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Jin Yan

Publications and source records attributed to Jin Yan.

80 records · Page 5Linked to original sources
arXiv2020

Distinguished correlation properties of Chebyshev dynamical systems and their generalisations

We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration and study a family of shifted Chebyshev maps, presenting analytic results for two-point and higher-order correlation functions. We also review results for the eigenvalues and eigenfunctions of the Perron-Frobenius operator of N-th order Chebyshev maps and their shifted generalisations. The spectrum is degenerate for odd N. Finally, we consider coupled map lattices (CMLs) of shifted Chebyshev maps and numerically investigate zeros of the temporal and spatial nearest-neighbour correlations, which are of interest in chaotically quantized field theories.

math.DS↗
arXiv2020

On directed version of the Sauer-Spender Theorem

Let $D=(V,A)$ be a digraph of order $n$ and let $W$ be any subset of $V$. We define the minimum semi-degree of $W$ in $D$ to be $δ^0(W)=\mbox{min}\{δ^+(W),δ^-(W)\}$, where $δ^+(W)$ is the minimum out-degree of $W$ in $D$ and $δ^-(W)$ is the minimum in-degree of $W$ in $D$. Let $k$ be an integer with $k\geq 1$. In this paper, we prove that for any positive integer partition $|W|=\sum_{i=1}^{k}n_i$ with $n_i\geq 2$ for each $i$, if $δ^0(W)\geq \frac{3n-3}{4}$, then there are $k$ vertex disjoint cycles $C_1,\ldots,C_k$ in $D$ such that each $C_i$ contains exactly $n_i$ vertices of $W$. Moreover, the lower bound of $δ^0(W)$ can be improved to $\frac{n}{2}$ if $k=1$, and $\frac{n}{2}+|W|-1$ if $n\geq 2|W|$. The minimum semi-degree condition $δ^0(W)\geq \frac{3n-3}{4}$ is sharp in some sense and this result partially confirms the conjecture posed by Wang [Graphs and Combinatorics 16 (2000) 453-462]. It is also a directed version of the Sauer-Spender Theorem on vertex disjoint cycles in graphs [J. Combin. Theory B, 25 (1978) 295-302].

math.CO↗
arXiv2019

Lichiardopol's conjecture on disjoint cycles in tournaments

In 2010, N. Lichiardopol conjectured for $q \geq 3$ and $k \geq 1$ that any tournament with minimum out-degree at least $(q-1)k-1$ contains $k$ disjoint cycles of length $q$. We prove this conjecture for $q \geq 5$. Since it is already known to hold for $q\le4$, this completes the proof of the conjecture.

math.CO↗
arXiv2019

Visual Natural Language Query Auto-Completion for Estimating Instance Probabilities

We present a new task of query auto-completion for estimating instance probabilities. We complete a user query prefix conditioned upon an image. Given the complete query, we fine tune a BERT embedding for estimating probabilities of a broad set of instances. The resulting instance probabilities are used for selection while being agnostic to the segmentation or attention mechanism. Our results demonstrate that auto-completion using both language and vision performs better than using only language, and that fine tuning a BERT embedding allows to efficiently rank instances in the image. In the spirit of reproducible research we make our data, models, and code available.

cs.CV↗
arXiv2018

Nonlinear Dynamics of Coupled Axion-Josephson Junction Systems

We study the classical dynamics of an axion field (the signal) that is coupling into a Josephson junction (the detector) by means of a capacitive coupling of arbitrary size. Depending on the size of the coupling constant and the initial conditions, we find a rich phase space structure of this nonlinear problem. We present general analytic solutions of the equations of motion in the limit of small amplitudes of the angle variables, and discuss both the case of no dissipation and the case of dissipation in the system. The effect of a magnetic field is investigated as well, leading to topological phase transitions in the phase space structure.

nlin.CD↗
arXiv2018

Partitioning a graph into cycles with a specified number of chords

For a graph $G$, let $σ_{2}(G)$ be the minimum degree sum of two non-adjacent vertices in $G$. A chord of a cycle in a graph $G$ is an edge of $G$ joining two non-consecutive vertices of the cycle. In this paper, we prove the following result, which is an extension of a result of Brandt et al. (J. Graph Theory 24 (1997) 165-173) for large graphs: For positive integers $k$ and $c$, there exists an integer $f(k,c)$ such that, if $G$ is a graph of order $n \ge f(k, c)$ and $σ_{2}(G) \ge n$, then $G$ can be partitioned into $k$ vertex-disjoint cycles, each of which has at least $c$ chords.

math.CO↗
arXiv2017

The confirmation of a conjecture on disjoint cycles in a graph

In this paper, we prove the following conjecture proposed by Gould, Hirohata and Keller [Discrete Math. submitted]: Let $G$ be a graph of sufficiently large order. If $σ_t(G) \geq 2kt - t + 1$ for any two integers $k \geq 2$ and $t \geq 5$, then $G$ contains $k$ disjoint cycles.

math.CO↗