arXiv subjects

Xiaowei Yu

Publications and source records attributed to Xiaowei Yu.

45 records · Page 3Linked to original sources

arXiv2022

Disentangling Spatial-Temporal Functional Brain Networks via Twin-Transformers

How to identify and characterize functional brain networks (BN) is fundamental to gain system-level insights into the mechanisms of brain organizational architecture. Current functional magnetic resonance (fMRI) analysis highly relies on prior knowledge of specific patterns in either spatial (e.g., resting-state network) or temporal (e.g., task stimulus) domain. In addition, most approaches aim to find group-wise common functional networks, individual-specific functional networks have been rarely studied. In this work, we propose a novel Twin-Transformers framework to simultaneously infer common and individual functional networks in both spatial and temporal space, in a self-supervised manner. The first transformer takes space-divided information as input and generates spatial features, while the second transformer takes time-related information as input and outputs temporal features. The spatial and temporal features are further separated into common and individual ones via interactions (weights sharing) and constraints between the two transformers. We applied our TwinTransformers to Human Connectome Project (HCP) motor task-fMRI dataset and identified multiple common brain networks, including both task-related and resting-state networks (e.g., default mode network). Interestingly, we also successfully recovered a set of individual-specific networks that are not related to task stimulus and only exist at the individual level.

q-bio.NC↗

arXiv2022

Representing Brain Anatomical Regularity and Variability by Few-Shot Embedding

Effective representation of brain anatomical architecture is fundamental in understanding brain regularity and variability. Despite numerous efforts, it is still difficult to infer reliable anatomical correspondence at finer scale, given the tremendous individual variability in cortical folding patterns. It is even more challenging to disentangle common and individual patterns when comparing brains at different neuro-developmental stages. In this work, we developed a novel learning-based few-shot embedding framework to encode the cortical folding patterns into a latent space represented by a group of anatomically meaningful embedding vectors. Specifically, we adopted 3-hinge (3HG) network as the substrate and designed an autoencoder-based embedding framework to learn a common embedding vector for each 3HG's multi-hop feature: each 3HG can be represented as a combination of these feature embeddings via a set of individual specific coefficients to characterize individualized anatomical information. That is, the regularity of folding patterns is encoded into the embeddings, while the individual variations are preserved by the multi=hop combination coefficients. To effectively learn the embeddings for the population with very limited samples, few-shot learning was adopted. We applied our method on adult HCP and pediatric datasets with 1,000+ brains (from 34 gestational weeks to young adult). Our experimental results show that: 1) the learned embedding vectors can quantitatively encode the commonality and individuality of cortical folding patterns; 2) with the embeddings we can robustly infer the complicated many-to-many anatomical correspondences among different brains and 3) our model can be successfully transferred to new populations with very limited training samples.

q-bio.NC↗

arXiv2021

Antimagic Orientation of Forests

An antimagic labeling of a digraph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,2,\cdots,m\}$ such that all $n$ oriented vertex-sums are pairwise distinct, where the oriented vertex-sum of a vertex is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. A graph $G$ admits an antimagic orientation if $G$ has an orientation $D$ such that $D$ has an antimagic labeling. Hefetz, M{ü}tze and Schwartz conjectured every connected graph admits an antimagic orientation. In this paper, we support this conjecture by proving that any forest obtained from a given forest with at most one isolated vertex by subdividing each edge at least once admits an antimagic orientation.

math.CO↗

arXiv2021

List star edge coloring of generalized Halin graphs

A star $k$-edge coloring is a proper edge coloring such that there are no bichromatic paths or cycles of length four. The smallest integer $k$ such that $G$ admits a star $k$-edge coloring is the star chromatic index of $G$. Deng \etal \cite{MR2933839}, and Bezegov{á} \etal \cite{MR3431294} independently proved that the star chromatic index of a tree is at most $\lfloor \frac{3Δ}{2} \rfloor$, and the bound is sharp. Han \etal \cite{MR3924408} strengthened the result to list version of star chromatic index, and proved that $\lfloor \frac{3Δ}{2} \rfloor$ is also the sharp upper bound for the list star chromatic index of trees. A generalized Halin graph is a plane graph that consists of a plane embedding of a tree $T$ with $Δ(T) \geq 3$, and a cycle $C$ connecting all the leaves of the tree such that $C$ is the boundary of the exterior face. In this paper, we prove that if $H := T \cup C$ is a generalized Halin graph with $|C| \neq 5$, then its list star chromatic index is at most \[ \max\left\{\left\lfloor\frac{θ(T) + Δ(T)}{2}\right\rfloor, 2 \left\lfloor\frac{Δ(T)}{2}\right\rfloor + 7\right\}, \] where $θ(T) = \max_{xy \in E(T)}\{d_{T}(x) + d_{T}(y)\}$. As a consequence, if $H$ is a (generalized) Halin graph with maximum degree $Δ\geq 13$, then the list star chromatic index is at most $\lfloor \frac{3Δ}{2} \rfloor$. Moreover, the upper bound for the list star chromatic index is sharp.

math.CO↗

arXiv2021

Representative Functional Connectivity Learning for Multiple Clinical groups in Alzheimer's Disease

Mild cognitive impairment (MCI) is a high-risk dementia condition which progresses to probable Alzheimer's disease (AD) at approximately 10% to 15% per year. Characterization of group-level differences between two subtypes of MCI - stable MCI (sMCI) and progressive MCI (pMCI) is the key step to understand the mechanisms of MCI progression and enable possible delay of transition from MCI to AD. Functional connectivity (FC) is considered as a promising way to study MCI progression since which may show alterations even in preclinical stages and provide substrates for AD progression. However, the representative FC patterns during AD development for different clinical groups, especially for sMCI and pMCI, have been understudied. In this work, we integrated autoencoder and multi-class classification into a single deep model and successfully learned a set of clinical group related feature vectors. Specifically, we trained two non-linear mappings which realized the mutual transformations between original FC space and the feature space. By mapping the learned clinical group related feature vectors to the original FC space, representative FCs were constructed for each group. Moreover, based on these feature vectors, our model achieves a high classification accuracy - 68% for multi-class classification (NC vs SMC vs sMCI vs pMCI vs AD).

q-bio.NC↗

arXiv2021

Improved bounds on the Ramsey number of fans

For a given graph $H$, the Ramsey number $r(H)$ is the minimum $N$ such that any 2-edge-coloring of the complete graph $K_N$ yields a monochromatic copy of $H$. Given a positive integer $n$, a \emph{fan }$F_n$ is a graph formed by $n$ triangles that share one common vertex. We show that ${9n}/{2}-5\le r(F_n)\le {11n}/{2} + 6$ for any $n$. This improves previous best bounds $r(F_n) \le 6n$ of Lin and Li and $r(F_n) \ge 4n+2$ of Zhang, Broersma and Chen.

math.CO↗

arXiv2017

Planar graphs without 4-cycles adjacent to triangles are DP-4-colorable

DP-coloring (also known as correspondence coloring) of a simple graph is a generalization of list coloring. It is known that planar graphs without 4-cycles adjacent to triangles are 4-choosable, and planar graphs without 4-cycles are DP-4-colorable. In this paper, we show that planar graphs without 4-cycles adjacent to triangles are DP-4-colorable, which is an extension of the two results above.

math.CO↗

arXiv2017

Antimagic orientation of biregular bipartite graphs

An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. An undirected graph $G$ is said to have an antimagic orientation if $G$ has an orientation which admits an antimagic labeling. Hefetz, M{ü}tze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation. In this paper, we support this conjecture by proving that every biregular bipartite graph admits an antimagic orientation.

math.CO↗

arXiv2004

Maxwell Equation for the Coupled Spin-Charge Wave Propagation

We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the 2+1 dimensional Maxwell equation. This analogy leads to a remarkable prediction that a density packet can spontaneously split into two counter propagation packets, each carrying the opposite spins. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse "photon". We propose both optical and purely electronic experiments to detect this effect.

cond-mat.mtrl-sci↗