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arXiv:2606.01863v1 Announce Type: cross Abstract: Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically ..

arXiv:2606.01877v1 Announce Type: cross Abstract: We found sets of exact analytic quasi-stationary states of a massive scalar field in a dyonic Kerr-Sen black hole~(DKSBH) background in the maximally extended spacetime region. A central novelty is the use of horizon-regular ingoing Eddington-Finkelstein coordinates, which enables a direct and unambiguous imposition of the ingoing boundary condition at the horizon. The exact radial solution....

arXiv:2606.01943v1 Announce Type: cross Abstract: Absolutely maximally entangled (AME) states and, more generally, $k$-uniform states in $(\C^q)^{\otimes n}$ are central objects in multipartite entanglement theory, with applications to quantum secret sharing, quantum masking, and quantum error correction. In the extremal case $k=\lfloor n/2\rfloor$, Scott (2004) proved a sharp nonexistence bound showing that AME states cannot exist once th....

arXiv:2606.01960v1 Announce Type: cross Abstract: We consider the problem of detecting a Return to Baseline (RtB) in high-frequency monitoring data preceding and following an intervention, where the aim is to identify the time at which the data-generating distribution realigns with its pre-intervention distribution. We propose a sequential, distribution-free testing procedure that does not rely on specifying a null model and provides anyti....

arXiv:2606.01963v1 Announce Type: cross Abstract: We study local pure coordination games on finite social networks, continuing the framework of Hutchcroft, Rospuskova, and Tamuz. They showed that low inefficiency in local coordination forces the underlying graph to be amenable, with a square-root loss in the amenability parameter. We improve this loss in the binary unbiased setting. Using Shapley values of a mutual-information game associa..

arXiv:2606.01965v1 Announce Type: cross Abstract: The separation of multicomponent signals with crossing instantaneous frequency (IF) curves remains a fundamental challenge in time-frequency analysis. Although the synchrosqueezed wavelet-chirplet transform (SWCT) enhances time-frequency readability by introducing a chirprate variable, its effectiveness is constrained by the underlying assumption of local linear chirp. Consequently, this me....

arXiv:2606.01979v1 Announce Type: cross Abstract: We provide a brief primer for the idea behind formalising hierarchical causality in the context of complex systems. Here actors are not simply agents. Actors instantiate causation classes. Agents implement local dynamics in given levels or organisation in a given system. Hierarchical causality then describes how actor-level roles constrain, select, and organise agent-level behaviour across ..

arXiv:2606.01990v1 Announce Type: cross Abstract: The Admixture Model describes genetic marker data by representing each individual's genome as a mixture of contributions from $K$ ancestral populations, with the individual admixture vector summarizing the corresponding ancestry proportions. In population and forensic genetics, a key question is whether an individual's genome supports a predominantly single-ancestry interpretation or whethe....

arXiv:2606.02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure. Specifically, CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation op....

arXiv:2606.02051v1 Announce Type: cross Abstract: We derive a fully 3-dimensional Summation-By-Parts scheme for a class of linear wave equations on hyperboloidal slices that meet future null infinity on a Minkowski background. The scheme is derived in spherical polar coordinates, with a major strength being that it is provably stable and allows having grid points at the origin and on the $z$-axis, despite coordinate singularities, and at i....

arXiv:2606.02065v1 Announce Type: cross Abstract: While it is well-known how to compute the cells of a Laguerre tessellation for a given set of weighted generator points, it is not obvious how to invert a Laguerre tessellation. That is, given that one observes a Laguerre tessellation, how can one retrieve the weighted generators corresponding to the observed cells. In this paper, we consider inversion of a class of random Laguerre tessella....

arXiv:2606.02223v1 Announce Type: cross Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning. It requires the identification of the latent connectivity structure, which is in general an NP-hard combinatorial problem due to the absence of canonical node labels. We address this challenge by allowing for probabilistic couplings, thereby relaxing the assignment problem....

arXiv:2606.02263v1 Announce Type: cross Abstract: We study exact uniform sampling of permutations of length $n$ whose longest increasing subsequence (LIS) has prescribed length $k$. For $k \in \Theta(n)$, we give a direct rejection sampler whose expected running time is $O(n\log\log n)$ in the word-RAM model. The sampler uses an expanded proposal space consisting of permutations together with a specified increasing subsequence, and accepts....

arXiv:2606.02290v1 Announce Type: cross Abstract: We investigate a three-dimensional ghostly Hamiltonian realisation of the fully degenerate resonant sixth-order Pais-Uhlenbeck oscillator. On the classical level, the phase-space flow is non-diagonalisable and decomposes into two complex-conjugate Jordan chains of length three, explaining the appearance of oscillatory solutions with secular terms. Upon quantisation, we construct intertwini....

arXiv:2606.02311v1 Announce Type: cross Abstract: In a recent paper the $\gamma$-Boost scheduling policy was shown to minimize the tail of the response time distribution in a light-tailed M/G/1-queue. This policy schedules jobs using a boosted arrival time, defined as the arrival time of a job minus its boost, where the boost of a job depends on its exact job size. The $\gamma$-Boost policy can also be used when only partial job size infor....

arXiv:2606.02315v1 Announce Type: cross Abstract: Reduced-order models (ROMs) are widely employed to describe complex system dynamics when simulations with full-order models (FOMs) are computationally prohibitive. This study presents POD-AS-PRS, a novel model-reduction framework based on the active subspaces (AS) technique, which performs dimensionality reduction in both the state and parameter spaces, enabling efficient and high-fidelity ....

arXiv:2606.02335v1 Announce Type: cross Abstract: The Neural Spectral Element Method (NSEM) evaluates each network only at fixed Legendre-Gauss-Lobatto quadrature nodes and replaces all derivative calls with precomputed spectral differentiation matrices. The resulting deterministic loss enables limited-memory BFGS (L-BFGS) to reach residuals of 10^-9 to 10^-10. A Kosloff-Tal-Ezer coordinate map resolves electrochemical boundary layers, whi....

arXiv:2606.02369v1 Announce Type: cross Abstract: Microwave linear analog computers (MiLACs) offer a transformative paradigm for future multiple-input multiple-output (MIMO) systems by shifting complex signal processing into the analog domain, thereby significantly reducing computational complexity, radio-frequency chains, and analog-digital converters, while speeding up computation. However, the practical deployment of MiLACs is severely ....

arXiv:2606.02381v1 Announce Type: cross Abstract: In this study, a generalized operator-based mathematical conflict framework is presented to explicitly represent structural discrepancies between raw data and contextual data. The proposed structure treats conflict as a local, directional, and context-sensitive quantity, integrating components such as weighting, scale behavior, and output mapping under a unified abstract operator. Without b..

arXiv:2606.02421v1 Announce Type: cross Abstract: Density cube theory extends the canonical quantum density matrix $\rho_{ij}$ with the addition of an extra index to $\rho_{ijk}$. The elements of the density cube with two different indices, $\rho_{iij}$ and $\rho_{ijj}$, correspond to the real and imaginary parts of the off-diagonal element $\rho_{ij}$ of the density matrix and describe double-path interference, while those with three diff..

arXiv:2606.02531v1 Announce Type: cross Abstract: Clifford codes are a natural generalization of quantum stabilizer codes based primarily on representation theory. This class of codes has previously been extended to the setting of quantum subsystem codes. We formulate a two-fold generalization of Clifford codes, for both the hybrid classical and quantum information and projective representation theory settings. This leads to new classes of..

arXiv:1703.02849v4 Announce Type: replace Abstract: In this paper, we develop motivic derived algebraic geometry, an enhancement of derived algebraic geometry adapted to the $\mathbb{A}^1$-homotopy theory of Morel and Voevodsky. We construct motivic model categories by imposing descent for a Grothendieck topology and invariance with respect to an interval object, and use them to formulate motivic versions of $\infty$-categories, $\infty$-t..

arXiv:1709.08464v3 Announce Type: replace Abstract: We study the controllability of linear control systems on connected solvable Lie groups with hyperbolic drift. Under a suitable splitting assumption on the control directions, we show that the controllability problem can be reduced to the controllability of induced systems on the positive and negative hyperbolic components of the group. We then establish sufficient conditions ensuring con..

arXiv:1902.07030v2 Announce Type: replace Abstract: Global sensitivity analysis (GSA) of numerical simulators aims at studying the global impact of the input uncertainties on the output. To perform the GSA, statistical tools based on inputs/output dependence measures are commonly used. We focus here on dependence measures based on reproducing kernel Hilbert spaces: the Hilbert-Schmidt Independence Criterion denoted HSIC. Sometimes, the pro....

arXiv:1904.09888v3 Announce Type: replace Abstract: Penney's game is a two-player zero-sum game in which each player chooses a three-flip pattern of heads and tails, and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose sequentially, the second mover has the advantage. In fact, for any three-flip pattern, there is another three-flip pattern that is strictly more likely to occu..

arXiv:2003.11419v2 Announce Type: replace Abstract: In this article, we introduce incomplete Lauricella matrix functions (ILMFs) of $n$ variables through application of the incomplete Pochhammer matrix symbols. Furthermore there is derivation of certain properties; matrix differential equation, integral formula, recursion formula and differentiation formula of the ILMFs. We also establish the connection between these matrix functions and o..

arXiv:2005.06813v3 Announce Type: replace Abstract: We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.

arXiv:2006.13218v3 Announce Type: replace Abstract: In 2011 Musiker, Schiffler and Williams obtained expansion formulae for cluster algebras from orientable surfaces. For singly and doubly notched arcs these formulae required the notion of $\gamma$-symmetric perfect matchings and $\gamma$-compatible pairs of $\gamma$-symmetric perfect matchings, respectively. We simplify and unify these approaches by considering good matchings of loop grap..

arXiv:2010.06759v4 Announce Type: replace Abstract: This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO) problems. Our main contribution is a novel nonconsecutive dual dynamic programming (NDDP) algorithm which explores different stages in an adaptive fashion. In contrast with the usual consecutive dual dynamic programming (CDDP) algorithm, we show that..

arXiv:2102.03384v5 Announce Type: replace Abstract: In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic relations between the solutions of the partial differential equations satisfied by the uniformizers. In particular, we give a proof of the full Ax-Schanuel Theorem with derivatives for uniformizers of simple projective structure on curv..

arXiv:2104.04408v3 Announce Type: replace Abstract: Let $f$ be a Laurent polynomial in $d$ commuting variables with integer coefficients. Associated to $f$ is the principal algebraic $\mathbb{Z}^d$-action $\alpha_f$ on a compact subgroup $X_f$ of $\mathbb{T}^{\mathbb{Z}^d}$ determined by $f$. Let $N\ge1$ and restrict points in $X_f$ to coordinates in $N\mathbb{Z}^d$. The resulting algebraic $N\mathbb{Z}^d$-action is again principal, and is....

arXiv:2107.14176v5 Announce Type: replace Abstract: In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational work of Benini et al. by providing a richer framework to detect and treat homotopical phenomena in quantum field theory. Our main technical tool is a new extension model structure on operadic algebras which is c..

arXiv:2112.14728v2 Announce Type: replace Abstract: Let $X$ be a smooth projective curve over a complete discretely valued field $K$. Let $L/K$ be the minimal extension such that $X \times_K L$ has a semi-stable model, and write $e(L/K)$ for the ramification index of $L/K$. Let $e(X)$ be the so-called ``stabilization index'' of $X$, defined by Halle and Nicaise as the lcm of the multiplicities of the ``principal'' irreducible components of..

arXiv:2204.11261v3 Announce Type: replace Abstract: We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (non-radial) data. We prove that global solutions are asymptotically given by a free wave and a weakly localized part. The proof is based on constructing in a new way the Free Channel Wave Operator, and further to..

arXiv:2206.15361v3 Announce Type: replace Abstract: The purpose of this article is to give a new construction of the map relating the Borel-Serre and the Baily-Borel compactifications of a Shimura variety (Zucker 1983), and to provide a close analysis of its main properties.

arXiv:2208.00336v2 Announce Type: replace Abstract: We prove irreducible components of moduli spaces of semistable representations of skewed-gentle algebras, and more generally, clannish algebras, are isomorphic to products of projective spaces. This is achieved by showing irreducible components of varieties of representations of clannish algebras can be viewed as irreducible components of skewed-gentle algebras, which we show are always n..

arXiv:2208.09128v5 Announce Type: replace Abstract: We study the totally nonnegative part of the complete flag variety and of its tropicalization. We show that Lusztig's notion of nonnegative complete flag variety coincides with the flags in the complete flag variety which have nonnegative Pl{\"u}cker coordinates. This mirrors the characterization of the totally nonnegative Grassmannian as those points in the Grassmannian whose Pl{\"u}cker..

arXiv:2208.13855v4 Announce Type: replace Abstract: We study rigidity without assuming general position. Given $n$ distinct labelled points and a set $\mathcal{P}\subseteq \binom{[n]}{2}$ of revealed pairs, we ask when the corresponding distances determine the configuration up to isometry. On the line, we prove an extremal result: if $|\mathcal{P}|=\Omega(n^{3/2})$, then there is an induced globally rigid subgraph on $\Omega(|\mathcal{P}|/....

arXiv:2209.07720v4 Announce Type: replace Abstract: In this note, we explore the cohomological property of the codimension of the center of a resolution. In particular, we define a resolution $f:X'\to X$ to be $q$-birational if the center of $f$ satisfies $\mathrm{codim} \,\mathrm{Cent}(f)\ge q+1$, and we prove that $R^if_*\mathcal{O}_X(E)=0$ for every $1\le i\le q-1$ and every $f$-anti-nef effective $f$-exceptional divisor $E$ on $X'$ if ..

arXiv:2303.10146v3 Announce Type: replace Abstract: We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex numbers and for a quotient stack, this recovers Grojnowski's equivariant elliptic cohomology of the analytification.

arXiv:2307.02816v2 Announce Type: replace Abstract: We prove that for every planar graph $X$ of treedepth $h$, there exists a positive integer $c$ such that for every $X$-minor-free graph $G$, there exists a graph $H$ of treewidth at most $f(h)$ such that $G$ is isomorphic to a subgraph of $H\boxtimes K_c$. This is a qualitative strengthening of the Grid-Minor Theorem of Robertson and Seymour (JCTB 1986), and treedepth is the optimal param..

arXiv:2307.08497v3 Announce Type: replace Abstract: It is an easy observation that if a graph~$G$ admits a path-decomposition whose parts have small radius, then $G$ contains no large subdivision of $K_{1,3}$ or $K^3$ as a (quasi-)geodesic subgraph. We show that these are in fact the only obstructions to such path-decompositions of small radial width, and we prove analogous results for decompositions modelled on cycles and subdivided stars..

arXiv:2307.16736v3 Announce Type: replace Abstract: Let $F$ be a totally real number field and $r=[F :\mathbb{Q}].$ Let $A_k(\mathfrak{N},\omega) $ be the space of holomorphic Hilbert cusp forms with respect to $K_1(\mathfrak{N})$, of weight $k=(k_1,\dots,k_r)$ such that $k_j>2$ for all $j$, and with central Hecke character $\omega$. For integral ideals $\mathfrak{N}$ and $\mathfrak{n}$ in $F$ such that $( \mathfrak{n}, \mathfrak{N}) = 1$,....

arXiv:2308.07591v4 Announce Type: replace Abstract: In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide a discretization based approximation method for MDPs with continuous spaces under average cost criteria, and provide error bounds for approximations when the dynamics are only weakly continuous (for asymptotic convergence of errors as the grid sizes vanish) or Wasserstein continuous (with ....

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