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Jin Yan

Publications and source records attributed to Jin Yan.

At least 37 records · Page 2Linked to original sources
arXiv2026

Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors

For two digraph properties $P_1$ and $P_2$, a $(P_1,P_2)$-arc-decomposition of a digraph $D$ is a partition $A(D)=A_1\mathbin{\dot\cup}A_2$ such that the spanning subdigraphs $D[A_1]$ and $D[A_2]$ have properties $P_1$ and $P_2$, respectively. For example, a (strong,strong)-arc-decomposition of a digraph $D=(V,A)$ is a partitioning $A=A_1\cup{}A_2$ of $A$ so that each of the spanning digraphs $D_i=(V,A_i)$, $i=1,2$ are strongly connected. We prove that it is NP-complete to decide whether a digraph admits an arc-decomposition with properties $(P_1,P_2)$ where $(P_1,P_2)\in \{$(is a perfect matching, having no odd directed cycle), (perfect matching, strong), (perfect matching, having an out-branching), (is a cycle factor, having no odd directed cycle)$\}$. These results settle some open problems posed by Bang-Jensen, Bessy, Gonçalves, and Picasarri-Arrieta [Theoret. Comput. Sci. 928 (2022), 167--182].

math.CO↗
arXiv2026

Efficient production of $^{229m,g}$Th via neutron capture in VUV-transparent crystals

The low-lying isomeric state of $^{229m}$Th, owing to its unique nuclear energy structure, has been widely regarded as one of the most promising candidates for the development of a nuclear clock. However, the limited availability of suitable $^{229}$Th sources with sufficiently high activity remains a major challenge for experimental investigations of the $^{229m}$Th isomer. We propose a neutron-capture-based approach for the in-situ production of $^{229m,g}$Th by doping $^{228}$Ra into crystal hosts, where $^{229m,g}$Th is generated through neutron-capture reactions followed by a sequence of radioactive decay processes. We systematically investigate the background contributions associated with the three doped crystal hosts, namely CaF$_2$, SrF$_2$, and LiF, and evaluate their impact on the detection and identification of $^{229m}$Th. Under a neutron flux of $10^{15}\ \mathrm{n/cm^{2}/s}$ and a $^{228}$Ra doping concentration of $10^{19}\ \mathrm{cm^{-3}}$, the proposed method is capable of producing on the order of $10^{12}$ $^{229}$Th and $^{229m}$Th nuclei within only 1 s of irradiation, with a signal-to-noise ratios as high as $10^5$. In addition, the influences of detector wavelength resolution and post-irradiation measurement time on the detectability of the $^{229m}$Th signal are systematically analyzed, and the corresponding optimal measurement conditions are identified. Furthermore, the spatial distribution of neutron-produced $^{229}$Th within the crystal is investigated, providing practical guidance for optimizing crystal geometry and illumination configuration in future continuous-wave VUV absorption spectroscopy experiments. These results suggest that the proposed scheme provides a promising alternative pathway for the production and detection of $^{229\mathrm{m,g}}$Th, which may facilitate future studies toward the realization of nuclear-clock-based technologies.

nucl-ex↗
arXiv2026

Spanning $H$-subdivisions with Prescribed Path Lengths

We study spanning $H$-subdivisions in dense graphs where the length of every subdivision path is prescribed in advance. This problem is motivated in part by a question of Pavez-Signé [Combin. Probab. Comput. 33 (2024), 121--128], who asked whether the subdivision paths in a spanning $H$-subdivision can be required to have similar lengths. Let $h\ge3$ be an integer and let $0<β\llα\ll1/h$. We prove that, for all sufficiently large $n$, every $n$-vertex graph $G$ with $δ(G)\ge n/2+\lfloor h/3\rfloor$ has the following property. For every graph $H$ with $h$ edges and no isolated vertices, write $E(H)=\{e_1,\ldots,e_h\}$, and every choice of integers $\ell_1,\ldots,\ell_h\ge4$ satisfying $\sum_{i=1}^h\ell_i=n-|V(H)|+h$ and $\sum_{\ell_i<αn}\ell_i\leβn$, the graph $G$ contains a spanning $H$-subdivision in which the $i$th edge of $H$ is replaced by a path of length exactly $\ell_i$. We also give a family of examples showing that a linear additive term in $h$ is necessary in general.

math.CO↗
arXiv2026

Nearly balanced spanning subdivisions in dense digraphs

Pavez-Signé [Combin. Probab. Comput. 33 (2024), 121--128] conjectured a Dirac-type condition for spanning $H$-subdivisions and asked whether the subdivision paths can additionally be required to have similar lengths. Lee [European J. Combin. 124 (2025), 104059] resolved the existence conjecture in the stronger setting of digraphs. We answer the length-control question in this stronger directed setting: for every $\varepsilon>0$, there exists a constant $C_0>0$ such that, for every digraph $H$ with $h$ arcs and no isolated vertices, every $n$-vertex digraph $D$ with $n\ge C_0h$ and $δ^0(D)\ge(1/2+\varepsilon)n$ contains a spanning $H$-subdivision whose subdivision paths have lengths differing by at most one.

math.CO↗
arXiv2026

Sparse spanning $k$-strong oriented subdigraphs in split digraphs

Jackson and Thomassen conjectured that every $2k$-strong digraph admits a spanning $k$-strong oriented subdigraph [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. The conjecture holds for $k=1$ but other than some partial results that have been obtained for general $k$ in some special families of digraphs, including symmetric digraphs, the conjecture remains wide open in general. Even the existence of an integer $K$ such that every $K$-strong digraph has a 2-strong spanning oriented subdigraph is open. As a natural optimization counterpart, the minimum spanning $k$-strong subdigraph (MSSS$_k$) problem, is to find the minimum number of arcs in a spanning $k$-strong subdigraph of a $k$-strong digraph. This problem is NP-hard already for $k=1$ as it generalizes the hamiltonian cycle problem. In this paper, we address both problems simultaneously for the class of split digraphs, by constructing sparse spanning $k$-strong oriented subdigraphs. Specifically, we prove that every $k$-strong split digraph $D = (V_1, V_2; A)$ with minimum semi-degree {$δ^0(D)\geq 26k+15$} contains a spanning $k$-strong oriented subdigraph with no more than $kn+k|V_1|+98k^2+38k+3$ arcs, where $kn + k|V_1|$ is tight and the $k^{2}$ term is tight up to a constant factor. For the class of $k$-strong tournaments with minimum semi-degree at least $26k+15$ our results improve the bound obtained by Kang in [Combin. Probab. Comput., 27:892-907, 2018].

math.CO↗
arXiv2026

Highly connected spanning oriented subdigraphs in generalizations of semicomplete digraphs

Let $k$ be a positive integer. Jackson and Thomassen conjectured in 1989 that there exists an integer function $f(k)$ such that every $f(k)$-strong digraph admits a spanning $k$-strong oriented subdigraph. They even conjectured that one can take $f(k)=2k$ [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. Already the existence of $f(2)$ is open for general digraphs. Thomassen proved that $f(2)=4$ for symmetric digraphs. For general $k$, the existence of $f(k)$ was only known for locally semicomplete digraphs and quasi-transitive digraphs. Guo proved that every ${(3k-2)}$-strong locally semicomplete digraph contains a spanning $k$-strong local tournament [Discrete Appl. Math. 79 (1997) 119--125]. One can deduce from Guo's result that we have $f(k)\leq 3k-2$ for quasi-transitive digraphs. In this paper, we prove the existence of $f(k)$ for two subclasses of the semicomplete multipartite digraphs, namely extended semicomplete digraphs and semicomplete split digraphs. We prove that every $(4k+1)$-strong extended semicomplete digraph contains a spanning $k$-strong oriented subdigraph and every $5k$-strong semicomplete split digraph contains a spanning $k$-strong oriented subdigraph. The first result implies that for the large class of digraphs which can be obtained from some semicomplete digraph $S$ on at least 3 vertices by substituting arbitrary digraphs for each vertex of $S$ we also have $f(k)\leq 4k+1$.

math.CO↗
arXiv2026

The exact total degree threshold for the square of a Hamilton cycle in digraphs

The Pósa-Seymour conjecture establishes the minimum degree threshold required to guarantee the presence of the $k$th power of a Hamilton cycle in a graph. Following numerous partial results, Komlós, Sárközy, and Szemerédi confirmed the conjecture holds for all sufficiently large graphs. Treglown later conjectured the analogous minimum semi-degree threshold for forcing the $k$th power of a Hamilton cycle in a digraph. Subsequently, DeBiasio et al. proposed a conjecture on the minimum total degree threshold for the same problem. In this paper we settle the conjecture of DeBiasio et al. for $k=2$. Specifically, we prove that every sufficiently large $n$-vertex digraph with minimum total degree at least $8n/5-c$ contains the square of a Hamilton cycle, where $c=2$ if $n\equiv2,4\pmod 5$, and $c=1$ otherwise.

math.CO↗
arXiv2026

K-Arc-Strong Orientations Of Semicomplete Digraphs

Results by Jackson and Frank imply that every 2k-arc-strong digraph D contains a spanning k-arc-strong oriented subdigraph. This is best possible, even for very dense digraphs. A digraph is semicomplete if at least one of the arcs xy,yx is present for every pair of distinct vertices x,y. A tournament has exactly one of xy,yx for every such pair. Clearly every semicomplete digraph D contains a spanning tournament T which is obtained by deleting one arc from every 2-cycle of D. We prove that every (2k-1)-arc-strong semicomplete digraph on at least 2k+1 vertices contains a spanning k-arc-strong tournament. Both bounds 2k-1 and 2k+1 are best possible. The proof uses Frank's general orientation theorem for graphs as well as counting arguments based on the semicomplete structure.

math.CO↗
arXiv2026

Basin Metamorphosis in Coupled Phase Oscillators

We investigate the global basin structure of twisted states in nearest-neighbor coupled phase oscillators with a common phase shift $α$. As $α$ increases, basin boundaries become progressively more complex, with their fractal dimension growing toward that of the full ambient phase space. We conjecture that the basins eventually become riddled-like as the system approaches the limit $α\to \fracπ{2}$, where the dynamics becomes volume-preserving. We characterize the transient dynamics via the stabilization time of the winding number and demonstrate that it grows with system size. The scaling accelerates at larger phase shifts, transitioning from logarithmic to power-law behavior. We further analyze the dynamical origin of these long transients. Our results demonstrate how a single phase-shift governs fractal basin complexity and provide new insights into the global geometry and transient dynamics of multistable, yet non-chaotic, coupled phase oscillators.

nlin.CD↗
arXiv2026

Polynomial Algorithms for Minimum Degree Partitions in Semicomplete Digraphs

A 2-partition of a digraph is a partition of its vertex set into two nonempty parts. Degree-constrained 2-partition problems are generally computationally difficult, even when the prescribed properties are expressed only in terms of minimum indegree, minimum outdegree, or minimum semidegree. Bang-Jensen and Christiansen~\cite{B-C} conjectured that the minimum-degree partition problems would be polynomial-time solvable on semicomplete digraphs when the degree thresholds are fixed, and Bang-Jensen and Gutin~\cite{B-G-Classes} posed the related Problems~2.8.15 and~2.8.16. We resolve this conjecture. More precisely, for every fixed pair of integers $k_1,k_2\ge 2$, we give deterministic polynomial-time algorithms that decide whether a given semicomplete digraph admits a $(δ^+\geq k_1,δ^-\geq k_2)$-partition, a $(δ^+\geq k_1,δ^0\geq k_2)$-partition, or a $(δ^0\geq k_1,δ^0\geq k_2)$-partition, and construct such a partition whenever one exists. Here, $δ^+,δ^-,δ^0$ represent the minimum out-, in-, semi-degree, respectively. The algorithms use small degree certificates, minimal cores, closure and protective-set arguments, and deterministic universal colorings with monotone recoloring, which develop a new method in partition algorithm construction.

cs.DM↗
arXiv2026

Investigation of regional variations in CO$_2$ growth rates : Integrating Emission Inventories and Atmospheric Observations

Atmospheric carbon dioxide (CO2) growth rates reflects the combined influence of anthropogenic emissions, biospheric carbon exchange, and climate variability. While climate mitigation is primarily evaluated using bottom-up emission inventories within political boundaries, there is a need to validate these emission reductions using atmospheric measurements. Here, we present a global top-down analysis of atmospheric CO2 growth rates using CAMS atmospheric CO2 reanalysis, EDGAR anthropogenic emissions, GOSIF dataset and the Southern Oscillation Index (SOI) as a measures of biospheric activity, to quantify the relative influence of human and natural drivers. We find that atmospheric CO2 growth rate varies substantially across space and time but is dominated by natural carbon-cycle processes and global background trends. Anthropogenic emission signals are frequently masked by natural variability, making regional top-down detection of human emission changes difficult. The COVID-19 emission reductions in 2020, despite occurring during a neutral ENSO year, were not consistently reflected in regional atmospheric CO2 growth rates, highlighting the dominant roles of biospheric dynamics and atmospheric transport. Using unsupervised clustering and persistence analysis, we identify five characteristic carbon-cycle regimes. Spatial averaging removes much of the regional variability, leaving large-scale climate as the dominant control in most regimes. The active biosphere is the main exception, where strong biogenic signals persist, underscoring the critical role of tropical forests in shaping atmospheric CO2 variability.

physics.ao-ph↗
arXiv2026

Ramsey-Turán Type Problem for Perfect Transitive Triangle Tilings in Digraphs

The classical Corrádi-Hajnal theorem states that for any multiple $n$ of $3$, if $G$ is a graph with $n$ vertices and $δ(G) \geq 2n/3$, then $G$ can be partitioned into $n/3$ vertex-disjoint copies of the triangle [\emph{Acta Math. Acad. Sci. Hung.}, 14:423-439, 1964]. Balogh, Molla and Sharifzadeh obtained a smaller lower bound by adding the independence number condition [\emph{Random Struct. Algorithms}, 49:669-693, 2016]. In this paper, we study perfect tilings in digraphs subject to conditions on the independence number and the degree. The independence number, $α(D)$, of $D$ is the maximum integer $k$ such that $D$ has an independent set of cardinality $k$. We show that if $D$ is an $n$-vertex digraph with $α(D)\leq o(1)n$ and $δ(D) \geq (1+o(1))n$, then $D$ has a perfect $T_3$-tiling, where $T_3$ denotes a transitive triangle. This minimum degree condition is asymptotically best possible. Moreover, our result implies the theorem of Balogh, Molla, and Sharifzadeh concerning perfect triangle tilings.

math.CO↗
arXiv2026

Oriented Discrepancy of The Square of Hamilton Cycles

For an oriented graph $G$, the oriented discrepancy problem concerns the existence of a spanning subgraph of $G$ with a large imbalance between its forward and backward edge orientations. Freschi and Lo proved the Dirac-type Hamilton cycle result in oriented graphs, and asked for an analogue for powers of Hamilton cycles under a minimum-degree condition. We show that, for sufficiently large $n$, every oriented graph $G$ on $n$ vertices with minimum degree $δ(G)\geq 2n/3$ contains the square of a Hamilton cycle $H$ with $σ_{\max}(H)$ guaranteed to exceed a function depending on $δ(G)$ and $n$.

math.CO↗
arXiv2026

On the Viscosity Solutions of Parabolic p-Laplacian Equations with Capillary-Type Boundary Conditions

In this paper, we establish the well-posedness and large-time asymptotic behavior of viscosity solutions to singular/degenerate parabolic $p$-Laplacian equations with general capillary-type boundary conditions, including Neumann and prescribed contact angle cases, on strictly convex domains. By establishing a gradient estimate independent of the $C^0$ norm of the solution via the maximum principle, and by analyzing the problem through an approximation procedure together with associated elliptic eigenvalue problems, we prove the existence, uniqueness, and asymptotic behavior of solutions. For the elliptic problem with Neumann boundary conditions, we first focus on flat domains with the zero Neumann condition. By reflecting $u$ across the flat boundary $T_1$ and then using inf- and sup-convolution arguments in the reflected domain, we obtain the $C^{1,α}$ result. For the general elliptic case, we obtain sharp global $C^{1,α}$ regularity by flattening the boundary and employing compactness arguments together with an ``improvement of flatness'' iteration. With an extra condition in the iteration, we can also deal with the singular case $1<p<2$. In the parabolic setting, the spatial Hölder regularity of $Du$ follows from elliptic estimates combined with the Lipschitz continuity of $u$ in time, which in turn yields joint Hölder continuity in $(x,t)$. Extensions to non-convex domains are also discussed by incorporating a suitable forcing term.

math.AP↗
arXiv2026

The $H$-linkage problems in sparse robustly expanding digraphs

The Nash-Williams conjecture establishes degree sequence conditions ensuring Hamilton cycles in digraphs. An asymptotic version of this conjecture for large digraphs was independently derived by several researchers. We strengthen these results by proving the following results under the same asymptotic degree sequence conditions. For any digraph $H$, a digraph $D$ is $(\mathcal{N}H)$-linked if there exists an integer $l_0$ such that for any vertex set $U$ of cardinality $|V(H)|$ and every integer set $\mathcal{N}=\{l_i\}_{i=1}^{|A(H)|}$ with $l_i\geq l_0$, $D$ contains an $H$-subdivision with $U$ as branch-vertex set and the values in $\mathcal{N}$ specifying the lengths of the subdivided paths. Let $D$ be a sufficiently large digraph of order $n$ with the out-degree sequence $d_1^+\leq\cdots\leq d_n^+$ and the in-degree sequence $d_1^-\leq\cdots\leq d_n^-$. We prove that if for every $γ\in(0, 1)$ and every integer $0\leq i<n/2$, the following conditions hold: (i) $d_i^+\geq i+γn$ or $d_{n-i-γn}^-\geq n-i$, and (ii) $d_i^-\geq i+γn$ or $d_{n-i-γn}^+\geq n-i$, then $D$ is $(\mathcal{N}H)$-linked, and also admits a perfect $H$-subdivision tiling with subdivision orders $\{n_1, \ldots, n_k\}$, where each $n_i\geq C_0$ for some integer $C_0$.

math.CO↗
arXiv2026

DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence

We present a preview version of DeepSeek-V4 series, including two strong Mixture-of-Experts (MoE) language models -- DeepSeek-V4-Pro with 1.6T parameters (49B activated) and DeepSeek-V4-Flash with 284B parameters (13B activated) -- both supporting a context length of one million tokens. DeepSeek-V4 series incorporate several key upgrades in architecture and optimization: (1) a hybrid attention architecture that combines Compressed Sparse Attention (CSA) and Heavily Compressed Attention (HCA) to improve long-context efficiency; (2) Manifold-Constrained Hyper-Connections (mHC) that enhance conventional residual connections; (3) and the Muon optimizer for faster convergence and greater training stability. We pre-train both models on more than 32T diverse and high-quality tokens, followed by a comprehensive post-training pipeline that unlocks and further enhances their capabilities. DeepSeek-V4-Pro-Max, the maximum reasoning effort mode of DeepSeek-V4-Pro, redefines the state-of-the-art for open models, outperforming its predecessors in core tasks. Meanwhile, DeepSeek-V4 series are highly efficient in long-context scenarios. In the one-million-token context setting, DeepSeek-V4-Pro requires only 27% of single-token inference FLOPs and 10% of KV cache compared with DeepSeek-V3.2. This enables us to routinely support one-million-token contexts, thereby making long-horizon tasks and further test-time scaling more feasible. The model checkpoints are available at https://huggingface.co/collections/deepseek-ai/deepseek-v4.

cs.CL↗
arXiv2026

Spanning $H$-subdivisions and perfect $H$-subdivision tilings in dense digraphs

Given a (di)graph $H$, we say that a (di)graph $H^\prime$ is an $H$-subdivision if $H^\prime$ is obtained from $H$ by replacing one or more edges with internally vertex-disjoint path(s). Pavez-Signé conjectured that for every $\varepsilon>0$, there exists a constant $C_0>0$ such that for every graph $H$ with $h$ edges and no isolated vertices, if $G$ is a graph on $n\geq C_0h$ vertices and minimum degree $δ(G)\geq(1+\varepsilon)\frac{n}{2}$, then $G$ contains a spanning $H$-subdivision. This conjecture was later resolved by Lee [European J. Combin. \textbf{124} (2025), 104059]. In this paper, we strengthen Lee's result. Specifically, we prove that for any digraph $D$ on $n\geq C_0h$ vertices, if the minimum semi-degree of $D$ is at least $\frac{n+h}{2}-1$, then $D$ contains a spanning $H$-subdivision. The lower bound on the minimum semi-degree is best possible. Furthermore, we show that there exist constants $C>0$ and $α, β\in(0, 1)$ such that for any integer partition $n=n_1+\cdots+n_m\geq Cm$ with $n_i\geq|V(H)|+3h$ for each $i$, and $\sum_{n_i<αn}n_i\leqβn$, if a digraph of order $n\geq Cm$ has minimum semi-degree at least $\frac{n+m+h}{2}-1$, then it contains $m$ vertex-disjoint $H$-subdivisions whose orders are $n_1, \ldots, n_m$, respectively. The bound $\frac{n+m+h}{2}-1$ is also optimal. This work partly answers a conjecture of Lee [Combin. Probab. Comput. \textbf{34} (2025), 421--444] and generalizes a recent result from the same paper.

math.CO↗