In the present paper we study minimization of energy integrals on sphere with a focus an interesting clustering phenomenon: for certain types potentials, optimal measures are discrete or supported small sets. particular, prove that support any minimizer p-frame has empty interior whenever p is not even integer. A similar effect also demonstrated energies analytic potentials which positive defin...

This paper provides an overview of categorical and gradient effects in islands, with a focus on English, argues that most islands are gradient. In some cases, the island is circumvented by construction type which extraction takes place, there growing evidence critical factor pragmatic nature, contrary to classic accounts favored generative circles this day. other effect malleable can weaken inc...

Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic replicator equations in the evolutionary game theory. However, intrinsic fluctuations arisen from the discreteness of populations lead to stochastic derivations from...

Demand for product characteristics is examined within the context of models that allow for both corner and interior solutions corresponding to zero and non-zero demand. Product attribute information is associated with marginal utility and curvature (satiation) parameters of various utility functions. Empirical applications demonstrate the need for incorporating characteristics in a fairly gener...

This paper presents a geometric approach to meaning representation within the framework of continuous mathematics. Meaning representation is a central issue in Natural Language Processing, in particular for tasks like word sense disambiguation or information extraction. We want here to discuss the relevance of using continuous models in semantics. We don’t want to argue the continuous or discre...

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrödinger and generalized Ablowitz-Ladik equations. PACS numbers: 03.40.Kf, 42.65.Tg, 63.20.Pw Typeset using REVTEX...

Are there temporal constraints on speech timing? Some have argued against them (Chomsky and Halle, 1968; van Santen, 1996) while others have claimed, for example, that languages come in two possible rhythm types, stressed-timed and syllable-timed (Abercrombie, 1967; Pike, 1943). We prefer to avoid for the moment, the question of a typology of rhythm types. Instead we will focus on styles of spe...

The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete ...

Surprising things happen when we take the discreteness of molecule number seriously, abandoning the notion that chemical concentrations may be treated as continuous variables. Here we will show how ideas of discreteness force us into dealing with issues of noise and randomness. We will arrive at a probabilistic description of reaction kinetics which, in the limit of large numbers, will reproduc...