Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

Good match exploration for thermal infrared face recognition based on YWF-SIFT with multi-scale fusion

Stable local feature detection is a critical prerequisite in the problem of infrared (IR) face recognition. Recently, Scale Invariant Feature Transform (SIFT) is introduced for feature detection in an infrared face frame, which is achieved by applying a simple and effective averaging window with SIFT termed as Y-styled Window Filter (YWF). However, the thermal IR face frame has an intrinsic characteristic such as lack of feature points (keypoints); therefore, the performance of the YWF-SIFT method will be inevitably influenced when it was used for IR face recognition. In this paper, we propose a novel method combining multi-scale fusion with YWF-SIFT to explore more good feature matches. The multi-scale fusion is performed on a thermal IR frame and a corresponding auxiliary visual frame generated from an off-the-shelf low-cost visual camera. The fused image is more informative, and typically contains much more stable features. Besides, the use of YWF-SIFT method enables us to establish feature correspondences more accurately. Quantitative experimental results demonstrate that our algorithm is able to significantly improve the quantity of feature points by approximately 38%. As a result, the performance of YWF-SIFT with multi-scale fusion is enhanced about 12% in infrared human face recognition.     

Operation principle of self-phase compensated optical waveguide isolator

A theory is developed for the self-phase compensated optical waveguide isolator recently reported in the literature. The operation principle of such device is explained in terms of synchronization of phase and power conversion. The effect of balancing phase mismatches of the two convertors on achieving a proper percentage of mode conversion is revealed. The way to make use of the phase mismatches of different sections to accommodate the different requirements in phase relationship for the reciprocal and nonreciprocal mode convertors is discussed. The theory is extended to the case where phase compensator is used. It is demonstrated that the introduction of phase compensator separates the adjustment of phase from the adjustment of power for the mode convertors so that relaxes fabrication tolerances of such devices. An isolator consists of three phase mismatched waveguide sections is designed and simulated. The simulation results confirm the self-phase compensation theory.     

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two suffcient and necessary conditions for such graphs to be 1- or 2-arc-regular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.     

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.