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We construct a universal decompressor $U$ for plain Kolmogorov complexity $\mathrm{C}_U$ such that the Halting Problem cannot be decided by any polynomial-time oracle machine with access to the set of random strings $R_{\mathrm{C}_U} = \{x : \mathrm{C}_U(x) \ge |x|\}$. This result resolves a problem posed by Eric Allender regarding the computational power of Kolmogorov complexity-based oracles.

Token serves as the fundamental unit of computation in modern autoregressive models, and generation length directly influences both inference cost and reasoning performance. Despite its importance, existing approaches lack fine-grained length modeling, operating primarily at the coarse-grained sequence level. We introduce the Length Value Model (LenVM), a token-level framework that models the remaining generation length. By formulating length modeling as a value estimation problem and assigning a constant negative reward to each generated token, LenVM predicts a bounded, discounted return that serves as a monotone proxy for the remaining generation horizon. This formulation yields supervision that is annotation-free, dense, unbiased, and scalable. Experiments on LLMs and VLMs demonstrate LenVM provides a highly effective signal at inference time. On the LIFEBench exact length matching task, applying LenVM to a 7B model improves the length score from 30.9 to 64.8, significantly outperforming frontier closed-source models. Furthermore, LenVM enables continuous control over the trade off between performance and efficiency. On GSM8K at a budget of 200 tokens, LenVM maintains 63% accura

We prove a new characterization of complex projective space using lengths of extremal rays.

Single-qubit gates on superconducting quantum processors are typically implemented using microwave pulses applied through dedicated control lines. However, these microwave pulses may also drive other qubits due to crosstalk arising from capacitive coupling and wavefunction overlap in systems with closely spaced transition frequencies. Crosstalk and frequency crowding increase errors during simultaneous single-qubit operations relative to isolated gates, thus forming a major bottleneck for scaling superconducting quantum processors. In this work, we combine model-based qubit frequency optimization with pulse shaping to demonstrate crosstalk error mitigation in single-qubit gates on a 49-qubit superconducting quantum processor. We introduce and experimentally verify an analytical model of simultaneous single-qubit gate error caused by microwave crosstalk that depends on a given pulse shape. By employing a model-based optimization strategy of qubit frequencies, we minimize the crosstalk-induced error across the processor and achieve a mean simultaneous single-qubit gate fidelity of 99.96% for a 16-ns gate duration, approaching the mean individual gate fidelity. To further reduce the s

Respiratory syncytial virus (RSV) is a leading cause of hospitalization among young children, with outbreaks strongly influenced by environmental conditions. This study developed a machine learning framework to predict RSV-associated hospitalizations in the United States (U.S.) by integrating wastewater surveillance, meteorological, and air quality data. The dataset combined weekly hospitalization rates, wastewater RSV levels, daily meteorological measurements, and air pollutant concentrations. Classification models, including CART, Random Forest, and Boosting, were trained to predict weekly RSV-associated hospitalization rates classified as \textit{Low risk}, \textit{Alert}, and \textit{Epidemic} levels. The wastewater RSV level was identified as the strongest predictor, followed by meteorological and air quality variables such as temperature, ozone levels, and specific humidity. Notably, the analysis also revealed significantly higher RSV-associated hospitalization rates among Native Americans and Alaska Natives. Further research is needed to better understand the drivers of RSV disparity in these communities to improve prevention strategies. Furthermore, states at high altitudes

World models that support controllable and editable spatiotemporal environments are valuable for robotics, enabling scalable training data, repro ducible evaluation, and flexible task design. While recent text-to-video models generate realistic dynam ics, they are constrained to 2D views and offer limited interaction. We introduce MorphoSim, a language guided framework that generates 4D scenes with multi-view consistency and object-level controls. From natural language instructions, MorphoSim produces dynamic environments where objects can be directed, recolored, or removed, and scenes can be observed from arbitrary viewpoints. The framework integrates trajectory-guided generation with feature field dis tillation, allowing edits to be applied interactively without full re-generation. Experiments show that Mor phoSim maintains high scene fidelity while enabling controllability and editability. The code is available at https://github.com/eric-ai-lab/Morph4D.

The role of Li-based batteries in the electrification of society cannot be understated, however their operational lifetime is often limited by the formation of dendrites, i.e. the localised deposition of Li that can cause shorts between the two electrodes leading to the failure of the battery. Nanocrystalline bimetallic current collectors can be used for anode-free Li-metal batteries, with improved Li plating and limited or suppressed formation of dendrites. Here, we demonstrate that the microstructure of an alpha-Brass current collector, Cu 63% Zn 37%, used in an anode-free Li-metal battery evolves during cycling. It initially had a nanocrystalline deformation layer approximately 80 nm in thickness after polishing. After 100 cycles, the initial deformed brass layer was partially converted to a ternary Laves phase Cu3ZnLi2 within a nanocrystalline brass matrix that grew to 200 - 250 nm in thickness. Upon Li stripping, the phase partially decomposes electrochemically, but what remains can sequester Li thus forming "dead Li" thereby contributing to capacity loss. We propose a mechanism for the microstructural evolution including dynamic recrystallization and phase formation. Since th

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

We show that klt Fano varieties and certain lc Fano varieties contain free higher-genus curves in their smooth loci. Our methods also allow us to find free curves on varieties in positive characteristic and on quasiprojective varieties, under a natural positivity condition on the tangent bundle. We then use the existence of free curves to deduce finiteness of the fundamental group of the smooth locus in these settings. The paper includes an appendix by de Jong that establishes the Künneth formula for tame étale fundamental groups.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations

We improve the Bend-and-Break result of Miyaoka and Mori by establishing the optimal degree bound. Our result also yields optimal bounds on lengths of extremal rays of log canonical pairs.

We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find that suitable generalizations of the unweighted theorems hold under a weighted null energy condition. Our results also provide further evidence in favour of a weighted scalar curvature that differs from the trace of the weighted Ricci curvature. When the synthetic dimension is a positive integer, these weighted curvatures have a natural interpretation in terms of warped product metrics.

In many auctions, bidders may be reluctant to reveal private information to the auctioneer and other bidders. Among deterministic bilateral communication protocols, reducing what bidders learn requires increasing what the auctioneer learns. A protocol implementing a given social choice rule is on the Privacy Frontier if no alternative protocol reveals less to both bidders and the auctioneer. For first-price auctions, the descending protocol and the sealed-bid protocol are both on the Privacy Frontier. For second-price auctions, the ascending protocol and the ascending-join protocol of Haupt and Hitzig (2025) are both on the Privacy Frontier, but the sealed-bid protocol is not. We provide sufficient conditions for a protocol to be on the Privacy Frontier and devise alternative protocols on the Privacy Frontier for first-price auctions that allow the designer to flexibly trade off between privacy from bidders and the auctioneer.

The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric Férard and François Rodier [4]) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.