arXiv subjects

Zemin Jin

Publications and source records attributed to Zemin Jin.

10 recordsLinked to original sources

arXiv2026

Robust Rank Aggregation for Multimodal Speech-Based Alzheimer's Disease Detection

Speech-based Alzheimer's disease (AD) detection has recently benefited from multimodal foundation-model representations that integrate complementary acoustic and linguistic information. However, conventional probability averaging over these complementary classifiers is unreliable, because their posterior probabilities exhibit mismatched scales: identical values may reflect different confidence levels across models. We propose a robust rank aggregation framework that aggregates normalized prediction ranks instead of posterior probabilities. Each subject is scored by its percentile within a fixed training-cohort distribution of out-of-fold predictions; since rank ordering is invariant to monotonic transformations, this avoids probability-scale mismatch while preserving classifier confidence ordering. A confidence-gated Random Forest further corrects residual errors using clinically interpretable linguistic features, overriding the rank prediction only when the two disagree and the RF is highly confident, without additional deep model training or explicit posterior-probability calibration. On ADReSS2020 and ADReSSo2021, the method achieves accuracies of 95.83% and 90.14%, respectively, comparing favorably with previously reported results.

cs.SD↗

arXiv2025

On the Anti-Ramsey Number Under Edge Deletion

According to a study by Erdős et al. in 1975, the anti-Ramsey number of a graph $G$, denoted as $AR(n, G)$, is defined as the maximum number of colors that can be used in an edge-coloring of the complete graph $K_n$ without creating a rainbow copy of $G$. In this paper, we investigate the anti-Ramsey number under edge deletion and demonstrate that both decreasing and unchanging are possible outcomes. For three non-negative integers $k$, $t$, and $n$, let $G = kP_4 \cup tP_2$. Let $E'$ be a subset of the edge set $E(G)$ such that every endpoint of these edges has a degree of two in $G$. We prove that if one of the conditions (i) $t \geq k + 1 \geq 2$ and $n \geq 8k + 2t - 4$; (ii) $k, t \geq 1$ and $n = 4k + 2t$; (iii) $k = 1$, $t \geq 1$, and $n \geq 2t + 4$, occurs then the behavior of the anti-Ramsey number remains consistent when the edges in $E'$ are removed from $G$, i.e., $AR(n, G) = AR(n, G - E')$. However, this is not the case when $k \geq 2$, $t = 0$, and $n=4k$. As a result, we calculate $AR(kP_4 \cup tP_2)$ for the cases: (i) $t \geq k + 1 \geq 2$ and $n \geq 8k + 2t - 4$; (ii) $k, t \geq 1$ and $n = 4k + 2t$; (iii) $k = 1$, $t \geq 0$, and $n \geq 2t + 4$; (iv) $k \geq 1$, $t = 0$, and $n = 4k$.

math.CO↗

arXiv2025

On Neutral Edge Sets in Anti-Ramsey Numbers

The anti-Ramsey number of a graph $G$, introduced by Erdős et al.\ in 1975, is the maximum number of colors in an edge-coloring of the complete graph $K_n$ that avoids a rainbow copy of $G$. We call a subset of edges of $G$ \emph{neutral} for the anti-Ramsey number if removing them does not alter the anti-Ramsey number of $G$. Let $k$, $t$, and $n$ be positive integers, and consider $G = kP_4 \cup tP_2$. Assume $S \subseteq E(G)$ consists of internal edges of the $P_4$ components in $G$. It is known that $S$ is neutral when $t \geq k+1 \geq 2$ and $n \geq 8k + 2t - 4$. In this paper, we identify values of $k \geq t$ such that, for all $n$ in a specific subinterval of $[8k + 2t - 4, \infty)$, $S$ remains neutral. Since the anti-Ramsey numbers for matchings are well understood, our results provide a complete determination of the anti-Ramsey number for $G$ under these conditions. Based on our findings, we conjecture that this neutrality may extend to the general case $t \geq 1$, $k \geq 1$, and $n \geq 4k + 2t$, but not when $t = 0$, $k \geq 2$, and $n \geq 4k$.

math.CO↗

arXiv2024

Kings and Kernels in Semicomplete Compositions

Let $k$ be an integer with $k\geq 2$. A $k$-king in a digraph $D$ is a vertex which can reach every other vertex by a directed path of length at most $k$ and a non-king is a vertex which is not a 3-king. A subset $K$ is $k$-independent if for every pair of vertices $x,y \in K$, we have $d_D(x, y), d_D(y, x)\geq k$; it is $\ell$-absorbent if for every $x\in V(D)\setminus K$ there exists $y\in K$ such that $d_D(x, y)\leq \ell$. A $k$-kernel of $D$ is a $k$-independent and $(k-1)$-absorbent subset of $V(D)$. A kernel is a 2-kernel. A set $K\subseteq V(D)$ is a quasi-kernel of $D$ if it is independent, and for every vertex $x\in V(D)\setminus K$, there exists $y\in K$ such that $d_D(x, y)\leq 2$. The problem {\sc $k$-Kernel} is determining whether a given digraph has a $k$-kernel. Let $Q=T[H_1, \dots, H_t]$ be the composition of $T$ and $H_i$ ($1\leq i\leq t, t\ge 2$), where $T$ is a digraph with $t$ vertices, and $H_1, \dots, H_t$ are pairwise disjoint digraphs. The composition $Q=T[H_1, \dots, H_t]$ is a semicomplete composition if $T$ is semicomplete. In this paper, we study kings and kernels in semicomplete compositions. For the topic of kings, we characterize digraph compositions with a $k$-king and digraph compositions all of whose vertices are $k$-kings, respectively. We also discuss the existence of 3-kings, and study the minimum number of 4-kings in a strong semicomplete composition. For the topic of kernels, we first study the existence of a pair of disjoint quasi-kernels in semicomplete compositions. We then deduce that the problem {\sc $k$-Kernel} restricted to strong semicomplete compositions is NP-complete when $k\in \{2,3\}$, and is polynomial-time solvable when $k\geq 4$. We also prove that when $k$ is divisible by 2 or 3, the problem {\sc $k$-Kernel} restricted to non-strong semicomplete compositions is NP-complete.

math.CO↗

arXiv2020

The normalized Laplacian and related indexes of graphs with edges blew up by cliques

In this paper, we introduce the clique-blew up graph $CL(G)$ of a given graph $G$, which is obtained from $G$ by replacing each edge of $G$ with a complete graph $K_n$. We characterize all the normalized Laplacian spectrum of the grpah $CL(G)$ in term of the given graph $G$. Based on the spectrum obtained, the formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of spanning trees of $CL(G)$ are derived well. Finally, the spectrum and indexes of the clique-blew up iterative graphs are present.

math.CO↗

arXiv2016

On $(2k+1, 2k+3)$-core partitions with distinct parts

In this paper, we are mainly concerned with the enumeration of $(2k+1, 2k+3)$-core partitions with distinct parts. We derive the number and the largest size of such partitions, confirming two conjectures posed by Straub.

math.CO↗

arXiv2007

Heterochromatic tree partition number of a complete multipartite graph

This paper has been withdrawn by the author(s), due an error in the proof.

math.CO↗

arXiv2007

Partitioning complete graphs by heterochromatic trees

A {\it heterochromatic tree} is an edge-colored tree in which any two edges have different colors. The {\it heterochromatic tree partition number} of an $r$-edge-colored graph $G$, denoted by $t_r(G)$, is the minimum positive integer $p$ such that whenever the edges of the graph $G$ are colored with $r$ colors, the vertices of $G$ can be covered by at most $p$ vertex-disjoint heterochromatic trees. In this paper we determine the heterochromatic tree partition number of an $r$-edge-colored complete graph.

math.CO↗

arXiv2006

Bipartite Rainbow Numbers of Matchings

Given two graphs $G$ and $H$, let $f(G,H)$ denote the maximum number $c$ for which there is a way to color the edges of $G$ with $c$ colors such that every subgraph $H$ of $G$ has at least two edges of the same color. Equivalently, any edge-coloring of $G$ with at least $rb(G,H)=f(G,H)+1$ colors contains a rainbow copy of $H$, where a rainbow subgraph of an edge-colored graph is such that no two edges of it have the same color. The number $rb(G,H)$ is called the {\it rainbow number of $H$ with respect to $G$}, and simply called the {\it bipartite rainbow number of $H$} if $G$ is the complete bipartite graph $K_{m,n}$. Erdős, Simonovits and Sós showed that $rb(K_n,K_3)=n$. In 2004, Schiermeyer determined the rainbow numbers $rb(K_n,K_k)$ for all $n\geq k\geq 4$, and the rainbow numbers $rb(K_n,kK_2)$ for all $k\geq 2$ and $n\geq 3k+3$. In this paper we will determine the rainbow numbers $rb(K_{m,n},kK_2)$ for all $k\geq 1$.

math.CO↗

arXiv2006

Generalization of matching extensions in graphs (II)

Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and $d$ be non-negative integers such that $n+2k+d\leq |V(G)|-2$ and $|V(G)|-n-d$ is even. If when deleting any $n$ vertices from $G$, the remaining subgraph $H$ of $G$ contains a $k$-matching and each such $k$- matching can be extended to a defect-$d$ matching in $H$, then $G$ is called an $(n,k,d)$-graph. In \cite{Liu}, the recursive relations for distinct parameters $n, k$ and $d$ were presented and the impact of adding or deleting an edge also was discussed for the case $d = 0$. In this paper, we continue the study begun in \cite{Liu} and obtain new recursive results for $(n,k,d)$-graphs in the general case $d \geq0$.

math.CO↗