The critical exponent conjecture for powers of doubly nonnegative matrices

Doubly nonnegative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. In this short note, we settle a recent conjecture by C.R. Johnson et al. [Charles R. Johnson, Brian Lins, Olivia Walch, The critical exponent for continuous conventional powers of doubly nonnegative matrices, Linear Algebra Appl. 435 (9) (2011) 2175–2182] by proving that the critical exponent beyond which all continuous conventional powers of n-by-n   doubly nonnegative matrices are doubly nonnegative is exactly n−2$n-2$. We show that the conjecture follows immediately by applying a general characterization from the literature. We prove a stronger form of the conjecture by classifying all powers preserving doubly nonnegative matrices, and proceed to generalize the conjecture for broad classes of functions. We also provide different approaches for settling the original conjecture.     

The impact of voters’ preference diversity on the probability of some electoral outcomes

Voting rules are known to exhibit various paradoxical or problematic behaviors, typically in the form of their failure to meet the Condorcet criterion or in their vulnerability to strategic voting. Our basic premise is that a decrease in the number of coalitions of voters that exist with similar preference rankings should generally lead to a reduced propensity of voting rules to yield undesired results. Surprisingly enough, conclusions that are reported by Felsenthal et al. (1990) in an early study do not corroborate this intuition. This study reconsiders and extends the Felsenthal et al. analysis by using a modified Impartial Anonymous Culture (IAC) model. It turns out that the results obtained with this probabilistic assumption are much more consistent with the stated intuitive premise.     

Markov Chain Approximations to Nonsymmetric Diffusions with Bounded Coefficients

We consider a certain class of nonsymmetric Markov chains and obtain heat kernel bounds and parabolic Harnack inequalities. Using the heat kernel estimates, we establish a sufficient condition for the family of Markov chains to converge to nonsymmetric diffusions. As an application, we approximate nonsymmetric diffusions in divergence form with bounded coefficients by nonsymmetric Markov chains. This extends the results by Stroock and Zheng to the nonsymmetric divergence forms. © 2012 Wiley Periodicals, Inc.     

Essential countability of treeable equivalence relations

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E   is essentially countable if and only if there is no continuous embedding of _E1${\mathbb{E}}_1$ into E. Our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations, and allow us to show that up to continuous Kakutani embeddability, there is a minimum Borel function which is not essentially countable-to-one.     

The Structural Nature of the Nerve Functor for n-Groupoids

Given a left exact category B, the construction of the nerve functor _n for n-groupoids in B is related to a certain property of the category S-S i m p l _{n – 1} B of the split (n – 1)-truncated simplicial objects in B, which allows us to define the split n-truncated simplicial objects in B completely internally to S-S i m p l _{n – 1} B and thus to construct intrisincally from it the category S-S i m p l _n B.     

Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes

The zero-mean process is said to be almost periodically correlated whenever its shifted covariance kernel is almost periodic in t uniformly with respect to . Then it admits a Fourier–Bohr decomposition: . This paper deals with the estimation of the spectral covariance a(λ,τ) from a discrete time observation of the process , when jitter and delay phenomena are present in conjunction with periodic sampling. Under mixing conditions, we establish the consistency and the asymptotic normality of empirical estimators as the sampling time step tends to 0 and the sampling period tends to infinity.      

Factorisation des polynômes de Poncelet

La condition pour qu’il existe des n-gones de Poncelet, inscrits dans un cercle, et circonscrits à un autre cercle, est polynomiale en les paramètres définissant ces deux cercles. Nous décomposons ces polynômes “de Poncelet” en facteurs irréductibles que nous interprétons géométriquement.     

A note on taxation,incentives and risk sharing

The necessary and sufficient conditions for a tax system to guarantee the consistency of private and public evaluation of risky projects are derived. A stochastic dominance approach is used.     

Determining the effective density of airborne nanoparticles using multiple charging correction in a tandem DMA/ELPI setup

The cysteamine-modified hyaluronic acid (HA) polymer was employed to coat quantum dots (QDs) through a convenient one-step reverse micelle method, with the final QDs hydrodynamic size of around 22.6 nm. The HA coating renders the QDs with very good stability in PBS for more than 140 days and resistant to large pH range of 2–12. Besides, the HA-coated QDs also show excellent fluorescence stability in BSA-containing cell culture medium. In addition, the cell culture assay indicates no significant cytotoxicity for MD-MB-231 breast cancer cells, and its targeting ability to cancer receptor CD44 has been demonstrated on two breast cancer cell lines. The targeting mechanism was further proved by the HA competition experiment. This work has established a new approach to help solve the stability and toxicity problems of QDs, and moreover render the QDs cancer targeting property. The current results indicate that the HA polymer-coated QDs hold the potential application for both in vitro and in vivo cancer imaging researches.