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cdbe84e2046817908027d7006949e820abbb0e9a10055b92f3ac9f8a1fa3889f
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2026-01-01T00:00:00-05:00
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Quasi-spherical metrics and the static Minkowski inequality
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arXiv:2403.06216v3 Announce Type: replace Abstract: We prove that equality within the Minkowski inequality for asymptotically flat static manifolds is achieved only by slices of Schwarzschild space.
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https://arxiv.org/abs/2403.06216
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5b98800765bf034cfac885475ff01878615d82c1ce276d9edf01d7f2d0ad1d4f
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2026-01-01T00:00:00-05:00
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Centrality of star and monotone factorisations
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arXiv:2403.08354v2 Announce Type: replace Abstract: A factorisation problem in the symmetric group is central if conjugate permutations always have the same number of factorisations. We give the first fully combinatorial proof of the centrality of transitive star factorisations that is valid in all genera, which answers a natural question of Goulden and Jackson from 2009. We begin by showing that the set of star factorisations is equinumerous with a certain set of monotone factorisations, a new result. We give more than one proof of this, and, crucially, one of our proofs is bijective. As a corollary we obtain new formulae for some monotone double Hurwitz factorisations, and a new relation between Hurwitz and monotone Hurwitz factorisations. We also generalise a theorem of Goulden and Jackson from 2009 that states that the transitive power of Jucys-Murphy elements are central. Our theorem states that the transitive image of any symmetric function evaluated at Jucys-Murphy elements is central, which gives a transitive version of Jucys' original result from 1974.
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https://arxiv.org/abs/2403.08354
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42e8ba80d53048b63d035c5d9b983e6e74d35ff6ce3c2e52eef131fbb3942a20
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2026-01-01T00:00:00-05:00
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On the temporal estimates for the incompressible Navier-Stokes equations and the Hall-magnetohydrodynamic equations
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arXiv:2404.16290v2 Announce Type: replace Abstract: In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting method with initial data in the space of pseudo-measures. Additionally, we investigate these equations with initial data in the Lei-Lin spaces and establish decay rates for those solutions.
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https://arxiv.org/abs/2404.16290
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aa8341715a960255876b60c48eb028dec90fb4a00b90be8bde5b51d2899b1874
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2026-01-01T00:00:00-05:00
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Constrained-degree percolation on the hypercubic lattice: uniqueness and some of its consequences
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arXiv:2405.09343v3 Announce Type: replace Abstract: We consider the constrained-degree percolation (CDP) model on the hypercubic lattice. This is a continuous-time percolation model defined by a sequence $(U_e)_{e\in\mathcal{E}^d}$ of i.i.d. uniform random variables and a positive integer $k$, referred to as the constraint. The model evolves as follows: each edge $e$ attempts to open at a random time $U_e$, independently of all other edges. It succeeds if, at time $U_e$, both of its end-vertices have degrees strictly smaller than $k$. It is known \cite{hartarsky2022weakly} that this model undergoes a phase transition when $d\geq3$ for most nontrivial values of $k$. In this work, we prove that, for any fixed constraint, the number of infinite clusters at any time $t\in[0,1)$ is almost surely either 0 or 1. This uniqueness result implies the continuity of the percolation function in the supercritical regime, $t\in(t_c,1)$, where $t_c$ denotes the percolation critical threshold. The proof relies on a key time-regularity property of the model: the law of the process is continuous with respect to time for local events. In fact, we establish differentiability in time, thereby extending the result of \cite{SSS} to the CDP setting.
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https://arxiv.org/abs/2405.09343
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72853cad0a0f27140ecfbfa81130c2bc28c7b365b74766f1c31a66edfe12bdf5
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2026-01-01T00:00:00-05:00
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On the Stieltjes Approximation Error to Logarithmic Integral
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arXiv:2406.12152v2 Announce Type: replace Abstract: We study the approximation error $\varepsilon(x)=\operatorname{li}_{*}(x)-\operatorname{li}(x)$ arising from the classical Stieltjes asymptotic expansion for the logarithmic integral. Our analysis is based on the discrete values $\varepsilon_k=\varepsilon(e^{k})$ and their increments $\Delta_k=\varepsilon_{k+1}-\varepsilon_k,$ for which we derive new unconditional analytic bounds. Using precise integral representations for each increment $\Delta_k$, together with sharp upper and lower estimates for the associated kernel integrals, we obtain computable and uniform bounds for $\varepsilon_k$ for all $k\ge 1$, and hence for $\varepsilon(x)$ for all $x\ge e$. We prove the following unconditional bounds: $$\begin{array}{l} \displaystyle \frac{1}{3}\sqrt{\frac{2\pi}{\ln(x)}} + o\left(\frac{1}{\sqrt{\ln(x)}}\right) \le \varepsilon(x) \le \frac{1}{3}\sqrt{\frac{2\pi}{\ln(x)}} + o\left(\frac{1}{\sqrt{\ln(x)}}\right) \text{for all } e \le x \le e^{1000}, \end{array} $$ $$\begin{array}{l} \displaystyle \frac{1}{3}\sqrt{\frac{2\pi}{\ln(x)}} + o\left(\frac{1}{\sqrt{\ln(x)}}\right) - C_{l} \le \varepsilon(x) \le \frac{1}{3}\sqrt{\frac{2\pi}{\ln(x)}} + o\left(\frac{1}{\sqrt{\ln(x)}}\right) + C_{r} \text{for all } x>e^{1000} \text{ with } C_{l} = 0.0000035462\text{ and } C_{r}=0.0000021511. \end{array}$$ These results establish the first fully explicit global bounds for the Stieltjes approximation error. Finally, our findings strongly support the conjectural behaviour: $$ \varepsilon(x) = \frac{1}{3}\sqrt{\frac{2\pi}{\ln(x)}} + o\!\left(\frac{1}{\sqrt{\ln(x)}}\right), \qquad x\ge e. $$
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https://arxiv.org/abs/2406.12152
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da7ffb21524d41c63b0c60dda0372c5d1d78c8931a914ad3619ed1e841f434bf
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2026-01-01T00:00:00-05:00
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Analyzing Dynamical Systems Inspired by Montgomery's Conjecture: Insights into Zeta Function Zeros and Chaos in Number Theory
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arXiv:2406.12852v2 Announce Type: replace Abstract: In this study, we analyze a novel dynamical system inspired by Montgomery's pair correlation conjecture, modeling the spacings between nontrivial zeros of the Riemann zeta function via the GUE kernel $g(u) = 1 - \left( \frac{\sin(\pi u)}{\pi u} \right)^2 + \delta(u)$. The recurrence $x_{n+1} = 1 - \left( \frac{\sin(\pi/x_n)}{\pi/x_n} \right)^2 + \frac{1}{x_n}$ emulates eigenvalue repulsion as a quantum operator analogue realizing the P\'olya-Hilbert conjecture. Bifurcation analysis and Lyapunov exponents reveal quantum-like chaos: near $x=0$, linearized dynamics $f(x) = 1 - \pi^2 x^2$ yield Gaussian Lyapunov function $V(x) = C_1 e^{-\pi^2 x^3/3}$ with LaSalle invariance bounding zeros in $[0,1]$; large $x$ exhibit exponential growth $\lambda_n \to \ln(\pi^2/6)$. Entropy analysis confirms GUE level repulsion with zero entropy for small initial conditions. Comparative validation against actual $\gamma_n$ achieves errors $<10^{-100}$, while spectral density $\rho(E) \sim \frac{\log E}{2\pi}$ matches zeta zero statistics. This bridges Montgomery pair correlation to quantum chaos, providing computational evidence for Riemann zero spacing distributions and supporting the quantum operator hypothesis for $\zeta(1/2+it)$.
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https://arxiv.org/abs/2406.12852
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eea6ec85d44c3101b4f7396b0adba30f6d9f7140337ba4cd31298e6516976cee
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2026-01-01T00:00:00-05:00
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Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces
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arXiv:2406.15114v3 Announce Type: replace Abstract: This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fractional derivative of order $0<\alpha\leq 1$, a closed linear operator generating a strongly continuous semigroup, and instantaneous state jumps governed by bounded linear impulse operators. We first derive an explicit representation of the mild solution by combining fractional solution operators with impulsive operators. Using this representation, we characterize the approximate controllability of the system through a necessary and sufficient condition expressed in terms of the convergence of an associated family of impulsive resolvent operators. This resolvent condition extends the classical criterion for approximate controllability to the fractional impulsive setting. To illustrate the applicability of our theoretical results, a concrete example is provided. The analysis presented here bridges the gap between the well-established theory for integer-order impulsive systems and the more complex fractional case, highlighting the distinct challenges and solutions arising from the interplay of fractional dynamics and impulsive effects.
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https://arxiv.org/abs/2406.15114
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6cbf9dc7cb32eeef6f119207d9fbc150c31f77e2e4685a5e0c29620c76536746
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2026-01-01T00:00:00-05:00
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The multiplicity of the ground state of a generalized particle system interacting with a massless Bose field
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arXiv:2407.13462v3 Announce Type: replace Abstract: A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists, its multiplicity is finite.
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https://arxiv.org/abs/2407.13462
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8de0ab634c02a709c45439ebb2eca2fd164286c9f291a395e8f0ad74ca7a1641
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2026-01-01T00:00:00-05:00
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Pseudodifferential damping estimates and stability of relaxation shocks
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arXiv:2407.14484v3 Announce Type: replace Abstract: A bottleneck in the theory of large-amplitude and multi-d viscous and relaxation shock stability is the development of nonlinear damping estimates controlling higher by lower derivatives. These have traditionally proceeded from time-evolution bounds based on Friedrichs symmetric and Kawashima or Goodman type energy estimates. Here, we propose an alternative program based on frequency-dependent pseudodifferential time-space damping estimates in the spirit of Kreiss. These are seen to be equivalent in the linear case to high-frequency spectral stability, and, just as for the constant-coefficient analysis of Kreiss, sharp in a pointwise, fixed-frequency, sense. This point of view leads to a number of simplifications and extensions using already-existing analysis. We point to the new issue of turning points, analogous to glancing points in the constant-coefficient case as an important direction for further development.
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https://arxiv.org/abs/2407.14484
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e5e063fbe90f4309fe79c60c11239349393502ac007813e8c2c04aa57d3f3728
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2026-01-01T00:00:00-05:00
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Simple Models of Randomization and Preservation Theorems
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arXiv:2408.15014v2 Announce Type: replace Abstract: The main purpose of this paper is to present a new and more uniform model-theoretic/combinatorial proof of the theorem ([5]): The randomization $T^{R}$ of a complete first-order theory $T$ with $NIP$ is a (complete) first-order continuous theory with $NIP$. The proof method is based on the significant use of a particular type of models of $T^{R}$, namely simple models, certain indiscernible arrays, and Rademacher mean width. Using simple models of $T^R$ gives the advantage of re-proving this theorem in a simpler and quantitative manner. We finally turn our attention to $NSOP$ in randomization. We show that based on the definition of $NSOP$ given [13], $T^R$ is stable if and only if it is $NIP$ and $NSOP$.
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https://arxiv.org/abs/2408.15014
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d39ada98c19784aad84e303da39ecf723675a8daada0bc27b926a82dfdd1d8e2
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2026-01-01T00:00:00-05:00
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$\mathcal{C}$-Hereditarily conjugacy separable groups and wreath products
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arXiv:2409.06200v2 Announce Type: replace Abstract: We provide a necessary and sufficient condition for the restricted wreath product $A\wr B$ to be $\mathcal{C}$-hereditarily conjugacy separable where $\mathcal{C}$ is an extension-closed pseudovariety of finite groups. Moreover, we prove that the Grigorchuk group is 2-hereditarily conjugacy separable. As an application, we demonstrate that the lamplighter groups and $\mathbb{Z} \wr \mathbb{Z}$ are hereditarily conjugacy separable (but not $p$-conjugacy separable for any prime $p$) which provides infinitely many new examples of solvable, non-polycyclic hereditarily conjugacy separable groups. Furthermore, we study wreath products of cyclic subgroup separable groups and the derived length of iterated wreath products of solvable groups with an abelian base group and, as an application, we give an explicit construction of non-polycyclic hereditarily conjugacy separable groups of arbitrary derived length as an iterated wreath products of abelian groups.
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https://arxiv.org/abs/2409.06200
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1efc371da6548ea37d30d723ac889653f953c24def7edcac6ff388ec675e92bc
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2026-01-01T00:00:00-05:00
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Expander estimates for cubes
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arXiv:2409.16795v2 Announce Type: replace Abstract: If $\mathscr A$ is a set of natural numbers of exponential density $\delta$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 \delta)$. This is a considerable improvement on the previous best lower bounds for this problem, obtained by Davenport more than 80 years ago. The result is the best possible for $\delta\ge \frac 45$.
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https://arxiv.org/abs/2409.16795
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2adb0ca1bdd6ce994d39a5e16fd8b13078deba213504e754b376273e40bf4f8f
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2026-01-01T00:00:00-05:00
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Functional Extreme-PLS
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arXiv:2410.05517v2 Announce Type: replace Abstract: We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and Sliced Inverse Regression techniques. As such, the method relies on the projection of the covariate onto a subspace and maximizes the covariance between its projection and the response conditionally to an extreme event driven by a random threshold to capture the tail-information. The covariate and the heavy-tailed response are supposed to be linked through a non-linear inverse single-index model and our goal is to infer the index in this regression framework. We propose a new family of estimators and show its asymptotic consistency with convergence rates under the model. Assuming mild conditions on the noise, most of the assumptions are stated in terms of regular variation unlike the standard literature on SIR and single-index regression. Finally, our results are illustrated on a finite-sample study with synthetic functional data as well as on real data from the financial realm, highlighting the effectiveness of the dimension reduction for estimating extreme risk measures.
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https://arxiv.org/abs/2410.05517
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ba75fadbe7d6b1b5cc5d6acd1bf3177090431ca70a86c69e7228e3acb2c711df
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2026-01-01T00:00:00-05:00
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Fej\'er* monotonicity in optimization algorithms
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arXiv:2410.08331v2 Announce Type: replace Abstract: Fej\'er monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fej\'er* monotonicity, which was initially proposed in [SIAM J. Optim., 34(3), 2535-2556 (2024)]. We discuss and explore its behavior within Hilbert spaces as a tool for optimization algorithms. Additionally, we investigate weak and strong convergence properties of this novel concept. Through illustrative examples and insightful results, we contrast Fej\'er* with weaker notions of quasi-Fej\'er-type monotonicity.
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https://arxiv.org/abs/2410.08331
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89a0f5070a2bd22ddbf471d5b65746295898f505e3708e9982f2149dab23bdec
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2026-01-01T00:00:00-05:00
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Witten genera of complete intersections
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arXiv:2410.21412v2 Announce Type: replace Abstract: We prove vanishing results for Witten genera of string generalized complete intersections in homogeneous $\text{Spin}^c$-manifolds and in other $\text{Spin}^c$-manifolds with Lie group actions. By applying these results to Fano manifolds with second Betti number equal to one we get new evidence for a conjecture of Stolz.
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https://arxiv.org/abs/2410.21412
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3021eb28abae2894af40207eb08506b86feb778ef8078a4613ecccfaae2c80bf
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2026-01-01T00:00:00-05:00
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On the geography of log-surfaces
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arXiv:2412.14635v2 Announce Type: replace Abstract: This survey focuses on the geometric problem of log-surfaces, which are pairs consisting of a smooth projective surface and a reduced non-empty boundary divisor. In the first part, we focus on the geography problem for complex log-surfaces associated with pairs of the form $(\mathbb{P}^{2}, C)$, where $C$ is an arrangement of smooth plane curves admitting ordinary singularities. Specifically, we focus on the case in which $C$ is an arrangement consisting of smooth rational curves as its irreducible components. In the second part, containing original new results, we study log-surfaces constructed as pairs consisting of a complex projective $K3$ surface and a rational curve arrangement. In particular, we provide some combinatorial conditions for such pairs to have the log-Chern slope equal to $3$. Our survey is illustrated with many explicit examples of log-surfaces.
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https://arxiv.org/abs/2412.14635
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bffa34ecb9cde87ab1a75b279df639abb424e056ff5db5db333a7c14c39925e4
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2026-01-01T00:00:00-05:00
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Maximizing Satisfied Vertex Requests in List Coloring
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arXiv:2412.15927v3 Announce Type: replace Abstract: Suppose $G$ is a graph and $L$ is a list assignment for $G$. A request of $L$ is a function $r$ with nonempty domain $D\subseteq V(G)$ such that $r(v) \in L(v)$ for each $v \in D$. The triple $(G,L,r)$ is $\epsilon$-satisfiable if there exists a proper $L$-coloring $f$ of $G$ such that $f(v) = r(v)$ for at least $\epsilon|D|$ vertices in $D$. We say $G$ is $(k, \epsilon)$-flexible if $(G,L',r')$ is $\epsilon$-satisfiable whenever $L'$ is a $k$-assignment for $G$ and $r'$ is a request of $L'$. It is known that a graph $G$ is not $(k, \epsilon)$-flexible for any $k$ if and only if $\epsilon > 1/ \rho(G)$ where $\rho(G)$ is the Hall ratio of $G$. The list flexibility number of a graph $G$, denoted $\chi_{\ell flex}(G)$, is the smallest $k$ such that $G$ is $(k,1/ \rho(G))$-flexible. A fundamental open question on list flexibility numbers asks: Is there a graph with list flexibility number greater than its coloring number? In this paper, we show that the list flexibility number of any complete multipartite graph $G$ is at most the coloring number of $G$. We also initiate the study of list epsilon flexibility functions of complete bipartite graphs which was first suggested by Kaul, Mathew, Mudrock, and Pelsmajer in 2024. Specifically, we completely determine the list epsilon flexibility function of $K_{m,n}$ when $m \in \{1,2\}$ and establish some additional bounds for small $m$. Our proofs reveal a connection to list coloring complete bipartite graphs with asymmetric list sizes which is a topic that was explored by Alon, Cambie, and Kang in 2021.
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https://arxiv.org/abs/2412.15927
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fec50c1ec978fc998fafa92dcf7b6d7553e00b802b0f0b2a5f6af0c3b6b6c51d
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2026-01-01T00:00:00-05:00
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Diophantine Graphs
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arXiv:2501.00640v2 Announce Type: replace Abstract: This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and their number of edges are computed. Some number-theoretic techniques are used to characterize vertices of maximum degree and nonadjacent vertices. Some necessary and sufficient conditions for vertices of equal degrees are found.
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https://arxiv.org/abs/2501.00640
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fad6d3d0f2040e8505907ba65752d32561bd6eed9c43ff5b64b003d74c1a9790
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2026-01-01T00:00:00-05:00
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Mean Field Backward Stochastic Differential Equations with Double Mean Reflections
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arXiv:2501.10939v3 Announce Type: replace Abstract: In this paper, we analyze the mean field backward stochastic differential equations (MFBSDEs) with double mean reflections, whose generator and constraints both depend on the distribution of the solution. When the generator is Lipschitz continuous, based on the backward Skorokhod problem with nonlinear constraints, we investigate the solvability of the doubly mean reflected MFBSDEs by constructing a contraction mapping. Furthermore, if the constraints are linear, the solution can also be constructed by a penalization method. For the case of quadratic growth, we obtain the existence and uniqueness results by using a fixed-point argument, the BMO martingale theory and the {\theta}-method.
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https://arxiv.org/abs/2501.10939
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b95811cb0319c0091fb61c2948bdfc680e2e89a891074db3c30b3d6607126223
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2026-01-01T00:00:00-05:00
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Emergent transfinite topological dynamics
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arXiv:2501.14963v3 Announce Type: replace Abstract: In a sequence $S=\{(X,f_n)\}_{n\in\mathbb{N}}$ of dynamical systems sharing a common ambient space, the point $f^k_n(x)$ visited by a certain $x\in X$ depends on the iteration order $k$ and on the index $n$ specifying the system in $S$. If the sequence of maps $\{f_n\}_{n\in\mathbb{N}}$ is eventually constant at every point, the $f_n$-orbits show an emergent poset structure. A maximal initial segment of this poset is isomorphic to a certain countable ordinal $\ge\omega$. We study this transfinite emergent structure from the point of view of topological dynamics, investigating orbits, recurrence, limit sets, attractors and conjugacy.
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https://arxiv.org/abs/2501.14963
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73f7416de11a3aecb0e84cb61b6e10de6b2c9a9b01ff77a760fe0ee5fc2504db
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2026-01-01T00:00:00-05:00
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A Gauge Set Framework for Flexible Robustness Design
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arXiv:2501.14989v3 Announce Type: replace Abstract: This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing robustness through a gauge set reweighting formulation brings many classical robustness paradigms under a single convex-analytic perspective. The corresponding dual problem, the upper approximator regularization model, reveals a direct connection between distributional perturbations and objective regularization via polar gauge sets. This framework decouples the design of the nominal distribution, distance metric, and reformulation method, components often entangled in classical approaches, thus enabling modular and composable robustness modeling. We further provide a gauge set algebra toolkit that supports intersection, summation, convex combination, and composition, enabling complex ambiguity structures to be assembled from simpler components. For computational tractability under continuously supported uncertainty, we introduce two general finite-dimensional reformulation methods. The functional parameterization approach guarantees any prescribed gauge-based robustness through flexible selection of function bases, while the envelope representation approach yields exact reformulations under empirical nominal distributions and is asymptotically exact for arbitrary nominal choices. A detailed case study demonstrates how the framework accommodates diverse robustness requirements while admitting multiple tractable reformulations.
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https://arxiv.org/abs/2501.14989
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0bfa627e9f54520624146d3dac43fa85ce4b15717af264a654d9720bf3773ed7
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2026-01-01T00:00:00-05:00
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Sample complexity and weak limits of nonsmooth multimarginal Schr\"{o}dinger system with application to optimal transport barycenter
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arXiv:2502.02726v2 Announce Type: replace Abstract: Multimarginal optimal transport (MOT) has emerged as a useful framework for many applied problems. However, compared to the well-studied classical two-marginal optimal transport theory, analysis of MOT is far more challenging and remains much less developed. In this paper, we study the statistical estimation and inference problems for the entropic MOT (EMOT), whose optimal solution is characterized by the multimarginal Schr\"{o}dinger system. Assuming only boundedness of the cost function, we derive sharp sample complexity for estimating several key quantities pertaining to EMOT (cost functional and Schr\"{o}dinger coupling) from point clouds that are randomly sampled from the input marginal distributions. Moreover, with substantially weaker smoothness assumption on the cost function than the existing literature, we derive distributional limits and bootstrap validity of various key EMOT objects. As an application, we propose the multimarginal Schr\"{o}dinger barycenter as a new and natural way to regularize the exact Wasserstein barycenter and demonstrate its statistical optimality.
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https://arxiv.org/abs/2502.02726
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c60a42a7411171591a18d79f857f5fd0a869327d4f5b3d4ebd668667b4f5865d
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2026-01-01T00:00:00-05:00
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A formalization of Borel determinacy in Lean
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arXiv:2502.03432v3 Announce Type: replace Abstract: We present a formalization of Borel determinacy in the Lean 4 theorem prover. The formalization includes a definition of Gale-Stewart games and a proof of Martin's theorem stating that Borel games are determined. The proof closely follows Martin's "A purely inductive proof of Borel determinacy".
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https://arxiv.org/abs/2502.03432
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37cff529e6b17c74ef5a182a9557a0c5d9acb976ae71323d36c2d17e9b686b52
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2026-01-01T00:00:00-05:00
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Algebraic independence of the solutions of the classical Lotka-Volterra system
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arXiv:2502.17194v2 Announce Type: replace Abstract: Let $(x_1,y_1),\ldots,(x_n,y_n)$ be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system \begin{equation}\notag \begin{split} x'&= axy + bx\\ y'&= cxy + dy, \end{split} \end{equation} where $a,b,c,d\in\mathbb{C}\setminus\{0\}$. We show that if $d$ and $b$ are linearly independent over $\mathbb{Q}$, then the solutions are algebraically independent over $\mathbb{C}$, that is $tr.deg_{\mathbb{C}}\mathbb{C}(x_1,y_1,\ldots,x_n,y_n)=2n$. As a main part of the proof, we show that the set defined by the system in universal differential fields, with $d$ and $b$ linearly independent over $\mathbb{Q}$, is strongly minimal and geometrically trivial. Our techniques also allows us to obtain partial results for some of the more general $2d$-Lotka-Volterra system.
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https://arxiv.org/abs/2502.17194
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67347123f71ee19556e37291c43fe5b4b6865e8529929d3564364917f03629eb
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2026-01-01T00:00:00-05:00
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Relationship between haptotaxis and chemotaxis in cell dynamics
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arXiv:2503.00280v2 Announce Type: replace Abstract: The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial differential equations involving nonlocal advection. In contrast, cell phenomena where cells communicate with other cells via chemical substances and arrange themselves appropriately are termed cell sorting through chemotaxis, typically modeled by chemotactic systems such as the Keller--Segel model. Although there are clear differences between haptotaxis and chemotaxis, similar behaviors are often observed. In this study, we investigate the relationship between haptotaxis and chemotaxis in cell sorting phenomena. Specifically, we analyze the connections between a nonlocal aggregation model for haptotaxis and a Keller--Segel type chemotaxis system. By demonstrating convergence under specific kernel approximations, we show how these distinct mechanisms can lead to comparable dynamic behaviors. In particular, we establish that the gradient of a given kernel can be approximated by linear combinations of gradients of fundamental solutions, which also provides a mathematical contribution of independent interest. This study provides a mathematical framework for understanding the interplay between haptotaxis and chemotaxis in cell sorting phenomena.
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https://arxiv.org/abs/2503.00280
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e15349d9a6360ac5ab21694f4819df0a2700d7ef1a0ebbf82632de4330818cb9
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2026-01-01T00:00:00-05:00
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Partition functions of determinantal point processes on polarized K\"ahler manifolds
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arXiv:2503.01524v5 Announce Type: replace Abstract: In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on K\"ahler metrics satisfying the cocycle identity, whose first variations can be expressed through the TYZ expansion coefficients of the Bergman kernel. In particular, these functionals naturally generalize the Mabuchi functional in K\"ahler geometry and the Liouville functional on Riemann surfaces. We further show that Futaki-type holomorphic invariants obstruct the existence of critical points of these geometric functionals, extending Lu's formula. We also verify that certain formulas remain valid up to the third coefficient without assuming polarization. Finally, we discuss the relation of our results to the quantum Hall effect (QHE), where the determinantal point process provides a microscopic model. In particular, we recover the higher-dimensional effective Chern-Simons actions derived in the physics literature and confirm a conjecture of Klevtsov on the form of the partition function asymptotics.
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https://arxiv.org/abs/2503.01524
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956f0175d736735d535955fcda03948cf74b1cfb4f264ea099e0cfc58e672667
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2026-01-01T00:00:00-05:00
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Constrained Reinforcement Learning for the Dynamic Inventory Routing Problem under Stochastic Supply and Demand
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arXiv:2503.05276v2 Announce Type: replace Abstract: Green hydrogen has multiple use cases and is produced from renewable energy, such as solar or wind energy. It can be stored in large quantities, decoupling renewable energy generation from its use, and is therefore considered essential for achieving a climate-neutral economy. The intermittency of renewable energy generation and the stochastic nature of demand are, however, challenging factors for the dynamic planning of hydrogen storage and transportation. This holds particularly in the early-adoption phase when hydrogen distribution occurs through vehicle-based networks. We therefore address the Dynamic Inventory Routing Problem (DIRP) under stochastic supply and demand with direct deliveries for the vehicle-based distribution of hydrogen. To solve this problem, we propose a Constrained Reinforcement Learning (CRL) framework that integrates constraints into the learning process and incorporates parameterized post-decision state value predictions. Additionally, we introduce Lookahead-based CRL (LCRL), which improves decision-making over a multi-period horizon to enhance short-term planning while maintaining the value predictions. Our computational experiments demonstrate the efficacy of CRL and LCRL across diverse instances. Our learning methods provide near-optimal solutions on small scale instances that are solved via value iteration. Furthermore, both methods outperform typical deep learning approaches such as Proximal Policy Optimization, as well as classical inventory heuristics, such as (s,S)-policy-based and Power-of-Two-based heuristics. Furthermore, LCRL achieves a 10% improvement over CRL on average, albeit with higher computational requirements. Analyses of optimal replenishment policies reveal that accounting for stochastic supply and demand influences these policies, showing the importance of our addition to the DIRP.
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https://arxiv.org/abs/2503.05276
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58a32ac691e1a07bc76df768f64166f0362d5d41d47c7a3c3fceccd7447c84d8
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2026-01-01T00:00:00-05:00
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Reachability for multiagent control systems via Lyapunov functions
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arXiv:2503.09179v2 Announce Type: replace Abstract: This paper concerns the problem of reachability of a given state for a multiagent control system in $\mathbb{R}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the position of the whole crowd of agents (modeled by a probability measure on $ \mathbb{R}^d$). The main contribution of the paper is to study the above reachability problem with a given rate of attainability through a Lyapunov method adapted to the Wasserstein space of probability measures. As a byproduct we obtain a new comparison result for viscosity solutions of Hamilton Jacobi equations in the Wasserstein space.
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https://arxiv.org/abs/2503.09179
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315b2183a7736e6c17b2c8e9365e21e851c883deea5cfaa0a2e352337a9b2b96
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2026-01-01T00:00:00-05:00
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Representation Theorems for Convex Expectations and Semigroups on Path Space
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arXiv:2503.10572v2 Announce Type: replace Abstract: The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis and convex expectations from probability theory. Our main result provides a one-to-one relation between these objects. As an application, we use the representation via penality functions and duality arguments to show that convex expectations are determined by their finite dimensional distributions. To illustrate this structural result, we show that Hu and Peng's axiomatic description of $G$-L\'evy processes in terms of finite dimensional distributions extends uniquely to the control approach introduced by Neufeld and Nutz. Finally, we show that convex expectations with a Markovian structure are fully determined by their one-dimensional distributions, which give rise to a classical semigroup on the state space. As an application of this result, we establish a Laplace principle for entropic risk measures associated to controlled diffusions.
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https://arxiv.org/abs/2503.10572
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6b4cf0b97b8540ef05e77d3f68f7d1c66581b0952114dc2f08fd99ec9bc4f6dd
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2026-01-01T00:00:00-05:00
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Symmetric square type $L$-series
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arXiv:2504.00972v2 Announce Type: replace Abstract: We construct symmetric square type $L$-series for vector-valued modular forms transforming under the Weil representation associated to a discriminant form. We study Hecke operators and integral representations to investigate their properties, deriving functional equations and infinite product expansions.
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https://arxiv.org/abs/2504.00972
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cc1d61050e94d0bf9d023895e9a73464bae50604d85b2c61e3f628f84f2777d5
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2026-01-01T00:00:00-05:00
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Arbitrary orientations of cycles in oriented graphs
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arXiv:2504.09794v2 Announce Type: replace Abstract: We show that every sufficiently large oriented graph $G$ with minimum indegree and outdegree both at least $(3|V(G)|-1)/8$ contains every orientation of a Hamilton cycle. This result improves the approximate bound established by Kelly and resolves a long-standing problem posed by H\"aggkvist and Thomason in 1995. The degree condition is tight and it can be improved to $(3|V(G)|-4)/8$ for Hamilton cycles that are nearly directed, generalizing a classic result by Keevash, K\"uhn and Osthus. Additionally, we derive a pancyclicity result for arbitrary orientations. More precisely, the above degree condition suffices to guarantee the existence of cycles of every possible orientation and every possible length unless $G$ is isomorphic to one of the exceptional oriented graphs.
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https://arxiv.org/abs/2504.09794
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5c4d6bc7457b89cdc8c058ce5d7c504bd90bde109bbec90ba4df69552a27c467
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2026-01-01T00:00:00-05:00
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Coniveau filtrations with Z/2 coefficients
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arXiv:2504.19388v2 Announce Type: replace Abstract: We show that two coniveau filtrations on the mod 2 cohomology group of a smooth projective complex variety differ.
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https://arxiv.org/abs/2504.19388
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f667822523fb1a9091cb43d777a8e6dd70560b9a6dc04b98982086640e23c014
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2026-01-01T00:00:00-05:00
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Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension
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arXiv:2505.10525v4 Announce Type: replace Abstract: We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to the setting of intermediate dimensions both the Gehring--V\"ais\"al\"a theorem on dilatation-dependent quasiconformal distortion of dimension and Kovalev's theorem on the nonexistence of metric spaces with conformal dimension strictly between zero and one. Applications include new contributions to the quasiconformal classification of Euclidean sets and a new sufficient condition for the vanishing of conformal box-counting dimension. We illustrate our conclusions with specific consequences for Bedford--McMullen carpets, samples of Mandelbrot percolation, and product sets containing a polynomially convergent sequence factor.
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https://arxiv.org/abs/2505.10525
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db04dd031590a5254f9395121f8d4b0f90f6e709fbe73f76d3e1ff0c13e9a841
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2026-01-01T00:00:00-05:00
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Consistent line clustering using geometric hypergraphs
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arXiv:2505.24868v2 Announce Type: replace Abstract: Many datasets are naturally modeled as graphs, where vertices denote entities and edges encode pairwise interactions. However, some problems exhibit higher-order structure that lies beyond this framework. Among the simplest examples is line clustering, in which points in a Euclidean space are grouped into clusters well approximated by line segments. As any two points trivially determine a line, the relevant structure emerges only when considering higher-order tuples. To capture this, we construct a 3-uniform hypergraph by treating sets of three points as hyperedges whenever they are approximately collinear. This geometric hypergraph encodes information about the underlying line segments, which can be extracted using community recovery algorithms. We characterize the fundamental limits of line clustering and establish the near-optimality of hypergraph-based methods. In particular, we derive information-theoretic thresholds for exact and almost exact recovery for noisy observations from intersecting lines in the plane. Finally, we introduce a polynomial-time spectral algorithm that succeeds up to polylogarithmic factors of the information-theoretic bounds.
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https://arxiv.org/abs/2505.24868
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98b695b8160decac31fc21ee1ac2de7d691d8ddb8dbdf221da11979a67eb0860
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2026-01-01T00:00:00-05:00
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Graph quandles: Generalized Cayley graphs of racks and right quasigroups
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arXiv:2506.04437v3 Announce Type: replace Abstract: We solve two open problems of Valeriy Bardakov about Cayley graphs of racks and graph-theoretic realizations of right quasigroups. We also extend Didier Caucal's classification of labeled Cayley digraphs to right quasigroups and related algebraic structures like quandles. First, we characterize markings of graphs that realize racks. As an application, we construct rack-theoretic (di)graph invariants from permutation representations of graph automorphism groups. We describe how to compute these invariants with general results for path graphs and cycle graphs. Second, we show that all right quasigroups are realizable by edgeless graphs and complete (di)graphs. Using Schreier (di)graphs, we also characterize Cayley (di)graphs of right quasigroups Q that realize Q. In particular, all racks are realizable by their full Cayley (di)graphs. Finally, we give a graph-theoretic characterization of labeled Cayley digraphs of right-cancellative magmas, right-divisible magmas, right quasigroups, racks, quandles, involutory racks, and kei.
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https://arxiv.org/abs/2506.04437
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6c54e504f234b176b14e33d8ca41d7b1c76bee160e876ea7c6558c5cb36715b7
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2026-01-01T00:00:00-05:00
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On solutions to Hardy-Sobolev equations on Riemannian manifolds
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arXiv:2506.20089v2 Announce Type: replace Abstract: Let $(M,g)$ be a closed Riemannian manifold of dimension at least $3$. Let $S$ be the union of the focal submanifolds of an isoparametric function on $(M,g)$. In this article we address the existence of solutions of the Hardy-Sobolev type equation $\Delta_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s}$, where $d_{S}(x)$ is the distance from $x$ to $S$ and $q>2$. In particular, we will prove the existence of infinite sign-changing solutions to the equation.
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https://arxiv.org/abs/2506.20089
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541a4f781b398143ce1543689f3942eaba098ea3fe0494802af2316da4a44d36
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2026-01-01T00:00:00-05:00
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On pre-local tabularity above $\mathrm{S4}\times \mathrm{S4}$
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arXiv:2506.20874v2 Announce Type: replace Abstract: We investigate pre-local tabularity in normal extensions of the logic $\mathrm{S4}\times \mathrm{S4}$. We show that there are exactly four pre-locally tabular logics in normal extensions of products of finite height, and that every non-locally tabular logic in this family is contained in one of them. We also give an axiomatic criterion of local tabularity above the logic of products with Noetherian skeletons. Finally, we discuss examples of pre-locally tabular extensions of $\mathrm{S4}\times \mathrm{S4}$ outside this class, including logics with the converse and universal modalities.
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https://arxiv.org/abs/2506.20874
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5494be9847e527a8cc90736eaeaf9d777d9330341164213b6190076cb597fd64
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2026-01-01T00:00:00-05:00
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On the zero sets of harmonic polynomials
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arXiv:2506.24116v4 Announce Type: replace Abstract: In this paper we consider nonzero harmonic functions vanishing on some subsets of $\mathbb R^n$. We give a positive solution to Problem 151 from the Scottish Book posed by R. Wavre in 1936. In more detail, we construct a nonzero harmonic polynomial that vanishes on the edges of the unit cube. Moreover, using harmonic morphisms we build new nontrivial families of harmonic polynomials that vanish at the same set in the unit ball in $\mathbb R^n$ for all $n \geq 4$. This extends certain results by Logunov and Malinnikova. We also present new results on harmonic functions in the space whose zero sets are unions of affine codimension two subspaces.
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https://arxiv.org/abs/2506.24116
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61bcac495db8f9dc13e124580f08ffe0e008ec391fe598f47e4eb46e5af01327
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2026-01-01T00:00:00-05:00
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Complete classification of the Dehn functions of Bestvina-Brady groups
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arXiv:2507.07566v2 Announce Type: replace Abstract: We prove that the Dehn function of every finitely presented Bestvina-Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina-Brady groups from admitting a CAT(0) structure.
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https://arxiv.org/abs/2507.07566
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5130ef8cd0fa7d171784a39c730aaac8d9edb2394ecbba01a7e1ad3c9728f97a
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2026-01-01T00:00:00-05:00
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Generalized Symmetries From Fusion Actions
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arXiv:2508.13063v3 Announce Type: replace Abstract: Let $A$ be a condensable algebra in a modular tensor category $\mathcal{C}$. We define an action of the fusion category $\mathcal{C}_A$ of $A$-modules in $\mathcal{C}$ on the morphism space $\mbox{Hom}_{\mathcal{C}}(x,A)$ for any $x$ in $\mathcal{C}$, whose characters are generalized Frobenius-Schur indicators. This fusion action can be considered on $A$, and we prove a categorical generalization of the Schur-Weyl duality for this action. For any fusion subcategory $\mathcal{B}$ of $\mathcal{C}_A$ containing all the local $A$-modules, we prove the invariant subobject $B=A^\mathcal{B}$ is a condensable subalgebra of $A$. The assignment of $\mathcal{B}$ to $A^\mathcal{B}$ defines a Galois correspondence between this kind of fusion subcategories of $\mathcal{C}_A$ and the condensable subalgebras of $A$. In the context of VOAs, we prove for any nice VOAs $U \subset A$, $U=A^{\mathcal{C}_A}$ where $\mathcal{C}=\mathcal{M}_U$ is the category of $U$-modules. In particular, if $U = A^G$ for some finite automorphism group $G$ of $A,$ the fusion action of $\mathcal{C}_A$ on $A$ is equivalent to the $G$-action on $A.$
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https://arxiv.org/abs/2508.13063
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2026-01-01T00:00:00-05:00
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Non-vanishing of Poincar\'e Series on Average
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arXiv:2508.17242v2 Announce Type: replace Abstract: We study when Poincar\'e series for congruence subgroups do not vanish identically. We show that almost all Poincar\'e series with suitable parameters do not vanish when either the weight $k$ or the index $m$ varies in a dyadic interval. Crucially, analyzing the problem `on average' over these weights or indices allows us to prove non-vanishing in ranges where the index $m$ is significantly larger than $k^2$ - a range in which proving non-vanishing for individual Poincar\'e series remains out of reach of current methods.
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https://arxiv.org/abs/2508.17242
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30c7de723d8839a40450d89b7342e216895e9178cb87be901fa42c685233aa98
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2026-01-01T00:00:00-05:00
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Sharp bilinear eigenfunction estimate, $L^\infty_{x_2}L^p_{t,x_1}$-type Strichartz estimate, and energy-critical NLS
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arXiv:2509.09565v3 Announce Type: replace Abstract: We establish sharp bilinear eigenfunction estimates for the Laplace-Beltrami operator on the standard three-sphere $\mathbb{S}^3$, eliminating the logarithmic loss that has persisted in the literature since the pioneering work of Burq, G\'erard, and Tzvetkov over twenty years ago. This completes the theory of multilinear eigenfunction estimates on the standard spheres. Our approach relies on viewing $\mathbb{S}^3$ as the compact Lie group $\mathrm{SU}(2)$ and exploiting its representation theory. Motivated by applications to the energy-critical nonlinear Schr\"odinger equation (NLS) on $\mathbb{R} \times \mathbb{S}^3$, we also prove a refined anisotropic Strichartz estimate on the cylindrical space $\mathbb{R}_{x_1} \times \mathbb{T}_{x_2}$ of $L^\infty_{x_2}L^4_{t,x_1}$-type, adapted to certain spectrally localized functions. The argument relies on multiple sharp measure estimates and a robust kernel decomposition method. Combining these two key ingredients, we derive a refined bilinear Strichartz estimate on $\mathbb{R} \times \mathbb{S}^3$, which in turn yields small-data global well-posedness for the above mentioned NLS in the energy space.
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https://arxiv.org/abs/2509.09565
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62c25ee4ded71e3befcafa5a5f60f7234a21b07151a76301895fb6bcfb0a68bf
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2026-01-01T00:00:00-05:00
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Generic Frameworks for Distributed Functional Optimization and Learning over Time-Varying Networks
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arXiv:2509.17554v2 Announce Type: replace Abstract: In this paper, we establish a distributed functional optimization (DFO) theory over time-varying networks. The vast majority of existing distributed optimization theories are developed based on Euclidean decision variables. However, for many scenarios in machine learning and statistical learning, such as reproducing kernel spaces or probability measure spaces that use functions or probability measures as fundamental variables, the development of existing distributed optimization theories exhibit obvious theoretical and technical deficiencies. This paper addresses these issues by developing a novel general DFO theory on Banach spaces, allowing functional learning problems in the aforementioned scenarios to be incorporated into our framework for resolution. We study both convex and nonconvex DFO problems and rigorously establish a comprehensive convergence theory of distributed functional mirror descent and distributed functional gradient descent algorithm to solve them. Satisfactory convergence rates are fully derived. The work has provided generic analyzing frameworks for DFO. The established theory is shown to have crucial application value in the kernel-based distributed learning theory over networks.
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https://arxiv.org/abs/2509.17554
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604f5219b061ed17ba494f10e4899cdf84a22c756e690dbebf8b29293af88d92
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2026-01-01T00:00:00-05:00
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A geometric perspective on the inextensible flows and energy of curves in 4-dimensional pseudo-Galilean space
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arXiv:2509.24036v2 Announce Type: replace Abstract: In this study, inextensible flows of curves in four-dimensional pseudo-Galilean space are expressed, and the necessary and sufficient conditions of these curve flows are given as partial differential equations. Also, the directional derivatives are defined in accordance with the Serret-Frenet frame in G41, the extended Serret-Frenet relations are expressed by using Frenet formulas in G41. Furthermore, the bending elastic energy functions are expressed for the same particle according to curve a(s,t).
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https://arxiv.org/abs/2509.24036
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927be103e241e4392d6aab9208a5df75f153c1d0527b4d3639df5dd1616ac0d5
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2026-01-01T00:00:00-05:00
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Homogeneity
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arXiv:2509.25227v2 Announce Type: replace Abstract: The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function $f$ changes under scaling or shifting of its arguments. These generalized homogeneity functions capture different scaling behaviors and establish fundamental properties. Such properties include how homogeneity is preserved under function operations and how it determines the transformation behavior of related constructions like quotient functions. This framework extends the classical concept of homogeneity to a wider class of functional symmetries, providing a unified approach to analyzing scaling properties in various mathematical contexts.
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https://arxiv.org/abs/2509.25227
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cb1f0a77338542574d739cc7e98ab1d46424dbeb9123905cbb0fee0478168043
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2026-01-01T00:00:00-05:00
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Non-Attainment of Minima in Non-Polyhedral Conic Optimization: A Robust SOCP Example
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arXiv:2510.00318v2 Announce Type: replace Abstract: A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this crucial guarantee does not extend to Second-Order Cone Programs (SOCPs), a workhorse model in robust and convex optimization. We construct and analyze a rigorous counterexample derived from a robust linear optimization problem with ellipsoidal uncertainty. The resulting SOCP possesses a non-empty feasible set, a bounded objective, and an objective function that is copositive on its recession cone. Despite satisfying these classical conditions for solvability, the problem admits no optimal solution; its infimum is finite but unattainable. We trace this pathology directly to the non-polyhedral geometry of the second-order cone, which causes the image of the feasible set under the linear objective to be non-closed. We interpret the example explicitly within the context of robust optimization, discuss its significant practical implications for modeling and computation, and propose effective mitigation strategies via polyhedral approximation or regularization.
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https://arxiv.org/abs/2510.00318
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413ff94b2c4c269c6a0ea5477a6f31ec07ade104b8dd7c7c2c9d5af37dd09444
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2026-01-01T00:00:00-05:00
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Hausdorff dimension and quasisymmetric minimality of homogeneous Moran sets
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arXiv:2510.00540v2 Announce Type: replace Abstract: In this paper, we study the quasisymmetric Hausdorff minimality of homogeneous Moran sets. First, we obtain the Hausdorff dimension formula of two classes of homogeneous Moran sets which satisfy some conditions. Second, we show two special classes of homogeneous Moran sets with Hausdorff dimension 1 are quasisymmetrically Hausdorff minimal.
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https://arxiv.org/abs/2510.00540
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Robustified Gaussian quasi-likelihood inference for volatility
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arXiv:2510.02666v3 Announce Type: replace Abstract: We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and H\"{o}lder-inequality-based normalization, we propose easy-to-implement, robustified versions of the conventional Gaussian quasi-maximum-likelihood estimator that require only a single tuning parameter. We prove their asymptotic mixed normality at the standard rate of $\sqrt{n}$. It is theoretically shown that these estimators are simultaneously robust against contamination in both the covariate and response processes. Additionally, under suitable conditions on the selection of the tuning parameter, the proposed estimators achieve the same asymptotic distribution as the conventional estimator in the contamination-free case. Illustrative simulation results highlight the estimators' insensitivity to the choice of the tuning parameter.
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https://arxiv.org/abs/2510.02666
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398e35d1ae87d793791f091e946f22fc265aff0197fc1ef7257e12648df36c79
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2026-01-01T00:00:00-05:00
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Concentration of the hypergraph's weak independence number
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arXiv:2510.15117v2 Announce Type: replace Abstract: In this note we generalize the results of the recent work by Tom Bohman and Jacob Hofstad on the independence number in G(n, p) to the case of the random k-uniform hypergraph. Concentration in two values occurs in the regime $p>n^{-(k-1)k/(k+1)+\varepsilon}$.
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https://arxiv.org/abs/2510.15117
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2026-01-01T00:00:00-05:00
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Nonradial Quenching Profile for a MEMS Model
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arXiv:2510.15246v2 Announce Type: replace Abstract: We construct a quenching solution to the parabolic MEMS model \[ u_t = \Delta u - \frac{1}{u^2} \quad \text{in } \mathcal{B} \times (0,T), \quad u|_{\partial \mathcal{B}} = 1, \] where $\mathcal{B}$ is the unit disc in $\mathbb{R}^2$, and $T > 0$ denotes the quenching time. The constructed solution quenches only at the origin and admits the final profile \[ u(x,T) \sim \left(x_1^2 x_2^2 + \theta(x_1^6 + x_2^6)\right)^{\frac{1}{3}} \quad \text{as } |x| \to 0, \] where $\theta \in (0, \theta^*)$ for some $\theta^* > 0$. To our knowledge, this is the first example of a quenching solution with a genuinely non-radial profile. The proof relies on the construction of a good approximate solution, using a perturbative expansion in self-similar variables. We then justify the true solution that remains close to this approximation through a spectral analysis combined with a robust energy method.
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https://arxiv.org/abs/2510.15246
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303927e031a5ecdcc0f7075e3153df202b70183944eb78d8703a323ac32f7d70
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2026-01-01T00:00:00-05:00
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On Type I blowup and $\varepsilon$-regularity criteria of suitable weak solutions to the 3D incompressible MHD equations
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arXiv:2510.25448v2 Announce Type: replace Abstract: We study interior $\varepsilon$-regularity and Type I blowup criteria for suitable weak solutions to the three-dimensional incompressible MHD equations. Our starting point is a direct iteration scheme for the classical Caffarelli--Kohn--Nirenberg scaled energy quantities $A,E,C$ and $D$, which yields $\varepsilon$-regularity criteria under smallness assumptions on the velocity field $u$ and boundedness assumptions on the magnetic field $b$, with the underlying scaling-invariant quantities chosen independently. As an intermediate step, we prove that finiteness of one such scaling-invariant quantity for each of $u$ and $b$ allows only Type I blowup, in the sense that $A(u,b;r)+E(u,b;r)+C(u,b;r)+D(p;r)<\infty$ for small $r$. This extends Seregin's Type I criteria for the Navier--Stokes equations to the MHD setting and provides a natural point of departure for the analysis of Type II blowup. By interpolation and embedding, we further obtain $\varepsilon$-regularity criteria and Type I characterisations in terms of general scaled mixed Lebesgue norms for $u$ and $b$, with independent exponent choices. While we do not aim to sharpen existing mixed-norm $\varepsilon$-regularity criteria, the present formulation offers a unified and comparatively direct route that is naturally compatible with the Type I framework; in particular, the mixed-norm Type I description does not follow from earlier mixed-norm $\varepsilon$-regularity proofs by a formal replacement of the smallness parameter.
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https://arxiv.org/abs/2510.25448
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a07c761bd3e1bf3755103c329bbb5295f2f87719c372680942ced2ec1c662d9e
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2026-01-01T00:00:00-05:00
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Exponential Stability of a Degenerate Euler-Bernoulli Beam with Axial Force and Delayed Boundary Control
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arXiv:2510.25484v2 Announce Type: replace Abstract: This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we establish the well-posedness of the system by constructing an appropriate energy space in weighted Sobolev settings. Using L\"umer-Phillips theorem, we prove that the linear operator associated with the problem generates a $\mathcal{C}_0$-semigroup of contractions. Second, we establish the uniform exponential stability of the system. By constructing a novel Lyapunov functional incorporating weighted integral terms, we demonstrate that the energy's system exponentially decays to zero and derive a precise decay rate estimate. This work provides a significant extension to the stability theory for complex distributed parameter systems.
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https://arxiv.org/abs/2510.25484
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975ba2bfcd3f9e9d0f79dcdef9b7d28873cde580d8118e1335045b492c4240aa
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2026-01-01T00:00:00-05:00
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Quenched coalescent for diploid population models with selfing and overlapping generations
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arXiv:2510.26115v2 Announce Type: replace Abstract: We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of $n$ genes as the population size $N$ tends to infinity. Unlike traditional approach in coalescent theory which considers the unconditional (annealed) law of the gene genealogies averaged over the population pedigree, here we study the conditional (quenched) law of gene genealogies given the pedigree. We focus on the case of high selfing probability and obtain that this conditional law converges to a random probability measure, given by the random law of a system of coalescing random walks on an exchangeable fragmentation-coalescence process of \cite{berestycki04}. This system contains the system of coalescing random walks on the ancestral recombination graph as a special case, and it sheds new light on the site-frequency spectrum (SFS) of genetic data by specifying how SFS depends on the pedigree. The convergence result is proved by means of a general characterization of weak convergence for random measures on the Skorokhod space with paths taking values in a locally compact Polish space.
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https://arxiv.org/abs/2510.26115
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a6d4303030fd68ee219dd21d77ddb63682465c27c099f6ef994247b55c635c8e
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2026-01-01T00:00:00-05:00
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Polynomial Approximation in Higher-Order Weighted Dirichlet Spaces
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arXiv:2510.26133v2 Announce Type: replace Abstract: Fej\'er's theorem guarantees norm convergence of Ces\`aro means of Taylor partial sums in the Hardy space, whereas such convergence generally fails in weighted Dirichlet-type spaces, especially in the higher-order setting. In this paper, we investigate summability problems in higher-order weighted Dirichlet spaces $\widehat{\mathcal{H}}_{\mu,m}$ and show that Taylor partial sums are not uniformly bounded in these spaces and may therefore diverge in norm. To restore convergence, we introduce a family of modified polynomials whose coefficients are adjusted by a suitable weight array. Under mild boundedness and variation assumptions on the weights, we establish norm convergence of the modified sums via a coefficient correspondence principle and a Local Douglas formula. As an application, when the weight measure $\mu$ is a finite sum of Dirac point masses, explicit formulas for the modified coefficients are obtained, yielding a Fej\'er-type summability theorem for higher-order weighted Dirichlet spaces.
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https://arxiv.org/abs/2510.26133
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26394e623078f72a2c58b757a6576166be7f986a0ebd6333a13a81238e7d3bd4
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2026-01-01T00:00:00-05:00
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A Group with Exactly One Noncommutator
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arXiv:2511.00541v2 Announce Type: replace Abstract: The question of whether there exists a finite group of order at least three in which every element except one is a commutator has remained unresolved in group theory. In this article, we address this open problem by developing an algorithmic approach that leverages several group theoretic properties of such groups. Specifically, we utilize a result of Frobenius and various necessary properties of such groups, combined with Plesken and Holt's extensive enumeration of finite perfect groups, to systematically examine all finite groups up to a certain order for the desired property. The computational core of our work is implemented using the computer system GAP (Groups, Algorithms, and Programming). We discover two nonisomorphic groups of order 368,640 that exhibit the desired property. Our investigation also establishes that this order is the minimum order for such a group to exist. As a result, this study provides a positive answer to Problem 17.76 in the Kourovka Notebook. In addition to the algorithmic framework, this paper provides a structural description of one of the two groups found.
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https://arxiv.org/abs/2511.00541
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18f1eb1b67ba1ab4e5517576b8dbef10fa7c8cd254463508798f366382897a9a
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2026-01-01T00:00:00-05:00
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New Algebraic Points on Curves
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arXiv:2511.15635v2 Announce Type: replace Abstract: Let $C$ be a smooth projective absolutely irreducible curve of genus at least 2, defined over the rationals. For a number field $L$, we define the set of $L$-new points on $C$ to be $C(L)_{new} = \{P \in C(L) : \mathbb{Q}(P)=L\}$; this is the set of points on $C$ defined over $L$ but not any strictly smaller field. Let $n$ be at least 2. We conjecture that $C(L)_{new}$ is empty for 100 percent of degree $n$ number fields $L$ when ordered by absolute discriminant. For degrees $n=2$, $3$, we give sufficient criteria for our conjecture to hold in terms of an explicit model for $C$. For general $n$ we prove a theorem that harmonises with the conjecture. In particular, we verify our conjecture for $n=2$ and $C=X_0(N)$ for the $18$ values $N \ne 37$ such that $X_0(N)$ is hyperelliptic, and also for $n=3$ and $C=X_0(23)$, $X_0(29)$, $X_0(31)$, $X_0(64)$. Moreover, we prove the analogue of our conjecture for the unit equation, again with $n=3$.
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https://arxiv.org/abs/2511.15635
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7c2ae2be3cf0e8f441703bf1096244b2c7e693167f95bf9e2fc9b981d2cc3ec4
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2026-01-01T00:00:00-05:00
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Classical localization problem: a survey
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arXiv:2511.18216v2 Announce Type: replace Abstract: We survey classical localization problems arising from quantum network models in symmetry class C and their mappings to history-dependent random walks on directed lattices. We describe how localization versus delocalization of trajectories can be analysed using percolation methods and combinatorial enumeration of path intersection patterns. In particular, we review results establishing almost sure finiteness of trajectories for parameters near criticality and polynomial bounds on the confinement length in cylindrical geometries.
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https://arxiv.org/abs/2511.18216
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422f77bcebb482b81e4a6d32a8f53184b944e72ab469284ae9a2974474b5e996
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2026-01-01T00:00:00-05:00
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Local Laws and Fluctuations for Super-Coulombic Riesz Gases
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arXiv:2511.18623v2 Announce Type: replace Abstract: We study the local statistical behavior of the super-Coulombic Riesz gas of particles in Euclidean space of arbitrary dimension, with inverse power distance repulsion integrable near $0$, and with a general confinement potential, in a certain regime of inverse temperature. Using a bootstrap procedure, we prove local laws on the next order energy and control on fluctuations of linear statistics that are valid down to the microscopic lengthscale, and provide controls for instance, on the number of particles in a (mesoscopic or microscopic) box, and the existence of a limit point process up to subsequences. As a consequence of the local laws, we derive an almost additivity of the free energy that allows us to exhibit for the first time a CLT for Riesz gases corresponding to small enough inverse powers, at small mesoscopic length scales, which can be interpreted as the convergence of the associated potential to a fractional Gaussian field. Compared to the Coulomb interaction case, the main new issues arise from the nonlocal aspect of the Riesz kernel. This manifests in (i) a novel technical difficulty in generalizing the transport approach of Lebl\'e and the second author to the Riesz gas which now requires analyzing a degenerate and singular elliptic PDE, (ii) the fact that the transport map is not localized, which makes it more delicate to localize the estimates, (iii) the need for coupling the local laws and the fluctuations control inside the same bootstrap procedure.
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https://arxiv.org/abs/2511.18623
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94f5c5340e422ee30478343b591081a9d8e7c96f608c0845b65d3d4f99f51655
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2026-01-01T00:00:00-05:00
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Generalized Latin Square Graphs of Semigroups: A Counting Framework for Regularity and Spectra
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arXiv:2511.23190v2 Announce Type: replace Abstract: We introduce the \emph{Generalized Latin Square Graph} $\Gamma(S)$ of a finite semigroup $S$. Since we record global factorization multiplicities and local alternative counts, we define three counting invariants $N_S,N_R,N_C$. This gives that we have a simple degree formula \[ \text{deg}(v)=2n-3+Q(v),\qquad Q(v)=N_S(s_k)-2N_R(v)-2N_C(v). \] We show that $\Gamma(S)$ is regular exactly when $Q$ is constant. We apply the framework to cancellative semigroups, bands, Brandt semigroups and null semigroups. For null semigroups, since we identify $\Gamma(S)\cong K_n\times K_n$, we compute the spectrum and energy. A concise computational appendix lists the \texttt{GAP} driver and representative outputs.
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https://arxiv.org/abs/2511.23190
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3dbf7c7b9037073ffb3513b609ddcf90bbaa15ad43462ea3f41469060eda10b9
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2026-01-01T00:00:00-05:00
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Avoidance of non-strict saddle points by blow-up
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arXiv:2511.23268v2 Announce Type: replace Abstract: It is an old idea to use gradient flows or time-discretized variants thereof as methods for solving minimization problems. In some applications, for example in machine learning contexts, it is important to know that for generic initial data, gradient flow trajectories do not get stuck at saddle points. There are classical results concerned with the non-degenerate situation. But if the Hessian of the objective function has a non-trivial kernel at the critical point, then these results are inconclusive in general. In this paper, we show how relevant information can be extracted by ``blowing up'' the objective function around the non-strict saddle point, i.e., by a suitable non-linear rescaling that makes the higher order geometry visible.
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https://arxiv.org/abs/2511.23268
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40854c9ffbf85f39656ad165d31e87a1fd5d1fd3cd870deba67a76d6e3c03314
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2026-01-01T00:00:00-05:00
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Hamiltonicity of optimal 2-planar graphs
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arXiv:2512.11535v2 Announce Type: replace Abstract: A classical result of Tutte shows that every 4-connected planar graph is Hamiltonian. In recent years, there has been growing interest in extending classical Hamiltonian results from planar graphs to sparse graphs with drawings allowing crossings, such as $k$-planar graphs, where each edge is crossed at most $k$ times. For example, using different approaches, Hud\'ak, Tom\'a\v{s} and Suzuki, as well as Noguchi and Suzuki, independently proved that every optimal 1-planar graph is Hamiltonian. Here, an optimal 1-planar graph refers to one that attains the maximum possible number of edges. In this paper, we establish results on the Hamiltonicity of optimal 2-planar graphs, that is, 2-planar graphs with the maximum number of edges. More precisely, we show that every 4-connected optimal 2-planar graph is Hamiltonian-connected. With vertex-connectivity 3, there exist infinitely many optimal 2-planar graphs that are non-Hamiltonian.
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https://arxiv.org/abs/2512.11535
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c6eda61d5f1fc8546340d1cc4969dd82950c1a4f5500c435a5ed4b13b364eafe
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2026-01-01T00:00:00-05:00
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Teleportation=Translation: Continuous recovery of black hole information
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arXiv:2512.11877v3 Announce Type: replace Abstract: The \textit{Teleportation=Translation} conjecture posits that the recovery of information from a black hole is dual to a geometric translation in the emergent spacetime. In this paper, we establish this equivalence by constructing a continuous family of unitaries that bridges the discrete algebraic teleportation protocol and modular flow. We resolve the failure of dynamic idempotency, inherent in Type III von Neumann algebras, by employing the Haagerup-Kosaki crosse-product construction. This lift to the semifinite envelope yields a canonical, dynamically consistent path whose unique self-adjoint generator $\tilde{G}$ is proven to be twice the modular Hamiltonian difference, $\tilde{G}=2(K_{\tilde{\mathcal{M}}}-K_{\tilde{\mathcal{N}}})$. We establish this identity as a closed operator equivalence using Nelson's analytic vector theorem and quantify its structural robustness via Kosaki's non-commutative $L^p$ theory. Our results provide a concrete analytic mechanism for probing emergent geometry from quantum information, offering a kinematic framework naturally extendable to include gravitational back-reaction.
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https://arxiv.org/abs/2512.11877
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1bc69f6969faa7847709739042d672b4fe5bbf7c0d35c477adf3b7707022914a
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2026-01-01T00:00:00-05:00
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Complements of discriminants of real parabolic function singularities. II
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arXiv:2512.12738v2 Announce Type: replace Abstract: We provide a complete list of the connected components of the spaces of non-discriminant functions within standard versal deformations of function singularities of classes $X_9$, $J_{10}$ and $P_8^1$ (as well as a partial list for the remaining class, $P_8^2$). Thus, we prove (and improve in one particular case) the corresponding conjectures from the previous work \cite{para} with the same title. As an application, we enumerate all local Petrovskii lacunas near arbitrary parabolic singularities of wavefronts of hyperbolic PDEs. In particular, we discover a new local lacuna at the $P_8^2$ singularities. We also show that the complements of the discriminant varieties of $X_9^+$ and $P_8^1$ singularities have nontrivial one-dimensional homology groups, unlike all simple singularities.
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https://arxiv.org/abs/2512.12738
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6c66087eb01d5367826ff239aac5b668d88e314d32fc1b576a4631257c381819
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2026-01-01T00:00:00-05:00
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Hyperbolic equations with fifth-order symmetries
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arXiv:2512.12789v2 Announce Type: replace Abstract: This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where $u(x,y)$ is the unknown function and $x,y$ are independent variables. The classification is based on the requirement for the existence of higher fifth-order symmetries. As a result, a list of four equations with the required conditions was obtained.
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https://arxiv.org/abs/2512.12789
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4c0eb734d6c81ab86a46ea132f6a965ff7afe7bce090502f8b521c00ed24a817
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2026-01-01T00:00:00-05:00
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Well-Posedness of Pseudo-Parabolic Gradient Systems with State-Dependent Dynamics
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arXiv:2512.15164v2 Announce Type: replace Abstract: This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fields in the governing energy functional. Such coefficients arise naturally in scientific and technological models, including state-dependent mobilities in KWC-type grain boundary motion and variable orientation-adaptation operators in anisotropic image denoising. We establish two main results: the existence of energy-dissipating solutions, and the uniqueness and continuous dependence on initial data. The proposed framework yields a general well-posedness theory for a broad class of nonlinear evolutionary systems driven by state-dependent operators. As illustrative applications, we present an anisotropic image-denoising model and a new pseudo-parabolic KWC-type model for anisotropic grain boundary motion, and prove that both fit naturally within the abstract structure of $(\mathrm{S})_\nu$.
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https://arxiv.org/abs/2512.15164
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6118263bd7853dfafdbbc304a6577bb02aeb43b7d207cec0dc2ce94415c7cbca
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2026-01-01T00:00:00-05:00
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Capillary $L_p$-Christoffel-Minkowski problem
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arXiv:2512.15464v2 Announce Type: replace Abstract: We solve the capillary $L_p$-Christoffel--Minkowski problem in the half-space for $1<k+1$ in the class of even hypersurfaces. A crucial ingredient is a non-collapsing estimate that yields lower bounds for both the height and the capillary support function. Our result extends the capillary Christoffel--Minkowski existence result of \cite{HIS25}.
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https://arxiv.org/abs/2512.15464
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57f68207b4bab4979c6d3b4736f48cea916ca320cac41f9186d1d197a7d620fa
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2026-01-01T00:00:00-05:00
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A semicircle law for the normalized Laplacian of sparse random graphs
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arXiv:2512.20146v2 Announce Type: replace Abstract: We study the limiting spectral distribution of the normalized Laplacian $\mathcal L$ of an Erd\H{o}s-R\'enyi graph $G(n,p)$. To account for the presence of isolated vertices in the sparse regime, we define $\mathcal L$ using the Moore-Penrose pseudoinverse of the degree matrix. Under this convention, we show that the empirical spectral distribution of a suitably normalized $\mathcal L$ converges weakly in probability to the semicircle law whenever $np\to\infty$, thereby providing a rigorous justification of a prediction made in (Akara-pipattana and Evnin, 2023). Moreover, if $np>\log n+\omega(1)$, so that $G(n,p)$ has no isolated vertices with high probability, the same conclusion holds for the standard definition of $\mathcal L$. We further strengthen this result to almost sure convergence when $np=\Omega(\log n)$. Finally, we extend our approach to the Chung-Lu random graph model, where we establish a semicircle law for $\mathcal L$ itself, improving upon (Chung, Lu, and Vu 2003), which obtained the semicircle law only for a proxy matrix.
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https://arxiv.org/abs/2512.20146
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e7a91764889ff90804b4bc9d146457b23f355624327acbba1822ed3f7f1dfbc6
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2026-01-01T00:00:00-05:00
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On the Euclidean Distance Degree of Quadratic Two-Neuron Neural Networks
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arXiv:2512.21016v3 Announce Type: replace Abstract: We study the Euclidean Distance degree of algebraic neural network models from the perspective of algebraic geometry. Focusing on shallow networks with two neurons, quadratic activation, and scalar output, we identify the associated neurovariety with the second secant variety of a quadratic Veronese embedding. We introduce and analyze the virtual Euclidean Distance degree, a projective invariant defined as the sum of the polar degrees of the variety, which coincides with the usual Euclidean Distance degree for a generic choice of scalar product. Using intersection theory, Chern-Mather classes, and the Nash blow-up provided by Kempf's resolution, we reduce the computation of the virtual Euclidean Distance degree to explicit intersection numbers on a Grassmannian. Applying equivariant localization, we prove that this invariant depends stably polynomially on the input dimension. Numerical experiments based on homotopy continuation illustrate the dependence of the Euclidean Distance degree on the chosen metric and highlight the distinction between the generic and nongeneric cases, such as the Bombieri-Weyl metric.
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https://arxiv.org/abs/2512.21016
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14145c5834405a2ea4822afecff45abd18b45a537cecbedadaa8f280ed9938bf
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2026-01-01T00:00:00-05:00
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A Sieve M-Estimator for Entropic Optimal Transport
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arXiv:2512.21981v2 Announce Type: replace Abstract: The entropically regularized optimal transport problem between probability measures on compact Euclidean subsets can be represented as an information projection with moment inequality constraints. This allows its Fenchel dual to be approximated by a sequence of convex, finite-dimensional problems using sieve methods, enabling tractable estimation of the primal value and dual optimizers from samples. Assuming only continuity of the cost function, I establish almost sure consistency of these estimators. I derive a finite-sample convergence rate for the primal value estimator, showing logarithmic dependence on sieve complexity, and quantify uncertainty for the dual optimal value estimator via matching stochastic bounds involving suprema of centered Gaussian processes. These results provide the first statistical guarantees for sieve-based estimators of entropic optimal transport, extending beyond the empirical Sinkhorn approach.
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https://arxiv.org/abs/2512.21981
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29c3db8088aa39be8e4e60f641b339a781d222f13969ee6223f206b0f874caad
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2026-01-01T00:00:00-05:00
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Tiling Triangles with $2\pi/3$ Angles
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arXiv:2512.22696v2 Announce Type: replace Abstract: Motivated by a question of Erd\"{o}s and inquiries by Beeson and Laczkovich, we explore the possible $N$ for which a triangle $T$ can tile into $N$ congruent copies of a triangle $R$. The \emph{reptile} cases (where $T$ is similar to $R$) and the \emph{commensurable-angles} cases (where all angles of $R$ are rational multiples of $\pi$) are well-understood. We tackle the most interesting remaining case, which is when $R$ contains an angle of $2\pi/3$ and when $T$ is one of $6$ ``sporadic'' specific triangles, of which only $2$ were known to have constructions. For each of these, we create a family of constructions and conjecture that they are the only possible $N$ that occur for these triangles.
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https://arxiv.org/abs/2512.22696
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b29d1db98a40a966e7b07eb03bd7f259d03f1d24fff7415c424dd779b883a7b2
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2026-01-01T00:00:00-05:00
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L\^e modules and hypersurfaces with one-dimensional singular sets
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arXiv:2512.23058v2 Announce Type: replace Abstract: By using our previous results on L\^e modules and an upper-bound on the betti numbers which we proved with L\^e, we investigate the cohomology of Milnor fibers and the internal local systems given by the vanishing cycles of hypersurfaces with one-dimensional singular sets.
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https://arxiv.org/abs/2512.23058
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8e0885a068fcf4157d44b970c85faf25f826a9504d79107ed464271c2906fb76
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Bounding the integral of the argument of the Riemann Zeta function
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arXiv:2512.23064v2 Announce Type: replace Abstract: This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the exact number of zeta zeros up to a given height.
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https://arxiv.org/abs/2512.23064
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d40e465c2a29bc67092114942beafac86bb4e11c63c743812691986b9fe07f56
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2026-01-01T00:00:00-05:00
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Intersections of sumsets in additive number theory
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arXiv:2512.23574v2 Announce Type: replace Abstract: Let $A$ be a subset of an additive abelian semigroup and let $hA$ be the $h$-fold sumset of $A$. The following question is considered: Let $(A_q)_{q=1}^{\infty}$ be a strictly decreasing sequence of sets in the semigroup and let $A = \bigcap_{q=1}^{\infty} A_q$. When does one have \[ hA = \bigcap_{q=1}^{\infty} hA_q \] for some or all $h \geq 2$?
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https://arxiv.org/abs/2512.23574
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2d84a8c31016c4262039d09b08d6827d3940595db9bd3d238cdb53b70575897d
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2026-01-01T00:00:00-05:00
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The Time-Periodic Cahn-Hilliard-Gurtin System on the Half Space as a Mixed-Order System with General Boundary Conditions
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arXiv:2512.23582v2 Announce Type: replace Abstract: A well-posedness and maximal regularity result for the time-periodic Cahn-Hilliard-Gurtin system in the half space is proved. For this purpose, we introduce a novel class of complementing boundary conditions, extending the classical Lopatinski\u{\i}-Shapiro conditions from elliptic and parabolic theory to time-periodic mixed-order systems with general boundary conditions. Moreover, we show that the classical Lopatinski\u{\i}-Shapiro conditions are in general insufficient for well-posedness of mixed-order systems.
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https://arxiv.org/abs/2512.23582
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d73597cfddf4bc0ae839ecab513922788df268dcbf38deadf037d222d67ccbf2
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2026-01-01T00:00:00-05:00
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Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises
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arXiv:2205.06070v5 Announce Type: replace-cross Abstract: We show how measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling, and causal relations for macroscopic quantities. Considering measurement of a field amplitude $\hat{x}$, we derive theorems that lead to an equivalence between a quantum phase-space probability distribution Q(x,p,t) and stochastic trajectories for real amplitudes x and p propagating backwards and forwards in time, respectively. We present forward-backward stochastic simulations that motivate a Q-based model of reality. Amplification plays a key role in measurement. With amplification, contributions due to interference become unobservable, leading to branches that correspond to distinct eigenvalues. This elucidates how the system evolves from a superposition to an eigenstate, from which Born's rule follows. We deduce a hybrid causal structure involving causal deterministic relations for amplified variables, along with microscopic noise inputs and hidden loops for unobservable quantities. Causal consistency is confirmed. The simulations allow evaluation of a state inferred for the system, conditioned on a particular branch, from which we deduce a model for projection and collapse of the wave function. The theory is extended to Einstein-Podolsky-Rosen and Bell nonlocality. We demonstrate consistency with three weak local realistic premises: the existence of real properties (defined after operations that fix measurement settings); a partial locality implying no-signaling; elements of reality that apply to the predictions of a system by a meter, once meter-settings are fixed. A mechanism for non-locality is identified. Our work shows how forward-backward stochastic simulations lead to a hybrid causal structure, involving both deterministic causal relations and hidden stochastic loops, explaining measurement and entanglement, with paradoxes associated with retrocausality avoided.
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https://arxiv.org/abs/2205.06070
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37c14013e745b273049e727e52a143f82eb1b7c14eeb87cd5f6c42417dc202c6
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2026-01-01T00:00:00-05:00
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Decomposition of $\mathcal{N}=1$ superconformal minimal models and their fractional quantum Hall wavefunctions
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arXiv:2303.10107v2 Announce Type: replace-cross Abstract: $\mathcal{N}=1$ superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal models using combinations of a parafermion theory, an Ising theory and a free boson theory. Supercurrent operators in the original theory also becomes sums of operators from each constituent theory. If we take our $\mathcal{N}=1$ superconformal theories as the neutral part of the edge theory of a fractional quantum Hall state, we present a systematic way of calculating its ground state wavefunction using free field methods. Each ground state wavefunction is known previously as a sum of polynomials with distinct clustering behaviours. Based on our decomposition, we find explicit expressions for each summand polynomial. A brief generalization to $S_3$ minimal models using coset construction is also included.
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https://arxiv.org/abs/2303.10107
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64281923cbce4c2a3c2e0132e9374c8ff1d702594503c334a01ca32b8d863d13
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2026-01-01T00:00:00-05:00
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Studentising Kendall's Tau: U-Statistic Estimators and Bias Correction for a Generalised Rank Variance-Covariance framework
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arXiv:2307.10973v2 Announce Type: replace-cross Abstract: Kemeny (1959) introduced a topologically complete metric space to study ordinal random variables, particularly in the context of Condorcet's paradox and the measurability of ties. Building on this, Emond & Mason (2002) reformulated Kemeny's framework into a rank correlation coefficient by embedding the metric space into a Hilbert structure. This transformation enables the analysis of data under weak order-preserving transformations (monotonically non-decreasing) within a linear probabilistic framework. However, the statistical properties of this rank correlation estimator, such as bias, estimation variance, and Type I error rates, have not been thoroughly evaluated. In this paper, we derive and prove a complete U-statistic estimator in the presence of ties for Kemeny's \(\tau_{\kappa}\), addressing the positive bias introduced by tied ranks. We also introduce a consistent population standard error estimator. The null distribution of the test statistic is shown to follow a \(t_{(N-2)}\)-distribution. Simulation results demonstrate that the proposed method outperforms Kendall's \(\tau_{b}\), offering a more accurate and robust measure of ordinal association which is topologically complete upon standard linear models.
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https://arxiv.org/abs/2307.10973
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ac88cdc88a74def0bfefbb9e9d730eb52bb1045ad08a9de9c8a620cc700a5e6b
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2026-01-01T00:00:00-05:00
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The Population Resemblance Statistic: A Chi-Square Measure of Fit for Banking
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arXiv:2307.11878v4 Announce Type: replace-cross Abstract: The Population Stability Index (PSI) is a widely used measure in credit risk modeling and monitoring within the banking industry. Its purpose is to monitor for changes in the population underlying a model, such as a scorecard, to ensure that the current population closely resembles the one used during model development. If substantial differences between populations are detected, model reconstruction may be necessary. Despite its widespread use, the origins and properties of the PSI are not well documented. Previous literature has suggested using arbitrary constants as a rule-of-thumb to assess resemblance (or "stability"), regardless of sample size. However, this approach too often calls for model reconstruction in small sample sizes while not detecting the need often enough in large sample sizes. This paper introduces an alternative discrepancy measure, the Population Resemblance statistic (PRS), based on the Pearson chi-square statistic. Properties of the PRS follow from the non-central chi-square distribution. Specifically, the PRS allows for critical values that are configured according to sample size and the number of risk categories. Implementation relies on the specification of a set of parameters, enabling practitioners to calibrate the procedure with their risk tolerance and sensitivity to population shifts. The PRS is demonstrated to be universally competent in a simulation study and with real-world examples.
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https://arxiv.org/abs/2307.11878
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fbbd01385ae49323355e16d00cdc8c909648d41c7dd9a8963be59cb7b2439c83
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2026-01-01T00:00:00-05:00
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Quantum Expander Mixing Lemma and its Structural Converse
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arXiv:2403.11454v2 Announce Type: replace-cross Abstract: Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory, quantum complexity, and noncommutative pseudorandomness. The classical expander mixing lemma plays a central role in graph theory, offering essential insights into edge distribution within graphs and aiding in the analysis of diverse network properties and algorithms. This paper establishes the quantum analogue of the classical expander mixing lemma and its structural converse for quantum expanders.
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https://arxiv.org/abs/2403.11454
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22cae4e650eb880be1447459b8efbed4bf826944f3adb3a4be83782403437cbc
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2026-01-01T00:00:00-05:00
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Binary Galton-Watson trees with mutations
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arXiv:2501.10951v2 Announce Type: replace-cross Abstract: We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and distributions of different types. This allows us in particular to estimate the proportions of different types in the long run, as well as the distribution of the first time of occurrence of a given type as the tree size or time increases. Our approach relies on the recursive computation of the joint distribution of types conditionally to the value of the total progeny. In comparison with the literature on related multitype models, we do not rely on approximations.
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https://arxiv.org/abs/2501.10951
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14f2683f4b1a2d9040c6883574b932cbe698507cf568a482b1a39b99c2b3087b
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2026-01-01T00:00:00-05:00
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Classical Estimation of the Free Energy and Quantum Gibbs Sampling from the Markov Entropy Decomposition
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arXiv:2504.17405v2 Announce Type: replace-cross Abstract: We revisit the Markov Entropy Decomposition, a classical convex relaxation algorithm introduced by Poulin and Hastings to approximate the free energy in quantum spin lattices. We identify a sufficient condition for its convergence, namely the decay of the effective interaction. The effective interaction, also known as Hamiltonians of mean force, is a widely established correlation measure, and we show our decay condition in 1D at any temperature as well as in the high-temperature regime under a certain commutativity condition on the Hamiltonian building on existing results. This yields polynomial and quasi-polynomial time approximation algorithms in these settings, respectively. Furthermore, the decay of the effective interaction implies the decay of the conditional mutual information for the Gibbs state of the system. We then use this fact to devise a rounding scheme that maps the solution of the convex relaxation to a global state and show that the scheme can be efficiently implemented on a quantum computer, thus proving efficiency of quantum Gibbs sampling under our assumption of decay of the effective interaction.
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https://arxiv.org/abs/2504.17405
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2d1e661840b0c7cd94b87079c887bd3027b80d1969f7e8336961727c7bd16359
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2026-01-01T00:00:00-05:00
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Gravitational radiation at infinity with negative cosmological constant and AdS$_4$ holography
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arXiv:2507.05826v4 Announce Type: replace-cross Abstract: The covariant characterization of the existence of gravitational radiation traversing infinity $\mathscr{J}$ in the presence of a negative cosmological constant is presented. It is coherent and consistent with the previous characterizations put forward for the cases of non-negative cosmological constant, relying on the properties of the asymptotic super-Poynting vector; or in more transparent terms, based on the intrinsic properties of the flux of tidal energy at infinity. The proposed characterization is fully satisfactory, it can be covariantly typified in terms of boundary data at infinity, and it can also be categorized according to the geometric properties of the rescaled Weyl tensor at $\mathscr{J}$. The cases with no incoming radiation entering from (or no outgoing radiation escaping at) $\mathscr{J}$ can similarly be determined in terms of the boundary data or geometric properties of the rescaled Weyl tensor. In particular, we identify the most general boundary conditions that, in an initial-boundary value problem, ensure absence of gravitational radiation traversing $\mathscr{J}$, namely (functional) proportionality between the Cotton-York tensor field and the holographic stress tensor field at $\mathscr{J}$. We also present novel conditions ensuring the absence of just incoming (outgoing) radiation at $\mathscr{J}$. These are given in a covariant way and also in terms of standard rescaled Weyl tensor scalars. The results are compatible with any matter content of the physical spacetime.
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https://arxiv.org/abs/2507.05826
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1f7c3d5113fa83beea445f94177ac0e68da8122c1ecc23e0bd44ece5b061d898
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2026-01-01T00:00:00-05:00
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Optically Controlled Skyrmion Number Current
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arXiv:2508.11209v2 Announce Type: replace-cross Abstract: We propose a mechanism to control the motion of magnetic Skyrmions through the generation of a Skyrmion number current. This current is induced and tuned by an explicitly time-dependent Hamiltonian that includes a Zeeman term arising from the interaction between the spin system and circularly polarized light. To capture the effect, we apply a first-order perturbation method to the Landau-Lifshitz-Gilbert equation, using a breathing Skyrmion ansatz based on the Belavin-Polyakov profile. This approach reveals that the time-dependent deformation of the Skyrmion boundary produces an anisotropic breathing mode, which in turn generates a nonzero Skyrmion number current. The resulting dynamics in momentum space form a limit cycle, whose characteristics depend on the external magnetic field amplitude, the Heisenberg exchange coupling, and the Gilbert damping constant. Our formulation not only clarifies the topological origin of optically driven Skyrmion motion but also points to Skyrmion number currents as a low-dissipation alternative to electric currents for efficient Skyrmion control.
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https://arxiv.org/abs/2508.11209
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6f13d9fe3c21f3eb71e3ebe1ea26fd5b1e95a21cad5542617bd78677a584c5ce
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2026-01-01T00:00:00-05:00
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Quiver superconformal index and giant gravitons: asymptotics and expansions
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arXiv:2509.12123v3 Announce Type: replace-cross Abstract: We study asymptotics of the $d=4$, $\mathcal{N}=1$ superconformal index for toric quiver gauge theories. Using graph-theoretic and algebraic factorization techniques, we obtain a cycle expansion for the large-$N$ index in terms of the $R$-charge-weighted adjacency matrix. Applying saddle-point techniques at the on-shell $R$-charges, we determine the asymptotic degeneracy in the univariate specialization for $\hat{A}_{m}$, and along the main diagonal for the bivariate index for $\mathcal{N}=4$ and $\hat{A}_{3}$. In these cases we find $\ln |c_{n}| \sim \gamma n^{\frac{1}{2}}+ \beta \ln n + \alpha$ (Hardy-Ramanujan type). We also identify polynomial growth for $dP3$, $Y^{3,3}$ and $Y^{p,0}$, and give numerical evidence for $\gamma$ in further $Y^{p,p}$ examples. Finally, we generalize Murthy's giant graviton expansion via the Hubbard-Stratonovich transformation and Borodin-Okounkov formula to multi-matrix models relevant for quivers.
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https://arxiv.org/abs/2509.12123
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d41605f7b3467e50102b06dfb1333fb955bdfaf7208b0ba2667c04f4ec483b66
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2026-01-01T00:00:00-05:00
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Quantum Signatures of Strange Attractors
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arXiv:2510.01416v3 Announce Type: replace-cross Abstract: In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate the quantum Duffing oscillator, a paradigmatic chaotic system, using the Caldirola-Kanai (CK) framework, where dissipation is integrated directly into a time-dependent Hamiltonian. By employing the Husimi distribution to represent the quantum state in phase space, we present the first visualization of a quantum strange attractor within this model. Our simulations demonstrate how an initially simple Gaussian wave packet is stretched, folded, and sculpted by the interplay of chaotic dynamics and energy loss, causing it to localize onto a structure that beautifully mirrors the classical attractor. This quantum "photograph" is inherently smoothed, blurring the infinitely fine fractal details of its classical counterpart as a direct consequence of the uncertainty principle. We supplement this analysis by examining the out-of-time-ordered correlator (OTOC), which shows that stronger dissipation clarifies the exponential growth associated with the classical Lyapunov exponent, thereby confirming the model's semiclassical behavior. This work offers a compelling geometric perspective on open chaotic quantum systems and sheds new light on the quantum-classical transition.
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https://arxiv.org/abs/2510.01416
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aa04d5e453bd7b98118405c81d044f5c25a67930cf039650328b332f4eeb037a
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2026-01-01T00:00:00-05:00
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The Popkov-Sch\"{u}tz two-lane lattice gas: Universality for general jump rates
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arXiv:2510.12678v2 Announce Type: replace-cross Abstract: We consider the asymmetric version of the Popkov-Sch\"{u}tz two-lane lattice gas with general jump rates, subject to the stationary measure being of product form. This still leaves five free parameters. At density 1/2 the eigenvalues of the flux Jacobian are degenerate. We compute the second order expansion of the average fluxes at density 1/2 and thereby identify the universality classes.
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https://arxiv.org/abs/2510.12678
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cf0d0a891889aacda129059ca68c7872a0749a4fa15f900b6df8ee8913d88aaf
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2026-01-01T00:00:00-05:00
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Results on Lorentzian metric spaces
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arXiv:2510.24423v2 Announce Type: replace-cross Abstract: We provide a short introduction to ``Lorentzian metric spaces" i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed, such as the continuity of the Lorentzian distance and the relative compactness of chronological diamonds. The latter condition is natural for interpreting these spaces as low-regularity versions of globally hyperbolic spacetimes. Confirming this interpretation, we prove that every Lorentzian metric space admits a Cauchy time function. The proof is constructive for this general setting and it provides a novel argument that is interesting already for smooth spacetimes.
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https://arxiv.org/abs/2510.24423
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a51b4a6daec37ae1e8a1b1ec5ae730bc657099bac6a2da8c7826d6e2031a621b
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2026-01-01T00:00:00-05:00
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Torus Knots in Adjoint Representation
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arXiv:2512.23095v2 Announce Type: replace-cross Abstract: We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.
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https://arxiv.org/abs/2512.23095
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faf3809ad0b1488d2374806680af801ce1f2835fec379f62af4c164ebfc93f71
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2026-01-01T00:00:00-05:00
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Lambda Expected Shortfall
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arXiv:2512.23139v2 Announce Type: replace-cross Abstract: The Lambda Value-at-Risk (Lambda$-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk measures alongside VaR because of its various desirable properties in the practice of optimization, risk management, and financial regulation. Analogously to the intimate relation between ES and VaR, we introduce the Lambda Expected Shortfall (Lambda-ES), as a generalization of ES and a counterpart to Lambda-VaR. Our definition of Lambda-ES has an explicit formula and many convenient properties, and we show that it is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR under mild assumptions. We examine further properties of Lambda-ES, its dual representation, and related optimization problems.
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https://arxiv.org/abs/2512.23139
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a61a28192c9b97294c89ccabbcc49be82cbeca7fff8c4f7973ad1a00b6536b3b
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2026-01-01T00:00:00-05:00
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Machine-Learning Classification of Neutron-Star Matter Composition from Macroscopic and Oscillation Observables
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arXiv:2512.23758v1 Announce Type: new Abstract: The microscopic composition of neutron star interiors remains uncertain, with possible scenarios including nucleonic matter, hyperonic matter, dark matter admixed cores, and strange self-bound matter. Traditional constraints on the equation of state rely on Tolman Oppenheimer Volkoff modelling and comparison with multimessenger observations, but machine learning provides a complementary pathway by learning composition dependent patterns directly from astrophysically accessible observables. This work presents a compact supervised learning framework for EOS family classification using stellar properties derived from TOV modelling, asteroseismology, and gravitational wave descriptors. A labelled dataset of neutron star configurations spanning four EOS families (nucleonic, strange matter, dark matter admixed, and hyperonic) is constructed using seven input features: gravitational mass, radius, fundamental f mode frequency, quadrupole moment, redshift, damping time, and characteristic strain. A multilayer perceptron is trained to infer the underlying matter composition. On a held out test set, the classifier achieves an accuracy of 97.4 percent with strong class wise precision and recall. Permutation based feature importance analysis shows that oscillation related quantities, especially the f mode frequency and damping time, dominate the discriminatory power, while mass and radius provide secondary support. Residual misclassifications occur in physically intuitive regions where different EOS families produce partially overlapping macroscopic signatures. These results show that lightweight neural models can reliably identify EOS family fingerprints from a modest set of observables, providing a reproducible baseline for future extensions incorporating Bayesian uncertainty and observational posteriors from NICER and gravitational wave events.
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https://arxiv.org/abs/2512.23758
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1752613fd97fd3b231a1df16f7e5e69870c6ddfff84ac38e90b79051ce52af04
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2026-01-01T00:00:00-05:00
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Clustering of cosmic string loops within a Milky-way like halo
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arXiv:2512.23811v1 Announce Type: new Abstract: Loops of cosmic string experience a recoil from anisotropic gravitational radiation, known as the rocket effect, which influences the extent to which they are captured by galaxies during structure formation. Analytical studies have reached different conclusions regarding loop capture in galaxies: early treatments argued for efficient capture, while later analyses incorporating the loop rocket force throughout halo formation found that capture efficiency is reduced and strongly dependent on loop size. In this work, we employ the N-body simulation code GADGET-4, introducing non-backreacting tracer particles subject to a constant recoil force to model cosmic string loops with the rocket effect. We simulate the formation of a Milky-Way-like halo from redshift $z=127$ to $z=0$, considering loop populations characterized by a range of length parameters $\xi$, inversely proportional to the rocket acceleration. We find that the number of captured loops exhibits a pronounced peak at $\xi_{\textrm{peak}}\simeq 12.5$, arising from the competition between rocket-driven ejection at small $\xi$ and the declining intrinsic loop abundance at large $\xi$. For fiducial string tensions, this corresponds to $\mathcal{O}(10^6)$ loops within the halo. We further find that loops with weak rocket forces closely trace the dark-matter distribution, while those subject to stronger recoil but still captured -- particularly the most abundant loops near $\xi_{\textrm{peak}}$ -- are preferentially concentrated toward the central regions of the halo.
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https://arxiv.org/abs/2512.23811
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3cc240742b5c5c02abd65c0150f48b7016f8d7093d425db4a622f8bc0e952793
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2026-01-01T00:00:00-05:00
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COBIPLANE: A Systematic Search for Compact Binary Millisecond Pulsars at Low Galactic Latitudes
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arXiv:2512.23815v1 Announce Type: new Abstract: We present the main results obtained from the COmpact BInary Pulsar search in the low-LAtitude NEighborhood (COBIPLANE), an optical photometric survey designed to find new `spider' binary millisecond pulsars. We conducted observations targeting 30 unidentified sources from the 4FGL-DR3 Fermi Large Area Telescope (Fermi-LAT) catalog, selected for their pulsar-like $\gamma$-ray properties. Extending to Galactic latitudes as low as $\pm3^{\circ}$, this survey reaches closer to the Galactic plane than its predecessor survey, the COmpact BInary PULsar SEarch (COBIPULSE). We report the discovery of five optical variables coincident with the localizations of 4FGL J0821.5-1436, 4FGL J1517.9-5233, 4FGL J1639.3-5146, 4FGL J1748.8-3915, and 4FGL J2056.4+3142. These systems show optical flux modulation at the presumed orbital periods of $0.41576(6) \ \mathrm{d}$, $0.305(2) \ \mathrm{d}$, $0.204(7) \ \mathrm{d}$, $0.3(2) \ \mathrm{d}$, and $0.4395(1) \ \mathrm{d}$, respectively, and photometric temperatures of $4000$--$6000 \ \mathrm{K}$, consistent with the companion stars of `redback' subtype of spider pulsar binaries. Based on their optical light curve shapes and X-ray properties characteristic for spider systems -- namely, a luminosity of $1.5 \times 10^{32} \ (D / 3.9 \ \mathrm{kpc})^2 \ \mathrm{erg} \ \mathrm{s}^{-1}$ ($0.3$--$10 \ \mathrm{keV}$) for 4FGL J1748.8-3915, and upper limits of $\sim10^{31}$--$10^{33} \ \mathrm{erg} \ \mathrm{s}^{-1}$ ($0.2$--$12 \ \mathrm{keV}$) for the others -- we classify these sources as new spider candidate systems.
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https://arxiv.org/abs/2512.23815
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060fb669df6752df64b45817d6d0830bfbb8b2a25b4f48c141eee9f7ec109cf4
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2026-01-01T00:00:00-05:00
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A secondary orbiter under collisions with an accretion disk
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arXiv:2512.23826v1 Announce Type: new Abstract: Dynamics of stellar orbits in dense stellar systems and nuclear star clusters (NSC) with an embedded supermassive black hole (SMBH) is governed a complex interplay of different forces. In particular, star--star gravitational collisions (relaxation), physical collisions between stars, and the hydrodynamical interaction with any surrounding gaseous environment, such as an accretion disk. These processes influence the stellar distribution, the feeding of the central black hole, and the generation of observable phenomena. Furthermore, the self-gravity of the accretion medium modulates the long-term evolution, adding significant complexity to the system's dynamics. By employing elementary arguments we outline the mentioned influences in their mutual competition.
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https://arxiv.org/abs/2512.23826
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febbe8a2af7b0926710c505fede97ce4619f0a184884a29ea6dd7101b8061fda
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2026-01-01T00:00:00-05:00
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A clustering-based search for substructures in the Galactic plane and bulge using RR Lyrae stars as tracers
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arXiv:2512.23846v1 Announce Type: new Abstract: Although many globular clusters (GCs) have been identified in the Galaxy, their population is estimated to be incomplete, especially in regions with strong crowding and interstellar extinction such as the Galactic bulge and plane.RR Lyrae stars, as bright standard candles and tracers of old stellar populations, are powerful tools for finding GCs in these regions, and large catalogs of such stars have recently become available. We aim to construct a sample of RR Lyrae stars with six-dimensional information (three-dimensional positions, proper motions, and metallicities) in the Galactic plane and bulge, and to exploit it using a hierarchical clustering algorithm to search for Galactic substructures. We build a sample of fundamental-mode RR Lyrae (RRab) stars with positions, distances, proper motions, and photometric metallicity estimates from Gaia and VVV data. Using a clustering algorithm calibrated to optimize GC recovery, we identify groups of RRab stars with similar locations in the six-dimensional parameter space. The most promising groups are selected by comparison with the properties of known GCs. We recover many RRab groups associated with known Galactic GCs and derive the first RR Lyrae-based distances for BH 140 and NGC 5986. We also detect small groups of two to three RRab stars at distances up to ~25 kpc that are not associated with any known GC, but display GC-like distributions in all six parameters. Several of these groups, mostly pairs, lie toward the Galactic bulge but show distinct proper motions or distances, suggesting they may not belong to the bulge population. Overall, our approach identifies dozens of GC-like RRab groups in the Galactic plane and bulge, which are excellent targets for follow-up observations. Future radial velocity measurements can test whether the RRab members of these groups are truly co-moving.
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https://arxiv.org/abs/2512.23846
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ae8f7a8763d526a34c34f5a5bcf60d2169a7365acb337d065fdb4b50ca59cd59
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2026-01-01T00:00:00-05:00
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The ionization structure and chemical history in isolated H ii regions of dwarf galaxies with VIMOS/IFU II. The Leo A galaxy
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arXiv:2512.23863v1 Announce Type: new Abstract: Study the ionized gas in metal-poor environments is key to understanding the mechanisms regulating galaxy evolution. However, most of the previous studies of extragalactic HII regions rely on unresolved observations of gaseous structures. We study the south-western, spatially resolved, HII region of Leo A, one of the most studied isolated dwarf galaxies in the Local Group. Using archival VIMOS-IFU/VLT data, we explored its gaseous structure through optical emission lines to gain insights into the present-day drivers of gas physics in this dIrr, and we place constraints on the chemical evolution scenario responsible for this low chemical enrichment. The emission line maps reveal that the strongest emission comes from the south-west region. A stratified distribution of ionic species was detected, likely powered by the young star cluster at the nebular centre. HST/ACS data show that the brightest star is in the centre of both the HII region and the star cluster. Photoionization production rates derived indicate that this star can sustain the ionization budget to power the HII region, although subject to the assumed electron density. Using the direct method, we derived a metallicity of $12+\log(\mathrm{O/H})=7.29\pm0.06$ dex, increasing to $7.46\pm0.09$ dex after correcting for temperature fluctuations, placing Leo A in the low-mass end of the MZR. Chemical evolution models suggest that, under constant accretion, the stellar mass growth and metal enrichment over the last 10 Gyr are successfully reproduced by both leaky-box and gas-regulator models. Those results are similar to those found in SagDIG, supporting a picture in which the present-day evolution of Leo A is dominated by stellar feedback processes. The combination of mass loss mechanisms and accretion events reproduces its chemical evolution, suggesting that Leo A has evolved under a gas equilibrium regime across its lifetime.
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https://arxiv.org/abs/2512.23863
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c086f4a14b5dadc8bfccd1ba23bba856e2de716e9e1935aef3f31fa32af4d43d
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2026-01-01T00:00:00-05:00
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The Tianlai-WIYN North Celestial Cap Redshift Survey
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arXiv:2512.23899v1 Announce Type: new Abstract: We present the results of a small, low redshift spectroscopic survey of galaxies within 3 degrees of the North Celestial Pole (NCP) selected using V-band photometry obtained from the North Celestial Cap Survey (NCCS) (Gorbikov & Brosch 2014). The purpose of the current survey is to create a redshift space template for 21 cm emission from neutral hydrogen with which to correlate radio line intensity observations by the Tianlai dish and cylinder interferometers. A total of 898 redshifts were obtained from the 2102 extended objects in the NCCS with m_V < 19 in the survey area. After accounting for extinction, the survey geometry and selection effects, the number density and clustering pattern of galaxies in the redshift catalog are consistent with other low redshift surveys. We were also able to identify 11 galaxy cluster candidates from this redshift catalog.
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https://arxiv.org/abs/2512.23899
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66d02fe7dfebca16ec460928beff2e44ae9d20b8e92b06d5900a50a218dec84f
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2026-01-01T00:00:00-05:00
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Variation of the 2175 {\AA} extinction feature in Andromeda galaxy
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arXiv:2512.23958v1 Announce Type: new Abstract: Extinction curves contain key information on interstellar dust composition and size distribution, with the 2175 {\AA} bump being the most prominent feature. We analyze 20 sightlines toward M31 using HST/STIS UV spectroscopy combined with multi-band photometry to characterize this feature. The extinction curves show substantial diversity, from MW-like shapes to flatter profiles with $R_V$ reaching up to $\sim5.8$. The strength of the 2175 {\AA} feature varies widely, including two sightlines where the bump is essentially absent. The bump central wavelength spans a broader range than previously reported, while its width remains consistent with earlier studies. A moderate positive correlation is found between bump strength ($c_3$) and width ($\gamma$). We derive an average UV extinction curve toward M31 with $R_V \approx 3.53$. These results provide new constraints on dust properties and their spatial variations in this galaxy.
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https://arxiv.org/abs/2512.23958
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a996b359c1f7a797cf0f5cbd7becb5549257a8cca8d2b2aecc46aef8e232d28e
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2026-01-01T00:00:00-05:00
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Time-Dependent Accretion Disks with Magnetically Driven Winds: Green's Function Solutions
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arXiv:2512.23999v1 Announce Type: new Abstract: We present Green's function solutions for a geometrically thin, one-dimensional Keplerian accretion disk that includes angular momentum extraction and mass loss due to magnetohydrodynamic (MHD) winds. The disk viscosity is assumed to vary radially as $\nu \propto r^{n}$. We derive solutions for three types of boundary conditions applied at the inner radius $r_{\rm in}$: (i) zero torque, (ii) zero mass accretion rate, and (iii) finite torque and finite accretion rate, and investigate the time evolution of a disk with an initial surface density represented by a Dirac-delta function. The mass accretion rate at the inner radius decays with time as $t^{-3/2}$ for $n = 1$ at late times in the absence of winds under the zero-torque condition, consistent with Lynden-Bell \& Pringle (1974), while the presence of winds leads to a steeper decay. All boundary conditions yield identical asymptotic time evolution for the accretion and wind mass-loss rates, though their radial profiles differ near $r_{\rm in}$. Applying our solutions to protoplanetary disks, we find that the disk follows distinct evolutionary tracks in the accretion rate-disk mass plane depending on $\psi$, a dimensionless parameter that regulates the strength of the vertical stress driving the wind, with the disk lifetime decreasing as $\psi$ increases due to enhanced wind-driven mass loss. The inner boundary condition influences the evolution for $\psi < 1$ but becomes negligible at higher $\psi$, indicating that strong magnetically driven winds dominate and limit mass inflow near the boundary. Our Green's function solutions offer a general framework to study the long-term evolution of accretion disks with magnetically driven winds.
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https://arxiv.org/abs/2512.23999
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Academic Papers
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229af6136a8b36c131d32a52a2038d0dc1fee84444e7ee51837404fef9d336ff
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2026-01-01T00:00:00-05:00
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Machine-learning approaches to dispersion measure estimation for fast radio bursts
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arXiv:2512.24003v1 Announce Type: new Abstract: Fast radio bursts (FRBs) are bright, mostly millisecond-duration transients of extragalactic origin whose emission mechanisms remain unknown. As FRB signals propagate through ionized media, they experience frequency-dependent delays quantified by the dispersion measure (DM), a key parameter for inferring source distances and local plasma conditions. Accurate DM estimation is therefore essential for characterizing FRB sources and testing physical models, yet current dedispersion methods can be computationally intensive and prone to human bias. In this proof-of-concept study, we develop and benchmark three deep-learning architectures, a conventional convolutional neural network (CNN), a fine-tuned ResNet-50, and a hybrid CNN-LSTM model, for automated DM estimation. All models are trained and validated on a large set of synthetic FRB dynamic spectra generated using CHIME/FRB-like specifications. The hybrid CNN-LSTM achieves the highest accuracy and stability while maintaining low computational cost across the investigated DM range. Although trained on simulated data, these models can be fine-tuned on real CHIME/FRB observations and extended to future facilities, offering a scalable pathway toward real-time, data-driven DM estimation in large FRB surveys.
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https://arxiv.org/abs/2512.24003
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Academic Papers
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0d9a7465700ef22101e21081304b42cdf93ca3cb407b102096be67d4559cd5f7
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2026-01-01T00:00:00-05:00
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Atmospheric Mass Flux as a Function of Ionospheric Emission on Unmagnetized Earth
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arXiv:2512.24004v1 Announce Type: new Abstract: We explore ion escape from, and solar ion deposition to, \hll{an unmagnetized Earth-like planet}. We use RHybrid, an ion-kinetic electron-fluid code to simulate the global plasma interaction of unmagnetized Earth with the solar wind. We vary the global ionospheric emission rate, and quantify the resultant planetary ion escape rates ($O^+$ and $H^+$) and the solar wind deposition rate ($H^+$). We use these results to compute the net mass flux to the atmosphere and find that the solar ion deposition rate could be comparable to planetary ion escape rates. For the emission rates simulated, our results show that under typical solar wind conditions ($v_{sw} = 400 \ km \ s^{-1}$, $n_{sw} = 5 \ cm^{-3}$), the mass of the atmosphere would decrease by less than 3\% over a billion years, indicating that Earth's intrinsic magnetic field may be unnecessary for retention of its atmosphere. Lastly, we present a hypothesis suggesting that ionospheric emission may evolve through time towards a critical emission rate that occurs at a net mass flux of zero.
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https://arxiv.org/abs/2512.24004
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Academic Papers
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