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Xiao-Song Yang

Publications and source records attributed to Xiao-Song Yang.

At least 19 recordsLinked to original sources
arXiv2026

Analysis of the two-body strong decays of the hidden-charm pentaquark states in QCD sum rules

In the present work, we study the two-body strong decays of the hidden-charm pentaquark states with the quark content $uudc\bar c$ and the quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ in the framework of the three-point QCD sum rules. The initial pentaquark states are described by four local diquark-diquark-antiquark type interpolating currents with definite isospin. We construct the three-point correlation functions for the decay channels $P_c\to \eta_c p$, $J/\psi p$, $\Lambda_c\bar D$, $\Lambda_c\bar D^{*}$ and $\Sigma_c\bar D$, and derive the corresponding QCD sum rules for the strong coupling constants. At the hadron side, the correlation functions are expressed in terms of the hadron masses, pole residues, decay constants and strong coupling constants. At the QCD side, they are calculated by carrying out the operator product expansion with the full quark propagators, where the vacuum condensates up to dimension 10 are taken into account. After matching the two representations and performing the double Borel transformations, we extract the strong coupling constants from the selected Lorentz structures. With the obtained coupling constants, we evaluate the partial decay widths and discuss the possible assignments of the corresponding pentaquark states. The numerical results indicate that two of the compact hidden-charm pentaquark states can be related to the $P_c(4312)$ and $P_c(4457)$, respectively, while the other two lower-mass states may be regarded as possible hidden-charm pentaquark candidates to be searched for in future experiments. The present results may be useful for identifying the hidden-charm pentaquark states in future experiments.

hep-ph↗
arXiv2026

Sharp regularity for the periodic Camassa--Holm equation in critical Triebel--Lizorkin spaces

We establish a sharp well-posedness and norm inflation theory for the Camassa--Holm equation in critical Triebel--Lizorkin $F^{1+1/p}_{p,q}(\mathbb{T})$. At the endpoint $p=1$, we prove local Hadamard well-posedness for $1\le q<\infty$. In contrast, we prove norm inflation for $1<p<\infty$ and $1\le q\le\infty$. We also complement the local well-posedness in the critical Besov spaces and higher-regularity Triebel--Lizorkin spaces. The positive results rely on a Lipschitz stability theorem for the periodic Green operator under degree-one Lagrangian flows. The negative result is based on a nested smooth atomic construction on the torus, adapted from its real-line counterpart.

math.AP↗
arXiv2026

On the mathematics table problem

In this paper we study the mathematical table problem from a geometric-topological point of view. We prove a zero-existence theorem on a cylinder, which gives a new proof of Fenn's square-table theorem under Fenn's boundary conditions, and establish a variant under different boundary conditions. We also prove that every square table admits a horizontal placement on saddle surfaces. Finally, we show that almost every level set of a smooth Fenn graph contains a rectangle similar to any prescribed rectangle and an orientation-preserving similar copy of every prescribed cyclic quadrilateral.

math.GT↗
arXiv2026

Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

In this paper, we study the universal approximation property of residual neural networks. For input and output dimensions $d_x$ and $d_y$, and LeakyReLU, ReLU, ReLU-like activation functions, the upper and lower bounds of the minimum block width are established. To achieve $L^p$ approximation $(1\leq p <+\infty)$ on any compact set, we show that the exact minimum block width is $\max\{d_x,d_y\}$ when each residual branch has inner width 1. Furthermore, we show that residual neural networks with block width $\min\{d_x+d_y, \max\{2d_x+1,d_y\}\}$ can achieve uniform approximation on any compact set under the constraint that each residual branch has inner width 1. Besides, for any activation function family, we prove that there exist functions that cannot be approximated by residual neural networks with block width less than $\max\{d_x, d_y\}$, both in the $L^p$ sense and the uniform sense, regardless of inner width. Consequently, for LeakyReLU, ReLU, ReLU-like activation functions and $d_y\geq 2d_x+1$, the exact minimum block width for uniform approximation is $d_y$ when each residual branch has inner width 1.

cs.LG↗
arXiv2026

Table Problem Revisited

We revisit Fenn's table theorem from a differential-topological point of view. We prove a zero-existence theorem on a cylinder, which gives a short proof of the horizontal square-table theorem under Fenn's boundary conditions, and We establish a theorem under more general boundary conditions. We also discuss square tables on saddle surfaces and conjecture that every sufficiently small square table can be placed horizontally on a saddle surface. We further conjecture that any prescribed rectangular table can be placed horizontally on a Fenn graph.

math.GT↗
arXiv2026

Topological Horseshoe Induced by Periodic Switching Between Non-Isochronous Planar Systems

We establish a criterion for the existence of a topological horseshoe in a class of planar systems generated by periodic switching between two subsystems, each admitting a family of closed orbits, where the mechanism for chaos arises from the non-isochronicity of each subsystem. Exploiting the relationship between the period function of a Hamiltonian system and the rate of change of the area enclosed by its periodic orbits, we derive a criterion, which can be checked by numerical methods, for the existence of horseshoe in planar systems obtained by switching between two Hamiltonian subsystems. Furthermore, by invoking monotonicity results for the period function in Newtonian Hamiltonian systems, we obtain an explicit and computable criterion that guarantees chaotic dynamics in planar systems generated by switching between two such subsystems.

math.DS↗
arXiv2026

Relocation of compact sets in $\mathbb{R}^n$ by diffeomorphisms and linear separability of datasets in $\mathbb{R}^n$

Relocation of compact sets in an $n$-dimensional manifold by self-diffeomorphism is of its own interest as well as significant potential applications to data classification in data science. This paper presents a theory for relocating a finite number of compact sets in $\mathbb{R}^n$ to be relocated to arbitrary target domains in $\mathbb{R}^n$ by diffeomorphisms of $\mathbb{R}^n$. Furthermore, we prove that for any such collection, there exists a differentiable embedding into $\mathbb{R}^{n+1}$ such that their images become linearly separable. As applications of the established theory, we show that a finite number of compact datasets in $\mathbb{R}^n$ can be made linearly separable by width-$n$ deep neural networks (DNNs) with Leaky-ReLU, ELU, or SELU activation functions, under a mild condition. In addition, we show that any finite number of mutually disjoint compact datasets in $\mathbb{R}^n$ can be made linearly separable in $\mathbb{R}^{n+1}$ by a width-$(n+1)$ DNN.

cs.LG↗
arXiv2026

Discrete homotopy and homology theories for finite posets

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is related to the discrete homotopy theory through a discrete analogue of the Hurewicz map.

math.CO↗
arXiv2025

Variation of entropy in the Duffing system with the amplitude of the external force

In this paper, we revisit the well-known perturbed Duffing system and investigate its chaotic dynamics by means of numerical Runge--Kutta method based on topological horseshoe theory. Precisely, we investigate chaos through the topological horseshoes associated with the first, second, and third return maps, obtained by varying the amplitude of an external force term while keeping all other parameters fixed. Our new finding demonstrates that, when the force amplitude exceeds a certain value, the topological (Smale) horseshoe degenerates into a pseudo-horseshoe, while chaotic invariant set persists. This phenomenon indicates that the lower bound of the topological entropy decreases as the force amplitude increases, thereby enriching the dynamics in the perturbed Duffing system. Furthermore, we identify a critical value of the force amplitude governing the attractivity of the chaotic invariant set. For amplitudes slightly below this value, the basin of attraction of the chaotic invariant set progressively shrinks as the amplitude increases. In contrast, for larger amplitudes, both Lyapunov exponents become negative while the topological horseshoe persists, suggesting that the chaotic invariant set loses attractivity as the amplitude grows.

nlin.CD↗
arXiv2025

Minimum Width of Deep Narrow Networks for Universal Approximation

Determining the minimum width of fully connected neural networks has become a fundamental problem in recent theoretical studies of deep neural networks. In this paper, we study the lower bounds and upper bounds of the minimum width required for fully connected neural networks in order to have universal approximation capability, which is important in network design and training. We show that $w_{min}\leq\max(2d_x+1, d_y)$ also holds true for networks with ELU, SELU activation functions, and the upper bound of this inequality is attained when $d_y=2d_x$, where $d_x$, $d_y$ denote the input and output dimensions, respectively. Besides, we show that $d_x+1\leq w_{min}\leq d_x+d_y$ for networks with LeakyReLU, ELU, CELU, SELU, Softplus activation functions, by proving that ReLU activation function can be approximated by these activation functions. In addition, in the case that the activation function is injective or can be uniformly approximated by a sequence of injective functions (e.g., ReLU), we present a new proof of the inequality $w_{min}\ge d_y+\mathbf{1}_{d_x<d_y\leq2d_x}$ by constructing a more intuitive example via a new geometric approach based on Poincaré-Miranda Theorem.

cs.LG↗
arXiv2025

Analysis of the strong decays of the $Y(4660)$ in tetraquark scenario via the QCD sum rules

Motivated by the enigmatic vector charmonium-like states, we investigate the strong decay behaviors of four kinds of vector tetraquark states, which are possible candidates for the $Y(4660)$, within the framework of three-point QCD sum rules based on rigorous quark-hadron duality. We take into account the vacuum condensates up to dimension 5 on the QCD side, and obtain the hadronic coupling constants therefore the partial decay widths of those states. The predicted total width $61.5\pm7.3\,\rm{MeV}$ is in excellent agreement with the experimental data for the $Y(4660)$, which supports its interpretation as a $[sc][\bar{s}\bar{c}]$ tetraquark state with the $J^{PC}=1^{--}$.

hep-ph↗
arXiv2025

Dimensionality reduction and width of deep neural networks based on topological degree theory

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the established theory, we provide some fascinating insights into classification and approximation problems in deep learning theory in the setting of deep neural networks.

math.GN↗
arXiv2025

On the inverse limits of finite posets

In this paper, we show that any finite simplicial complex is homeomorphic to the inverse limit of a sequence of finite posets, which is an extension of Claders result.

math.CO↗
arXiv2025

An RRT* algorithm based on Riemannian metric model for optimal path planning

This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based on constructing a new Riemannian metric on a two-dimensional projection plane, which is induced by the high-dimensional Euclidean metric on two-dimensional smooth submanifold and reflects the environmental information of the robot. The optimal path planning problem in high-dimensional space is therefore transformed into a geometric problem on the two-dimensional plane with new Riemannian metric. Based on the new Riemannian metric, we proposed an incremental algorithm RRT*-R on the projection plane. The experimental results show that the proposed algorithm is suitable for scenarios with uneven fields in multiple dimensions. The proposed algorithm can help the robot to effectively avoid areas with drastic changes in height, ground resistance and other environmental factors. More importantly, the RRT*-R algorithm shows better smoothness and optimization properties compared with the original RRT* algorithm using Euclidean distance in high-dimensional workspace. The length of the entire path by RRT*-R is a good approximation of the theoretical minimum geodesic distance on projection plane.

cs.RO↗
arXiv2025

RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric

The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous studies have focused on the Dijkstra algorithm due to its potential application. However, its application in surface path planning for mobile robots remains largely unexplored. In this letter, a surface optimal path planning algorithm called RM-Dijkstra is proposed, which is based on Riemannian metric model. By constructing a new Riemannian metric on the 2D projection plane, the surface optimal path planning problem is therefore transformed into a geometric problem on the 2D plane with new Riemannian metric. Induced by the standard Euclidean metric on surface, the constructed new metric reflects environmental information of the robot and ensures that the projection map is an isometric immersion. By conducting a series of simulation tests, the experimental results demonstrate that the RM-Dijkstra algorithm not only effectively solves the optimal path planning problem on surfaces, but also outperforms traditional path planning algorithms in terms of path accuracy and smoothness, particularly in complex scenarios.

cs.RO↗
arXiv2025

Two-body strong decays of the hidden-charm tetraquark molecular states via the QCD sum rules

In this work, we extend our previous work on the $D^*\bar{D}^*$ molecular states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$ to investigate their two-body strong decays via the QCD sum rules based on rigorous quark-hadron duality. We obtain the partial decay widths therefore total widths of the ground states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$, which indicate that it is reasonable to assign the $X_2(4014)$ as the $D^*\bar{D}^*$ tetraquark molecular states with the $J^{PC}=2^{++}$.

hep-ph↗
arXiv2025

Reconstruction of mapping spaces by inverse limits

Extending the results of reconstruction of compact metric spaces by inverse limits, we show that if $(X, d), (Y, d)$ are compact metric spaces, then the mapping space $Y^X$ is homotopy equivalent to the inverse limit of an inverse system of finite $T_0$-spaces which depends only on the finite open covers of $X$ and $Y$. Applying our tools, we obtain that if $H$ is an isotopy of a compact metric space $(X, d)$, then $H_1H^{-1}_0$ can be approximated in terms of moves of a finite $T_0$-space.

math.CO↗