We construct a continuous nowhere monotone and nondifferentiable function depending on single parameter q0 ? (0; 1). For functions from this continual class, we describe their structural, variational, fractal, integrodifferential properties.

Domains in Continuous Constraint Programming (CP) are generally represented with intervals whose n-ary Cartesian product (box) approximates the solution space. This paper proposes a new representation for continuous variable domains based on octagons. We generalize local consistency and split to this octagon representation, and we propose an octagonal-based branch and prune algorithm. Prelimina...

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...

We train a variational autoencoder to convert discrete representations of molecules to and from a multidimensional continuous representation. This continuous representation allow us to automatically generate novel chemical structures by performing simple operations in the latent space, such as decoding random vectors, perturbing known chemical structures, or interpolating between molecules. Con...

In this paper we describe a probabilistic image matching scheme in which the im age representation is continuous and the similarity measure and distance computation are also de ned in the continuous domain Each image is rst represented as a Gaus sian mixture distribution and images are compared and matched via a probabilistic measure of similarity between distributions A common probabilistic an...

Many of the modern systems integrate components specific to different application domains. Frequently these systems combine continuous and discrete sub-systems and therefore their design involves solving specific global modeling and simulation problems. This paper addresses the formal representation of a continuous/discrete global synchronization model and the corresponding simulation interface...

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis technique to maps which come from discretization of continuous nonlinear polynomial problems in accelerator physics. Our main point is generalization of wavele...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

ion and Representation of Continuous Variables in Connectionist Networks Eric Saund Department of Brain and Cognitive Sciences and the Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge, Massachusetts 02139