Reference counting bugs in Linux kernel drivers can lead to severe resource mismanagement and security vulnerabilities. We introduce DrvHorn, a novel automated tool to detect these bugs by reducing reference counting verification to an assertion checking problem leveraging the Linux driver interface. Through efficient modeling of the Linux kernel and aggressive program slicing, DrvHorn discovered 545 bugs, of which 424 were previously unknown, across all platform drivers in v6.6 Linux kernel, with a lower false positive rate of 29.9% compared to prior studies. To address the root causes of these newly discovered bugs, we submitted patches to the Linux kernel, and 45 of them were merged.

Income inequality is a major contributor to health disparities, yet its effects often vary by geography and are commonly represented as compositional distributions (e.g., proportions of households across income brackets). Existing spatial regression methods struggle in this setting: they typically assume smooth spatial variation, cannot accommodate abrupt spatial heterogeneity, and lack principled treatment of compositional covariates. We propose a geographically weighted penalized compositional regression model that addresses these challenges simultaneously. Our method adopts a pairwise fusion penalty that enables detection of both contiguous and noncontiguous regional clusters with shared regression effects, thereby relaxing strong assumptions of spatial smoothness and geographic contiguity. This allows regions with similar underlying socioeconomic structures to be identified even when they are not geographically adjacent. By incorporating nonconvex penalties, such as the minimax concave penalty (MCP), the approach achieves improved estimation accuracy, interpretability, and scalability in high-dimensional spatial settings. We illustrate the method through an analysis linking U.S. income composition to chronic obstructive pulmonary disease (COPD) prevalence, revealing spatially heterogeneous associations that are obscured by conventional models. The proposed framework provides a flexible and robust tool for spatial data analysis involving compositional predictors and region-specific heterogeneity.

An \emph{outer-string representation} of a graph $G$ is an intersection representation of $G$ where vertices are represented by curves (strings) inside the unit disk and each curve has exactly one endpoint on the boundary of the unit disk (the anchor of the curve). Additionally, if each two curves are allowed to cross at most once, we call this an \emph{outer-$1$-string representation} of $G$. If we impose a cyclic ordering on the vertices of $G$ and require the cyclic order of the anchors to respect this cyclic order, such a representation is called a \emph{constrained outer-string representation}. In this paper, we present two results about graphs admitting outer-string representations. Firstly, we show that for a bipartite graph $G$ (and, more generally, for any $\{C_3,C_5\}$-free graph $G$) with a given cyclic order of vertices, we can decide in polynomial time whether $G$ admits a constrained outer-string representation. Our algorithm follows from a characterization by a single forbidden configuration, similar to that of Biedl et al. [GD 2024] for chordal graphs. Secondly, we answer an open question from the same authors and show that determining whether a given graph admits an outer-1-string representation is NP-hard. More generally, we show that it is NP-hard to determine if a given graph $G$ admits an outer-$k$-string representation for any fixed $k\ge1$.

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over underactuated systems. To obtain a continuous and numerically tractable formulation, we introduce an entropic regularization by adding small noise aligned with the control directions and study the associated Schrodinger bridge problem. The resulting reference process is a degenerate diffusion on the sub-Riemannian manifold. Under bracket-generating hypotheses we obtain smooth, strictly positive transition densities and a forward--backward characterization of the optimal bridge. This leads to a practical Sinkhorn-type algorithm for the Schrodinger potentials and, as the noise level vanishes, a recovery of the deterministic sub-Riemannian optimal transport problem. We demonstrate with a numerical example.

\noindent In this work, new measurements of absolute X-ray yields for several transitions in kaonic copper and, for the first time, in kaonic fluorine are reported. The data were collected by the SIDDHARTA-2 collaboration at the DA$Φ$NE collider using a novel room-temperature Cadmium Zinc Telluride (CZT) detection system. Detection efficiencies were evaluated through a dedicated Geant4 Monte Carlo simulation of the full experimental setup, enabling the extraction of absolute yields per stopped kaon. \noindent The measured yields exhibit a systematic dependence on the principal quantum number, reflecting the interplay between radiative transitions, Auger de-excitation, and strong-interaction-induced nuclear capture. In kaonic fluorine, a suppression of the 4$\to$3 transition yield relative to higher-n transitions is observed, providing evidence for the onset of strong-interaction effects already at the $n=4$ level. From this behaviour, a conservative lower limit on the corresponding strong-interaction width is derived. \noindent These results provide new quantitative constraints for cascade models of exotic atoms and extend experimental access to intermediate atomic levels where strong-interaction effects are not directly observable via level shifts and widths. They also establish CZT-based detection as a powerful and versatile approach for high-resolution X-ray spectroscopy of kaonic atoms in collider environments.

In this chapter, the use of machine learning (ML) in redshifted 21 cm cosmology is discussed, especially for the cosmic dawn, the Epoch of Reionization, and the scientific program of SKA-Low. The 21 cm signal is useful because it can directly probe diffuse neutral hydrogen. At the same time, it is a difficult signal, since the observable depends on density, ionization, heating, radiation backgrounds, and instrumental response in a nonlinear way. The first part of this chapter reviews the basic physical ingredients needed for the later discussion, including the global signal, spatial fluctuations, morphology-aware summaries, and the 21 cm forest. The next part describes the main difficulties for realistic analysis, such as bright foregrounds, radio-frequency interference, ionospheric and calibration effects, incomplete sampling, and the cost of forward modeling in large parameter spaces. Based on this background, ML applications are grouped by their role in the analysis pipeline. Observation-domain methods work on contaminated data products; theory-domain methods accelerate or compress forward modeling; and inference-domain methods connect observables to astrophysical and cosmological constraints. The 21 cm forest is also discussed as a case where one-dimensional spectra, small-scale information, and uncertain source populations make ML useful.

We prove global smooth continuation for smooth finite-energy solutions of the three-dimensional incompressible Navier--Stokes equations by a two-part first-threshold argument. Part I proves the axisymmetric-with-swirl theorem in the exact five-dimensional lifted formulation. The central variables are the lifted vorticity ratio \(G=ω_θ/r\), the regularized swirl derivative \(F=u^θ/r\), and the squared source density \(H=F^2\). In these variables the derivative source in the \(G\)-equation and the compressive feedback generated by the recovered strain \(U=u^r/r\) form a single pair-transfer mechanism. The proof combines localized energy identities, Hardy--Littlewood--Sobolev and Sobolev interpolation estimates, pair-threshold absorption, finite-overlap descendant exclusion, localized temporal source-to-score estimates, compactness of endpoint profiles, projected Pohozaev--Morawetz strictness, and an auxiliary recovery estimate for \(F\). Part II gives a full three-dimensional finite-threshold front-end. Starting from a hypothetical singular terminal packet, it removes leakage, shell, pressure, tail, fragmentation, passive-strain, angular phase-lock, and transfer-active temporal channels by finite-overlap descendants or strict terminal loss. A zero final defect forces the active frame measure into either a constant-frame locally two-dimensional class or a physical azimuthal orbit around one fixed axis. The first alternative is excluded by the classical two-dimensional Navier--Stokes theory, and the second is precisely the axisymmetric-with-swirl class proved in Part I.

We investigate the thermal and structural properties of knotted diblock copolymer rings using a coarse-grained lattice model in an implicit solvent. The system is studied by means of the Wang--Landau Monte Carlo algorithm, allowing us to analyze thermodynamic and conformational responses over a wide temperature range. Different knot topologies, including the unknot, trefoil, figure-eight, and pentafoil knots, are considered for both symmetric and asymmetric monomer compositions. In the AB model employed here, A-type monomers are self-repulsive, B-type monomers are self-attractive, and A-B interactions are neutral, such that the solvent is effectively good for A-type monomers and poor for B-type monomers at low temperatures. We analyze several key observables, including the heat capacity, the radius of gyration, and its temperature derivative for both the entire copolymer ring and the individual blocks, and the probability that a monomer belongs to the knotted region. Our results show that the interplay between knot topology, monomer composition, and temperature strongly influences polymer conformations. Small variations in the B-block length induce nonmonotonic, reentrant-like conformational behavior as a function of temperature, including transitions between knot localization and delocalization at low temperatures. These effects arise from the competition between energetic and entropic contributions imposed by topological constraints.

Code authorship attribution (CAA) supports software forensics, plagiarism detection, and intellectual property protection. However, existing supervised CAA approaches suffer from scarce training data and closed-world assumptions: they require sufficient labeled code from fixed candidate-author sets, making training difficult in low-data cases and predictions unreliable for open-world test pairs with unseen samples, or heterogeneous code pairs. Large language models remove task-specific training, but direct prompting depends on costly expert-designed prompts, can hallucinate over complex heterogeneous code pairs, and rarely yields auditable evidence traces. We propose MACAA, a belief-revision-based multi-agent framework for training-free code authorship verification. MACAA comprises a Coordinator and four Expert Agents analyzing layout, lexical, syntactic, and programming-pattern evidence. The Coordinator gathers expert signals for expansion, discounts unreliable evidence through contraction, and resolves conflicts through revision to preserve belief consistency, replacing direct LLM judgment with auditable hypothesis refinement. MACAA achieves 89.15\% F1 on same-language benchmarks and 80.00\% on mixed cross-language pairs, outperforming the baselines overall in both same-language and cross-language evaluations.

Understanding the evolution of nuclear size away from stability remains a central challenge in nuclear physics. In neutron-deficient systems, charge radii can be highly sensitive to the interplay between strong and electromagnetic interactions, and the effects of weak binding, giving rise to exotic nuclear phenomena. However, experimental data on these systems has been limited by short lifetimes and low production rates. Here we report the first laser-spectroscopy measurements of nuclear charge radii along the neutron-deficient aluminium isotopic chain, from $^{25}$Al to the proton-drip-line nucleus $^{22}$Al, using the {Resonance Ionization Spectroscopy Experiment} (RISE) at the {Facility for Rare Isotope Beams} (FRIB). Our measurements reveal a step-like increase in charge radius toward the drip line, with similar radii for $^{22,\,23}$Al. A comparison of our results with those of their mirror partners reveals an almost identical correlation with the calculated proton skins and is consistent with the systematic trend of well-bound nuclei. These results offer insight for understanding the evolution of nuclear size at the proton dripline and place important constraints on modern nuclear theory. They also demonstrate the unique combined capabilities of RISE and FRIB to probe the structures of previously inaccessible nuclei at the limits of existence.

Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology bulk-deformed by the Chern character. We do this by giving an explicit model for the complexified homotopy groups of the MU-module spectrum associated to a complex-oriented flow category and proving a ``homotopy coherent'' version of the classical Grothedieck-Riemann-Roch theorem. Using the aforementioned relation, we establish a computable cohomological criterion, in terms of the pair-of-pants product and the BV operator on symplectic cohomology, for when this MU lift cannot be obtained via base change from the sphere spectrum; moreover, we give examples where this holds. Finally, we use this non-base change criterion to detect examples of non-trivial higher-dimensional complex cobordism classes of relative Gromov-Witten type moduli spaces in the context of a smooth complex projective variety relative to an ample smooth divisor.

Large language models (LLMs) are rapidly transforming knowledge work by improving the quality and efficiency of tasks such as writing, coding, and data analysis. However, their growing use in education has exposed a learning-performance paradox: while they can enhance short-term task performance, they may also undermine genuine learning, including cognitive growth, knowledge transfer, and metacognitive development. This paper addresses the question of how artificial intelligence should be designed and used to support learning rather than merely improve immediate outputs. We introduce the concept of AI learning companions, defined as adaptive, pedagogically informed, LLM-powered agents designed for integration into learning environments. We propose a framework for their design built on three interrelated foundations: a pedagogical foundation focused on how students learn with AI, an adaptive foundation focused on how AI learns about students, and a responsible design foundation ensuring systems remain transparent, accountable, inclusive, and secure. The framework is illustrated through five case studies spanning diverse educational contexts, levels, and tool designs, revealing both the promise and current limitations of existing tools. We conclude that there is a necessary shift away from LLMs designed for task-oriented performance, and beyond simply prompting them to act as tutors, toward deliberately developed AI learning companions that are pedagogically sound, adapt to their learners, and foster durable understanding, metacognitive growth, and learner agency.

The genus number of a number field is a fundamental invariant which measures the contribution of ramification to its ideal class group. In this paper, we establish the statistics for the genus number for $S_3\times C_q$-fields for $q\neq 3$ a prime number, $D_4$-fields and pure quartic fields. We also obtain precise results on the average and higher moments of the genus distribution within the family of $S_3\times C_q$-fields. Finally, based on heuristics, we formulate a conjecture identifying families for which one should expect the genus density to be zero, i.e., only a density zero subset of fields in the family attains any fixed genus number.

We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.

We study a contest-theoretic model of adversarial investment in which an attacker and a defender allocate resources to AI-augmented capabilities across multiple attack surfaces. The attacker's investment operates through two channels: it amplifies offensive potency unconditionally and erodes defensive effectiveness conditionally, generating an adversarial discount that deepens endogenously with the defender's own investment. We derive a closed-form arms race ratio decomposing the relative marginal effectiveness of offensive and defensive investment into six structural primitives and establish equilibrium uniqueness and global convergence under a continuous best-response dynamic. The central result concerns signal cross-correlation, the degree to which threat intelligence on one surface informs detection on another. With full cross-correlation, the arms race ratio is independent of the number of attack surfaces: the attacker's structural advantage from surface proliferation is completely neutralized. Under the benchmark full-dilution case, without cross-correlation, per-surface defense effectiveness vanishes as the attack surface grows. Extending the analysis to heterogeneous defenders facing an attacker who targets by expected value, we argue that the model points to a dual inefficiency: overinvestment in private defense (a zero-sum redirective externality) and underinvestment in shared signal correlation (a public good). These formal results, together with public-good reasoning outside the base model, characterize when collective information aggregation can dominate private capability investment as the decisive margin in adversarial contests.

Sequential hypothesis tests are widely adopted as a principled way to perform multiple tests on data that arrives over time. In particular, researchers frequently utilize group sequential hypothesis tests (GST) to test the same hypotheses at K times or "groups" while data arrives sequentially. In this setting, many methods have been proposed to allow researchers to uniformly control type-1 error across K checks (often known as various alpha-spending budgets). Although these methods are all successfully valid in controlling uniform type-1 error, it is not clear which of these methods are optimal when trying to reject the null as soon as possible. In this paper, we directly optimize the rejection criterion in the GST setting under the same constraints of controlling type-1 and type-2 errors. We use a sample average approximation combined with mixed integer linear programming (S-MILP) approach for this problem and show how our S-MILP approach dominates classical GST procedures such as Lan-DeMets, Pocock, and O'Brien-Fleming methods. We also find that the optimal solution typically aggressively spends the alpha-budget early, shedding insight to the long-standing debate of which alpha-spending budgets are more efficient. We finally apply our optimal S-MILP approach to a recent study on acute kidney injury interventions and find our optimal S-MILP approach can reach the same statistically significant conclusion faster than the original study and other GST methods.

This study investigates non-adiabatic wave dynamics in condensed media and the transition from adiabatic stability to spectral chaos. We introduce a dimensionless parameter, as a universal metric to quantify phase-mode redistribution at sub-wavelength inhomogeneities. Our framework treats defects as localized sites of adiabaticity violation triggering non-adiabatic parametric excitation of the ground state. Numerical validation in an expanded 50-level bosonic basis demonstrates that the framework accurately distinguishes between adiabatic regimes in ENZ-metamaterials and non-adiabatic transitions in ultrafast magnetic media. We establish a universal scaling law governed by the non-adiabaticity-to-regulation ratio, proving that the proposed metric remains a robust metrological tool for identifying sub-wavelength inhomogeneities across diverse material classes. Computational singularities observed at extreme loads identify the rigorous operational boundaries for coherent mode-mixing. The robustness of the proposed framework is numerically validated, proving the method's reliability for a wide class of non-linear condensed media satisfying the stability criterion. This result provides a rigorous physical justification for the dynamic Hilbert space truncation (effective fermion-like dynamics), ensuring metrological consistency in complex structural environments. These results provide a theoretical foundation for probing ultrafast collective excitations and latent internal stresses, extending structural analysis beyond the traditional diffraction barrier.

For a phenomenon $\boldsymbol{f}$ that is a function of $n$ factors, defined on a finite abelian group $G$, we derive its population statistics solely from its Fourier transform $\hat{\boldsymbol{f}}$. Our main result is an $m$-Coefficient/Index Annihilation Theorem: the $m$th moment of $\boldsymbol{f}$ becomes a series of terms, each with precisely $m$ Fourier coefficients --- and surprisingly, the coefficient indices in each term sum to zero under group addition. This condition acts like a filter, limiting which terms appear in the Fourier domain, and can reveal deeper relationships between the variables driving $\boldsymbol{f}$. These techniques can also be used as an analytical/design tool, or as a feasibility constraint in search algorithms. For functions defined on $\mathbb{Z}_2^n$, we show how the skew, kurtosis, etc. of a binomial distribution can be derived from the Fourier domain. Several other examples are presented.

This is the first paper in a two-part direct-threshold series on large-data global regularity for the three-dimensional Navier--Stokes equations. We prove a direct first-threshold continuation theorem for the axisymmetric class with swirl. The proof is written entirely in the lifted variables \[ Γ=ru_θ,\qquad G=ω_θ/r,\qquad dμ_5=r^3\,dr\,dz, \] and uses the five-dimensional full-Dirichlet visibility \(\mathcal V_χ\) as the local coercive quantity. The argument is organized by a finite first-threshold stopping time. We define a critical axis score envelope, follow it to a first possible threshold time, and prove that the corresponding normalized packet cannot exist. The proof has three quantitative ingredients. First, a small-envelope continuation theorem converts bounded score and regularized source size into smooth continuation. Second, a finite-overlap descendant-extraction theorem shows that every large collar leakage, exterior tail, low-frequency residue, source concentration, or fragmentation channel either produces a smaller descendant packet or is perturbative. Third, in the remaining coherent case, the strict full-Dirichlet bridge \[ |\mathcal T_{G,χ}[G]| \le θ\mathcal V_χ[G]+C\mathfrak E_{\rm dir}[G], \qquad 0<θ<1, \] and a coefficient-calibrated local balance contract the selected packet. Consequently no first threshold occurs, the critical envelope stays

Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains significant. We propose quantum simulation of nanographene $π$-systems as relevant and scalable problems to span the gap between early and large-scale fault-tolerant quantum computing. We examine the efficiency of Trotterized quantum simulation, present a detailed analysis of worst-case, average-case and energy eigenvalue Trotter errors, and show that these Trotter error estimates vary by orders of magnitude. Trotter eigenvalue errors are obtained from a novel tensor-network-based approach which allows spectral analysis of product formulas for systems beyond brute-force calculation. Notably, we observe a Trotter error cancellation phenomenon whereby the Trotter error for energy differences between low-lying eigenstates is significantly smaller than the Trotter error for absolute energies, resulting in approximately an order of magnitude circuit depth reduction for quantum phase estimation calculation of energy gaps. This is a significant result because for most chemical applications, only energy differences are of practical relevance. We estimate that calculation of energy gaps to chemical accuracy between the ground- and excited-states within the Pariser--Parr--Pople model for large 2D nanographenes (up to 140 spin orbitals) requires circuits with $< 3.2 \times 10^7$ Toffoli gates. This work shows that considering details of chemically-relevant applications and exploiting error cancellation can lead to substantial reductions in resource requirements.

The Petz recovery map (1986) provably reverses a noisy quantum channel on a reference state, but its algorithmic relevance to real, dissipation-dominated platforms has remained unclear. Using the open-source \texttt{organic-qc-bench} simulation package, we benchmark a Petz-style covariant-purification quantum error correction (CQEC) protocol across four engineered organic qubit platforms operated \emph{without any magnetic field}: a flavin-nitroxide radical-pair reservoir (P1); perchlorotriphenylmethyl radicals in a covalent organic framework (P2); the SVILC qubit [Wakaura2017] on $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br (P3, conditional on SVILC confirmation); and a Su-Schrieffer-Heeger soliton on \emph{trans}-polyacetylene (P4). Across five quantum algorithms (QKAN, qDRIFT, control-free QPE, Shor-Regev, Bernstein-Vazirani) and two ML tasks, CQEC gains are significant ($p\!<\!10^{-5}$; Wilcoxon, Bonferroni $α\!=\!0.05/44$) for all sixteen path$\times$algorithm pairs. The central finding is the \emph{$γ_c$-peak}: the fidelity gain $ΔF$ is maximised \emph{at} the entanglement-breaking threshold $γ_c$, with $ΔF_{\rm max}\!=\!+0.303$ at $d\!=\!64$ and a linear $\log_2 d$ scaling over $d=2$-$64$ -- algorithmically confirming the prediction [Wakaura2026LQBH] that Petz recovery preserves coherence beyond this threshold. Bernstein-Vazirani also yields a $7.6$-$31\times$ provable quantum advantage at $n\!=\!3$-$5$, diarylethene-photoswitch CZ fidelities reach $F_{CZ}\!\ge\!0.987$ for P2-P4, and projected manufacturing costs are 10-40$\times$ lower with 10-200$\times$ less operating power than superconducting platforms. The $γ_c$-peak establishes Petz-style recovery as a practically relevant primitive at the dissipation-coherence boundary and identifies PTM-COF (P2) as the highest-priority experimental target.

We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic. The class of models contains the recently introduced model of Han--Huang--Komargodski--Lucas--Popov (arXiv:2503.22789), by which our work is inspired. The proof uses Pirogov--Sinai theory and the key input is a Peierls bound.

New observations from the Gaia spacecraft have traced an emerging demographic of low-mass associations disconnected from larger associations or GMCs. The first of these associations were recently characterized, but the star-forming environments they trace remain unknown. Using new velocities and ages alongside literature catalogs, we uncover the origins of 16 low-mass associations ($M\lesssim100$ M$_{\odot}$, $τ\lesssim50$ Myr) using dynamical traceback. We reveal that three groups of currently disparate populations share common formation sites, comprising the Leo, CaNMoS, and AquENS associations. Twelve of 16 associations have plausible connections to larger complexes, six of which form while moving outward from well-established multi-generational star-forming events that drive known or suspected bubbles. We find that feedback from the oldest co-spatial and co-moving relatives of these associations can explain the current morphologies of the Local and Orion-Eridanus Bubbles, along with the formation of related associations like Sco-Cen and Orion OB1. Most remaining populations show evidence for triggered star formation. In the Leo Association, high vertical velocities and a deceleration signature suggest that it formed out of an intermediate velocity cloud colliding with gas in Orion, which would make it the first known case of star formation in one of these clouds. The other newly defined associations show similar asymmetric velocity signatures, such as CaNMoS, which may trace bubble-driven acceleration or a cloud collision. We conclude that the lowest-mass young associations remain undiscovered, and that these populations may have a critical role revealing the small gas overdensities that trace the processes sculpting galactic star formation.

This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games (MFG). We reformulate the game as a regenerative problem with deterministic cycles, which allows policy evaluation (PE), policy improvement (PI), and population measure estimation to be carried out cycle by cycle. Within this formulation, we approximate the population measure by a particle system and update it using a one-step random mapping induced by the Euler-Maruyama discretization of the state dynamics. This update transports a mini-batch of particles from one cycle to the next, avoiding sequential trajectory simulation over the entire time horizon at each iteration. The PE and PI subproblems are formulated through the relation between consecutive cycles, with adversarial training used for evaluation and averaged optimization used for improvement. The resulting method is efficient and scalable in high dimensions, as it avoids the direct solution of the coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, the full simulation of trajectories to estimate the population measure, the explicit computation of conditional expectations in policy evaluation, and pointwise optimization in policy improvement. Numerical experiments demonstrate that the proposed method effectively handles dimensions up to 10,000.

We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem for Alexandroff topological groups. Motivated by this obstruction, we turn to the broader setting of Alexandroff paratopological groups. We establish several fundamental properties of these spaces and provide explicit non-compact $T_0$ examples, showing that the Alexandroff framework is rich enough to capture nontrivial paratopological phenomena. As applications, we address two classical open questions concerning feebly bounded subsets in paratopological groups, proving that non-compact Alexandroff paratopological groups offer a positive solution both for products of feebly bounded sets and for the feebly boundedness of $B^2$ when $B$ is a feebly bounded subset.

We study two-point correlation functions of heavy scalar fields in the Nariai geometry. Utilizing the heat kernel formalism, we obtain this result from a geodesic approximation to the two-point function on a product of spheres. By analytically continuing one of the spheres, we obtain the correlation function in the Nariai geometry. This result involves a sum over complex geodesics, extending previous results in pure de Sitter space. We emphasize the important role of the phase of each geodesic contribution, which needs to be taken into account to avoid spurious singularities in the correlator.

This paper proposes a deep reinforcement learning (DRL)-based event-triggered controller design for networked artificial pancreas (AP) systems. Although existing DRL-based AP controllers typically assume periodic control updates, networked control systems (NCSs) require a reduction in communication frequency to achieve energy-efficient operation, which is directly tied to control updates. However, jointly learning both insulin dosing and update timing significantly increases the complexity of the learning problem. To alleviate this complexity, we develop a practical DRL-based controller design that avoids explicitly learning update timing by introducing a rule-based criterion defined by changes in blood glucose. As a result, decision-making occurs at irregular intervals, and the problem is naturally formulated as a semi-Markov decision process (SMDP), for which we extend a standard DRL algorithm. Numerical experiments demonstrate that the proposed method improves communication efficiency while maintaining control performance.

Accurate quantification of protein-nanoparticle interactions is essential for applications in nanobiotechnology, nanomedicine, and drug delivery. Motivated by recent computational and experimental work, we combine coarse-grained united-atom (UA) models with molecular docking to characterize protein adsorption on SiO_2 nanoparticles. We construct orientation-resolved heatmaps in which polar and azimuthal angles uniquely specify the relative protein-nanoparticle pose, and the map amplitude reports binding propensity via the minimum UA adsorption energy or the docking score. Each angular bin corresponds to a distinct docked complex, enabling systematic comparison of binding geometries across models. To relate docking score landscapes to Boltzmann-averaged UA adsorption energetics, we analyze eight birch pollen allergen proteins previously studied experimentally. Similarity between the two orientational distributions is quantified using the Jensen-Shannon divergence (JSD). We find encouraging agreement between the two approaches in several cases, while also identifying limitations and routes for improvement, including optimized angular resolution and iterative refinement of interaction parameters. Overall, this framework provides a quantitative bridge between coarse-grained energetics and docking outputs at protein-nanoparticle interfaces, supporting improved predictive modeling and mechanistic insight into protein-nanoparticle binding landscapes.

Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base ring of $K$-integers. For every $K$-point $x$ in $X$, we introduce the minimal invariant locus $\operatorname{MinInvLoc}_x$ and the semistable reduction translation locus $\operatorname{SSRL}_x$ in the translation space $\operatorname{BT}_G(K)$ associated with $G_K$, which is a variant of Bruhat-Tits building, and establish not only the coincidence of those loci but, under a mild completeness assumption, also their non-emptiness. In the dynamical setting which has been studied by Szpiro--Tepper--Williams and Rumely, the coincidence result is already new in higher dimensions, and the non-emptiness result includes Rumely's $1$-dimensional result at least in the spherical complete case.

It is known that the classical information like strings of bits can be copied. In 1982, Wootters and Zurek proposed the quantum no-cloning principle. No-cloning principle says that it is impossible to make an identical copy of an arbitrary unknown quantum pure state by using unitary evolution. In this paper, we call U $|ψ>$, where U is any unitary operator, a U-copy of the state $|ψ>$ and show it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.