In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices I...

This paper deals with the design and analysis of dynamical systems on directed graphs (digraphs) that achieve weight-balanced and doubly stochastic assignments. Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of coordination problems, including formation control, agreement, and distributed optimization. We refer to a digraph as...

We consider the problem of multiuser detection for DSCDMA in doubly-selective (timeand frequency-selective) channels, and propose a time-varying multiuser detector (TVMUD) to solve this problem. Using a basis expansion model (BEM) to model the doubly-selective channel and the TVMUD, we derive a closed-form expression for the BEM coefficients of the TV-MUD as a function of the BEM coefficients o...

A construction based on Legendre sequences is presented for a doubly-extended binary linear code of length 2p + 2 and dimension p+1. This code has a double circulant structure. For p = 4k +3, we obtain a doubly-even self-dual code. Another construction is given for a class of triply extended rate 1/3 codes of length 3p + 3 and dimension p + 1. For p = 4k + 1, these codes are doubly-even selfort...

Abstract. In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions...

Recently, there has been a growing interest in the methods addressing volatility in computational finance and econometrics. Peiris et al. [8] have introduced doubly stochastic volatility models with GARCH innovations. Random coefficient autoregressive sequences are special case of doubly stochastic time series. In this paper, we consider some doubly stochastic stationary time series with GARCH ...

The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not behave analogously to smooth surfaces with respect to negative curvature. We extend this curvature to vertices and faces in such a way that the problems with co...

Nonaccidental properties (NAPs) are image properties that are invariant over orientation in depth and are distinguished from metric properties (MPs) that can change continuously with variations over depth orientation. To a large extent NAPs allow facile recognition of objects at novel viewpoints. Two match-to-sample experiments with 2D or 3D appearing geons assessed sensitivity to NAP vs. MP di...

The time course of categorization was investigated in four experiments, which revealed graded competitive effects in a categorization task. Participants clicked one of two categories (e.g., mammal or fish) in response to atypical or typical exemplars (e.g., whale or cat) in the form of words (Experiments 1 and 2) or pictures (Experiments 3 and 4). Streaming x, y coordinates of mouse movement tr...

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles > 2π. With an additional condition, we can weaken the requirement on one metric to ‘no conjugate points.’