It has been known for some years that the uniform-density problem for neural networks has a positive answer: Any real-valued, continuous function on a compact subset of R d can be uniformly approximated by a neural network with one hidden layer. We contribute here to the related complexity problem. We call an activation function : R ! R nearly exponential if, after suitable aane transformations...

In this paper we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems. The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts. Parabolic partial differential equations and their spatial discretization are typical examples. The second class consists of highl...

The additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is studied. This channel can be considered as an exponential version of the discrete memoryless channel with state known non-causally at the encoder considered by Gelfand and Pinsker. We make use of Gelf’and-Pinsker’s classic capacity Theorem to derive inner and outer b...

We propose extreme value analogues of natural exponential families and exponential dispersionmodels and introduce the hazard slope as an analogue of the variance function. The set of quadraticand power hazard slopes is characterized, and is shown to include well-known distributions such asthe Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fréchet famili...

In that paper, we prove an equivalence between Nash-type inequalities and an exponential decay (in the sense of the definition 2.2) for symmetric submarkovian semigroups. This exponential decay generalizes the notion of spectral gap where this number is replaced by a function. We discuss different formulations of the decay associated to the usual Nash inequality in terms of Lyapunov-type functi...

This paper challenges the conventional wisdom dominating social sciences and philosophy regarding temporal discounting, practice of discounting value future utility when making decisions. Although there are sharp disagreements about a kind standard model has arisen, one that begins with normative how we should make intertemporal comparisons utility. demands in so far as is rational discounts ut...

We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX +Z where a is a positive constant and Z is independent of X. To obtain exponentia...

In this article, we study a system of viscoelastic parabolic type Kirchhoff equation with multiple nonlinearities. We obtain finite time blow up solutions and exponential growth solution negative initial energy.

Mikolov et al. (2013) introduced the skip-gram formulation for neural word embeddings, wherein one tries to predict the context of a given word. Their negative-sampling algorithm improved the computational feasibility of training the embeddings. Due to their state-of-the-art performance on a number of tasks, there has been much research aimed at better understanding it. Goldberg and Levy (2014)...