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In this paper, our main goal is to define the class of weakly Demi Dunford-Pettis applications. We also study their relationship with the classes of weakly Dunford-Pettis and Demi Dunford-Pettis operators, including a condition where these operators coincide with Demi Dunford-Pettis and Demicompacts. In the last section, we study some of the behavior of this class in the Banach Lattice environment.

Recent advances in foundational models have yielded reasoning systems capable of achieving a gold-medal standard at the International Mathematical Olympiad. The transition from competition-level problem-solving to professional research, however, requires navigating vast literature and constructing long-horizon proofs. In this work, we introduce Aletheia, a math research agent that iteratively generates, verifies, and revises solutions end-to-end in natural language. Specifically, Aletheia is powered by an advanced version of Gemini Deep Think for challenging reasoning problems, a novel inference-time scaling law that extends beyond Olympiad-level problems, and intensive tool use to navigate the complexities of mathematical research. We demonstrate the capability of Aletheia from Olympiad problems to PhD-level exercises and most notably, through several distinct milestones in AI-assisted mathematics research: (a) a research paper (Feng26) generated by AI without any human intervention in calculating certain structure constants in arithmetic geometry called eigenweights; (b) a research paper (LeeSeo26) demonstrating human-AI collaboration in proving bounds on systems of interacting p

We present a new method for combining e-variables through demi-supermartingales, which settles an old conjecture in the literature on nonparametric mean testing. It also provides an explicit concentration bound for a certain Kullback--Leibler-type statistic arising in the stochastic multi-armed bandit literature. All of these combination results hold for independent e-variables as well as for the class of co-valid e-variables, whose dependence structure lies somewhere between independence and sequential validity. The results are further generalized to compound e-variables. The proofs proceed by analyzing elementary symmetric polynomials and their behavior as nonnegative demi-supermartingales.

Scientific discovery is driven by scientists generating novel hypotheses for complex problems that undergo rigorous experimental validation. To augment this process, we introduce Co-Scientist, a multi-agent AI system built on Gemini for structured scientific thinking and hypothesis generation. Co-Scientist aims to help scientists discover new original knowledge. Conditioned on their research objectives and prior scientific evidence, it formulates demonstrably novel research hypotheses for experimental verification. The system's design involves agents continuously generating, critiquing and refining hypotheses accelerated by scaling test-time compute. Key contributions include: (1) a multi-agent architecture with an asynchronous task execution framework for flexible compute scaling; (2) a tournament evolution process for self-improving hypotheses generation. Automated evaluations show continued benefits of test-time compute scaling, improving hypothesis quality over time. While general purpose, we focus the validation in three biomedical applications: drug repurposing, novel target discovery, and explaining mechanisms of anti-microbial resistance. Specifically, Co-Scientist helped i

We introduce SIMA 2, a generalist embodied agent that understands and acts in a wide variety of 3D virtual worlds. Built upon a Gemini foundation model, SIMA 2 represents a significant step toward active, goal-directed interaction within an embodied environment. Unlike prior work (e.g., SIMA 1) limited to simple language commands, SIMA 2 acts as an interactive partner, capable of reasoning about high-level goals, conversing with the user, and handling complex instructions given through language and images. Across a diverse portfolio of games, SIMA 2 substantially closes the gap with human performance and demonstrates robust generalization to previously unseen environments, all while retaining the base model's core reasoning capabilities. Furthermore, we demonstrate a capacity for open-ended self-improvement: by leveraging Gemini to generate tasks and provide rewards, SIMA 2 can autonomously learn new skills from scratch in a new environment. This work validates a path toward creating versatile and continuously learning agents for both virtual and, eventually, physical worlds.

Given a circuit $G: \{0, 1\}^n \to \{0, 1\}^m$ with $m > n$, the *range avoidance* problem ($\text{Avoid}$) asks to output a string $y\in \{0, 1\}^m$ that is not in the range of $G$. Besides its profound connection to circuit complexity and explicit construction problems, this problem is also related to the existence of *proof complexity generators* -- circuits $G: \{0, 1\}^n \to \{0, 1\}^m$ where $m > n$ but for every $y\in \{0, 1\}^m$, it is infeasible to prove the statement "$y ot\in\mathrm{Range}(G)$" in a given propositional proof system. This paper connects these two problems with the existence of *demi-bits generators*, a fundamental cryptographic primitive against nondeterministic adversaries introduced by Rudich (RANDOM '97). $\bullet$ We show that the existence of demi-bits generators implies $\text{Avoid}$ is hard for nondeterministic algorithms. This resolves an open problem raised by Chen and Li (STOC '24). Furthermore, assuming the demi-hardness of certain LPN-style generators or Goldreich' PRG, we prove the hardness of $\text{Avoid}$ even when the instances are constant-degree polynomials over $\mathbb{F}_2$. $\bullet$ We show that the dual weak pigeonhole prin

High quality-factor (Q) dielectric metasurfaces operating in the visible to near-infrared range usually require sub-200 nm features, limiting their fabrication to expensive, low-throughput electron beam lithography. Here, we demonstrate wafer-scale metasurfaces fabricated using deep ultraviolet lithography (DUVL), a workhorse technology in the semiconductor industry. Using a radius and depth perturbation technique in a hole array patterned into a silicon nitride slab, we achieve quasi-bound states in the continuum (qBIC) resonances with measured Q-factors of 150. Critically, we introduce DUV exposure dose as a Q-factor engineering parameter and demonstrate how hole depth control circumvents DUVL resolution limits. Despite stochastic nanoscale variations, the fabricated metasurfaces exhibit spatial uniformity, a consequence of the nonlocal nature of the qBIC resonances. Proof of concept refractive index sensing demonstrates 129 nm/RIU sensitivity while maintaining simple CMOS camera-based resonance shift interrogation. This work bridges scalable semiconductor manufacturing with high-performance nanophotonics, establishing a practical pathway for commercializing metasurface-based sen

Wide field of view and light weight optics are critical for advanced eyewear, with applications in augmented/virtual reality and night vision. Conventional refractive lenses are often stacked to correct aberrations at wide field of view, leading to limited performance and increased size and weight. In particular, simultaneously achieving wide field of view and large aperture for light collection is desirable but challenging to realize in a compact form-factor. Here, we demonstrate a wide field of view (greater than 60$^\circ$) meta-optic doublet eyepiece with an entrance aperture of 2.1 cm. At the design wavelength of 633 nm, the meta-optic doublet achieves comparable performance to a refractive lens-based eyepiece system. This meta-doublet eyepiece illustrates the potential for meta-optics to play an important role in the development of high-quality monochrome near-eye display and night vision systems.

In this paper, we introduce and study a new concept of unbounded order demi Dunford-Pettis operators. Namely, we investigate some properties for this new class of operators and we study its connection with other known operators, we also establish important results about power unbounded order demi Dunford-Pettis operators, and domination property.

Computational design of protein-binding proteins is a fundamental capability with broad utility in biomedical research and biotechnology. Recent methods have made strides against some target proteins, but on-demand creation of high-affinity binders without multiple rounds of experimental testing remains an unsolved challenge. This technical report introduces AlphaProteo, a family of machine learning models for protein design, and details its performance on the de novo binder design problem. With AlphaProteo, we achieve 3- to 300-fold better binding affinities and higher experimental success rates than the best existing methods on seven target proteins. Our results suggest that AlphaProteo can generate binders "ready-to-use" for many research applications using only one round of medium-throughput screening and no further optimization.

Free-space time domain THz spectroscopy accesses electrodynamic responses in a frequency regime ideally matched to interacting condensed matter systems. However, THz spectroscopy is challenging when samples are physically smaller than the diffraction limit of ~0.5 mm, as is typical, for example, in van der Waals materials and heterostructures. Here, we present an on-chip, time-domain THz spectrometer based on semiconducting photoconductive switches with a bandwidth of 200 GHz to 750 GHz. We measure the optical conductivity of a 7.5-$μ$m wide NbN film across the superconducting transition, demonstrating spectroscopic signatures of the superconducting gap in a sample smaller than 2% of the Rayleigh diffraction limit. Our spectrometer features an interchangeable sample architecture, making it ideal for probing superconductivity, magnetism, and charge order in strongly correlated van der Waals materials.

Artificial Intelligence (AI) systems have made remarkable progress, attaining super-human performance across various domains. This presents us with an opportunity to further human knowledge and improve human expert performance by leveraging the hidden knowledge encoded within these highly performant AI systems. Yet, this knowledge is often hard to extract, and may be hard to understand or learn from. Here, we show that this is possible by proposing a new method that allows us to extract new chess concepts in AlphaZero, an AI system that mastered the game of chess via self-play without human supervision. Our analysis indicates that AlphaZero may encode knowledge that extends beyond the existing human knowledge, but knowledge that is ultimately not beyond human grasp, and can be successfully learned from. In a human study, we show that these concepts are learnable by top human experts, as four top chess grandmasters show improvements in solving the presented concept prototype positions. This marks an important first milestone in advancing the frontier of human knowledge by leveraging AI; a development that could bear profound implications and help us shape how we interact with AI sys

Identifying key patterns of tactics implemented by rival teams, and developing effective responses, lies at the heart of modern football. However, doing so algorithmically remains an open research challenge. To address this unmet need, we propose TacticAI, an AI football tactics assistant developed and evaluated in close collaboration with domain experts from Liverpool FC. We focus on analysing corner kicks, as they offer coaches the most direct opportunities for interventions and improvements. TacticAI incorporates both a predictive and a generative component, allowing the coaches to effectively sample and explore alternative player setups for each corner kick routine and to select those with the highest predicted likelihood of success. We validate TacticAI on a number of relevant benchmark tasks: predicting receivers and shot attempts and recommending player position adjustments. The utility of TacticAI is validated by a qualitative study conducted with football domain experts at Liverpool FC. We show that TacticAI's model suggestions are not only indistinguishable from real tactics, but also favoured over existing tactics 90% of the time, and that TacticAI offers an effective co

Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers.

In recent years, Artificial Intelligence (AI) systems have surpassed human intelligence in a variety of computational tasks. However, AI systems, like humans, make mistakes, have blind spots, hallucinate, and struggle to generalize to new situations. This work explores whether AI can benefit from creative decision-making mechanisms when pushed to the limits of its computational rationality. In particular, we investigate whether a team of diverse AI systems can outperform a single AI in challenging tasks by generating more ideas as a group and then selecting the best ones. We study this question in the game of chess, the so-called drosophila of AI. We build on AlphaZero (AZ) and extend it to represent a league of agents via a latent-conditioned architecture, which we call AZ_db. We train AZ_db to generate a wider range of ideas using behavioral diversity techniques and select the most promising ones with sub-additive planning. Our experiments suggest that AZ_db plays chess in diverse ways, solves more puzzles as a group and outperforms a more homogeneous team. Notably, AZ_db solves twice as many challenging puzzles as AZ, including the challenging Penrose positions. When playing che

We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity. Specifically, we show the following: *Demi-bit stretch*: Super-bits and demi-bits are variants of cryptographic pseudorandom generators which are secure against nondeterministic statistical tests (Rudich 1997). They were introduced to rule out certain approaches to proving strong complexity lower bounds beyond the limitations set out by the Natural Proofs barrier (Rudich and Razborov 1997). Whether demi-bits are stretchable at all had been an open problem since their introduction. We answer this question affirmatively by showing that: every demi-bit $b:\{0,1\}^n\to \{0,1\}^{n+1}$ can be stretched into sublinear many demi-bits $b':\{0,1\}^{n}\to \{0,1\}^{n+n^{c}}$, for every constant $0<c<1$. >>> see rest of abstract in paper.

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics