Using reductions from structured P-matrix violation search to classical NP-complete formulations such as 3-SAT and Subset Sum, we examine the relationship between representational expansion, auxiliary variables, local inferability, and information accessibility. Rather than viewing reductions purely as computational transformations, we interpret them as mechanisms that redistribute hidden witness information across enlarged representations. From this perspective, reductions, gadgets, and auxiliary structures may expose globally encoded witness information to local propagation and inference, while search algorithms act as decoding procedures attempting to recover the original hidden witness. The resulting observations suggest that representational expansion may improve local inferability by introducing auxiliary variables and consistency structures, while preserving the need to recover the underlying witness information. This work is exploratory in nature and proposes a conceptual framework for understanding how reductions reshape information accessibility in NP search.

We formulate a Maxwell version of the codimension-three Riesz/Gaussian quadratic-form representation for perfectly conducting parallel plates. This paper is the Maxwell follow-up to the scalar codimension-three Riesz/Gaussian representation theorem presented earlier in arXiv:2605.06693(2026): the same transverse Riesz reduction and prescribed-covariance quadratic-form mechanism are carried over here to the physical parallel-plate Maxwell operator. The construction is carried out in finite lateral volume $Ω_{L,a}=T_L^2\times[0,a]$, using the physical electric-field Hilbert space of divergence-free fields satisfying the perfect-conductor tangential condition $n\times E=0$, with the static normal zero mode removed. The Maxwell curl-curl operator is defined by its closed quadratic form, and an explicit Fourier-domain analysis proves the finite-volume spectral gap, compact resolvent, and heat-trace admissibility needed for the stochastic construction. For this reduced Maxwell operator $\mathcal L_{\mathrm{Mx}}$, the codimension-three Riesz integral gives the transversely reduced Riesz mediator $g\mathcal L_{\mathrm{Mx}}^{-1}$. A prescribed heat-regularized Gaussian source with covariance $(\hbar c/g)\mathcal L_{\mathrm{Mx}}^{3/2}e^{-τ\mathcal L_{\mathrm{Mx}}}$ then has expected quadratic Green energy equal to the heat-regularized physical Maxwell trace. The finite-volume trace is shown to be spectrally equivalent to a scalar Dirichlet channel plus a scalar Neumann channel with its constant zero mode removed. Under the standard parallel-plate interaction finite-part prescription, the large-area energy density is $$ -\frac{π^2\hbar c}{720a^3}. $$ The result is a representation theorem for the Maxwell parallel-plate trace under a prescribed covariance in the flat-plate geometry considered here.

On the n x n chessboard, the move totals of distinct pieces satisfy a small number of striking arithmetic identities. The total diagonal mobility of the bishop and the total 8-neighbor mobility of the king are exactly proportional, with constant n/12, valid for every n. Among nontrivial boards, the strengths of two distinct pieces drawn from a natural thirteen-piece alphabet coincide only for n in {6, 8, 12}. We define the strength of a piece P on the n x n board as the probability that a uniformly random ordered pair of distinct squares forms a legal P-move on the empty board, and prove four main results. (1) An asymptotic dichotomy classifies pieces into riders (Theta(1/n) strength) and leapers (Theta(1/n^2) strength), with explicit rational leading constants. (2) A stable-ordering theorem identifies the threshold n* = 24 beyond which the strength order becomes fixed, with a complete tabulation of every transition for 4 <= n <= 24. (3) A complete classification of strength coincidences shows they occur only at the three magic boards n in {6, 8, 12}, accompanied by the closed-form identity str(K) - str(N) = 12/(n^2(n+1)), the unique near-coincidence between bishop and knight at n = 10 (gap 0.0606%), and the bishop-king proportionality str(B)/str(K) = n/12. (4) A Strength Algebra Theorem expresses the strength of any compound army as a linear functional of a four-dimensional atomic vector, and confines strength coincidences between distinct single pieces to the three magic boards. As immediate consequences we obtain explicit strength-preserving single-piece substitution rules on each magic board, and a characterization of the 8 x 8 board as the unique nontrivial board on which the rook attains a strength matched by another piece in the alphabet (the archbishop).

This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed framework to elementary functions. Derivatives of rational power, exponential, logarithmic, trigonometric, and inverse trigonometric functions are constructed through the geometric interpretation of the tangent line, inverse symmetry, and local linear structure, without treating the limit as the initial defining mechanism. Within the proposed approach, the derivative is introduced from the outset as a functional correspondence assigning to each point the slope coefficient of the tangent line. The paper demonstrates that the classical differentiation formulas arise naturally from interconnected geometric and algebraic structures and are subsequently consistent with standard limit-based analysis. From a methodological perspective, the study proposes the logical sequence: Tangent, Local Linear Structure, Limit formalisation. Thus, the paper presents a conceptual bridge between geometric intuition, algebraic construction, and classical differential calculus.

In this paper we study cosmological perturbations with $f(R)$ gravity scalaron. We consider epoch of transition from early general relativity (GR) phase to late time non-GR phase of cosmogenic history for a viable $f(R)$ gravity Lagrangian close to the $Λ$CDM theory at early cosmic history. We study deviation in matter power spectra from $Λ$CDM scenario. Galaxy power spectra multipoles are generated using galaxy bias, velocity dispersion and modified gravity parameters. While monopole and quadrupole matter power in $f(R)$ theory increase towards larger $k$ (small scales), quadrupole power spectrum remains elevated relative to $Λ$CDM for smaller $k$ (large scales), upto $k\approx 0.02$. These power spectra provide observables for testing gravity through the current and future galaxy survey missions such as DESI, EUCLID, 4MOST and PFS. We report appropriate GR limit of scalaron mass in galactic and massive black hole scales. Evolution of the scalaron mass and its general relativistic limit for various cosmic structures are reported. Deviation from GR in cosmogenic evolution is attributed to decrease in scalaron mass with cosmic time.

This essay argues that Alice Ambrose precedes key elements later critiques by Quine, first of Truth by convention (Quine 1936) and later of the analytic-synthetic distinction (Quine 1951). I demonstrate how Ambrose identifies in writing as early as in 1931: (1) the paradox of treating logical principles as mere conventions, (2) the infinite regress in stipulative definitions, (3) the preconditional role of logic for any convention, and (4) the instability of the analytic/synthetic divide. Ambrose, therefore, prefigures Margaret Macdonald (1934) unpublished dissertation (Cf. Spinney 2025) and predates some major contributions to the philosophy of logic by Quine a few years before he made them popular.

Drawing primarily on her early work (1931-1934), I argue that Alice Ambrose develops a philosophical project centered on preserving the rigor of extensional logic while rejecting the metaphysical and epistemological endorsements of logicism because of its commitment to the notion of material infinity. Positioning Ambrose as a transitional figure between formalism (Russell) and the constructivist turn represented by intuitionism (Brouwer), I demonstrate how Ambrose offers a practice oriented statement of finitist extensionalism. Employing only extensional methods (considering classes, relations, and propositions by reference to their members and truth values instead of mental processes), Ambrose reformulates an existential claim about pi as an explicit infinite disjunction of concrete instances insisting, against intensional projects, that such claims gain meaning only through a finite stopping rule that produces a witness.

The Connes-van Suijlekom truncated Weil quadratic form, indexed by a cutoff parameter $c$ that controls the primes $p\leq c$ entering the operator, has a ground state whose Fourier-Mellin zeros provably lie on the critical line; whether they converge to the Riemann zeros as $c\to\infty$ is open (Connes 2026; Connes-Consani-Moscovici 2025). We present, to our knowledge, the first public implementation of the CvS Galerkin matrix at sixteen cutoffs ($c=13$ through $67$, plus $c=100$). Across $c=13$ through $c=67$ at $N=100$, the first-zero absolute error $|γ_1-γ_1^{\mathrm{Riemann}}|$ shrinks monotonically from $\sim 2\times 10^{-55}$ to $\sim 1.5\times 10^{-168}$ -- a 113-OOM convergence across fifteen cutoffs. The smallest-positive even-sector eigenvalue $λ_{\min}^{\mathrm{even}}$ separately reaches $\sim 10^{-334}$ at $c=100$, $N=250$ (275-OOM span from $c=13$), and the same eigenvector recovers $γ_1,\ldots,γ_{10}$ to 307-329 matching digits at $N=250$, $\mathrm{dps}=500$. Under the unitary equivalence with CCM 2025 Lemma 5.1, each $γ_k$ is (modulo a hypothesis-status caveat at $c=100$) an eigenvalue of the CCM rank-one operator $D_{\log}^{(λ,N)}$ at $λ=\sqrt c$. On the four-point $N$-sweep at $c=100$, Aitken-$Δ^2$ on two consecutive triples gives $\log_{10}|λ_\infty^{\mathrm{even}}|\approx -536.76$ and $\approx -533.70$, approaching the Connes 2026 Section 6.4 heuristic continuum prediction ($\approx -530.38$) monotonically with $N$. The empirical fit $|\log_{10}λ_{\min}|\approx 13.24 c^{0.634}$ on $c\leq 67$, $N=100$ is shown to be a finite-$N$ rate, falsified at $c=100, N=200$ by 49 OOM. The raw spectrum at $c=100$ carries 3, 5, 8, 11 negative-sign eigenvalues for $N=100,150,200,250$; continuum positivity of $QW_λ$ is RH-equivalent and we do not assume it at $λ=\sqrt{100}$. We make no claim of proof.

We develop an observation-driven framework that reverses the standard wormhole approach: instead of assuming a Morris--Thorne traversable wormhole geometry and deriving the supporting matter, we reconstruct the wormhole metric directly from the observed rotation curve of the spiral galaxy \mbox{NGC\,3198}. Using SPARC data ($D=13.8\,\mathrm{Mpc}$; 43 measurements over $0.32$--$44.08\,\mathrm{kpc}$), we fit four dark-matter halo profiles -- Hernquist, Navarro--Frenk--White (NFW), Burkert, and Einasto -- through $χ^2$ minimisation with the Nelder--Mead algorithm. For each best-fit density profile $ρ(r)$, the redshift function is reconstructed from the circular geodesic relation $f'(r)=v^2(r)/r$, while the shape function follows from the Einstein field equations, $b'(r)=8πGρ(r)r^2/c^2$. We define the dimensionless wormhole indicator $\mathcal{W}(r)=b(r)/r$ and evaluate it across the observed galactic domain. All four profiles satisfy $\mathcal{W}(r)\ll1$, implying that the observed region lies entirely within the traversable exterior of the reconstructed wormhole geometry. The flare-out condition $b'(r)<1$ is satisfied everywhere by several orders of magnitude. The cored Burkert and Einasto profiles exhibit null energy condition (NEC) violation near the galactic centre, indicating effective exotic matter compatible with wormhole support, whereas the cuspy Hernquist and NFW profiles preserve the NEC. Among all models, the Burkert profile provides the best fit ($χ^2_{\rm dof}=2.545$), the largest wormhole indicator ($\mathcal{W}_{\max}=5.62\times10^{-7}$), and the strongest NEC violation, suggesting that the observationally favoured dark-matter distribution can also sustain a traversable wormhole. These results establish galactic rotation curves as a potential observational probe of wormhole physics.

Hierarchically designed mechanical metamaterials involve nested levels of structural organization, mimicking natural structures (such as bones, wood, and bird feathers) to create advanced functional materials. Compositional hierarchy, a specific type of hierarchical strategy that involves the methodical assembly of discrete building blocks, offers unique advantages in engineering design due to its modular nature. This involves proper selection and spatial arrangements of distinct microstructures, as a result of which the desired macro-scale mechanical behavior can be achieved. Towards the design of such compositional hierarchical metamaterials, this paper presents a two-step design framework. First, material optimization of the design domain is performed using a parameterized elasticity matrix to obtain optimal conceptual designs. Second, building-block microstructure geometries are selected from a qualitative library and subjected to shape-size refinement to satisfy the desired kinematic or stiffness requirements. To construct the qualitative library, a novel parametrization scheme is initially introduced, which categorizes the planar orthotropic elasticity matrix into four distinct classes. Utilizing a kinetostatic load flow visualization technique, the candidate microstructure geometries are then populated within these four classes. The framework is validated for the design of a cantilever beam with a specified lateral stiffness requirement and the design of planar sheets that exhibit specified target deformation patterns. Thus, the present work provides a systematic and physically intuitive methodology applicable to arbitrary kinematic deformation and stiffness requirements.

We solve the following problem of W.H. Besant using a formula for the coefficients of an ellipse inscribed in a quadrilateral, $Q$: \enquote{If an ellipse be inscribed in a quadrilateral so that one focus is equidistant from the four vertices(call that point $EP$), the other focus must be at the intersection of the diagonals(call that point $IP$).} We also prove somewhat more than just solving Besant's problem itself, though it would be nice to see the details of the geometric approach proposed by Besant. More precisely, we also prove the converse result and additional results when $Q$ is a trapezoid. Finally, we show that such an inscribed ellipse exists if and only if $Q$ is orthodiagonal.

The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic system can describe said conjecture. In this work, we construct explicit Turing machines that search for a solution to Brocard's problem greater than 7 and a Fermat prime beyond the 4th which halt if and only if such a solution exists.

We study a translation-invariant mean-field game on the flat torus with interaction $F(x,m)=γ(K*m)(x)$, where $K$ is smooth, even, and mean-zero. The interaction is of potential type, arising as the first variation of a quadratic energy, though the stationary system is not treated variationally. Linearizing around the uniform equilibrium yields mode-wise $2\times 2$ systems with dispersion $σ_ξ(γ)=ν^2(2π|ξ|)^4+γ(2π|ξ|)^2\hat K(ξ)$. If $\hat K$ is negative for some mode, a finite threshold \[ γ_c=\min_{\hat K(ξ)<0}\frac{ν^2(2π|ξ|)^2}{|\hat K(ξ)|} \] marks loss of stability; otherwise $γ_c=+\infty$. Near criticality, the spectral gap scales as $ρ(γ)\sim C_*\sqrt{γ_c-γ}$. For $γ<γ_c$, the uniform state is exponentially stable in the turnpike sense for finite-horizon problems, with rate $ρ(γ)$. At $γ=γ_c$, the gap closes and, after phase fixing and center-manifold reduction, one obtains algebraic midpoint decay of order $T^{-1/2}$. For $γ>γ_c$, a branch of nonuniform stationary solutions bifurcates via a pitchfork-type amplitude equation, with translations generating the full family. Finally, under standard asymptotic-consistency assumptions on symmetric $N$-player equilibria in the subcritical regime, we obtain qualitative propagation of chaos, without quantitative rates.

This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key results from real-valued convex analysis to the complex domain, establishing the validity of the minimax theorem and the preservation of saddle-point structure. Building on this foundation, we formulate a complex zero-sum game model that enables mixed strategies to interact with the real and imaginary components of the payoff matrix, and we characterize its saddle-point equilibrium through associated primal and dual problems. To incorporate uncertainty, we introduce a complex chance-constrained zero-sum game model (3CP) that handles individual probabilistic constraints defined by complex linear functionals. We first study the 3CP formulation under known exact distributions, focusing on Complex Elliptically Symmetric random variables, which generalize the complex Gaussian family. The framework is then extended to moments-based ambiguity sets, including: (i) distributions with known first two moments, (ii) distributions with unknown second-order moments, and (iii) fully distributed with unknown moments. In all cases, the probabilistic constraints admit deterministic second-order cone representations, ensuring convex feasible strategy sets and enabling explicit characterization of the complex game value. Numerical experiments, including a transmitter--jammer waveform interaction model, show how the proposed framework captures the behavior of complex mixed strategies. Additionally, we evaluate out-of-sample rates and confirm that practical behavior closely aligns with the theoretical guarantees.

Automated insulin delivery (AID) and artificial pancreas systems increasingly serve as safety-critical cyber-physical technologies in clinical care, integrating sensors, algorithms, software, and insulin-delivery hardware to automate a life-sustaining therapy. While regulated commercial systems are supported by formal approval pathways, manufacturer governance, and post-market surveillance, clinicians are also encountering patients who rely on do-it-yourself (DIY) artificial pancreas systems that operate outside conventional regulatory and institutional control structures. This paper examines how routine clinical handling practices intersect with cyberbiosecurity risk across both regulated and DIY AID systems. When insulin delivery systems are fundamentally reconfigured into a bespoke AID system, with the patient-user becoming the primary threat vector by assuming manufacturer-level roles without mandated governance, the entire ecosystem of stakeholders is placed in legal and clinical uncertainty.

Patients often struggle to communicate coherent accounts of their health histories during time-constrained clinical encounters. These accounts, which we refer to as health stories, include both clinical events and lived experiences. Existing systems prioritize structured, clinician-centered data and provide limited support for eliciting and communicating patient-generated narratives. We present HealthTale, a patient-centric visualization system designed to elicit health stories from patients and structure them to facilitate communication during initial clinical conversations. Its design arises from a multi-stage qualitative investigation across domain expert discussions, online narratives (n=20), patient (n=11) and clinician (n=6) interviews, and elicited health stories (n=22), identifying recurring patterns in how individuals construct and communicate their health stories. HealthTale transforms freeform narratives into structured timeline representations, grounded in a data abstraction that models health stories as events that are grouped by health concern and time, capturing both clinical and contextual information, with the flexibility to handle temporally imprecise data and non-linear distributions of events across time. Through evaluation with patients (n=34) and clinicians (n=3), we find that HealthTale supports recall, organization, and self-advocacy, while enabling clinicians to rapidly interpret patient-generated narratives and establish a shared understanding.

Creating supportive technologies for people living with multiple chronic conditions is extremely challenging. These patients are often faced with substantial visible and invisible treatment work as well as their everyday responsibilities, including coordinating across providers, tracking information, and repeating communication in emotionally charged contexts. In the Cumulative Complexity Model (CuCoM), the balance between patient workload and patient capacity shapes what patients can realistically take on, including whether a digital tool can be adopted and sustained. In this paper, we report engagement lessons from implementing MyCareCompass, a patient-facing digital health intervention (DHI) intended to support day-to-day self-management for people living with multiple chronic conditions. We define engagement as patient uptake and sustained use during a two-month pilot study of our platform, drawing on usage analytics and follow-up feedback, and distill three implementation lessons for designing for engagement in complex chronic care.

AI tools are enabling engineers to absorb roles previously distributed across cross-functional squads, yet there is little structured evidence on how to design or evaluate such a one-person squad in a regulated enterprise setting. Without that evidence, organizations adopting this model lack guidance on which design decisions make it viable and which conditions cause it to break down. We report a case study in which a single staff engineer, supported by four AI agents under a Spec-Driven Development workflow, delivered a brownfield product initiative scoped for a four-person squad in half the planned time, with 90\% acceptance of AI-generated code on first review, full integration test pass rates, and an above-85\% reduction in direct staffing cost. The results indicate that AI does not replace team members it multiplies the throughput of the experienced engineer who remains, making specification quality and institutional knowledge, not model capability, the binding constraints on one-person squad success.

The k-defensive domination problem is a powerful modeling tool for strategic decision-making in network security and disaster/emergency management, where multiple nodes may be simultaneously under attack. Despite its practical relevance, the problem has been poorly studied, largely due to its high computational difficulty. This study investigates the application of Benders decomposition to the k-defensive domination problem, aiming to improve computational efficiency over standard integer programming formulations. Several cut generation strategies, including a combinatorial approach and the simultaneous addition of multiple cuts, are proposed. Theoretical results on the strength of feasibility cuts are presented. In addition, two novel enhancement strategies are proposed: a clique-cover-based heuristic, the first feasible solution method in the literature for this problem, achieving up to 98% improvement over the trivial upper bound, and an initial cut generation heuristic that in some cases resolves the problem without further branching. Experiments on Erdos-Renyi, chordal, and Barabasi-Albert instances show that the algorithm variant involving all of the proposed components is able to solve instances that remain out of reach for classical formulations and standard Benders decomposition.

The academic journal zoning system is central to evaluating research talent, funding, and institutions. The CAS journal partition system, one of East Asia's most widely used tools, will cease operation in March 2026, creating a policy gap. Existing alternatives have major limitations: JCR depends on paid databases and excludes conferences; Scimago/CiteScore relies on Elsevier proprietary data; expert-based rankings such as CCF and CORE lack quantitative foundations and update slowly. This paper proposes the General Science Ranking (GSR), a multidimensional bibliometric framework built entirely on open-source data. GSR covers 500 computer science venues (397 journals and 103 conferences) and 500 medical journals using OpenAlex and Semantic Scholar. Scores combine four indicators: field-weighted citation impact (FWCI), two-year impact factor (IF2), five-year h-index (h5), and citation CAGR. For CS conferences lacking citation time-series data, IF2-approx was estimated from calibration on 1.41 million OpenAlex journal papers. Rankings adopt fixed quotas: Q1 (1-50), Q2 (51-100), Q3 (101-200), and Q4 (201+). All code and data are open source. In CS rankings, conferences and journals each occupy 25 of the top 50 Q1 positions. The leading conferences are NeurIPS, ICCV, ICLR, and CVPR. In medicine, CA: A Cancer Journal for Clinicians ranks first, followed by New England Journal of Medicine and The Lancet. Agreement with JCR Q1 reaches 84 percent in medicine and 71 percent in CS. Sensitivity analysis shows only 1.7 percent to 2.5 percent of CS conferences change partitions, indicating robustness. GSR provides a free, reproducible, field-normalized ranking system covering both journals and conferences, making it suitable for institutional evaluation policies.

Enterprise software development is a continuous evolutionary process, characterized by incremental additions, architectural revisions, production deployments and rigorous maintenance. These activities generate valuable data that modern LLMs could be finetuned on, to unlock additional tool possibilities for enterprise software engineering. While frontier LLMs are already very capable, this form of customization offers a compelling path for enterprise-specific optimization. We introduce Gemini for Google (GfG)}, an adaptation of Gemini specialized for Google's internal software engineering ecosystem. This paper details the model's end-to-end development, from curating a trillion-token proprietary dataset to implementing a mid-training strategy that mitigates catastrophic forgetting. In a large-scale blind A/B study across 29,000 developers, Gemini for Google significantly outperformed baselines: reducing the mean number of iterations per turn by 23\%, and increasing code survival rates by about 17%. Beyond metrics, we provide a comprehensive blueprint for enterprise model adaptation, covering: (1)The extraction of high-value signals from software engineering data, (2)Data preparation strategies, (3)Full-stack model tuning (continued pre-training and post-training), and (4)The deployment of downstream applications. We believe this methodology offers a replicable path for other organizations to unlock the full potential of their internal engineering data.

Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation networks. However, reconstructing these latent states is challenging because the signals are coupled across higher-order topologies, while high dimensionality, nonlinear observations, and unknown structures increase the difficulty. To address this, we propose a topology-aware state space framework derived from stochastic partial differential equations on cell complexes. State evolution follows heat-like topological diffusion, with perturbations propagating along boundary operators. Under partial observability, we model observations using a cell complex convolution of latent states coupled with a nonlinear mapping. We perform recursive state estimation via an Extended Kalman Filter, simultaneously learning model parameters and uncertainties through an online Expectation-Maximization algorithm. Finally, for scenarios where only lower-order topological structure is known, e.g., nodes and edges, as in critical infrastructure networks, we introduce a heuristic cell identification algorithm to explicitly infer the second-order cell structures. Validations on synthetic and real datasets from water, sensor and transportation networks demonstrate that our approach yields reliable estimates under partial observability and successfully recovers the underlying topological structures.

Recent developments in 3D generative AI enable users to create bespoke 3D models from text or image prompts. However, these approaches provide limited control over spatial structure, making them ill suited for tasks requiring precise geometric composition. We present MiXR, an XR system for in-situ compositional modeling that enables users to create new 3D models by harvesting geometry from their environment. Users extract segments from captured objects and assemble new artifacts through direct 3D manipulation, while generative AI synthesizes a coherent model from the user-defined composition. This hybrid workflow allows users to define spatial structure explicitly while delegating geometric refinement to generative models, enabling them to specify spatial intent that is difficult to express through verbal prompts alone. In a controlled user study ($N=12$), participants using MiXR rated their designs as significantly closer to the target, felt more in control, and experienced lower cognitive workload compared to a generative composition baseline.

Wake-Up Radio (WUR) enables resource-constrained, battery-powered sensor nodes to remain in a low-power deep sleep state while continuously listening for a Wake-Up Signal (WUS). Sensor nodes only wake and transmit data after receiving the WUS, significantly reducing energy consumption. However, polling nodes whose transmitted data provides little or no meaningful update to the remote monitor can still result in unnecessary energy usage and increased storage overhead. To address this issue, this paper uses the Age of Incorrect Information (AoII) metric to prioritise the polling of nodes that provide informative updates to the remote monitor. Determining the optimal set of nodes to poll based on AoII can be formulated as a Restless Multi-Armed Bandit (RMAB) problem, which traditionally requires prior knowledge of the monitored process transition dynamics. Since such dynamics are often unknown in practical deployments, we propose an online learning framework based on state estimation to derive Whittle Index AoII (WAoII) and Fair Whittle Index AoII (FWAoII) policies without assuming known transition probabilities. The proposed policies efficiently schedule node polling while adapting to unknown process behaviour. Experimental evaluation using both real-world and synthetic datasets demonstrates that the proposed online WAoII policy can reduce packet transmissions by up to 70\% compared to the widely used Round Robin (RR) polling strategy, while maintaining Root Mean Squared Error (RMSE) values within acceptable application error tolerances. These results demonstrate the effectiveness of WAoII and FWAoII as energy-efficient polling techniques for low-power WUR sensor networks.

Telegram has emerged as a major platform for large-scale video piracy, where copyrighted content is rapidly distributed among users. Despite its prominence, the structural and operational dynamics of this ecosystem remain insufficiently understood. To address this gap, we present the first large-scale study of video piracy on Telegram through a mixed-method analysis of 1,057 channels that shared 209k unique posts between December 2023 and January 2026 - systematically characterizing their content, distribution strategies, and how the ecosystem is sustained at scale. Central to our approach is the development of a fine-grained taxonomy that enables a structured understanding of the activity and intent of these channels on a per-post level. The channels collectively distributed 19,033 unique copyrighted titles originating from 175 countries, accumulating over 4.85B unique views and resulting in a lower-bound estimated financial loss of $17.49B for content rights holders. We also find that this ecosystem is deliberately engineered to be resilient against takedown efforts, frequently redirecting users through chains of intermediary channels and automated bots that collectively handle hosting, access control, monetization, and channel discovery. The scale and persistence of this ecosystem motivated the development of Anti-RIP, a real-time framework for detecting emerging video piracy communities on Telegram. Anti-RIP utilizes our taxonomy to generate contextual, interpretable insights that stakeholders confirmed improve the triaging action against reported posts and channels. Over a 61-day period, the framework facilitated the takedown of 524 previously unknown piracy channels and 71 bots. To support reproducibility and future research, we open-source both the dataset and the Anti-RIP framework.

Machine learning nowadays becomes a useful instrument in many subjects. In this paper we use interpretable machine learning to build quantum algorithm. By studying the parameters of the machine learning algorithm we were able to construct universal shortest analytic quantum algorithm for arbitrary diagonal matrix of any size.

We systematically investigate the entanglement and information dynamics of quasiperiodic systems across their extended, critical, and localized phases, aiming to identify dynamical signatures that can reveal the multifractal spatial structure of critical states and distinguish critical phases from the extended and localized regimes. Focusing on the generalized Aubry-André-Harper model, we complement the half-chain entanglement entropy with the spatially resolved subsystem information capacity (SIC) and demonstrate that critical states exhibit pronounced spatial heterogeneity absent in the extended and localized phases. In the steady state, the SIC reveals a stepwise ramp as a function of subsystem size, reflecting an underlying fragmentation of the chain into weakly connected subregions. Dynamically, information initially localized within such a subregion can undergo coherent long-lived oscillations, dubbed subregion echoes, whose period scales with the subregion length, in quantitative agreement with a quasiparticle picture of confined quasiparticle reflections. We trace this internal fragmentation to the incommensurately distributed zeros (IDZs) in the off-diagonal hopping terms of the Hamiltonian. To establish the generality of the SIC as a diagnostic tool, we further apply it to a mobility-edge phase with coexisting extended and localized states and to a critical phase that does not originate from IDZ fragmentation, and show that the SIC can cleanly distinguish these scenarios through their distinct steady-state profiles, initial-site sensitivities, and the presence or absence of subregion echoes. Our results establish the SIC as a powerful real-space probe for diagnosing critical phases and uncovering the bottlenecked connectivity that underlies the multifractal structure of critical states.

Retrieval-Augmented Generation (RAG) has become the standard approach for grounding large language models in information that was not available during training. While existing datasets and benchmarks focus on web or other public sources, there is still no widely adopted dataset that realistically reflects the nature of company-internal knowledge. Meanwhile, startups, enterprises, and researchers are increasingly developing AI Agents designed to operate over exactly this kind of proprietary data. To close this gap, we release a synthetic enterprise corpus, its generation framework, and a leaderboard. We present EnterpriseRAG-Bench, a dataset consisting of approximately 500,000 documents spanning nine enterprise source types (Slack, Gmail, Linear, Google Drive, HubSpot, Fireflies, GitHub, Jira, and Confluence) and 500 questions across ten categories that test distinct retrieval and reasoning capabilities. The corpus is generated with cross-document coherence (grounded in shared projects, people, and initiatives) and augmented with realistic noise such as misfiled documents, near-duplicates, and conflicting information. The question set ranges from simple single-document lookups to multi-document reasoning, constrained retrieval, conflict resolution, and recognizing when information is absent. The generation framework lets teams generate variants tailored to their own industry, scale, and source mix. The dataset, code, evaluation harness, and leaderboard are available at https://github.com/onyx-dot-app/EnterpriseRAG-Bench.

We study a minimal model of collective light emission from an incoherently driven ensemble of atoms where incoherent drive is applied to only a subset of the atoms and show that both the linewidth and the photon statistics can be controlled within a single framework. In this setting, collective dissipation induces correlations between the pumped and unpumped parts of the system, leading to interference between their emission contributions. By introducing a relative phase between these contributions and tuning the pump rate, we demonstrate that the properties of the emitted light can be varied over a broad range. In particular, the linewidth can be made either independent of system size or scale extensively with it, while the photon statistics can be tuned from antibunched or quantum to bunched. We further show that the role of the relative phase in controlling the interference can alternatively be played by the coherent interaction. By tuning the interaction strength together with the pump rate, one can access the same regimes as in the dissipation-only model. In addition, coherent interactions stabilize regimes of coherent emission with narrow linewidth, reminiscent of superradiant lasing. Our results illustrate how interference in partially driven collective systems provides a flexible mechanism for tailoring both spectral and statistical properties of light.

Vortices in fluids and superfluids are fundamental to phenomena ranging from Bose-Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where background geometry often plays an important role. Curvature can induce vortex motion distinct from planar domains. We study Hamiltonian vortex motion on a catenoid, a minimal surface of variable negative curvature, and derive explicit equations of motion and conserved quantities for co-rotating vortex pairs. For two identical vortices we find an exact analytic solution in which the pair rotates rigidly at fixed latitude, with angular velocity $Ω=(Γ/16π)\,K'(V)/\sqrt{-K(V)}$, where $K(V)$ is the Gaussian curvature. Thus the motion is governed by the curvature gradient rather than the curvature itself. This state is linearly unstable, with growth rate $λ=\sqrt{3}|Ω|$, in agreement with numerical simulations. For generic co-rotating pairs, conservation of the Hamiltonian and rotational momentum reduces the nonlinear dynamics to a single quadrature, yielding bounded relative oscillations together with a secular azimuthal drift. Simulations of the full equations confirm this and reveal the same curvature-induced azimuthal drift in a localized many-vortex cluster, motivating a broader theory of collective vortex drift on curved surfaces.