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We calculated a fixed strategy that minimizes the average number of guesses (minimum strategy) for the number-guessing game MOO by exhaustive search. Although the minimum strategy for a similar game, mastermind, has been reported, this study seems to be the first to find the minimum strategy for MOO with a larger search space. When two players play against each other in MOO, the minimum strategy is not always the strongest fixed strategy. First, we compute a fixed strategy that has the maximum winning rate when played against the minimum strategy. Then we confirm that there is no fixed strategy with a winning rate exceeding 0.5 against this strategy. This result shows that MOO is a game with the strongest fixed strategy.

In this document we update the status of U.S. community inputs for the European Strategy for Particle Physics Update (ESPPU) since April 1, 2025, and offer responses to the revised questions. Major new inputs include a long-term strategy report from the National Academies of Sciences, Engineering, and Medicine and the formal formation of a U.S. Muon Collider Collaboration.

This article develops the concept of Autonomous Business Models (ABMs) as a distinct managerial and strategic logic in the age of agentic AI. While most firms still operate within human-driven or AI-augmented models, we argue that we are now entering a phase where agentic AI (systems capable of initiating, coordinating, and adapting actions autonomously) can increasingly execute the core mechanisms of value creation, delivery, and capture. This shift reframes AI not as a tool to support strategy, but as the strategy itself. Using two illustrative cases, getswan.ai, an Israeli startup pursuing autonomy by design, and a hypothetical reconfiguration of Ryanair as an AI-driven incumbent, we depict the evolution from augmented to autonomous business models. We show how ABMs reshape competitive advantage through agentic execution, continuous adaptation, and the gradual offloading of human decision-making. This transition introduces new forms of competition between AI-led firms, which we term synthetic competition, where strategic interactions occur at rapid, machine-level speed and scale. It also challenges foundational assumptions in strategy, organizational design, and governance. By p

Grand-strategy games such as Civilization pose a distinctive long-horizon planning problem: an agent must divide one shared resource pool among six competing domains -- technology, government, diplomacy, city development, expansion, and military -- under partial observability, with no feedback except a delayed final score. Current LLM agents fall short in three ways: 1) they cannot infer spatial relations from raw coordinates; 2) they allocate resources poorly, because feeding the entire growing state into one prompt and planning all domains in a single output diffuses attention and biases decisions toward urgent events; and 3) they cannot improve, as the delayed score gives no signal within or across games. We present SAGA, an LLM multi-agent framework pairing one mechanism with each weakness: (i) a Map-Semantic Scene Graph turning coordinates into per-entity statements of distance, direction, and threat; (ii) a Tool-Augmented Planner that retrieves only the state a decision needs, cutting the order of magnitude of its input, and issues a separate plan per domain to six specialist controllers, so urgent events do not derail long-term plans; and (iii) a Dual-Horizon Feedback Loop s

Executive Summary: The Habitable Worlds Observatory (HWO) is the first astrophysics flagship mission with a key cross-divisional astrobiology science goal of searching for signs of life on rocky planets beyond our solar system. The Living Worlds Working Group under the Science, Technology, and Architecture Review Team (START) was charged with investigating how HWO could characterize potentially habitable exoplanets orbiting stars in the solar neighborhood, search for signs of life, and interpret potential biosignatures within a false positive and false negative framework. In particular, we focused on (1) identifying biosignatures that have spectral features in the UV-Vis-NIR wavelength range and defining their measurement requirements, (2) determining additional information needed from the planet and planet system to interpret biosignatures and assess the likelihood of false positives, and (3) assembling current knowledge of likely HWO target stars and identify which properties of host stars and systems are most critical to know in advance of HWO. The Living Worlds atmospheric biosignatures science case is considered one of the key drivers in the design of the observatory. An addit

This paper proposes a novel computationally efficient algorithm for optimal sizing of Battery Energy Storage Systems (BESS) considering renewable energy bidding strategies. Unlike existing two-stage methods, our algorithm enables the cooptimization of both by updating the BESS size during the training of the bidding policy, leveraging an extended reinforcement learning (RL) framework inspired by advancements in embodied cognition. By integrating the Deep Recurrent Q-Network (DRQN) with a distributed RL framework, the proposed algorithm effectively manages uncertainties in renewable generation and market prices while enabling parallel computation for efficiently handling long-term data.

The enterprises today are faced with the tough challenge of processing, storing large amounts of data in a secure, scalable manner and enabling decision makers to make quick, informed data driven decisions. This paper addresses this challenge and develops an effective enterprise data strategy in the cloud. Various components of an effective data strategy are discussed and architectures addressing security, scalability and privacy aspects are provided.

This document represents a contribution of the United States early career collider physics community to the 2025--2026 update to the European Strategy for Particle Physics. Preferences with regard to different future collider options and R&D priorities were assessed via a survey. The early career community was defined as anyone who is a graduate student, postdoctoral researcher, untenured faculty member, or research scientist under 40 years of age. In total, 105 participants responded to the survey between February and March 10th, 2025. Questions were formulated primarily to gauge the enthusiasm and preferences for different collider options in line with the recommendations of the United States' P5 report, relevant to the European Strategy Update.

Aiming at the shortcomings of the gazelle optimization algorithm, such as the imbalance between exploration and exploitation and the insufficient information exchange within the population, this paper proposes a multi-strategy improved gazelle optimization algorithm (MSIGOA). To address these issues, MSIGOA proposes an iteration-based updating framework that switches between exploitation and exploration according to the optimization process, which effectively enhances the balance between local exploitation and global exploration in the optimization process and improves the convergence speed. Two adaptive parameter tuning strategies improve the applicability of the algorithm and promote a smoother optimization process. The dominant population-based restart strategy enhances the algorithms ability to escape from local optima and avoid its premature convergence. These enhancements significantly improve the exploration and exploitation capabilities of MSIGOA, bringing superior convergence and efficiency in dealing with complex problems. In this paper, the parameter sensitivity, strategy effectiveness, convergence and stability of the proposed method are evaluated on two benchmark test

ECG foundation models are increasingly popular due to their adaptability across various tasks. However, their clinical applicability is often limited by performance gaps compared to task-specific models, even after pre-training on large ECG datasets and fine-tuning on target data. This limitation is likely due to the lack of an effective post-training strategy. In this paper, we propose a simple yet effective post-training approach to enhance ECG foundation models. We evaluate it on a publicly available Transformer-based foundation model. Experiments across multiple ECG tasks show that our method consistently outperforms baseline fine-tuning. On the PTB-XL benchmarks, it improves macro AUROC by 0.7%-8.9% and macro AUPRC by 23.3%-77.9%, also outperforming several recent state-of-the-art approaches, including task-specific and advanced architectures. Further analyses demonstrate improved training dynamics and data efficiency, with only 30% of the training data outperforming the baseline trained on the full dataset. Ablation studies highlight the importance of stochastic depth and preview linear probing. These findings underscore the potential of post-training strategies to improve EC

Axions and other very weakly interacting slim (with $m <$ 1 GeV) particles (WISPs) are a common feature of several extensions of the Standard Model of Particle Physics. The search of WISPs was already recommended in the last update of the European strategy on particle physics (ESPP). After that, the physics case for WISPs has gained additional momentum. Indeed, WISPs may provide a new paradigm to explain the nature of dark matter and puzzling astrophysical and particle physics observations. This document briefly summarizes current searches for WISPs and the perspectives in this research field for the next decade, ranging from their theoretical underpinning, over their indirect observational consequences in astrophysics, to their search in laboratory experiments. It is stressed that in Europe a rich, diverse, and low-cost experimental program is already underway with the potential for one or more game-changing discoveries. In this context, it is also reported the role of the EU funded COST Action ''Cosmic WISPers in the Dark Universe: Theory, astrophysics, and experiments'' (CA21106, https://www.cost.eu/actions/CA21106) in coordinating and supporting WISPs searches in Europe, sha

Heavy-flavour physics is an essential component of the particle-physics programme, offering critical tests of the Standard Model and far-reaching sensitivity to physics beyond it. Experiments such as LHCb, Belle II, and BESIII drive progress in the field, along with contributions from ATLAS and CMS. The LHCb Upgrade II and upgraded Belle II experiments will provide unique and highly sensitive measurements for decades, playing a key role in the searches for new physics. Future facilities with significant heavy-flavour capabilities will further expand these opportunities. We advocate for a European Strategy that fully supports Upgrade II of LHCb and an upgrade of Belle II, along with their subsequent exploitation. Additionally, we support a long-term plan that fully integrates flavour physics in an $e^+e^-$ collider to run as a $Z$ factory.

Statistical model checking delivers quantitative verification results with statistical guarantees. It scales to model sizes and model types that are out of reach for exhaustive, analytical techniques. So far, it has been used to evaluate one property value at a time only. Many practical problems, however, require finding the Pareto front of optimal tradeoffs between multiple objectives. In this paper, we present the first statistical model checking approach for such multi-objective Pareto queries, based on lightweight strategy sampling. We introduce an incremental scheme that almost surely converges to a statistically sound confidence band around the true Pareto front in the long run. To obtain a close underapproximation of the true front in finite time, we propose three heuristic approaches that try to make the best of an a-priori fixed sampling budget. We implement our new techniques in the modes simulator of the Modest Toolset, and show their effectiveness on benchmarks from the literature.

The European Strategy for Particle Physics (ESPP) - 2026 update is taking place in a turbulent international climate. Many of the norms that have governed relations between states for decades are being broken or challenged. The future progress of science in general, and particle physics in particular, will depend on our ability to maintain peaceful international scientific collaboration in the face of political pressures. We plead that the ESPP 2026 update acknowledge explicitly the importance of peaceful international scientific collaboration, not only for the progress of science, but also as a precious bridge between geopolitical blocs. "Scientific thought is the common heritage of mankind" - Abdus Salam

The Brazilian High-Energy Physics (HEP) community has expanded remarkably since its first involvement at CERN and Fermilab in the 1980s. Its recent organization under the Brazilian Network for High-Energy Physics (RENAFAE), since 2008, has further strengthened its scientific and technological goals, particularly in detector instrumentation, computing, and industry partnerships. In 2024, Brazil became an Associate Member State of CERN, opening new opportunities for deeper engagement in accelerator and detector R&D. This input to the 2026 update of the European Strategy for Particle Physics highlights Brazil's current participation in LHC experiments as well as ongoing developments in detector and accelerator technology, and details the community's view towards future colliders. The potential for expanded scientific and industrial collaborations between Brazil and CERN is also discussed.

This document is being submitted to the 2024-2026 European Strategy for Particle Physics Update (ESPPU) process on behalf of the US Muon Collider community, with its preparation coordinated by the interim US Muon Collider Coordination Group. The US Muon Collider Community comprises a few hundred American scientists. The purpose of the document is to inform ESPPU about the US plans for Muon Collider research and development (R&D), explain how these efforts align with the broader international R&D initiatives, and present the US community vision for the future realization of this transformative project.

The LISA mission is an international collaboration between ESA, its member states, and NASA, for the detection of gravitational waves from space. It was adopted in January 2024 and is scheduled for launch in the mid-2030's. It will be a constellation of three identical spacecraft forming a near-equilateral triangle in an heliocentric orbit, transferring laser beams over $2.5 \cdot 10^6$ km long arms. Laser interferometry is used to track separations between test masses, thus measuring spacetime strain variations as a function of time. LISA Science Objectives tackle many open questions in astrophysics, fundamental physics and cosmology, including ESA's Cosmic Vision questions "What are the fundamental laws of the universe?" and "How did the universe originate and of what is it made?". In this contribution, based on the LISA Red Book, we present a summary of the LISA Science Objectives relevant for the European Strategy for Particle Physics.

The paper presents a multi-resource load balancing strategy which can be utilised within an agent-based system. This approach can assist system designers in their attempts to optimise the structure for complex enterprise architectures. In this system, the social behaviour of the agent and its adaptation abilities are applied to determine an optimal setup for a given configuration. All the methods have been developed to allow the agent's self-assessment. The proposed agent system has been implemented and the experiment results are presented here.

In view of the European Strategy for Particle Physics process, the French HEP community has organized a national process of collecting written contributions and has pursued a series of workshops culminating with a national symposium held in Paris on January 20-21, 2025 that involved over 280 scientists https://indico.in2p3.fr/event/34662/. The present document summarises the main conclusions of this bottom-up approach centred on the physics and technology motivations.