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Maximum Matching and Related Problems in Catalytic Logspace
arXiv:2604.24275v2 Announce Type: replace Abstract: Understanding the power of space-bounded computation with access to catalytic space has been an important theme in complexity theory over the recent years. One of the key algorithmic results in this area is that bipartite maximum matching can be computed in catalytic logspace with a polynomial-time bound, Agarwala and Mertz (2025). In this paper, we show that we can construct a \emph{maximum matching} in \emph{general graphs} in CL, and, in...
Schools could get maximum temperature limits if needed to deal with heatwaves
Schools could get maximum temperature limits if needed to deal with heatwaves EXCLUSIVE: Bridget Phillipson said she will 'look closely' at what schools need after last week’s record-breaking temperatures triggered calls from teaching unions for action Schools could be given maximum temperatures if it becomes necessary to deal with heatwaves, Bridget Phillipson has suggested. The Education Secretary said she will “look closely” at what schools need after last week’s record-breaking...
Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings
Announce Type: replace Abstract: Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states.
Quaternion Maximum-Volume Submatrix Selection with Applications to Multichannel Imaging and Visual Data
arXiv:2606.08175v1 Announce Type: new Abstract: Low-rank approximation based on selected rows and columns is a useful alternative to singular value decompositions when the goal is an interpretable and compact matrix representation. A standard way to choose these rows and columns is the maximum-volume principle: it selects submatrices with large volume, which usually leads to stable interpolation coefficients and accurate CUR-type approximations. In this paper, we study this idea for...
Consistent and Distinctive: LLM Benchmark Efficiency via Maximum Independent Set Prompt Selection on Similarity Graphs
arXiv:2606.01400v1 Announce Type: new Abstract: Evaluating large language models (LLMs) across comprehensive benchmarks is expensive and time-consuming. We propose a graph-based prompt selection framework that models each benchmark as a similarity graph -- nodes are prompts connected if their embedding-space distance falls above a configurable threshold -- and applies Maximum Independent Set (MIS) algorithms to select a maximally diverse, non-redundant subset. We evaluate four MIS solvers...
Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
arXiv:2507.22597v2 Announce Type: replace-cross Abstract: We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre-like bound holds with equality for weighted projective spaces when the first weight is one, and when considering polynomials whose...
A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation
arXiv:2504.18352v2 Announce Type: replace Abstract: Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with linear running time. Our result improves the previous two-and-a-half-decades-old algorithm by de Berg, Cheong, Devillers, van Kreveld, and Teillaud (1998), which ran in $O((n+m)\log(n+m))$ time, as well as...
Multiparameter Maximum Information States for Coherent Diffraction Measurements
arXiv:2606.01445v1 Announce Type: new Abstract: In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the...
Multiparameter Maximum Information States for Coherent Diffraction Measurements
arXiv:2606.01445v2 Announce Type: replace Abstract: In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the...
Learned Non-Maximum Suppression for 3D Object Detection
arXiv:2606.03568v1 Announce Type: new Abstract: Post-processing is a critical stage in LiDAR-based 3D object detection, where dense and overlapping proposals must be filtered for compact and reliable perception. This work introduces two learned filtering modules that replace heuristic non-maximum suppression (NMS) by leveraging relations among detections. D2D-Rescore employs transformer-based detection-to-detection (D2D) attention, while GossipNet3D adapts the 2D GossipNet concept to 3D...