On noisy intermediate-scale quantum (NISQ) devices, expectation values of many observables are obtained through sampling-based approximations to trace-like quantities. A central limitation of this approach is destructive cancellation under near-uniform ensembles, which can render physically relevant signals effectively unresolvable. Here we show that this limitation is not simply statistical, but reflects a structural mismatch between ensemble weights and the operator-dependent sign structure of the measured correlator. We introduce a general framework for mitigating this effect through quantum ensemble engineering, in which the sampling distribution is encoded directly in the prepared quantum state. By reformulating correlators in a basis-resolved representation, we make the origin of cancellation explicit and derive strategies for aligning ensemble weights with operator structure. We realize this approach using two complementary circuit constructions: a Grover-type amplitude amplification protocol that provides a structure-aligned benchmark, and an oracle-free shallow circuit designed for near-term hardware constraints. Using the infinite-temperature correlation function as a representative setting, we demonstrate on IBM quantum processors with up to 20 qubits that engineered ensembles expose operator-resolved contributions that are strongly suppressed under uniform averaging. We identify a practical tradeoff between amplification strength and noise robustness, extend the framework to multi-qubit diagonal observables, and outline a path toward non-diagonal generalizations. These results position ensemble engineering as a new tool for improving measurement efficiency in near-term quantum algorithms.

Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question using a multi-agent system with spatially constrained interactions in which agents sense neighboring light signals through exteroceptors and act by switching their own light on or off, thereby forming a dynamical interaction network at the macroscopic level. The agents' internal states are themselves governed by a reservoir dynamical system at the microscopic level. By varying the microscopic parameters around dynamical criticality, together with the macroscopic interaction topology, we systematically investigate the relation between the two levels. We find that near-critical dynamics within individual agents is not sufficient to produce collective critical-like avalanche statistics. Instead, scale-free behavior depends on the effective connectivity of the macroscopic interaction network, which controls activity propagation. As a result, macroscopic critical-like dynamics are enabled by microscopic regimes that deviate from criticality, with the required deviation depending on the properties of the interaction network. Investigating this relation, we find that slightly subcritical micro-level regimes support near-critical dynamics across a wider range of macroscopic parameters. These results show that in this multi-agent system, collective near-critical behavior depends on the interplay between internal dynamics and the interaction structure that governs activity propagation.

The chiral magnetic effect consists in the induction of the electric current along the direction of the magnetic field. The corresponding transport coefficient $b_0$, known as the chiral magnetic conductivity, is proportional to the chiral imbalance in the medium. In many systems, such as quark-gluon plasma, $b_0$ is time-dependent. This paper studies the effect of the time variation of $b_0$ on the particle spectra and energy loss produced through the chiral Cherenkov and associated processes in Abelian and non-Abelian systems. The rates of all processes are derived in the ultra-relativistic approximation. The results are applied to the relativistic heavy-ion collisions utilizing a specific model describing the relaxation of the initial $P$-odd domain within the quark-gluon plasma. The corresponding energy loss is computed. The results suggest strong polarization of jets in quark-gluon plasma.

We study the computation of Hylland--Zeckhauser (HZ) equilibria beyond the bi-valued setting. First, we give a polynomial-time algorithm that, for general multi-valued utilities, computes an $1/e$-approximate HZ equilibrium. This yields, to our knowledge, the first polynomial-time constant-error approximation guarantee for this setting. The key technical ingredient is a utility-stratification construction that embeds a multi-valued market into a structured bi-valued instance, allowing us to apply the exact algorithm of Vazirani and Yannakakis. Second, we show that the rational structure of exact equilibria breaks down already for tri-valued utilities: there exists a $5\times5$ HZ instance with utilities in $\{0,\frac12,1\}$ such that all of whose equilibria are irrational. Taken together, these results show that while the bi-valued case can be used as a base for approximation algorithms, rational exact equilibria cannot be guaranteed even for tri-valued utilities.

Speech-based Alzheimer's Disease (AD) detection is constrained by scarce pathological speech data. To address this, we propose CoSTA, a Text-to-Speech (TTS)-based data augmentation framework. Specifically, we first develop two Cognitive-State-Conditioned (CS-Cond) TTS models by adapting CosyVoice2 and F5-TTS to synthesize speech with distinct AD and Healthy Control characteristics. Furthermore, by constructing a transcript pool comprising Manual Transcripts (MT) and 36 Automatic Speech Recognition (ASR) transcripts, we investigate the impact of text sources on TTS-based augmentation. We also perform augmentation-factor analysis and test-time augmentation. Experiments on the ADReSS dataset show that CS-Cond TTS significantly improves synthetic speech utility, and ASR-driven augmentation frequently outperforms MT-driven augmentation. Finally, CoSTA yields a 4.16% gain over the baseline, achieving an audio-only accuracy of 85.83% on the ADReSS test set and outperforming prior methods.

This paper studies how market informedness affects market makers' profitability in a computational market environment with heterogeneous learning agents. We develop an agent-based market model in which market makers differ in their information sets and inventory-risk aversion, prices form endogenously, fundamental values evolve exogenously, and market-taker order flow follows a state-dependent self-exciting process. The model provides a controlled computational laboratory for analyzing the interaction between informed trading, adverse selection, price discovery, and liquidity provision. We establish finite-horizon stability properties of the market-taker order-flow process and solve the market-making problem using multi-agent reinforcement learning with centralized training and decentralized execution. The results show that informed market order flow is particularly harmful when aggregate market informedness is low, exposing market makers to severe adverse-selection risk. However, as market informedness increases, market-maker profitability displays an overall upward trend despite local non-monotonicities arising from complex market dynamics and stochastic learning. This suggests that the price-discovery benefits of informed trading can offset its adverse-selection costs. The findings contribute to computational economics by showing how agent heterogeneity, endogenous price formation, and learning-based liquidity provision jointly shape market outcomes.

Long-period transients (LPTs) challenge our knowledge of the mechanism producing radio periodic pulsations in compact objects. Some LPTs have been associated with systems hosting a white dwarf and a low-mass star in a detached binary. Recently, a new LPT (ASKAP\,J174508.9-505149) has been classified as an accreting cataclysmic variable (CV). In the present letter, we report on the detailed study of the X-ray variability of ASKAP\,J174508.9-505149 as observed by \emph{XMM-Newton} and \emph{Einstein Probe} between September 2025 and May 2026. Simultaneous optical and radio observations are also presented. We studied the timing variability of the source, and estimated an X-ray periodicity of $P=4868(22)$\,s, consistent with radio and optical periods. We also observe the same periodicity in the hardness ratio extracted from the \emph{XMM-Newton} observation, peaking at the minimum of the modulation. A long-term modulation is also present in the X-rays and in the B-band photometry, but it is poorly constrained by the current dataset. Spectral X-ray analysis shows the presence of a black-body component ($\sim$0.1\,keV), a collisionally ionised plasma ($\sim$15\,keV), and an absorption feature at 0.77 keV (possibly due to Oxygen-VII). This is the third LPT detected in the X-ray band, the second with a detected X-ray periodicity and variable X-ray emission, and the first conclusively recognised as an accreting magnetic CV.

Decentralized Federated Learning (FL) removes reliance on centralized coordinators but remains vulnerable to model poisoning, unreliable validation, and high validation overhead. This paper introduces Proof of Contribution Quality (PoCQ), a blockchain-based consensus framework designed to secure decentralized FL through reputation-aware validation and aggregation. PoCQ evaluates client updates using cryptographic commitments and lightweight norm-based validation, enabling efficient detection of malicious contributions while limiting validation cost. A reputation-driven consensus mechanism dynamically adjusts the influence of participants based on their historical contribution quality, while the blockchain stores only compact audit metadata to preserve scalability. Extensive experiments under poisoning scenarios across three benchmark datasets demonstrate that PoCQ outperforms the strongest state-of-the-art methods, achieving accuracy gains of 34.1% on challenging medical datasets in highly non-iid settings and an 11% improvement in global average accuracy. In addition, PoCQ reduces validation time by 21.27% on average per round, highlighting its effectiveness in jointly enhancing robustness and efficiency for fully decentralized federated learning.

We exhibit a counterexample to a conjecture of Bhatt--Lurie on the cohomological dimension of the Hodge--Tate locus for regular local rings. The example arises from a non-excellent discrete valuation ring constructed by Datta--Smith, closely related to an earlier example of Bosch--Lütkebohmert--Raynaud. We also explain how the same mechanism yields broader families of counterexamples, while the expected bound is recovered under an excellence hypothesis.

This paper studies the problem of detecting a change in the distribution of a sequence of independent observations when the post-change distribution is unknown. We propose a novel change detection algorithm, termed Predictive-Mixture CuSum (PM-CuSum), which combines predictive distributions constructed from sliding windows of different lengths within a CuSum recursion. The predictive distributions are aggregated using adaptive weights based on their recent predictive performance. We show that PM-CuSum achieves first-order asymptotic optimality under mild conditions, and that its asymptotic delay bound has a smaller remainder order than what is achieved procedures using a single fixed (even oracle) window. Numerical simulations demonstrate that PM-CuSum performs well compared to existing methods. Moreover, it is demonstrated that forming likelihood ratios using full predictive distributions can substantially improve performance compared to plug-in likelihoods.

We revisit the path integral quantization of the null bosonic string from the viewpoint that all local gauge symmetries of the Carrollian worldsheet must be gauge fixed before the quantum theory is defined. In the tensile-string construction the $bc$ ghosts are the Faddeev-Popov determinant for fixing $\mathrm{Diff}\times\mathrm{Weyl}$. In the ILST null string this logic gives the BMS $bc$ system. However, a Carrollian worldsheet admits an additional volume-preserving Carroll-Weyl scaling, whose Hamiltonian generator is $C_3=P\cdot X$. Keeping this scaling as a genuine local gauge symmetry adds one more Faddeev-Popov row. The correct ghost system is therefore a $bcs$ system: the BMS $bc$ ghosts plus a scalar ghost $s$ and scalar antighost $b^s$ for Carroll-Weyl scaling. We derive the revised path integral, the $bcs$-ghost action, its residual symmetry equations, mode expansion, and its relation to the extended BMS algebra. The result changes the BRST complex and the anomaly problem: the usual $D=26$ check based only on the old BMS $bc$ ghosts is a partially gauge-fixed calculation, while the Carroll-Weyl covariant quantum theory must include the $s,b^s$ sector.

We explore an extension to Newtonian gravity through a generalised Lagrangian function with the introduction of a second dynamical scalar field. Building on previous research into gravity with variable gravitational coupling, the work derives the complete field equations and applies a weak-field approximation. This leads to an effective post-Newtonian gravitational potential that includes key aspects of relativistic theories. The resulting N-body equations of motion highlight differences among inertial and gravitational masses, which can constrain the theory's free parameter through data from the Nordtvedt effect. By employing the method of osculating orbits for a two-body system, the study calculates the secular variation of the orbital pericenter and aligns this with the latest data on Mercury's perihelion shift, for another observational constraint on the model. Furthermore, a few examples of theories are discussed.

Spectral characterizations of algebraic structure have a long history in the theory of Banach algebras. It is known that weak spectral information may force strong algebraic consequences, such as commutativity throughout the algebra or centrality of a single element. In this paper we study when spectral invariance, applied to the Jordan product $x \circ y = (xy + yx)/2$, forces commutativity or centrality in a semisimple Banach algebra $A$. We first investigate permutations of three elements, proving that equality of the spectral radii $ρ(xyz)=ρ(xzy)$ for all $x,y,z\in A$ implies $A$ is commutative, thereby complementing earlier cardinality and diameter results of Braatvedt et al. We next consider Jordan products and show that if the spectrum (or spectral radius) cannot distinguish the Jordan product from the ordinary product then $A$ must be commutative. By using representation-theoretic methods, we also obtain local spectral characterizations of central elements, showing that boundedness or omission properties of the spectrum (or spectral argument) of the Jordan product $x\circ(ax^{-1})$, as $x$ runs through the exponential group of $A$, imply $a$ belongs to the center of $A$. These results show that coarse spectral data associated with the Jordan product can determine commutativity and centrality.

Informationally complete (IC) measurements are a useful class of measurements, as their outcome statistics uniquely determine an unknown quantum state. Hence, they are important for certain tasks such as quantum state tomography, quantum process tomography, etc. In this work, we study the quantification of informational completeness for arbitrary quantum measurements by introducing and characterizing a faithful measure for it. We explicitly evaluate the informational completeness of qubit symmetric informationally complete (SIC) measurements and show that it is an upper bound for all qubit minimal informationally complete measurements. Furthermore, by introducing a faithful measure, we try to quantify and characterize the ability of an arbitrary quantum channel to preserve the informational completeness of any IC measurement when the channel acts on it in the Heisenberg picture. We call this measure informational completeness-preservability (IC preservability) of quantum channels. After studying its properties, we establish its relation to another quantity, namely, the absolute output coherence of a quantum channel, which quantifies the minimum amount of coherence (w.r.t. an arbitrary incoherent basis) that can always be obtained from the output of that channel. Finally, we illustrate our results with an example from light-matter interaction scenarios. Thus, in this work, not only do we try to provide a quantitative framework for studying both the informational completeness of quantum measurements and the ability of quantum channels to preserve it, but we also try to offer key insight into the conceptual relation between informational completeness and quantum coherence.

We investigate Nielsen's geometric approach to quantum complexity in the presence of multiple cost factors, extending the standard framework where a single penalty distinguishes easy from hard directions of the group manifold. By introducing a hierarchy of penalties associated with different degrees of non-locality, we develop a generalized right-invariant complexity geometry and analyze its implications for geodesic evolution. We derive the modified Euler-Arnold and Jacobi equations and study how multiple cost factors reshape the structure and scaling of conjugate points, where geodesic optimality breaks down. The formalism is illustrated in two settings: a single-qubit system with two cost factors, where we derive approximate analytic solutions for the complexity growth and its dependence on penalty hierarchies, and SYK-type models, where we analyze both free and chaotic regimes. In these many-body systems, we show that distinct non-local sectors generate multiple families of conjugate points whose occurrence depends on both the cost hierarchy and the system size. Our results highlight how refining the penalty structure provides a richer and more realistic description of quantum complexity and its dynamical behavior.

We generalize the augmented Roothaan-Hall (ARH) Hessian formalism to the self-consistent field (SCF) optimization of spin-restricted open-shell (RO) wavefunctions, encompassing high-spin, low-spin, and two-determinant electronic states. A detailed ARH formulation is presented. We demonstrate that ARH is a highly efficient optimization algorithm for rapidly identifying accurate SCF minima, primarily owing to its systematic construction of an effective Hessian, particularly in the case of Euclidean quadratic energy functions. The ARH is built upon a universal energy formulation, including grid-based integration, for spin-restricted closed-shell, spin-unrestricted and RO density functional theory (DFT), thereby unifying and simplifying their numerical implementation. The performance of the present method is evaluated using two benchmarking studies. First, for a series of iron-sulfur clusters exhibiting different spin states, which represent notoriously challenging SCF problems, the ARH algorithm demonstrates superior convergence efficiency relative to L-BFGS and truncated Newton methods, requiring much fewer RO-SCF iterations to achieve convergence. Second, the ARH approach avoids convergence to higher-energy stationary points in two-determinant RO-SCF calculations for singlet excited states of selected photoactive compounds. Finally, an application of the ARH-based RO-SCF is illustrated by an investigation of the mechanistic origin of the spin-crossover phenomenon in Ni(II)-porphyrin complex utilized as a contrast agent.

Hydrogen embrittlement (HE) has persisted for more than a century as one of the most intractable problems in materials science. The prevailing view1 that diffusive H governs embrittlement has fostered the widespread assumption that H trapping at crystal defects mitigates HE. Here we overturn this conventional paradigm. Using plasma/ion irradiation of tungsten, we decouple -- for the first time -- H-induced crack nucleation from subsequent cavity propagation, and reveal nucleation as a two-stage mechanochemical fracture instability enabled by trapped H in the absence of diffusive H. In the first stage, H accumulation to a critical occupancy at dislocation cores acts as a chemical fuse, collapsing the local cohesive strength to a threshold at which infinitesimal external loads can trigger atomic decohesion. This bond rupture instantaneously enables the second stage: confined recombination of atomic hydrogen into molecular form. The abrupt release of chemical energy within an atomically restricted volume generates a transient inflation pressure that drives a dynamic, brittle jump to an internal macroscopic cavity. By separating mechanical decohesion triggering from energetic crack driving, our results provide a deterministic framework for the onset of H-induced crack nucleation under low-stress conditions. Furthermore, we place experimentally the classical H-enhanced decohesion model on an atomistic foundation and elevate it from phenomenology to prediction. Finally, by shifting the focus from experimentally elusive diffusive H to directly measurable trapped H, this work reframes HE as a deterministic, quantifiable instability, establishing a new paradigm for understanding and mitigating H-induced failure in high-strength metals.

Altermagnetism, characterized by momentum-dependent spin splitting and zero net magnetization, has so far been explored mainly in weakly or moderately correlated d-electron systems. How symmetry-allowed altermagnetic band splitting manifests in heavy-fermion materials, where magnetic exchange competes with Kondo correlations, remains unclear. Here we use high-resolution angle-resolved photoemission spectroscopy (ARPES) to investigate CeNiAsO, a Kondo-lattice system that was predicted to be a candidate for p-wave altermagnetism. Fermi surface mapping and polarization-dependent ARPES show that the experimentally observed itinerant bands are mainly derived from Ni 3d orbitals, while resonant photoemission reveals that the Ce 4f states remain predominantly localized with residual c-f hybridization. Ultra-low-temperature measurements reveal no resolvable near-Fermi-level p-wave-like exchange splitting on the Ni 3d-derived conduction bands across the successive antiferromagnetic transitions. These experimental observations cannot be captured by an itinerant-4f band-structure description, which predicts a sizable p-wave splitting in the itinerant bands. When the localized Ce 4f character is incorporated, our band structure calculations indicate that the itinerant Ce 4f band weight is shifted away from the Fermi level and the p-wave-like splitting on the Ni 3d-derived bands is reduced to the few-meV scale. These results establish CeNiAsO as a strongly correlated f-electron setting in which the magnetic symmetry allows p-wave-like band splitting, but localized 4f electrons strongly suppress its observable itinerant single-particle signature.

In this work we present a pedagogically motivated analysis of spin-correlation calculations in a quantum system composed of two spin-$1/2$ particles. Rather than aiming at new physical results, our purpose is to clarify and bring attention to different strategies for evaluating expectation values of the form $\langle ψ| S^{(1)}_{\hat{\boldsymbol{u}}} S^{(2)}_{\hat{\boldsymbol{v}}} | ψ\rangle$, which play an important role in discussions of entanglement and Bell-type correlations. We compare three complementary approaches. The first follows a direct algebraic evaluation in the product basis, closely related to standard textbook methods. The second uses a matrix representation of bipartite states, in which the tensor-product structure is expressed in terms of $2\times2$ complex matrices. This representation keeps the calculation close to the familiar Pauli-matrix algebra and makes the independent action of operators on each subsystem more transparent. The third explores a symmetry-based argument, highlighting both its usefulness and its limitations when applied beyond the singlet state. We show explicitly that the singlet state is rotationally invariant, which explains why the symmetry argument successfully reproduces its correlation function, while a naive extension fails for triplet states. The discussion illustrates how entanglement, tensor-product structure, and rotational symmetry interplay in spin correlations.

Coherent electron shuttling is a key requirement for realizing scalable silicon quantum computing architectures. However, in silicon qubits, the existence of nearly degenerate conduction-band valleys poses a significant challenge because non-adiabatic transitions to excited valley states cause spin dephasing via spin-valley mixing. In this paper, we propose a smooth velocity shuttling protocol to suppress these valley excitations. By mapping the time-domain design of the shuttling velocity profile onto the design problem of window functions in signal processing, we establish an analytical and intuitive design guideline that does not require computationally expensive numerical optimization. We demonstrate that the high-frequency sidelobes of the shuttling velocity spectrum can be effectively suppressed by applying a frequency-modulated gate voltage based on the Tukey window. Through statistical numerical simulations incorporating realistic spatial randomness of the valley landscape, we show that the proposed smooth velocity control significantly reduces the average spin infidelity in the moderate-to-low disorder regime ($|Δ_0|/σ_Δ\simeq \mathcal{O}(1)$). Our results underscore that this simple, control-level velocity shaping provides a robust pathway toward high-fidelity spin transport in large-scale silicon quantum processors.

Ciliary arrays pump fluid at low Reynolds number through non-reciprocal beating and phase coordination between neighbouring cilia. Previous studies have demonstrated that antiplectic metachronal waves are more effective than symplectic waves in enhancing transport, and have proposed several physically intuitive explanations for this preference. What remains incomplete is a predictive analytical understanding of how hydrodynamic coupling and beat geometry determine the flow-maximising phase difference. Here, we address this problem in two steps: we first use reinforcement learning to identify flow-maximising coordination in a bead--spring cilia model, and then introduce an analytically tractable reduced model, termed a tilted-slider model, to analyse the weak-coupling limit. Reinforcement learning identifies antiplectic coordination as the flow-maximising state in linear arrays, and shows that the phase difference between neighbouring cilia accounts for most of the flow enhancement. We then use the tilted-slider model to show that a shift of the time-averaged position opposite to the effective-stroke direction enhances fluid transport through its coupling with the elastic restoring force. The reduced model further reveals that antiplectic coordination can be optimal, consistent with previous studies, whereas symplectic coordination can instead become optimal depending on beat geometry. These results identify a simple elastohydrodynamic mechanism underlying flow-maximising metachronal coordination.

Cryptocurrencies are increasingly adopted as investment assets, making their interactions with traditional financial markets central to cross-asset diversification and systemic risk. This paper studies the integration of cryptocurrencies, fiat currencies, and S&P500 equities using a balanced panel of 381 assets from October 2017 to February 2024. We combine rolling correlation networks, community structure, market-specific and system-wide Turbulence Indices, and VAR-based connectedness analysis to examine how market stress, network structure, and shock transmission vary across financial regimes. The results show that cross-asset integration is episodic. In calm periods, the three asset classes remain relatively segmented, whereas under stress, local clustering increases, modular separation weakens, and communities become more compositionally mixed across asset classes. Connectedness analysis further shows that regime shifts alter the structure of transmission rather than simply increasing spillover magnitudes. In high-turbulence states, fiat-market turbulence becomes the dominant propagation channel, while network clustering and modularity play a greater role in transmitting forecast uncertainty. These findings support the interpretation of network structure as an emergent, state-dependent transmission layer rather than a persistent exogenous driver of turbulence. The results highlight the need for regime-aware risk monitoring, since full-sample connectedness estimates can understate the cross-asset coupling that emerges precisely when diversification benefits are most fragile.

With the multitude of gravitational wave observations that have been made in the past ten years, probing the dynamical and nonlinear nature of strong gravity is becoming more and more feasible. One promising way to test the nonlinear nature of Einstein's theory of general relativity (GR) is through the gravitational wave null memory effect: a nonlinear prediction of GR which corresponds to initially comoving observers being permanently displaced due to a burst of gravitational radiation. Previous studies have shown that, while it is unlikely that the memory effect will be observed in a single event by the LIGO-Virgo-KAGRA (LVK) detectors, evidence for memory in the population of LVK events should be attainable after $\sim$2,000 gravitational wave detections. These works, however, largely relied on Bayes factors to perform their memory analyses: an approach that can depend sensitively on the analysis priors and, when naively multiplied across many events, can even favor incorrect conclusions. In this work, using the GWTC-5.0 catalog of binary black hole observations, we instead perform hierarchical Bayesian inference -- which is not subject to the issues associated with Bayes factors -- to measure the evidence for memory in current LVK observations. We find that we can constrain what we call the memory enhancement factor -- the constant appearing in front of the contribution to the strain from the supermomentum flux -- to $0.26_{-4.08}^{+4.09}$ (with $\pm$ values denoting the 68\% credible interval), consistent with its GR value of 1. We also forecast that $\sim$2,000 detections will be needed to constrain the memory enhancement factor away from zero at the $1σ$ level.

Nuclear quantum effects and non-Born--Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear--electronic orbital time-dependent density functional theory (RT-NEO-TDDFT), the electronic and nuclear densities are propagated numerically in time according to the time-dependent Schrödinger equation. In this framework, specified protons are treated quantum mechanically on the same level as the electrons. The classical nuclei can be propagated on the instantaneous NEO vibronic surface using Ehrenfest dynamics. A traveling proton basis (TPB) can be used to describe the dynamics of moving protons in conjunction with Gaussian-type protonic and electronic basis sets for each quantum proton. Herein, we present a constrained TPB (c-TPB) approach that ensures each protonic basis function center coincides with the corresponding proton position expectation value during the dynamics. This approach produces accurate nuclear--electronic quantum dynamics and rigorously conserves energy. We demonstrate the accuracy and stability of this approach for computing molecular vibrational frequencies as well as simulating excited-state intramolecular proton transfer and double proton transfer in the o-hydroxybenzaldehyde and [2,2$'$-bipyridyl]-3,3$'$-diol molecules. These applications show that the c-TPB method provides accurate dynamics, conserves energy, and is computationally efficient.

LIGO, Virgo, KAGRA, and GEO 600 form a network of gravitational-wave observatories. Data and analysis results from this network are made publicly available through the Gravitational Wave Open Science Center (GWOSC). This paper describes open data from this network, including the addition of data from the second part of the fourth observing run (O4b) and selected periods from the preceding engineering run (ER16), which were collected from times spanning April 6th, 2024 to January 28th, 2025. The public data set includes calibrated strain time series for each instrument, data from additional channels used for noise subtraction and detector characterization, and new analysis data products in the online GWOSC release associated with version 5.0 of the Gravitational-Wave Transient Catalog.

Applying the concepts and formalism from Evolutionary Game Theory to the data regime, the fundamental paradigms of Evolutionary Data Theory are introduced. It is shown that essential definitions and results such as replicator equations, evolutionary strategies, the Bishop-Cannings theorem and the analogy to Lotka-Volterra systems can be mapped to the data interpretation. Understanding data in matrix form as evolutionary entities, input data is mapped to genes and organisms. Steered by genetic fitness and two evolutionary strategies, Dominant-Balanced and Altruistic-Selfish, data records and features conduct an evolutionary game. It is shown that this evolutionary interpretation remains universally meaningful, by proving convergence to a unique rest point, where all data features persist in the population. A basic example of multi-objective optimization is shown as well as a related distribution problem and machine learning applications.

To define the intrinsic reference frame and multipole moments of angular-momentum-$J$-conserving many-body wave functions, we introduce two-body conditional probabilities of finding two nucleons at different positions in space. In this way, quadrupole deformations of states with $J\leq1/2$, which are not accessible via spectroscopic one-body quadrupole moments, can be characterized. We illustrate the method with nuclear density functional theory calculations for $J=0$ states of $^{16}$O and $^{20}$Ne, the latter obtained by restoring rotational symmetry of prolate or oblate intrinsic configurations. We show that the two-body quadrupole shape characterizations differ from one-body moments obtained from broken-symmetry states.

Context. Hydrodynamical cosmological simulations based on the $Λ$-Cold Dark Matter ($Λ$CDM) model predict that $\sim$40% of the baryons in the local Universe are missing. These missing baryons are predicted to lie in low-density filamentary structures that trace connections between galaxies. This so-called warm-hot intergalactic medium (WHIM) is predicted to be observable in the far-ultraviolet (FUV) and soft X-ray regimes, and detectable in ion species with transitions in these bands. Aims. We investigate the capability of the X-ray Integral Field Unit (X-IFU) on NewAthena to detect this WHIM through O vii absorption lines imprinted on bright power-law sources in soft X-rays (0.3-1.0 keV) by examining the parameter space of different observing conditions. Methods. Through advanced simulations of the X-IFU detector, a multidimensional approach is taken to investigate the relationship between source parameters and their impacts on the significance of detection of a single absorption feature. By first studying the effect of line placement (redshift) for an observation of fixed length, followed by varying the observation length, the required counts for 3$σ$ and 5$σ$ detections are calculated for various photon indices and local Galactic absorptions. The rest-frame equivalent widths of the imprinted absorption features are then varied, and the same requirements are calculated for each line strength. Results. We discuss the detection and recovery of the imprinted WHIM features. Another method is used to derive count requirements for detecting these features at different levels of significance, which is then compared to the previously obtained requirements. Using publicly available data from the Swift archives, various non-transient sources are analysed for their suitability to detect WHIM features in absorption.

We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal T^{op} \to \mathbf{Prob},$ we consider the associated conditional expectation transport functor $\mathcal E \circ F : \mathcal T^{op} \to \mathbf{Ban},$ and the canonical distortion $dF(i) := (\mathcal E \circ F)(i)(1),$ which measures the failure of constant functions to be preserved under non-measure-preserving transitions. Motivated by the multiplicative transport structure of $dF$, we introduce a simplicial distortion operator defined recursively on the nerve $N_\bullet(\mathcal T)$ of the time category. This construction describes recursively accumulated transported distortions along composable chains of morphisms and leads naturally to a notion of holonomy along loops. We interpret non-trivial holonomy as a global inconsistency invisible at the level of individual transitions, analogous to the Aharonov-Bohm effect in physics. This yields a notion of AB arbitrage, in which arbitrage opportunities arise from global loop effects rather than local price discrepancies. We further introduce simplicial admissibility conditions ensuring that recursively accumulated distortions remain integrable, and show how non-trivial holonomy can be translated into predictable self-financing trading strategies through executable loop dynamics. This establishes a connection between categorical holonomy structures and economically realizable arbitrage. The framework developed here suggests a global and homological perspective on arbitrage theory, in which market inconsistencies are encoded by recursively accumulated simplicial distortions and their holonomy along loops in the underlying time category.

Late-interaction retrieval (ColBERT, ColPali) scores a query against a document via the MaxSim operator. The standard PyTorch implementation materialises the full query-token x document-token similarity tensor only to reduce it away. At ColPali scale this is the single largest tensor in the pipeline (e.g. 21 GB in FP16 for 10K documents) and limits both candidate set size at inference and batch size during contrastive training. We present Flash-MaxSim (FM), an IO-aware fused GPU kernel that computes the same MaxSim scores without ever materialising the tensor, and extends the same principle to the training backward. At ColPali scale on A100 this cuts inference memory up to 9x and training memory by two orders of magnitude, unlocking candidate sets and contrastive batch sizes a single GPU could not previously reach. The kernel is a drop-in replacement, exact up to floating-point evaluation order under its stated FP32-accumulation protocol: rankings match the FP32 reference within 5e-4 of nDCG@10 on BEIR and REAL-MM-RAG. A separate INT8 path trades exactness for halved index storage at high fidelity. Released open-source.