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Jian Shen

Publications and source records attributed to Jian Shen.

85 records · Page 5Linked to original sources
arXiv2012

Growth diagram and magnetic properties of hexagonal LuFe$_2$O$_4$ thin films

A growth diagram of Lu-Fe-O compounds on MgO (111) substrates using pulsed laser deposition is constructed based on extensive growth experiments. The LuFe$_2$O$_4$ phase can only be grown in a small range of temperature and O$_2$ pressure conditions. An understanding of the growth mechanism of Lu-Fe-O compound films is offered in terms of the thermochemistry at the surface. Superparamagnetism is observed in LuFe$_2$O$_4$ film and is explained in terms of the effect of the impurity h-LuFeO$_3$ phase and structural defects .

cond-mat.mtrl-sci↗
arXiv2011

Acyclic Subgraphs in $k$-Majority Tournaments

A $k$-majority digraph is a directed graph created by combining $k$ individual rankings on the same ground set to form a consensus where edges point in the direction indicated by a strict majority of the rankings. The $k$-majority digraph is used to model voting scenarios, where the vertices correspond to options ranked by $k$ voters. When $k$ is odd, the resulting digraph is always a tournament, called $k$-majority tournament. Let $f_k(n)$ be the minimum, over all $k$-majority tournaments with $n$ vertices, of the maximum order of an induced transitive sub-tournament. Recently, Milans, Schreiber, and West proved that $\sqrt n \le f_3(n) \le 2 \sqrt n +1 $. In this paper, we improve the upper bound of $f_3(n)$ by showing that $f_3(n) < \sqrt {2n} +\frac 12 $.

math.CO↗
arXiv2011

Three layer $Q_2$-free families in the Boolean lattice

We prove that the largest $Q_2$-free family of subsets of $[n]$ which contains sets of at most three different sizes has at most $(3 + 2\sqrt {3})N/3 + o(N) \approx 2.1547N + o(N)$ members, where $N = {n \choose {\lfloor n/2 \rfloor}}$. This improves an earlier bound of $2.207N + o(N)$ by Axenovich, Manske, and Martin.

math.CO↗
arXiv2011

Thermodynamics of Information Retrieval

In this work, we suggest a parameterized statistical model (the gamma distribution) for the frequency of word occurrences in long strings of English text and use this model to build a corresponding thermodynamic picture by constructing the partition function. We then use our partition function to compute thermodynamic quantities such as the free energy and the specific heat. In this approach, the parameters of the word frequency model vary from word to word so that each word has a different corresponding thermodynamics and we suggest that differences in the specific heat reflect differences in how the words are used in language, differentiating keywords from common and function words. Finally, we apply our thermodynamic picture to the problem of retrieval of texts based on keywords and suggest some advantages over traditional information retrieval methods.

cs.IT↗
arXiv2011

Bistability in a differential equation model of oyster reef height and sediment accumulation

Native oyster populations in Chesapeake Bay have been the focus of three decades of restoration attempts, which have generally failed to rebuild the populations and oyster reef structure. Recent restoration successes and field experiments suggest that high-relief reefs offset heavy sedimentation and promote oyster survival, disease resistance and growth, in contrast to low-relief reefs which degrade in just a few years. These findings suggest the existence of alternative stable states in oyster reef populations. We developed a mathematical model consisting of three differential equations that represent volumes of live oysters, dead oyster shells (= accreting reef), and sediment. Bifurcation analysis and numerical simulations demonstrated that multiple nonnegative equilibria can exist for live oyster, accreting reef and sediment volume at an ecologically reasonable range of parameter values; the initial height of oyster reefs determined which equilibrium was reached. This investigation thus provides a conceptual framework for alternative stable states in native oyster populations, and can be used as a tool to improve the likelihood of success in restoration efforts.

q-bio.PE↗
arXiv2009

On the Spectrum of Middle-Cubes

A middle-cube is an induced subgraph consisting of nodes at the middle two layers of a hypercube. The middle-cubes are related to the well-known Revolving Door (Middle Levels) conjecture. We study the middle-cube graph by completely characterizing its spectrum. Specifically, we first present a simple proof of its spectrum utilizing the fact that the graph is related to Johnson graphs which are distance-regular graphs and whose eigenvalues can be computed using the association schemes. We then give a second proof from a pure graph theory point of view without using its distance regular property and the technique of association schemes.

math.CO↗
arXiv2009

A bound on the scrambling index of a primitive matrix using Boolean rank

The scrambling index of an $n\times n$ primitive matrix $A$ is the smallest positive integer $k$ such that $A^k(A^{t})^k=J$, where $A^t$ denotes the transpose of $A$ and $J$ denotes the $n\times n$ all ones matrix. For an $m\times n$ Boolean matrix $M$, its {\it Boolean rank} $b(M)$ is the smallest positive integer $b$ such that $M=AB$ for some $m \times b$ Boolean matrix $A$ and $b\times n$ Boolean matrix $B$. In this paper, we give an upper bound on the scrambling index of an $n\times n$ primitive matrix $M$ in terms of its Boolean rank $b(M)$. Furthermore we characterize all primitive matrices that achieve the upper bound.

math.CO↗
arXiv2009

On the Borel-Cantelli Lemma and its Generalization

Let $\{A_n\}_{n=1}^{\infty}$ be a sequence of events on a probability space $(Ω,\mathcal{F},\mathbf{P})$. We show that if $\lim_{m\to\infty}\sum_{n=1}^{m}w_n\mathbf{P}(A_n)=\infty$ where each $w_n\in\mathbb{R}$, then \[{\mathbf{P}}(\limsup A_n)\geq\limsup_{n\to\infty} \frac{\displaystyle\big(\sum_{k=1}^n{w_k\mathbf{P}}(A_k)\big)^2}{\displaystyle\sum_{i=1}^n\sum_{j=1}^nw_iw_j{\mathbf{P}}(A_i\cap A_j)}.\]

math.PR↗
arXiv2009

On the Chudnovsky-Seymour-Sullivan Conjecture on Cycles in Triangle-free Digraphs

For a simple digraph $G$ without directed triangles or digons, let $β(G)$ be the size of the smallest subset $X \subseteq E(G)$ such that $G\setminus X$ has no directed cycles, and let $γ(G)$ be the number of unordered pairs of nonadjacent vertices in $G$. In 2008, Chudnovsky, Seymour, and Sullivan showed that $β(G) \le γ(G)$, and conjectured that $β(G) \le γ(G)/2$. Recently, Dunkum, Hamburger, and Pór proved that $β(G) \le 0.88 γ(G)$. In this note, we prove that $β(G) \le 0.8616 γ(G)$.

math.CO↗
arXiv2009

The kth Upper Bases of Primitive Non-powerful Signed Digraphs

In this paper, we study the kth upper bases of primitive non-powerful signed digraphs. A bound on the kth upper bases of all primitive non-powerful signed digraphs is obtained, and the equality case of the bound is characterized. We also show that there exists "gap" in the kth upper base set of primitive non-powerful signed digraphs.

math.CO↗
arXiv2009

Analyzing the Accuracy of the Fitch Method for Reconstructing Ancestral States on Ultrametric Phylogenies

Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we analyze the convergence of the accuracy of reconstructing the root state in a complete binary tree of $2^n$ as $n$ goes to infinity and also give a lower bound on the accuracy of reconstructing the root state in an ultrametric tree.

q-bio.PE↗
arXiv2002

Self-assembly of Nanometer-scale Magnetic Dots with Narrow Size Distributions on an Insulating Substrate

The self-assembly of iron dots on the insulating surface of NaCl(001) is investigated experimentally and theoretically. Under proper growth conditions, nanometer-scale magnetic iron dots with remarkably narrow size distributions can be achieved in the absence of a wetting layer Furthermore, both the vertical and lateral sizes of the dots can be tuned with the iron dosage without introducing apparent size broadening, even though the clustering is clearly in the strong coarsening regime. These observations are interpreted using a phenomenological mean-field theory, in which a coverage-dependent optimal dot size is selected by strain-mediated dot-dot interactions.

cond-mat.mtrl-sci↗