We study the dynamics of a simple bistable system driven by multiplicative correlated noise. Such system mimics the dynamics of classical attractor neural networks with an additional source of noise associated, for instance, with the stochasticity of synaptic transmission. We found that the multiplicative noise, which performs as a fluctuating barrier separating the stable solutions, strongly i...

Matching on one of two possibly interacting exposures can increase power and efficiency to estimate multiplicative interactions in case-control studies. We recently introduced the concept of flexible matching strategies with varying proportions of a dichotomous matching factor among controls to further increase power and efficiency. In order to facilitate the application of this concept, we dev...

We study the computational complexity of two Boolean non-linearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time 2 O(n) given the truth table of length 2 n , in fact under the same assumption it is impossible to approximate the multiplicative complexity within a factor of (2 −...

In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly related, so it is wise to make multiplicative unit learn relations among mor...

We study the model theory of (F;<χ) where the field F is an algebraic closure of a finite field and <χ is an ordering on the multiplicative group F× induced by a group embedding χ ∶ F× → C×. Using number-theoretic bounds on multiplicative character sums over finite fields and Weyl’s criterion for equidistribution, we establish a number of properties about the interaction between <χ and the unde...

We show that the rule that allows the inference of A from A B is admissible in many of the basic multiplicative (intensional) systems. By adding this rule to these systems we get, therefore, conservative extensions in which the tensor behaves as classical conjunction. Among the systems obtained in this way the one derived from RMIm (= multiplicative linear logic together with contraction and it...

In this paper we obtain asymptotic expansion for the geometric mean of values positive strongly multiplicative function $f$ satisfying $f(p)=\alpha(d)\,p^d+O(p^{d-\delta})$ any prime $p$ with $d$ real and $\alpha(d),\delta>0$.

In the last lecture, we considered thematrix scaling problem: Given non-negativematrices X, T ∈ ’n×n + , our goal was to find non-negative diagonal matrices D1 ,D2 so that D1XD2 had the same row and column sums as the target matrix T. In other words, we sought to weight the rows and columns of X by positive numbers in order to achieve this. We used entropy optimization to prove the following th...

Background: For psychiatric disorders, comorbidity is a rule rather than exception. Thus it is particularly important to study additive and multiplicative effects of multiple mental disorders on suicidal behaviors. Objectives: The aim of this study was to investigate the ethnic differences in multiplicative effects of mental disorders on suicidal ideation among Black adults in the United States...

The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic dynamical regimes and the role of the external noise on the probability distribution of the local field. Population dynamics attracted a lot of attention in recent...