arXiv subjects

Yan Zhuang

Publications and source records attributed to Yan Zhuang.

79 records · Page 5Linked to original sources

arXiv2016

Counting permutations by runs

In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem to allow for a much wider variety of restrictions on increasing run lengths, and use it to complete the enumeration of permutations with parity restrictions on peaks and valleys, and to give a systematic method for obtaining generating functions for permutation statistics that are expressible in terms of increasing runs. Our methods can also be used to obtain analogous results for alternating runs in permutations.

math.CO↗

arXiv2016

Human Gender Classification: A Review

Gender contains a wide range of information regarding to the characteristics difference between male and female. Successful gender recognition is essential and critical for many applications in the commercial domains such as applications of human-computer interaction and computer-aided physiological or psychological analysis. Some have proposed various approaches for automatic gender classification using the features derived from human bodies and/or behaviors. First, this paper introduces the challenge and application for gender classification research. Then, the development and framework of gender classification are described. Besides, we compare these state-of-the-art approaches, including vision-based methods, biological information-based method, and social network information-based method, to provide a comprehensive review in the area of gender classification. In mean time, we highlight the strength and discuss the limitation of each method. Finally, this review also discusses several promising applications for the future work.

cs.AI↗

arXiv2015

Strain-induced energy band gap opening in two-dimensional bilayered silicon film

This work presents a theoretical study of the structural and electronic properties of bilayered silicon films under in-plane biaxial strain/stress using density functional theory. Atomic structures of the two-dimensional silicon films are optimized by using both the local-density approximation and generalized gradient approximation. In the absence of strain/stress, five buckled hexagonal honeycomb structures of the bilayered silicon film have been obtained as local energy minima and their structural stability has been verified. These structures present a Dirac-cone shaped energy band diagram with zero energy band gaps. Applying tensile biaxial strain leads to a reduction of the buckling height. Atomically flat structures with zero bucking height have been observed when the AA-stacking structures are under a critical biaxial strain. Increase of the strain between 10.7% ~ 15.4% results in a band-gap opening with a maximum energy band gap opening of ~168.0 meV obtained when 14.3% strain is applied. Energy band diagram, electron transmission efficiency, and the charge transport property are calculated.

cond-mat.mtrl-sci↗

arXiv2014

Counting permutations by alternating descents

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can be expressed as the reciprocal of a sum involving Euler numbers. We give two proofs of the formula. The first uses a system of differential equations. The second proof derives the generating function directly from general permutation enumeration techniques, using noncommutative symmetric functions. The generating function is an "alternating" analogue of David and Barton's generating function for permutations with no increasing runs of length 3 or more. Our general results give further alternating analogues of permutation enumeration formulas, including results of Chebikin and Remmel.

math.CO↗

arXiv2013

Shattering Thresholds for Random Systems of Sets, Words, and Permutations

This paper considers a problem that relates to the theories of covering arrays, permutation patterns, Vapnik-Chervonenkis (VC) classes, and probability thresholds. Specifically, we want to find the number of subsets of [n]:={1,2,....,n} we need to randomly select, in a certain probability space, so as to respectively "shatter" all t-subsets of [n]. Moving from subsets to words, we ask for the number of n-letter words on a q-letter alphabet that are needed to shatter all t-subwords of the q^n words of length n. Finally, we explore the number of random permutations of [n] needed to shatter (specializing to t=3), all length 3 permutation patterns in specified positions. We uncover a very sharp zero-one probability threshold for the emergence of such shattering; Talagrand's isoperimetric inequality in product spaces is used as a key tool.

math.CO↗

arXiv2013

Properties of Two-Dimensional Silicon grown on Graphene Substrate

The structure and electrical properties of a two-dimensional (2D) sheet of silicon on a graphene substrate are studied using first-principles calculations. A new corrugated rectangular structure of silicon is proposed to be the most energetically favorable structure. The shifting of the Fermi energy level indicates self-doping. Calculation of electron density shows a weak coupling between the silicon layer and graphene substrate. The 2D silicon sheet turns to be metallic and has a much higher value of transmission efficiency (TE) than the underlying graphene substrate.

cond-mat.mes-hall↗

arXiv2013

Logarithmic Representability of Integers as k-Sums

A set A=A_{k,n} in [n]\cup{0} is said to be an additive k-basis if each element in {0,1,...,kn} can be written as a k-sum of elements of A in at least one way. Seeking multiple representations as k-sums, and given any function phi(n), with lim(phi(n))=infinity, we say that A is a truncated phi(n)-representative k-basis for [n] if for each j in [alpha n, (k-alpha)n] the number of ways that j can be represented as a k-sum of elements of A_{k,n} is Theta(phi(n)). In this paper, we follow tradition and focus on the case phi(n)=log n, and show that a randomly selected set in an appropriate probability space is a truncated log-representative basis with probability that tends to one as n tends to infinity. This result is a finite version of a result proved by Erdos (1956) and extended by Erdos and Tetali (1990).

math.PR↗