It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu [5], the only remaining relevant situation for the multiplicative strong unimodality of stable laws is the one-sided. In this paper, we show that positive α−stable laws are multiplicative strongly ...

One of the simplest ways of optimizing a problem without knowledge of its gradient, is to iteratively and randomly pick a sequence of candidate solutions that improve on the fitness. This paper shows mathematically that to exhaust the optimum of a problem, the search-range from which the candidate solutions are picked, must be decreased during an optimization run. A simple technique for doing t...

In this paper we prove that any sequence of n real numbers contains a unimodal subsequence of length at least [(3n-3/4) " '-fj and that this bound is best possible.

Time-symmetric cycles are defined. Unimodal time-symmetric cycles are classified. A one-parameter family of maps of the closed unit interval that exhibits this classification is given. 1. Introduction. In one-dimensional dynamics, the maps that are studied are usually noninvertible. The initial reason for studying these maps was that they had complicated behavior that was reminiscent of diffeom...

In this paper, we prove undecidability and the lack of finite model property for a certain class of unimodal logics. To do this, we adapt the technique from [7], where products of transitive modal logics were investigated, for the unimodal case. As a particular corollary, we present an undecidable unimodal fragment of Halpern and Shoham’s Interval Temporal Logic.

Loss of a sensory modality elicits both unimodal changes in the deprived cortex and cross-modal alterations in the remaining sensory systems. Unimodal changes are proposed to recruit the deprived cortex for processing the remaining senses, while cross-modal changes are thought to refine processing of spared senses. Hence coordinated unimodal and cross-modal changes are likely beneficial. Despit...

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, oc...

In this paper, we study, in some new ways, the estimation of unimodal densities. Several methods for estimating unimodal densities are proposed: plug-in MLE, pregrouping techniques, linear spline MLE. Based on the maximum likelihood method, an automatic procedure for estimating a unimodal density as well as its mode is proposed. We also give asymptotic theory for the proposed estimators. An imp...

The current study assessed the relative effectiveness with which unimodal tactile, unimodal touch-produced auditory, and bimodal tactile + auditory cues contribute to the performance of an absolute texture identification task via remote touch. The study contributes to our fundamental understanding of the unimodal perception and intersensory integration of multimodal surface texture cues generat...