Recent observations of metal-poor, star-forming dwarf galaxies reveal He III regions, traced by nebular He II 4686 emission that require a strong source of extreme-ultraviolet (EUV) radiation. The origin of this hard ionizing radiation remains poorly understood, as standard stellar populations fail to account for it, posing key implications for the understanding of early galaxy formation. We present a systematic Chandra X-ray study of 21 nearby star-forming galaxies with He II emission but lacking Wolf-Rayet spectral signatures. Using 7 new and 36 archival Chandra X-ray observations combined with optical stellar population synthesis modelling, we constrain the ionizing continuum required to sustain the observed He II line, the ionizing continuum available from X-ray objects, and the properties of the host H II regions. We find that the inferred EUV output from accreting X-ray sources in our sample is systematically lower than what is required to produce the observed He II emission. Our sample is consistent with established empirical scaling relations for X-ray luminosity, indicating that this discrepancy cannot be attributed to an anomalously low number or luminosity of X-ray sources. These results indicate that accreting X-ray sources alone cannot account for the observed He II-ionizing photon budget, pointing to additional or alternative sources of hard EUV radiation in metal-poor star-forming environments. Potential alternative or additional contributors are discussed.

Particle-mesh methods, such as the particle-in-cell (PIC) method, cannot retain exact pairwise interaction at sub-cell scales. For dense nonneutral relativistic electron bunches, this makes it difficult to accurately capture the inter-particle electromagnetic interaction and the associated bunch divergence. In this work, the previously developed electromagnetic particle-particle (EM-PP) model for relativistic two-particle interaction is extended to many-particle electron bunch transport in the Earth's magnetosphere. The method combines the Liénard--Wiechert fields, an improved retarded-time evaluation procedure, and a relativistic particle pusher, and adopts a two-stage strategy to couple the dense early self-field-dominated evolution to the later long-range geomagnetic-field-controlled transport. The method provides a practical mesh-free approach for accurately simulating long-range transport of relativistic electron bunches when short-range electromagnetic interaction is important.

We study fibres of the fertility map $Φ$ from decorated rooted trees to decorated multi-index monomials. For a multi-index $\mathbf{k}$ of weight $-1$, the fibre $\mathcal F_{\mathbf{k}}=\{\,t:Φ(t)=\xx^{\mathbf{k}}\,\}$ consists of all rooted trees with decoration--fertility profile $\mathbf{k}$. We consider its ordinary cardinality $F_{\mathbf{k}}$, its symmetry-weighted cardinality $W_{\mathbf{k}}$, and the coefficient mass $J_{\mathbf{k}}$ appearing in the tree expansion of the transposed embedding $\jmath$. We obtain an explicit formula and a functional equation for the weighted counts, and an exact multiset recursion together with a cycle-index functional equation for the ordinary counts. We also introduce coefficient generating functions for the lowering derivation $\bar\partial$, derive recursive and transport-array formulas for the corresponding coefficients, and use them to refine the admissible-cut formula for the coproduct in the LOT Hopf algebra.

This paper introduces the Statverse, a Metaverse framework designed to revolutionize statistical education in the digital age. Our key goal is to report our progress and encourage others to integrate similar strategies into their programs. The proposed framework seamlessly integrates the physical and digital realms to provide an immersive environment for the nuanced representation of complex statistical concepts. Finally, we discuss the potential impact of Statverse on advancing Statistical Education, offering a transformative approach to teaching and learning in the digital age. Statverse is the outcome of an academic partnership between Universidad Técnica Federico Santa María (UTFSM) and the University of Edinburgh (UoE).

Astrophysical formation channels of stellar-mass binary black holes (sBBHs) can induce significant orbital eccentricities in their early inspiral. We analyze the implications on the stochastic gravitational-wave background (SGWB) from unresolved sBBHs, which can be detected with the Laser Interferometer Space Antenna (LISA). We develop an improved SGWB model for the case of an idealized Dirac-delta eccentricity distribution, and extend it to the more astrophysical case of a thermal distribution. Using a fully Bayesian framework, we find that, if all binaries have a high initial eccentricity $e_0 \gtrsim 0.9$ at an orbital frequency of $f_{\rm orb} = 10^{-4}\,\mathrm{Hz}$, the resulting SGWB can be robustly distinguished from a background of quasi-circular sBBHs. For a thermal eccentricity distribution, the SGWB is consistent with a circular model when binaries form at $f_{\rm orb} = 10^{-5}\,\mathrm{Hz}$, but leads to significant systematic biases if formation occurs at $f_{\rm orb} = 10^{-4}\,\mathrm{Hz}$. We also show that, when eccentricity is properly accounted for, environmental effects such as dynamical friction can be distinguished from vacuum evolution, but only for sufficiently dense environments with gas densities $ρ\gtrsim 10^{-7}\,\mathrm{g\,cm^{-3}}$. Finally, we show that a LISA detection of the sBBH SGWB would place an upper bound on the maximum eccentricity of the sBBH population in the band of ground-based detectors, with direct implications for template modeling and data analysis. Our results highlight the importance of incorporating eccentricity in SGWB modeling to enable accurate astrophysical interpretation of LISA observations.

Logical query plan rewriting transforms a relational database query into an equivalent but more efficient form and is crucial to the performance of database-backed applications. In existing systems, rewrite rules are typically implemented manually, tightly coupled to specific execution engines, and often lack formal correctness guarantees. Consequently, developing a new engine requires reimplementing both legacy and new rules, incurring significant engineering cost, limiting portability, and every new implementation is an opportunity for introducing new bugs. We introduce Rulescript, an engine-agnostic domain-specific language (DSL) for developing query rewrite rules. Rulescript separates rule definition from execution infrastructure via a relational algebra-inspired core language and an explicit decomposition of rules into matching and transformation phases. Developers express rewrites by pattern-matching query plans using Rulescript's core operators and constructing semantically equivalent transformed plans, with all rewrites automatically verified formally to ensure correctness. Rulescript is extensible: users can define custom operators in terms of the core language to capture engine-specific semantics. To integrate with an existing system, developers need only implement a lightweight adapter that maps Rulescript's core and custom operators to the operators implemented in the target engine. We evaluate Rulescript by reimplementing 33 rewrite rules from Apache Calcite and extending the language with several custom operators. To demonstrate portability, we automatically deploy these rules to CockroachDB and Apache Data Fusion, two engines with substantially different backends. Our results show that Rulescript enables "write once, deploy everywhere" paradigm for query plan rewriting, with minimal effort required to deploy previously written rules on a new data engine.

We investigate the thermodynamic and emergent thermomechanical properties of fermions confined to a one-dimensional quantum ring with effective spin--orbit interactions induced by nonminimal couplings to antisymmetric tensor fields. Using the exact spectrum obtained in the companion work, we develop canonical and grand-canonical descriptions and show that the coupling parameter~$ξ$ deforms the angular-momentum branches, reorganizing the low-energy spectrum and leaving clear signatures in the internal energy, entropy, heat capacity, and spin--orbit response functions. We also formulate an effective thermomechanical description by treating the ring circumference as a quasi-static thermodynamic variable. This leads to a pressure-like quantity and associated response coefficients, directly linked to the microscopic spectrum. In the grand-canonical ensemble, Fermi statistics strongly enhance the response, producing coupling-dependent instabilities and sign changes reminiscent of mesoscopic de~Haas--van Alphen oscillations. Finally, we introduce a phenomenological interacting extension based on an exponential resummation of the free energy, showing that collective effects can sharpen the thermomechanical response and induce anomalous thermal contraction. Our results connect spectral deformation, finite-size thermodynamics, and emergent mechanical behavior in spin--orbit-active quantum rings.

Effective security logging is crucial for the timely and accurate detection of cyber threats; however, the relative effectiveness of various industry-standard logging frameworks remains understudied. This paper addresses this critical gap by presenting the first systematic evaluation of modern security logging standards utilizing a novel methodology built upon the automated Security Exploit Telemetry Collection (SETC) framework. SETC systematically generates reproducible exploit scenarios in containerized environments, collecting rich telemetry across multiple logging standards, including CIM (Common Information Model), OCSF (Open Cybersecurity Schema Framework), and ECS (Elastic Common Schema). The detection efficacy of each logging standard is quantified by measuring telemetry completeness and exploit detectability across standardized logs through detailed experiments involving 50 diverse remote code execution vulnerabilities. The resulting findings identify critical gaps and reveal significant differences in logging standards' abilities to capture key attack indicators. Our contributions include a novel evaluation methodology that enables scalable and reproducible analysis of exploit telemetry, as well as new findings that provide clear, evidence-based guidance for security practitioners to make informed decisions about adopting logging standards.

Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone into speeding up the high-dimensional coefficient update step, insufficient attention has been given to the potential poor mixing of the global scale parameter $τ$ and of the overall sampler. One proposed remedy has been to marginalize out the coefficients when updating $τ$. Here we show that, while this collapsed update was previously thought to require a Metropolis step, we can in fact sample directly and efficiently from the collapsed density. This is made possible by careful linear algebraic manipulations and a strategic per-Gibbs-scan spectral decomposition, allowing subsequent evaluations of the collapsed density across hundreds of values of $τ$ at negligible cost. We combine this computational trick with adaptive numerical integration and inverse transform sampling to construct a direct sampler. This eliminates the need to tune Metropolis proposals and yields faster convergence and improved mixing. We demonstrate our method on two big data applications, fitting logistic regression under the horseshoe prior to datasets with design matrices of size 120,000 x 1,379 and 1,980 x 17,848.

As edge computing expands, serving multiple deep neural network (DNN) models on a single shared GPU has become a common yet challenging scenario, where each scheduling decision affects the tail latency of all concurrent queues. Existing schedulers rely on local heuristics and fail to capture this global impact, while GPU spatial-sharing approaches sacrifice latency predictability. In this paper, we propose EdgeServing, a deadline-aware multi-DNN serving system for edge devices. EdgeServing adopts time-division GPU sharing with early-exit inference for high inference predictability, and introduces a stability score to quantify how each candidate scheduling decision impacts the future queue status. At runtime, it cohesively selects the model, exit point, and batch size to minimize predicted system-wide SLO impact. Experimental results on multiple hardware platforms show that EdgeServing consistently outperforms representative baselines in both SLO violation ratio and P95 latency, enabled by early-exit mechanism, which expands the scheduling action space under tight latency constraints.

Counterfactual utilities evaluate decisions not only by the realized outcome under a given decision, but also by the counterfactual outcomes that would arise under alternative decisions. By generalizing standard utility frameworks, they allow decision-makers to encode asymmetric criteria, such as avoiding harm and anticipating regret. Recent work, however, has raised fundamental concerns about the coherence and transitivity of counterfactual utilities. We address these concerns by extending the von Neumann-Morgenstern (vNM) framework to preferences defined on the extended space of all potential outcomes rather than realized outcomes alone. We show that expected counterfactual utility satisfies the vNM axioms on this extended domain, thereby admitting a coherent preference representation. We further examine how counterfactual preferences map onto the realized outcome space through menu-dependent and context-dependent projections. This axiomatic framework reconciles apparent inconsistencies highlighted by the Russian roulette example in the statistics literature and resolves the well-known Allais paradox from behavioral economics. We also derive an additional axiom required to reduce counterfactual utilities to standard utilities on the same potential outcome space, and establish an axiomatic foundation for additive counterfactual utilities, which satisfy a necessary and sufficient condition for point identification. Finally, we show that our results hold regardless of whether individual potential outcomes are deterministic or stochastic.

Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve randomised measurements induced by sampling uniformly randomly from a compact group, a situation which is now quite well understood. In this work we go beyond this standard assumption, studying the classical shadow protocols occasioned by sampling uniformly randomly from the so-called compact symmetric spaces. We uncover a unifying theory of such protocols, extending the extent to which the general theory of classical shadows is understood at a mathematical level. Interestingly, for the estimation of observables sampled from certain distributions we further find that some of these protocols allow for slight improvements in sample-complexity over existing shadow schemes.

In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of the system can be reconstructed up to quadratures from the critical points of the reduced variational principle. Also, we characterize the mentioned critical points in terms of a set of ordinary differential equations which are the scaling analogue of the Lagrange-Poincaré equations. Finally, we study if the homogeneous Lagrangian systems are naturally related or not with the Herglotz variational principle.

Certain antiferromagnets composed of antiferromagnetic spin dimers exhibit a zero-magnetization plateau despite that the single-ion anisotropy of their magnetic ions is negligible. The cause for this observation was investigated by analyzing how a magnetic field affects the energy spectrum of an antiferromagnetic chain composed of antiferromagnetic spin dimers made up of two spin-half ions and by carrying out specific heat measurements for potassium copper chloride as a function magnetic field at 2 K.

Kirch topology on $\mathbb N$ goes back to 1969, and is remarkable for being Hausdorff, connected, and locally connected. In this sense, it is analogous to the usual topology on $\mathbb C,$ yet, to the author's knowledge, there have been no Kirch topology analogs of the sheaf of complex-analytic functions until very recently. In our latest paper we constructed such natural sheaf of rings, the sheaf of locally LIP functions. In this paper we investigate some of its basic properties, primarily regarding zeroth and first cohomology and Cech cohomology with respect to covers by basic open sets.

Age verification before accessing restricted content is critical to protecting minors from exposure to harmful material such as pornography, gambling, violence, hateful speech, and substance purchases like alcohol and tobacco. Currently, the absence of reliable age-checking mechanisms allows children extensive access to such adult content, posing significant risks to their worldview and mental development. While regulatory efforts like the European Union's Digital Services Act promote using Digital Wallets or Age Verification Apps, relying solely on government-based solutions raises concerns about data sensitivity and privacy risks. Effective age verification must therefore be trustworthy, user-friendly, privacy-preserving, and offer flexible assurance levels. We analyze currently implemented (UK or Australia) and proposed (UE) solutions from different angles, pointing out the weaknesses and threats, and come up with an alternative. Our proposal addresses these challenges by leveraging open standards - such as Privacy Pass and Privacy Access Tokens - and cryptographic techniques to enable secure, privacy-conscious age verification without requiring specialized software installation. This approach empowers users to select trusted providers from multiple options, reducing the risk of data breaches and ensuring a safer digital environment for minors.

We develop a unified framework for testing gravity beyond General Relativity (GR) with continuous gravitational waves (CWs) from individual supermassive black hole binaries (SMBHBs). These long-lived, nearly monochromatic nanohertz signals offer unique strengths for precision tests of gravity, since their coherent phase evolution and inter-pulsar correlations in pulsar timing arrays (PTAs) retain detailed information about departures from GR over cosmological propagation distances. We consider three representative classes of deviations from GR: additional polarization states, modified dispersion relations, and parity-violating birefringence. For each, we derive the inter-pulsar cross correlation, the modified antenna response, and the propagation-induced pulsar-term phase delay. For non-tensorial polarizations, the CW cross correlation scales linearly in the alternative-polarization amplitude, compared to the quadratic scaling of the gravitational-wave background (GWB), provided the beyond-GR modes are sub-dominant. PTAs are also competitive for modified dispersion relations, where low frequencies enhance both the antenna-pattern modification and the pulsar-term phase delay. Birefringence, by contrast, is suppressed at nanohertz frequencies for most parity-violating theories. We validate the framework with injection-and-recovery simulations for breathing-mode and massive-graviton signals at current observational limits, recovering the injected beyond-GR parameters and distinguishing the CW signal from both correlated and uncorrelated background models. We further show that a pure-GR CW template recovers source parameters without significant bias when beyond-GR physics is present in the data, supporting a two-stage analysis strategy: identify candidates under GR, then test for deviations.

Large language models (LLMs) are increasingly being integrated into web browsers to create agentic browsing systems that execute actions on behalf of the user. Prior work considering the security of agentic browsers focuses exclusively on indirect prompt-injection attacks. However, by failing to consider traditional web attacks, previous agentic browser threat models have a blind spot to web social engineering attacks originally designed to trick humans. In this paper, we propose the first web-focused threat model for agentic browsers and use it to derive a taxonomy of 20 attacks across both the web and LLM space, and implement 18 of the attacks. Our threat model extends the original See$\rightarrow$Act browser agent model to account for all components of a browser, and frames the agent as a confused deputy unable to distinguish task steps from traditional web attacks. We show that 10 web threats can reemerge often in amplified forms once an agent can be influenced by untrusted page content. We further conduct a generalizability study on 14 of the 20 attacks, showing that our attacks reproduce across 4 major LLM models spanning multiple vendors. We show that agentic browsers exhibit five major failure modes when facing traditional and LLM web threats, demonstrating the need to rearchitect agentic browsers before they are ready for the current web.

Current machine learning models are evaluated through behavioral snapshots, with benchmark accuracies, win rates and outcome-based metrics. Model explanations and evaluations, however, are fundamentally intertwined: understanding why a model produces a behavior can be as important as measuring what it produces. If we trusted interpretability, we argue that it can serve not merely as diagnostics but as a richer and more principled form of model evaluation beyond surface-level performance metrics. We explore three ways interpretability can function evaluatively: (1) fixing problems by identifying the root causes of unwanted behavior, (2) detecting subtly faulty mechanisms that invalidate model outputs, and (3) predicting potential issues before they arise by fully understanding the model's weaknesses. To fulfill its evaluative potential, we argue that interpretability methods must generate claims that are falsifiable, reproducible, and predictive -- that is, interpretability must meet scientific standards.

In this article, we present a novel formulation for the load-dependent traveling salesman problem (LD-TSP), in which travel cost (or energy expended) depends on the vehicle's current load. This problem is relevant for package delivery and urban air mobility, where vehicles must transport and drop cargo at specified locations. The challenge lies in modeling the cost, which varies with both route sequence and onboard load. Our key contributions are: (i) formulating an energy dissipation model and proving energy expenditure depends linearly on vehicle mass and distance; and (ii) formulating a mixed-integer nonlinear programming formulation and providing a novel relaxation to obtain a mixed-integer linear program. Extensive numerical results show that optimal solutions for most instances with up to 50 targets are obtained within one minute. For unsolved instances within a 10-minute limit, optimality gaps are under 13%, highlighting the formulation's tightness. We further benchmark our approach against three proposed baseline formulations and another algorithm from a related problem, and demonstrate that our formulation outperforms all baselines.

We develop an exact theory of plasmon scattering at the boundary between gated and ungated regions of a two-dimensional electron system (2DES). Using the Wiener-Hopf technique, we derive analytical expressions for the complex reflection and transmission coefficients of plasmons incident from both sides of the interface. The theory fully accounts for evanescent fields at the gate edge and radiative losses into free-space electromagnetic waves. In the non-retarded limit and for small gate-2DES separation, the reflected plasmon dominates the total electric field, while radiative losses are negligible when plasmon scattering. The amplitudes and phases of the reflection and transmission coefficients for plasmons incident from both sides have a complex dependence from 2DES-gate separation and conductivity of 2DES. Our results provide a rigorous foundation for modeling tunable plasmonic crystals based on 2DES for terahertz detection and modulation.

Airborne Wind Energy Systems (AWES) have emerged as a promising renewable energy technology that exploits stronger, more consistent high-altitude winds via tethered airborne devices. Among the various concepts, crosswind systems, where efficient flight control is essential to maximise energy output, offer significant potential. This paper addresses the problem of reference selection for crosswind flight control, focusing on the design of power-maximising geometric flight paths for the reel-out phase of Groundgen systems. To overcome the computational challenges associated with optimal control approaches, a computationally tractable framework is proposed in which a path-planning problem is formulated as a nonlinear program. The method optimises the parameters of a Lissajous curve to maximise the average power production over the reel-out phase, while incorporating curvature constraints. The proposed approach provides an efficient alternative to existing optimal control and learning-based methods.

Security operations centers (SOCs) are beginning to use large language models (LLMs) as copilots to draft incident-response plans. These plans may include actions that are valid per the catalog but still violate mandatory steps, required ordering, or approval gates before analyst review. SOCpilot makes this compliance question measurable at the plan boundary. It fixes the incident package, action catalog, policy rules, verifier, and public evidence surface. Next, it verifies the copilot's proposed action trace. We evaluate two LLM providers on 200 real incidents from an anonymized production SOC in a financial-sector case study. We compare their plans to paired analyst-authored references from the same security orchestration, automation, and response (SOAR) cases. An identical inline policy text moves the two providers in opposite directions. A deterministic verifier removes 466 non-compliant, approval-gated actions, without reducing baseline-task recall. Aggregate rates remain stable across 3 reruns of the fixed corpus. The official evidence focuses on approval-gated decisions regarding recovery and containment. Separately, the artifact exposes zero-cost readiness checks for mandatory and ordering repairs. We release the runnable artifact so independent reviewers can rederive the public results without access to private incident data.

It is a classical fact that every $n$-element set of positive reals has at least $\binom{n+1}{2}+1$ distinct subset sums, with equality exactly for homogeneous arithmetic progressions (when $n\geq 4$). We establish stability versions of this inverse theorem in two regimes. First, for any parameter $M \leq n-4$, we precisely characterize the $n$-element sets of positive reals with at most $\binom{n+1}{2}+1+M$ subset sums. Second, for any constant $C$, we provide a characterization, sharp up to constants, of the $n$-element sets of positive reals with at most $Cn^2$ distinct subset sums. Along the way, we constrain (for any fixed $d \geq 2$) the structure of $n$-element subsets of $\mathbb{R}^d$ with $o(n^{d+1})$ subset sums.

While GPUs dominate massively parallel computing through the single-instruction, multiple-thread (SIMT) programming model, their underlying single-instruction, multiple-data (SIMD) execution incurs substantial energy overhead from frequent register file (RF) accesses and complex control logic. We present DICE, a novel architecture that addresses these inefficiencies by replacing the SIMD backend with minimal-overhead, statically scheduled coarse-grained reconfigurable arrays (CGRAs). Unlike SIMD units that execute warps of threads in lockstep, DICE dispatches active threads in a pipelined manner onto the CGRA fabric, where data flow directly between processing elements (PEs), reducing RF accesses for intermediate values. To handle operations with runtime dynamism, such as variable-latency memory loads and data-dependent control flow, while preserving static scheduling, DICE compiles programs into "p-graphs" by partitioning dynamic dependence edges across separate CGRA configurations. DICE further introduces several key optimizations: double-buffered configuration memory to hide reconfiguration latency, compile-time p-graph unrolling to enhance resource utilization, and a temporal memory coalescing unit (TMCU) to merge memory requests from consecutive, pipelined threads. Evaluations on Rodinia benchmarks in Accel-sim demonstrate that DICE reduces register file accesses by 68% on average. With equivalent computation and memory resources, DICE's CGRA Processors (CPs) achieve a geometric mean of 1.77-1.90x dynamic energy efficiency and 42.0%-45.9% average power reduction compared to the modeled NVIDIA Turing Streaming Multiprocessors (SMs), while the full DICE system achieves performance comparable to the modeled Turing GPU baselines. DICE demonstrates that spatial pipeline execution can deliver substantial energy savings without sacrificing performance.

Commercial treatment planning systems for electron FLASH radiotherapy are unavailable, and the dosimetric precision required for ultra-high dose rate delivery makes Monte Carlo (MC) simulation the gold standard approach. This work establishes a methodology for generating pulse-width-specific phase space (PHSP) files for the Mobetron UHDR system (9 MeV), accounting for systematic beam quality shifts caused by RF waveguide loading across pulse widths of 1.2-4.0 microsecond. Using GAMOS 6.2.0, source parameters were iteratively refined against experimental targets: mean energy was optimized by matching phantom-measured R50 in the fall-off region, while energy spread was refined using surface dose and build-up gradients. Relationships derived from a mid-range 6 cm aperture were applied across all clinical configurations (2.5-10 cm) to test the aperture-independence of beam loading effects. Mean energy decreased exponentially from 9.58 to 9.04 MeV (R^2=0.99) with increasing pulse width, while energy spread increased quadratically (R^2=0.99), with a strong negative correlation (r=-0.98). Cross-aperture validation confirmed that energy shifts are independent of downstream collimation. The geometric mean pulse width (2.28 microsecond) was evaluated as a universal clinical reference, yielding 9.32 MeV mean energy. Across experimental extremes, R50 deviations were within 1.3 mm and critical depth-dose parameters remained within 2.0 mm, meeting AAPM TG-106 tolerances. Validated regression models enable beam parameter prediction at arbitrary pulse widths, and the universal reference reduces computational burden by 75% while maintaining clinical accuracy.

In this paper we establish Hölder continuity estimates for viscosity solutions to first order Hamilton-Jacobi equations linked to linear control systems satisfying the Kalman rank condition. Our model Hamiltonians are non-convex in the generalised momentum variable and - more importantly - they lack coercivity in certain directions. Therefore, all previously available results from the literature cannot be applied to these degenerate settings. In order to overcome these obstructions, we design a geometric argument, dictated by the linear control system. As a result of this, the obtained Hölder estimates are quantified in an anisotropic way within this geometric framework. The estimates hold true for unbounded source terms, for which one part of our analysis is inspired by a recent result on De Giorgi type methods for hypoelliptic operators.

We identify a systematic distortion of the gain-vs.-frequency function of radio telescopes caused by digital flattening ("whitening") of the signal's spectrum followed by re-quantization, a common pair of processes in the signal processing of modern telescopes. Wide-bandwidth telescopes often have a large variation of signal power over frequency. Flattening of the spectrum allows samples of the channelized signal to be represented in a small number of bits, allowing efficient downstream processing. However, we show that this produces subtle systematic error in the measured spectra. We explore this effect in data from the Owens Valley Radio Observatory's Long Wavelength Array (OVRO-LWA) and through detailed semi-analytic simulations. Although the effect can be small so that it has heretofore been unrecognized, we demonstrate that it produces distortion of the spectrum at a level that is problematic for some science, in particular 21 cm cosmology. Finally, we explore mitigation strategies, showing that the effect can be substantially reduced by careful choice of the gain distribution along the signal path or by incorporating dithering in the re-quantization step.

Although machine learning (ML)-based performance outcome prediction is an important topic in contemporary sports science, one important issue is the limited understanding of the cross-individual generalizability of ML models in sports contexts. To address this issue, this study aimed to evaluate the cross-individual generalizability of ML models for predicting ball speed in baseball pitching. A dataset comprising 50 pitchers from various competitive levels was analyzed. Cross-individual generalizability was assessed using leave-one-subject-out cross-validation. Specifically, the effects of expertise level and restrictions on spatiotemporal motion information were examined to identify factors influencing model generalizability. The results revealed that, under cross-individual evaluation, (1) predictive performance was markedly lower than under within-individual evaluation, with R-squared value decreasing from 0.91 to 0.38; (2) the model tended to overestimate the performance of Intermediate pitchers relative to Expert pitchers, with a significant group difference in signed prediction error (p < .05); and (3) the trunk and pivot leg demonstrated relatively high generalization performance, with the pivot leg showing notable generalizability even during the weight-shift initiation phase (R-squared value > 0.25). These findings underscore the importance of cross-individual evaluation in enhancing the practical applicability of ML in sports settings and contribute to a deeper understanding of the biomechanical factors underlying the target movement.

We demonstrate that the conversion gain of a superconducting hot-electron bolometer (HEB) mixer can be increased by biasing the device within the negative differential resistance (NDR) region of its current-voltage characteristic. Although NDR biasing has historically been avoided due to MHz-range resistive oscillations, we show that these oscillations arise from an LC resonance formed by the bias-T inductance and the effective thermal capacitance of the HEB. By applying stability criteria analogous to those developed for tunnel diodes, we redesigned the embedding circuit to suppress this resonance and achieve stable NDR operation. Direct measurements using two monochromatic 2.5-THz sources confirm the predicted gain enhancement. These results establish NDR biasing as a viable method for improving HEB mixer performance and motivate further studies of noise behavior and circuit optimization.