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given.Comment: 14 page

A new algorithm for finding the nilpotency class of a finite p-group describing the upper central series

In this paper we describe an algorithm for finding the nilpotency class, and the upper central series of the maximal normal p-subgroup N(G) of the automorphism group, Aut(G) of a bounded (or finite) abelian p-group G. This is the first part of two papers devoted to compute the nilpotency class of N(G) using formulas, and algorithms that work in almost all groups. Here, we prove that for p>2 the algorithm always runs. The algorithm describes a sequence of ideals of the Jacobson radical, J, and because N(G)=J+1, this sequence induces the upper central series in N(G).Comment: 15 pages, sending to a Journa

Simulation of Probabilistic Sequential Systems

In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical Systems is an important and interesting problem. The notion of homomorphism of our new model, is a natural extension of homomorphism of sequential dynamical systems introduced and developed by Laubenbacher and Paregeis in several papers. Our model, give the possibility to describe the dynamic of the systems using Markov chains and all the advantage of stochastic theory. The notion of simulation is introduced using the concept of homomorphisms, as usual. Several examples of homomorphisms, subsystems and simulations are given

Distributions on symmetric cones II: Beta-Riesz distribution

This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In addition, introduce a kind of generalised beta distribution termed beta-Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some properties are studied.Comment: Several properties of q_{\kappa} have been modified and their consequences in the rest of the manuscrip

A probabilistic regulatory network for the human immune system

In this paper we made a review of some papers about probabilistic regulatory networks (PRN), in particular we introduce our concept of homomorphisms of PRN with an example of projection of a regulatory network to a smaller one. We apply the model PRN (or Probabilistic Boolean Network) to the immune system, the PRN works with two functions. The model called ""The B/T-cells interaction"" is Boolean, so we are really working with a Probabilistic Boolean Network. Using Markov Chains we determine the state of equilibrium of the immune response.Comment: 9 page