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Efficient Importance Sampling for Wrong Exit Probabilities over Combinatorially Many Rare Regions
Yanglei Song, Georgios Fellouris
https://arxiv.org/abs/2509.14596 https://

Efficient Importance Sampling for Wrong Exit Probabilities over Combinatorially Many Rare Regions
We consider importance sampling for estimating the probability that a light-tailed $d$-dimensional random walk exits through one of many disjoint rare-event regions before reaching an anticipated target. This problem arises in sequential multiple hypothesis testing, where the number of such regions may grow combinatorially and in some cases exponentially with the dimension. While mixtures over all associated exponential tilts are asymptotically efficient, they become computationally infeasible …

Some remarks on invariants
Martin Cederwall, Jessica Hutomo, Sergei M. Kuzenko, Kurt Lechner, Dmitri P. Sorokin
https://arxiv.org/abs/2509.14350 https://ar…

Some remarks on invariants
The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In mathematical terms the problem can be formulated as follows. Given a semi-simple finite-dimensional Lie algebra $\mathfrak g$ and a $\mathfrak g$-module $V$, one may ask about the structure of the sub-ring of $\mathfrak g$-invariants inside the ring freely g…

Should We Relax Stability in Matching Markets?
Dimitris Bertsimas, Carol Gao
https://arxiv.org/abs/2509.14475 https://arxiv.org/pdf/2509.14475

Should We Relax Stability in Matching Markets?
Centralized assignment markets have historically relied on Deferred-Acceptance (DA) algorithms, which do not incorporate multiple objectives into the assignment. In this work, we propose an optimization-based many-to-one assignment algorithm that explores the trade-offs between minimizing the number of blocking pairs in the match and other important objectives. In order to scale to high-dimensional problems, we develop an algorithm using inverse optimization to obtain the optimal cost vector th…

A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization
Hideaki Kim, Tomoharu Iwata
https://arxiv.org/abs/2510.08916 https://ar…

A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization
The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. In this paper, we address the problem of estimating the latent triggering kernels--functions that encode the interac…

Appell Functions for General Lattices
Aradhita Chattopadhyaya, Jan Manschot
https://arxiv.org/abs/2510.10204 https://arxiv.org/pdf/2510.10204

Appell Functions for General Lattices
We study Appell functions associated to an arbitrary positive definite lattice $Λ$ and a choice of $M\leq {\rm dim}(Λ)$ linearly independent vectors $d_r\in Λ$, $r=1,\dots,M$. These functions are instances of multi-variable quasi-elliptic functions, and specific examples have appeared at various places in mathematics and theoretical physics. For example, if $Λ$ is chosen to be one-dimensional, these functions reduce to the classical Appell function, which is a prominent example in the theor…

Does the Manipulation Process Matter? RITA: Reasoning Composite Image Manipulations via Reversely-Ordered Incremental-Transition Autoregression
Xuekang Zhu, Ji-Zhe Zhou, Kaiwen Feng, Chenfan Qu, Yunfei Wang, Liting Zhou, Jian liu
https://arxiv.org/abs/2509.20006

Does the Manipulation Process Matter? RITA: Reasoning Composite Image Manipulations via Reversely-Ordered Incremental-Transition Autoregression
Image manipulations often entail a complex manipulation process, comprising a series of editing operations to create a deceptive image, exhibiting sequentiality and hierarchical characteristics. However, existing IML methods remain manipulation-process-agnostic, directly producing localization masks in a one-shot prediction paradigm without modeling the underlying editing steps. This one-shot paradigm compresses the high-dimensional compositional space into a single binary mask, inducing severe…

Self-attention enabled quantum path analysis of high-harmonic generation in solids
Cong Zhao, Xiaozhou Zou
https://arxiv.org/abs/2510.12443 https://arxiv.o…

Self-attention enabled quantum path analysis of high-harmonic generation in solids
High-harmonic generation (HHG) in solids provides a powerful platform to probe ultrafast electron dynamics and interband--intraband coupling. However, disentangling the complex many-body contributions in the HHG spectrum remains challenging. Here we introduce a machine-learning approach based on a Transformer encoder to analyze and reconstruct HHG signals computed from a one-dimensional Kronig--Penney model. The self-attention mechanism inherently highlights correlations between temporal dipole…

A new proof of Poincar\'e-Miranda theorem based on the classification of one-dimensional manifolds
Xiao-Song Yang
https://arxiv.org/abs/2511.06828 https://arxiv.org/pdf/2511.06828 https://arxiv.org/html/2511.06828
arXiv:2511.06828v1 Announce Type: new
Abstract: This note gives a new elementary proof of Poincar\'e-Miranda theorem based on Sard's theorem and the simple classification of one-dimensional manifolds.
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Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
Kunal Vyas, Fengping Jin, Hans De Raedt, Kristel Michielsen
https://arxiv.org/abs/2510.02141

Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum algorithms for solving such many-body problems. The focus of our current work is on the one-dimensional model which is integrable, meaning that there exist analytical results for determining its ground state. In particular, we demonstrate how to perform a gate-ba…

Multiwinner Voting with Interval Preferences under Incomplete Information
Drew Springham, Edith Elkind, Bart de Keijzer, Maria Polukarov
https://arxiv.org/abs/2510.11625 https:/…

Multiwinner Voting with Interval Preferences under Incomplete Information
In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under reduced communication. In this paper, we consider voters with one-dimensional preferences: voters and candidates are associated with points in $\mathbb R$, and each voter's approval set forms an interval of $\mathbb R$. We put forward a probabilistic preferen…