Generative AI has enabled novice designers to quickly create professional-looking visual representations for product concepts. However, novices have limited domain knowledge that could constrain their ability to write prompts that effectively explore a product design space. To understand how experts explore and communicate about design spaces, we conducted a formative study with 12 experienced product designers and found that experts -- and their less-versed clients -- often use visual references to guide co-design discussions rather than written descriptions. These insights inspired DesignWeaver, an interface that helps novices generate prompts for a text-to-image model by surfacing key product design dimensions from generated images into a palette for quick selection. In a study with 52 novices, DesignWeaver enabled participants to craft longer prompts with more domain-specific vocabularies, resulting in more diverse, innovative product designs. However, the nuanced prompts heightened participants' expectations beyond what current text-to-image models could deliver. We discuss implications for AI-based product design support tools.

The increasing availability of large-scale observational data and the rapid development of artificial intelligence (AI) provide unprecedented opportunities to enhance our understanding of the global carbon cycle and other biogeochemical processes. However, retrieving mechanistic knowledge from these large-scale data remains a challenge. Here, we develop a Biogeochemistry-Informed Neural Network (BINN) that seamlessly integrates a vectorized process-based soil carbon cycle model (i.e., Community Land Model version 5, CLM5) into a neural network (NN) structure to examine mechanisms governing soil organic carbon (SOC) storage from big data. BINN demonstrates high accuracy in retrieving biogeochemical parameter values from synthetic data in a parameter recovery experiment. Furthermore, by incorporating Monte Carlo (MC) dropout to generate posterior distributions, we demonstrate that BINN can effectively quantify uncertainty in estimated parameters. We use BINN to predict six major processes (or components in process-based models) regulating the soil carbon cycle from 25,925 observed SOC profiles across the contiguous US and compare them with the same processes previously retrieved by a Bayesian inference-based PROcess-guided deep learning and DAta-driven modeling (PRODA) approach. The good agreement between the spatial patterns retrieved by BINN and PRODA (average correlation coefficient = 0.86) suggests that BINN's ability of capturing mechanistic knowledge is consistent with the established Bayesian-based methods. Additionally, the integration of neural networks and process-based models in BINN improves computational efficiency by more than 50 times over PRODA. We conclude that BINN is an efficient framework that harnesses the power of both AI, large-scale data, and process-based modeling to understand large scale soil carbon cycle.

The scientific community increasingly relies on machine learning (ML) for near-sensor processing, leveraging its strengths in tasks such as pattern recognition, anomaly detection, and real-time decision-making. These deployments demand accelerators that combine extremely high performance with programmability, ease of integration, and straightforward verification. We present cgra4ml, an open-source, modular framework that generates parameterizable CGRA accelerators in synthesizable SystemVerilog RTL, tailored to common ML compute patterns found in scientific applications. The framework supports seamless system integration through AXI-compliant interfaces and open-source DMA components, and it includes automatic firmware generation for programming the accelerator. A comprehensive verification suite and a runtime firmware stack further support deployment across diverse SoC platforms. cgra4ml provides a modular, full-stack infrastructure, including a Python API, SystemVerilog hardware, TCL toolflows, and a C runtime, which facilitates easy integration and experimentation, allowing scientists to focus on innovation rather than dealing with the intricacies of hardware design and optimization. We demonstrate the effectiveness of cgra4ml to implement common scientific edge neural networks using ASIC and FPGA design flows.

When blazars flare, their optical position moves. We show this by combining Gaia DR3 proper motions with epoch photometry for blazars with strong optical jet emission. In 60 of 74 sources with significant proper motion, rising flux drives the centroid upstream while fading flux drives it downstream - a near-universal pattern captured by a simple two-component model of constant extended emission and a flaring region. Using this connection, we geometrically localize the optical flares to within <1 mas of the VLBI position - a few parsecs at typical blazar distances - placing them in the innermost jet or accretion disk. This purely geometric method requires no multi-wavelength correlations or model-dependent assumptions, and provides an independent spatial anchor for localizing higher-energy flares. Per-epoch astrometry from Gaia DR4 is set to tighten our constraints even further.

Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown $n$-qubit Hamiltonians $H$ and $H_0$ with operator norm bounded by $M$, our certification protocol distinguishes whether $\|H-H_0\|_F\geqε$ or $\|H-H_0\|_F\leq O(ε/\sqrt{n})$ with sample complexity $O(nM^2\ln(1/δ)/ε^2)$ and total evolution time $O(nM\ln(1/δ)/ε^2)$. We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of $O(nM\ln(M\mathbb{E}_\infty[T])/ε^2)$, matching the known asymptotically optimal scaling with respect to false alarm run time $\mathbb{E}_\infty[T]$. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.

Focal plane arrays (FPAs) promise robust solid-state beam steering for LiDAR and free-space optical communications. However, the need for external collimation lenses hinders chip-scale compactness. Discrete switching between FPA elements further introduces blind spots and limits the number of resolvable points, restricting applications that require continuous tracking. Here, we demonstrate a silicon photonic beam steerer based on a metalens FPA that monolithically integrates the collimation lens on-chip. Thermo-optic prisms enable continuous fine-tuning, eliminating blind spots and tripling the number of resolvable points. Continuous steering over a 62° field of view is achieved while maintaining high beam quality, with an average sidelobe suppression ratio of 19 dB.

We construct a complete Riemannian surface $Σ$ that admits no triangulation $G\subset Σ$ such that the inclusion $G^{(1)} \hookrightarrow Σ$ is a quasi-isometry, where $G^{(1)}$ is the simplicial 1-skeleton of $G$. Our construction is without boundary, has arbitrarily large systole, and furthermore, there is no embedded graph $G\subsetΣ$ such that $G^{(1)} \hookrightarrow Σ$ is a quasi-isometry. This answers a question of Georgakopoulos.

This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a self-similar behaviour of the fundamental solution. Here fundamental solution means a Dirac distribution initial datum which moreover governs the large time asymptotics of a large class of solutions. Using a self-similar change of variables, the equation becomes a nonlinear kinetic Fokker-Planck equation with harmonic confinement and the intermediate asymptotics regime is transformed into a stability property of a special stationary solution, which attracts the solutions for large times. In the homogeneous case (pure nonlinear diffusion), the problem is reduced to a classical nonlinear diffusion equation with Barenblatt-Pattle self-similar profiles. Unexpectedly, this beautiful structure is preserved at kinetic level, with remarkable consequences for relative entropy estimates, detailed intermediate asymptotics and nonlinear diffusion limits in adapted functional spaces.

Chiral plasmonic nanostructures are rapidly emerging as ideal substrates for enantioselective sensing, chiral near-field engineering, and plasmon-assisted catalysis, owing to their exceptional sensitivity to structural handedness. However, the physical origin of plasmonic chirality, whether intrinsically quantum or primarily governed by collective electrodynamics, remains an open question, limiting the development of predictive theoretical methods for the design of novel chiral plasmonic architectures. Here, we show that a fully atomistic classical electrodynamic model, coupling intraband charge transport and interband polarization, quantitatively reproduces state-of-the-art \textit{ab initio} and experimental chiroptical spectra across the quantum-to-classical regime, from atomistically defined chiral Ag and Au nanostructures to DNA-origami-assembled Au nanorods containing up to $\sim 10^5$ atoms. Our results support a unified electrodynamic origin of plasmonic chirality, providing the missing foundation to connect local structural motifs to chiroptical response and local chiral near fields, and paving the way for the atomistically defined, rational design of chiral plasmonic nanostructures optimized for targeted applications.

We introduce the canonical, parameter-free, and efficiently computable notion of peel neighborhoods in a finite metric space of strict negative type. Using a soft threshold to upper bound their radius or cardinality allows peel neighborhoods to be computed at scale, enabling useful microscopic descriptions of geometry and topology. As an example of their utility, peel neighborhoods enable efficient and performant estimates of local dimension and detections of singularities in samples from stratified manifolds.

We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly sampled and fixed hidden parameters, the computation reduces to a linear least squares problem for the output coefficients, which avoids gradient based nonconvex optimization. This construction retains the dimensionality reduction of boundary integral equations and the linear solution structure of the random feature method. For elliptic problems, we establish convergence analysis by combining kernel-based method with random feature approximation, and obtain error bounds on both the boundary and the interior solution. Numerical experiments on Laplace and Helmholtz problems, including interior and exterior cases, show that the proposed method achieves competitive accuracy relative to the boundary element method and favorable performance relative to boundary integral neural networks in the tested settings with only few neurons. Overall, the proposed method provides a practical framework for combining boundary integral equations with neural network for problems on complex geometries and unbounded domains.

We investigate how a localized curvature affects the dynamics of massless Dirac fermions in a curved surface. We consider a smooth bump with axial symmetry, adopting two specific geometric models, namely a Gaussian and a volcano-like bumps. By considering a minimal coupling between the spinor and the surface geometry, described by the vielbeins and the spin connection, we study the behavior of the wave function over the surface. By using appropriate numerical methods, we find a linear discrete energy spectrum for the Dirac fermions and its corresponding wavefunctions when the Fermi velocity is considered. It turns out that, since the curvature vanishes asymptotically, the electron states are free waves far from the bumps, but around the curved points, the wave function increases its probability density.

Merging binary black holes embedded in gaseous environments, such as supermassive black hole binaries following gas-rich galaxy mergers, are promising sources of multi-messenger transients in the upcoming age of space-based gravitational wave detections. In case a gravitational radiation recoil is imparted to the merger remnant, subsequent interactions between the recoiled black hole and its circumbinary disk may lead to unique post-merger electromagnetic counterparts. We present the first general relativistic magnetohydrodynamic simulations of a recoiling black hole interacting with a magnetically arrested circumbinary disk the evolution of which has been consistently tracked through the inspiral phase. We show that the post-merger accretion dynamics, depending on the recoil geometry, exhibits qualitatively disparate jet and disk behavior. For recoils perpendicular to the disk, the inner disk remains gravitationally bound and sustains relativistic jets, while in-plane recoils lead to copious shock heating and potential jet quenching for black holes directly colliding with the disk. Oblique recoils, on the other hand, produce intermittent outbursts from jet-disk interactions owing to the tilt introduced in the accretion disk. Multi-wavelength monitoring of these electromagnetic counterparts, in conjunction with the coincident gravitational wave detection, will be able to aid in characterizing the physical conditions of the merger environment.

Single-event upset (SEU) fault tolerance for systems-on-chip (SoCs) in radiation-heavy environments is often addressed by architectural fault-tolerance approaches protecting individual SoC components (e.g., cores, memories) in isolation. However, the protection of voting logic and interconnections among components is also critical, as these become single points of failure in the design. We investigate combining multiple fault-tolerance approaches targeting individual SoC components, including interconnect and voting logic to ensure end-to-end SoC-level architectural SEU fault tolerance, while minimizing implementation area overheads. Enforcing an overlap between the protection methods ensures hardening of the whole design without gaps, while curtailing overheads. We demonstrate our approach on a RISC-V microcontroller SoC. SEU fault-tolerance is assessed with simulation-based fault injection. Overheads are assessed with full physical implementation. Tolerance to over 99.9% of faults in both RTL and implemented netlist is demonstrated. Furthermore, the design exhibits 22% lower implementation overhead compared to a single global fault-tolerance method, such as fine-grained triplication.

Traditional wireless power transfer (WPT) systems are largely limited to 1-D charging pads or 2-D charging surfaces and therefore do not support a truly ubiquitous device-powering experience. Although room-scale WPT based on multimode quasistatic cavity resonance (QSCR) has demonstrated full-volume coverage by leveraging multiple resonant modes, existing high-coverage implementations require obstructive internal conductive structures, such as a central pole. This letter presents a new structure, termed the patched-wall QSCR, that eliminates such internal obstructions while preserving full-volume coverage. By using conductive wall segments interconnected by capacitors, the proposed structure supports two complementary resonant modes that cover both the peripheral and central regions without obstructions within the charging volume. Electromagnetic simulations show that, by selectively exciting these two resonant modes, the proposed structure achieves a minimum power-transfer efficiency of 48.1% across the evaluated 54 m^3 charging volume while preserving an unobstructed interior space.

As large language models are deployed as autonomous agents, their capacity for strategic deception raises core questions for coordination, reliability, and safety in multi-goal, multi-agent systems. We study deception and communication in L2LM agents through the social deduction game Among Us, a cooperative-competitive environment. Across 1,100 games, autonomous agents produced over one million tokens of meeting dialogue. Using speech act theory and interpersonal deception theory, we find that all agents rely mainly on directive language, while impostor agents shift slightly toward representative acts such as explanations and denials. Deception appears primarily as equivocation rather than outright lies, increasing under social pressure but rarely improving win rates. Our contributions are a large-scale analysis of role-conditioned deceptive behavior in LLM agents and empirical evidence that current agents favor low-risk ambiguity that is linguistically subtle yet strategically limited, revealing a fundamental tension between truthfulness and utility in autonomous communication.

The hydrogen positions and magnetic structure of goethite $α$-FeOOH, a key component of iron rust, were examined through neutron diffraction. All symmetry-allowed magnetic structures under the space group $Pnma$ with the magnetic wavevector $\vec{q}_{\rm m} = (0, 0, 0)$ r.l.u. were analysed using irreducible representation and magnetic space group approaches. The magnetic moments aligned along the $b$-axis form antiferromagnetic spin arrangements, as reproduced by first-principles calculations. Accurately determining the hydrogen positions is crucial for understanding the mechanism of catalytic reduction of CO$_2$ in $α$-FeOOH. These positions were precisely identified through diffraction and calculations, highlighting the effectiveness of using both methods for undeuterated compounds.

The trilinear Higgs self-coupling provides a unique probe of the structure of the Higgs potential and of the nature of the electroweak phase transition, and constitutes a key target for future collider experiments. Recent studies have shown that confronting theoretical predictions for the trilinear Higgs coupling with current experimental bounds offers a powerful and complementary way to test effects of physics beyond the Standard Model (BSM), in particular those arising from extended Higgs sectors. Meanwhile, substantial progress has been achieved in the precise calculation and automation of the trilinear Higgs coupling in a wide class of BSM models. This contribution discusses several BSM scenarios, compatible with existing constraints, in which sizeable deviations in the trilinear Higgs coupling w.r.t. the Standard Model (SM) value are predicted, while other Higgs observables remain close to their SM expectations and are therefore difficult to probe experimentally. These results highlight the strong physics motivation for a precise measurement of the trilinear Higgs coupling at a future Higgs factory.

As the sociological theory of homophily suggests, people tend to interact with those of similar preferences. Motivated by this well-established phenomenon, today's online sellers, such as Amazon,~seek~to learn a new buyer's private preference from his friends' purchase records. Although such learning allows the seller to enable personalized pricing and boost revenue, buyers are also increasingly aware of these practices and may alter their social behaviors accordingly. This paper presents the first study regarding how buyers strategically manipulate their social interaction signals considering their preference correlations, and how a seller can take buyers' strategic social behaviors into consideration when designing the pricing scheme. Starting with the fundamental two-buyer network, we propose and analyze a parsimonious model that uniquely captures the double-layered information asymmetry between the seller and buyers, integrating both individual buyer information and inter-buyer correlation information. Our analysis reveals that only high-preference buyers tend to manipulate their social interactions to evade the seller's personalized pricing, but surprisingly, their payoffs may actually worsen as a result. Moreover, we demonstrate that the seller can considerably benefit from the learning practice, regardless of whether the buyers are aware of this fact or not. Indeed, our analysis reveals that buyers' learning-aware strategic manipulation has only a slight impact on the seller's revenue. In light of the tightening regulatory policies concerning data access, it is advisable for sellers to maintain transparency with buyers regarding their access to buyers' social interaction data for learning purposes. This finding aligns well with current informed-consent industry practices for data sharing.

Massive Internet-of-Things (IoT) deployments must simultaneously support monitoring, control, and safety-critical communication over shared wireless infrastructure. Classical timeliness metrics, such as Age of Information and its variants, quantify the freshness of received updates but do not account for deterministic safety timing requirements that arise in cyber-physical systems. Consequently, freshness-oriented metrics may indicate satisfactory performance even when worst-case timing guarantees required by functional safety standards are violated. This paper introduces the Unified Safety--Age Metric (USAM), a safety-aware timeliness metric that integrates information freshness, deadline reliability, and deterministic response-time feasibility into a single architecture-aware performance measure. We consider heterogeneous IoT traffic served by a gateway with intermittent receiver readiness and analyze system behavior in the ultra-sparse regime typical of massive machine-type communications. The analysis shows that, as device activity decreases, queueing delays become negligible and system timeliness becomes dominated by infrastructure readiness and deterministic response-time constraints. In this regime, feasibility is determined primarily by the receiver duty cycle rather than by average traffic load. Numerical results illustrate the safety-blindness of classical freshness metrics and demonstrate that USAM explicitly captures the feasibility boundary imposed by heterogeneous traffic requirements. The proposed framework provides a foundation for analyzing safety-aware communication architectures in large-scale IoT systems.

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in high-dimensional regimes or at fine resolution. Nonlinear phenomena such as turbulence are notoriously difficult to predict because of their extreme sensitivity to small variations in initial conditions, except when certain stability conditions are fulfilled. Indeed, stability allows us to achieve reliable approximate dynamics, since it determines whether small perturbations remain bounded or are amplified, potentially leading to markedly different long-term behavior. Here, we investigate the stability of dissipative partial differential equations with second-order nonlinearities. By analyzing the time evolution of solution norms in Sobolev spaces, we establish a sufficient condition for stability that links the characteristics of the linear dissipative operator, the quadratic nonlinear term, and the external forcing. The resulting criterion is expressed as an explicit inequality that guarantees stability for a wide range of initial conditions. As an illustration, we apply the framework to fluid-dynamical models governed by nonlinear partial differential equations. In particular, for the Burgers equation, the condition admits a natural interpretation in terms of the Reynolds number, thereby directly linking the stability threshold to the competition between viscous dissipation and inertial advection. We further demonstrate the scope of the approach by extending the analysis to the KPP-Fisher and Kuramoto-Sivashinsky equations.

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there remains an open conjecture that they can all be proved to have a canonical standard form. We very this conjecture for several new classes of nilpotent groups, including those corresponding to the positive subalgebra of almost all classical and exceptional types, curiously excluding those of type C.

We establish local and global well-posedness for the Cauchy problem of a generalized Camassa-Holm equation where orders of the momentum and the nonlinearity can be arbitrarily high. More precisely, we consider the equation \begin{equation*} m_t + m_x u^p + b m u^{p-1}u_x = -(g(u))_x + (b+1)u^p u_x, \quad m = (1-\partial_x^2)^k u, \end{equation*} where $p \geq 1$, $k \geq 1$ are arbitrary, $b$ is a real parameter, and $g(u)$ is a smooth function. %The standard Camassa-Holm equation corresponds to $k=1$, $p=1$, $b=2$, and $g(u)=0$. The local well-posedness is shown by using Kato's semigroup approach, where we treat the nonlinearity directly using commutator estimates and the fractional Leibniz rule without having to transform it in any specific differential form. This well-posedness is obtained in the phase space $H^s$ for $s > 2(k-1) + 3/2$, which is consistent with the results for the classical Camassa-Holm equation. We also prove the global existence of solutions by obtaining conserved quantity and applying the same idea from our local theory.

Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with time-dependent frequency (one degree of freedom); geodesics of a spheroid (two degrees of freedom); Calogero-Moser-Sutherland system of interacting particles (three degrees of freedom). For each system, a local generalization of Liouville integrability is shown. Specifically, the variational point symmetries in a Lagrangian setting lead to corresponding locally conserved integrals which are found to commute in the Poisson bracket imported from the equivalent Hamiltonian setting. Action-angle variables are then introduced in the Lagrangian setting, which leads to explicit integration of the Euler-Lagrange equations of motion locally in time.

We report on the status of an update of our collaboration's previous computation of light and strange quark masses in QCD with $N_{f}=2+1$ dynamical flavours. Bare quark masses are extracted from CLS ensembles, using $O(a)$-improved Wilson fermions, and the mass renormalization is performed non-perturbatively in the Schrödinger functional scheme over a wide range of scales to make safe contact with perturbation theory. Results for five lattice spacings, down to $a\sim 0.038 \textrm{ fm}$, and pion masses reaching the physical value are included in the analysis. This allows for the exploration of different models for cutoff and chiral effects, and a controlled extrapolation to the physical point.

The nozzle of an aircraft is a major source of radar scattering from the rear aspect of the aircraft, which undergoes higher operational temperatures. In order to reduce the radar scattering of these nozzles, high temperature radar absorbing materials (RAM) are essential. The thickness of these RAM typically increases to attain RCS reduction at lower frequencies, which subsequently leads to a higher weight of the structure. Therefore, this research study investigates the weight advantages of a star auxetic (SA) lattice made up of barium titanate to reduce the RCS of aircraft exhaust nozzles in the frequency range of 8-18 GHz. Modelling of SA with a complicated aircraft structure may lead to complexities in terms of Computer Aided Design and electromagnetic modelling and higher computational time for solving the electromagnetic problem using exact solvers. In order to simplify the computational problem, a homogenization and modified transfer matrix method is used to generate the RL performance. The RL from the proposed in-house tools is also compared with the Floquet port analysis. The RL performance obtained from the proposed method is also validated against experimental data. Comparative analyses are performed between SA and solid pure block (PB) barium titanate samples over 32761 SA and PB thickness combinations. Results show that selected SA samples with the same thickness achieve weight saving of approximately 60%, with 20dB lower RL than PB. The median RCS of the nozzle rear aspect also indicates that the SA-based barium titanate has an advantage in terms of weight penalty with similar or better RCS performance. The study demonstrates that auxetic metamaterials will be a multifunctional, lightweight, thermally stable, and radar absorbent structure for high temperature aircraft applications.

Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective compromise, as they can capture complex, typically non-convex geometries while maintaining an algebraic structure suitable for further manipulation. Building on this, we propose novel nonlinear encodings that provide sufficient conditions for testing inclusion between two CPZs and adapt them for seamless integration within optimization frameworks.

For independent multi-outcome events under multiplicative parlay pricing, we give a short exact proof of the optimal Kelly strategy using the implicit-cash viewpoint. The proof is entirely eventwise. One first solves each event in isolation. The full simultaneous optimizer over the entire menu of singles, doubles, triples, and higher parlays is then obtained by taking the outer product of the one-event Kelly strategies. Equivalently, the optimal terminal wealth factorizes across events. This yields an immediate active-leg criterion: a parlay is active if and only if each of its legs is active in the corresponding one-event problem. The result recovers, in a more transparent state-price form, the log-utility equivalence between simultaneous multibetting and sequential Kelly betting. We then study what is lost when one forbids parlays and allows only singles. In a low-edge regime and on a fixed active support, the exact parlay optimizer supplies the natural reference point. The singles-only problem is a first-order truncation of the factorized wealth formula. A perturbative expansion shows that the growth-rate loss from forbidding parlays is $\OO(\eps^4)$, while the optimal singles stakes deviate from the isolated one-event Kelly stakes only at cubic order. This yields a clean explanation of Whitrow's empirical near-proportionality phenomenon: the simultaneous singles-only optimizer is obtained from the isolated eventwise optimizer by an event-specific cubic shrinkage, so the portfolios agree through second order and differ only by a small blockwise drag.

The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio, depend explicitly on both the Hamiltonian and the initial state, rendering their connection to fundamental quantum resources such as entanglement and quantum coherence subtle. We establish quantitative bounds relating Krylov-space spreading to the entanglement of the evolved state and to the quantum coherence of the initial state. For bipartite systems, we have shown that the entanglement of the evolved state is upper bounded in terms of the entanglement of the Krylov basis vectors and the spread complexity. In the case of multipartite systems, analogous bounds are obtained for the inverse participation ratio, a quantifier of the delocalization of a quantum state in the Krylov basis, in terms of the geometric measures. Furthermore, for qubit and qutrit systems, we derive relations between the quantum coherence of the initial state in the energy eigenbasis and the spread complexity, valid for arbitrary Hamiltonians. Our results provide quantitative constraints linking Krylov-space complexity growth to fundamental quantum resources.

In multivariate extreme value statistics, the first step in understanding the dependence structure of extremes is identifying the directions in which they occur. The novelty of this paper is the analysis of high-dimensional extreme value models in which both the model dimension and the number of bias directions go to infinity as the number of observations tends to infinity; we estimate the number of extremal directions. To address the curse of dimensionality, we extend and investigate the information criteria (AIC, BICU, BICL, QAIC and MSEIC) from the fixed-dimensional case (Butsch and Fasen-Hartmann, 2025a; Meyer and Wintenberger, 2023), which employ the concept of sparse regular variation that is closely related to multivariate regular variation, for the estimation of the number of extremal directions. For all information criteria, we derive sufficient conditions for consistency. Unlike in the fixed-dimensional case, where only the Bayesian information criteria (BICU and BICL) and the QAIC are consistent, the AIC and MSEIC are also consistent in high dimensions under certain model assumptions. We compare the performance of the different information criteria in a simulation study that includes a detailed analysis of the model assumptions and the necessary and sufficient conditions for consistency.