Maximum Independent Set
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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...
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Announce Type: new Abstract: Johnson graph are a family of graphs that play an important role in the theory of constant-weight codes, extremal combinatorics, and combinatorial geometry. We study signed analogues of classical Johnson graphs, denoted by $J_\pm(n,k)$, whose vertices are vectors of the form $\pm e_{i_1}\pm\cdots\pm e_{i_k}$, where two vertices are adjacent whenever their dot product equals $k-1$. We are particularly interested in maximum independent sets in the case $k=4$. An...
Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances
new Abstract: The distance-d variants of Independent Set and Dominating Set problems have been extensively studied from different algorithmic viewpoints. In particular, the complexity of these problems are well understood on bounded-treewidth graphs [Katsikarelis, Lampis, and Paschos, Discret. Math 2022][Borradaile and Le, IPEC 2016]: given a tree decomposition of width t, the two problems can be solved in time $d^t \cdot n^{O(1)}$ and $(2d + 1)t \cdot n^{O(1)}$, respectively.
Penalty-free quantum optimization applied to lattice protein folding
Announce Type: cross Abstract: Identifying minimum-energy structures of lattice proteins is a challenging discrete optimization problem. Quantum approaches such as analog quantum annealing and the gate-based quantum approximate optimization algorithm (QAOA) can address this problem after mapping it to a binary representation, which typically involves introducing penalty terms to enforce valid chain configurations. However, in this and many related problems, the use of quadratic penalty terms...
Penalty-free quantum optimization applied to lattice protein folding
arXiv:2606.02104v2 Announce Type: replace-cross Abstract: Identifying minimum-energy structures of lattice proteins is a challenging discrete optimization problem. Quantum approaches such as analog quantum annealing and the gate-based quantum approximate optimization algorithm (QAOA) can address this problem after mapping it to a binary representation, which typically involves introducing penalty terms to enforce valid chain configurations.
Diverse binding poses of agonistic neurotoxins on human Na<sub>v</sub>1.6
Abstract Voltage-gated sodium (Nav) channels are key targets of various venomous toxins. Deciphering the binding poses and mechanisms of action of representative toxins will help to dissect the functional mechanism of the channels and facilitate therapeutic development targeting Nav channels1,2. Here we present cryo-electron microscopy (cryo-EM) structures of distinct binding poses of three agonistic peptide toxins on the human Nav1.6–β1 channel complex.
Kling-Gupta linear regression
arXiv:2606.09391v1 Announce Type: cross Abstract: Although the Kling-Gupta efficiency ($\mathrm{KGE}$) is widely adopted for model evaluation in hydrology, its properties as a statistical estimator remain unexplored. Investigating these properties is necessary because parameter estimation and forecast evaluation are inherently linked. To address this, we formalize the negatively oriented Kling-Gupta loss $L_\mathrm{KG} = (1 - \mathrm{KGE})^2$ within an extremum estimation framework...
Deep learning four decades of human migration
Abstract Human migration is a fundamental driver of global demographic change, shaping population structure, labour markets and social policy across countries1,2,3. Although long-term migration patterns are often linked to economic development4, they can shift rapidly in response to shocks such as conflict, environmental crises and political change5. Despite its importance, migration remains difficult to measure consistently: existing data are sparse, concentrated in high-income settings and...
Drivers only slightly exceeding the speed limit will avoid fines with new Colorado law
Drivers only slightly exceeding the speed limit will avoid fines with new Colorado law A local news investigation into the Centennial State’s photo radar system led to two towns voiding thousands of tickets and issuing about $2.3 million in refunds - Bookmark - CommentsGo to comments A new Colorado law passed this week prohibits speed camera tickets for drivers going 5 mph or less over the speed limit. Set to take effect August 12, the legislation, signed by Governor Jared Polis, also...
Apple’s Orwellian device controls for tots also mean more work for parents
Apple is turning parents into a corporate IT help desk, with rigid new monitoring and compliance tools for their children’s iPhones and iPads that will prompt for mom and dad's approval each time their kids visit a new website or want a new app. Apple's new trust and safety features for kids and teens will also automatically block nudity and gore from appearing on apps, even during live Facetime calls, while giving parents more control over the amount of time their tots spend glued to...