Papers

Spatial cognition supports how people interpret spatial relationships and navigate their surroundings. Although vision plays a dominant role, other sensory modalities, including olfaction, may also contribute under limited visual conditions. This paper investigates the role of olfactory cues in location recognition during virtual reality (VR) navigation. We conducted two formal studies using a wearable olfactory prototype. Study 1 examined whether olfactory cues and ventilation influenced users' recognition of encountered locations during \HDY{teleportation-} and dash-based navigation. Study 2 extended this investigation to repeated navigation and examined whether ventilation duration influenced recognition performance and user experience across successive movements. Results show that olfactory cues can support recognition of encountered locations during navigation, while ventilation was associated with reduced residual interference and improved usability. However, longer ventilation did not clearly improve recognition accuracy in repeated navigation. These findings suggest the potential of olfactory cues as contextual signals during VR navigation, while also highlighting the importance of scent management for maintaining perceptual clarity and user comfort.

Electrostatic (ES) field enhancement at sharp conducting structures plays a central role in lightning protection, corona discharge, electrical breakdown in vacuum (for example in particle accelerators), and more generally in technological applications of field electron emitters. A canonical geometry for studying this ES effect is the hemisphere-on-cylindrical-post (HCP) model, in the regime where the structure stands on a planar conductor of large lateral extent, and a large gap exists between the structure and the counter-electrode. A parameter of major interest is the apex field enhancement factor (AFEF) (apex-ES-field/background-ES-field). For this (and other) structures, a formula for the AFEF can be written in the form AFEF = ASC x ASR, where the apex sharpness ratio (ASR) is given by the ratio (post-height/apex-radius-of-curvature), and the apex sharpness coefficient (ASC) depends on the post shape. For the HCP model, no exact analytical formulas for the ASC or the AFEF are currently known. (Quite possibly none exist.) This paper develops a compact analytical approximation for the ASC and hence for the AFEF. This compact formula has a logarithmic-style structure, rather than the power-style structure used in previous approximations. When compared with precise finite-element analyses of the HCP model, over the computationally accessible range 1 to 1000 for the ASR, this logarithmic-style formula has a maximum error-magnitude of 0.15 percent, which is significantly better than older approximations.

We study probability measures minimizing the energy with kernel $|x\cdot y|^p$ on the real unit sphere. For every positive rational $p=a/b$, each minimizer admits a finitely supported minimizing replacement. If $a/b$ is reduced and $b\ge d$, every minimizer on $\mathbb S^{d-1}$ is finitely supported. The latter assertion follows from a finite-rank algebraic lift, Nash curve selection, and a Wronskian multiplicity bound. For irrational exponents, we prove that a positive semidefinite restriction of finite rank cannot have infinite compact support. We also establish local stability and a quantitative support bound under positive-definite Hessians at every contact of every limiting minimizer. This hypothesis is stronger than finite support and does not prove unconditional openness of the discreteness regime. Finally, subtracting a single suitably scaled high even power produces a uniformly nearby kernel whose every minimizer has finite support. We identify the atomic-purity selection of these approximants and prove a target-centered recovery theorem, separating finite approximation from discreteness of the limiting problem.

Adversarial consensus simulators require not only a model of message delivery but also a model of time. For timeout-sensitive protocols, coupling protocol-time progression to scheduler activity can allow communication scheduling to influence when failure detectors expire. We study this interaction in VeriProtocol using controlled Multi-Paxos and Raft experiments. In the primary Multi-Paxos study, we compare EventCoupled timing, where every scheduler opportunity advances protocol time, with RoundTick timing, which decouples individual scheduler events from timeout progression. At N=5, increasing the bounded message-delay budget from K=6 to K=14 increased the observed EventCoupled leadership-instability rate from 5% to 100% across the tested grid, while no additional valid leader elections occurred in any of the corresponding 140 RoundTick executions. At K=0, neither model produced additional elections. Matched-trace analysis identifies the mechanism: under EventCoupled timing, scheduler activity used to perturb communication also directly advances failure-detector state. Under RoundTick, comparable scheduler activity does not imply equivalent protocol-time progression. A targeted heartbeat-delay control confirms that RoundTick does not suppress timeout-driven elections; an additional election remains reachable when leader contact is unavailable across sufficient logical time.

Accurate forecasting of river discharge and floods is very challenging. River dynamics are affected by storage, meteorological forcing, and flow propagation at different spatial and temporal scales. Forecasting thus requires a framework that considers the upstream-to-downstream flow through river networks across grid cells and catchments. This modeling is known in hydrology as distributed modeling and routing. Existing deep learning approaches either ignore this topology, operate on lumped catchments, or route predicted physical quantities through a separate graph or physical routing model. We instead introduce feature-space routing: a topology-aware state-space operator embedded directly in the forecasting dynamics. At every forecast step, the operator gathers latent states from upstream grid cells and causally updates the downstream state according to the known river network. This preserves the physical connectivity of the river system while allowing the propagated state itself to be learned end-to-end and allows the model to predict river discharge considering both local dynamics and neighboring upstream contributions. To address uncertainty and provide probabilistic forecasts, we minimize the fair continuous ranked probability score (fCRPS) as a training objective. Our experiments on the European Flood Awareness System (EFAS) and observational data for river discharge forecasting demonstrate that encoding the physical structure of river networks explicitly in the feature space substantially improves the forecasting skill, particularly in an ungauged setting. Our approach achieves state-of-the-art results on both reanalysis and observational data and is able to forecast maps of river discharge at 1 arcminute and 6-hourly resolution up to 10 days lead time.

Minimax optimization is a fundamental framework in machine learning, robust optimization, and game theory, yet finding first-order stationary points of general nonconvex-nonconcave minimax problems remains challenging without additional structural assumptions. Existing guarantees often rely on global PL- or KL-type conditions that connect max-player stationarity to global inner optimality, or on Minty-type conditions that impose a global relation on the game gradient field relative to a reference solution; local KL variants relax the former requirement but typically require initialization and tracking within a near-optimal region. Such conditions may be difficult to satisfy in many applications. In contrast, we develop a first-order method that finds an $\epsilon$-stationary point within $\widetilde{O}(\epsilon^{-2})$ first-order iterations under a local inverse-Lipschitz regularity condition around approximate max-player stationary points, together with a compactness condition on a penalty sublevel set. Our condition places no optimality requirement on stationary points of the inner maximization problem: they need not be globally, or even locally, maximizing. We further provide sufficient conditions for the required regularity. In the unconstrained setting, it follows from uniform nonsingularity of the maximization-variable Hessian near stationary points; for constrained upper Moreau envelopes, it follows from standard KKT regularity conditions. These results establish first-order complexity guarantees for classes of nonconvex-nonconcave minimax problems not covered by the above PL-, KL-, or Minty-type frameworks.

Given a finite transitive group $G\leq \operatorname{Sym}(\Omega)$, the derangement graph $\Gamma_G$ is the graph whose vertex set is $G$, and two vertices $g$ and $h$ are adjacent if the ratio $h^{-1}g$ is a fixed-point-free permutation. In this paper, we show that the automorphism group of the derangement graph of the transitive permutation group corresponding to the natural action of $\operatorname{PGL}_{2}(q)$ on the projective line $\operatorname{PG}_{1}(q)$ is \begin{align*} \operatorname{Aut}(\Gamma_{\operatorname{PGL}_{2}({q})}) = \left(L_{\operatorname{PGL}_2(q)}\times R_{\operatorname{PGL}_2(q)}\right) \rtimes \left(\langle \psi \rangle \times \gamma_{\operatorname{Aut}(\mathbb{F}_q)}\right), \end{align*} where $L_{\operatorname{PGL}_2(q)}$ is the left-regular representation of $\operatorname{PGL}_2(q)$, $R_{\operatorname{PGL}_2(q)}$ is the right-regular representation of $\operatorname{PGL}_2(q)$, $\gamma_{\operatorname{Aut}(\mathbb{F}_q)}$ is the group of conjugation by elements of $\operatorname{Aut}(\mathbb{F}_q)$, and $\psi: \operatorname{PGL}_2(q) \to \operatorname{PGL}_2(q)$ such that $\psi(x) = x^{-1}$.

How can local multiplet signatures, collective core-hole screening, and an extended photoelectron be reconciled in Ce $L_3$ x-ray absorption near-edge spectra? Motivated by the question raised by Kvashnina [Chem. Eur. J. 30, e202400755 (2024)], we address this challenge using XSpectruplet, which couples local multiplet dynamics to continuum photoelectron propagation in self-consistent Kohn–Sham screening potentials. For Ce$^{4+}$ in CeO$_2$, our heuristic search identifies primary and secondary stationary screening states whose calculated white-line maxima lie about 7.3~eV apart after including their independently calculated total-energy difference, yet both retain the same effective local spectroscopic $4f^0$ sector. Their squared overlaps with the unrelaxed sudden reference give approximate statistical weights of 63% and 30%, respectively, within an independent-channel description. Their contrasting screening responses arise from collective rehybridization of occupied orbitals, rather than occupation of an additional localized $4f$ spectator, and produce contributions in both the main white-line and satellite regions. Ce$^{3+}$ in monazite CePO$_4$ provides the contrasting case of a localized $4f^1$ spectator participating explicitly in the multiplet dynamics. Independent relaxation of neutral $4f$ and white-line states gives a CeO$_2$ pre-edge–white-line gap of 10.51~eV, close to the experimental separation of approximately 10.7~eV. Its excess over the fixed-background spectral gap defines a net correction, which we transfer heuristically to CePO$_4$ without changing its local multiplet structure. This gives an estimated CePO$_4$ gap of 6.38~eV, compared with approximately 8.1~eV experimentally. Distinct spectral contributions can thus arise from collective screening without a change in the effective local configuration.

This paper analyzes finite element approximations for Maxwell's equations with time-dependent coefficients and nonlinear E-H coupling in both the total current density and the Silver-Müller-type boundary condition. The nonlinear coupling and the time-varying material parameters prevent the use of standard analytical tools, including the discrete compactness property and the Minty-Browder argument, making the numerical analysis particularly challenging. As the main novelty, we establish two primary contributions: Uniform convergence on every finite time interval $[0,T]$ and exponential stability on the infinite time horizon $[0,\infty)$. The uniform convergence is established via a Cauchy-type argument within a time-dependent Hilbert space framework that entirely bypasses Minty's trick and the discrete compactness argument. Furthermore, under a positive homogeneity assumption on the nonlinearities, the exponential stability is analyzed by means of a nonlinear sup-max problem arising from ratios of consecutive discrete energies. With this strategy, we ultimately prove a fully discrete unconditional exponential decay result under a specific sufficient condition. In the absence of this condition, a concrete counterexample shows that the energy decay fails to hold. Numerical experiments are provided to validate the theoretical findings.

Reinforcement learning (RL) trains representations on data selected by the agent's policy, which then uses the resulting returns to guide its next choices. We show that this loop can sustain a lower-return policy even when representation fitting is globally optimal on those data. In a self-confirming superposition trap, every optimal code assigns overlapping directions to features that rarely occur together under the current policy. An alternative action brings them together, causing interference that lowers its return and reinforces avoidance, although refitting to that action would yield more return at the same capacity. We characterize the dimensions admitting a trap in a tied two-step model and show separately that equal feature frequencies, continued visitation, and independent controller learning need not prevent it. Because fitting weights errors by visitation, an avoided action can lose its return advantage at little cost to the objective. In a finite-action model, we bound this distortion and derive a replay condition: sufficient training weight on the best separately adapted action preserves its ranking despite residual error. Neural PPO experiments show how the feedback develops during learning: agents initialized toward different actions develop different interference patterns, opposite mean return rankings, and different final policies at the same capacity. We therefore test whether retaining access to neglected states can improve control. Keeping these states in training reduces measured interference and improves sequential return, with gains even when the encoder is frozen. Related interventions on state access, replay weights, and feature overlap improve control on MiniGrid and DMControl. For agents that learn through a world model, protected fitting improves DreamerV3–Crafter's cumulative training scores at unchanged capacity.

Multiple agents may often conflict in an organization: for example, one coding agent changes an interface in a repository, but another continues to develop on the old version where existing tests become stale. A conversation can resolve the episode, but when the participants change, what makes the lesson continue to govern the team? We introduce Relic, which turns recurring collaboration failures into organization-owned, executable protocols. Members reflect on visible work, propose rules, and govern their adoption. Adopted protocols bind triggers, responsibilities, required evidence, and execution consequences to the runtime, while remaining open to revision and retirement. In one traced case, repeated integration friction produces an interface-review rule that governs later pull requests and is revised as work continues. Across 360 controlled runs over ten software workloads and three models, Relic raises complete-contract delivery from 14.06% to 19.76% (+5.71 percentage points) over a matched structured team without the protocol lifecycle, improving all four verified production endpoints in every model stratum. Under fresh-member transfer, behavioral correctness is 25.4% with no inherited protocol, 34.6% with the same rules provided as readable text, and 41.2% with executable bindings, a +6.5-point advantage over text alone. On the full CooperBench benchmark, after excluding 183 broken benchmark pairs, Relic achieves 371/469 (79.1%), establishing the best reported result among peer-structured systems. On the 47-pair same-model subset, Relic also exceeds Solo (28/47 vs. 26/47), reversing the coordination loss exhibited by the official peer baseline. Together, these results show how collaboration experience can become persistent organizational state that remains useful beyond the members who created it.

Language models (LMs) often hallucinate by committing to confident answers rather than abstaining, even when they do not have enough information to answer reliably. A large body of existing work mitigates hallucination through detection or abstention mechanisms, but leaves open how models internally arrive at the decision to commit or abstain in the first place. We study this decision through mechanistic analysis, framing hallucination as unsupported commitment: the model commits despite exhibiting signals of unanswerability. Using causal gating, we identify a Commit-Abstain Circuit (CAC), a sparse, causally localised subset of attention heads and MLP sublayers underlying this decision. Across ten LMs (3B-14B) from five families and three benchmarks, the CAC exhibits a recurring accumulate-yet-undercorrect pattern: commitment-promoting components build up commitment in earlier layers, while abstention-promoting components act later as corrective signals that are often insufficient to overturn the accumulated commitment. Building on this finding, a lightweight policy trained on CAC activations improves decision accuracy by 12.2 points over the model's intrinsic commit-abstain margin, reduces false abstentions by 2.5 times, transfers to unseen benchmarks, and extends to larger models (27B-35B). The CAC is both diagnostic, clarifying how models overcommit, and practical, enabling improved abstention decisions.

Scientific output is growing rapidly, but it is unclear whether the expanding literature remains original or is increasingly repeating itself. Originality has many dimensions. One dimension can now be measured directly: how textually distinct a paper is from the work that came before it. Using semantic language models, we screened more than 26,000 full-text papers across eight fields in the CORE database (2015–2025) for passages resembling recent literature. We compared every paper against a fixed-size sample of earlier work, so increases in resemblance are not a by-product of literature growth. We find that the share of a paper's text resembling recent work was stable before 2021, then rose sharply, more than tripling by 2025. The increase came not from a few papers borrowing more heavily but from resemblance spreading across the literature: more papers now contain passages that echo recent work, and almost none of this growth is explained by cited work. We also found an analogous increase in passages expressing the same scientific idea. The pattern held across robustness checks and replicated in a second, independent database. Along this one measurable axis of originality, scientific writing has become less distinct from the work preceding it.

Gradient clipping is widely used to stabilize training, but it need not improve the statistical accuracy of averaged SGD, even under heavy-tailed noise. We derive a finite-sample comparison of clipped and unclipped Polyak-Ruppert averaged SGD under finite conditional $p$-th moments, $p\ge2$. Our main result gives explicit accuracy and confidence conditions under which, for $p>2$, the Gaussian term dominates the unclipped deviation bound, so clipping need not improve its leading order. By balancing clipping bias and concentration, we obtain a bound in which the heavy-tail correction depends logarithmically rather than polynomially on the inverse failure probability. At $p=2$, this improves the confidence dependence of the leading bound. We establish sharpness of the unclipped heavy-tail term through an exact one-dimensional quadratic recursion and extend the comparison to projected convex SGD. We also prove concrete costs of clipping: every fixed finite threshold increases asymptotic variance on a scalar Gaussian quadratic, while whole-gradient clipping can shift the limiting point under asymmetric noise.

As LLM agents tackle longer tasks, they increasingly compress growing histories of reasoning, actions, and tool outputs. Compression can reduce token use, but it also changes the information available for later decisions. Existing agentic harnesses bundle decisions about what to compress, when to compress, and how much to remove into fixed policies. A systematic characterization is needed to disentangle these decisions and reveal how each affects task success and execution cost. We systematically vary these decisions across three open-weight models on SWE-bench Verified and Terminal-Bench 1.0. Across nearly 35,000 agent runs, we measure task success, token use, end-to-end latency, and estimated cost. We find that fewer tokens need not mean faster or cheaper execution: on Terminal-Bench with Qwen, policies using roughly one-third as many tokens can take 20-80% longer than the uncompressed agent. Policies with similar overall success can solve different tasks, while the same policy can perform quite differently across models. Our results motivate evaluating compression by its effects on agent execution and tailoring policies to the task, model, and workload.

The proliferation of generative and agentic artificial intelligence (AI) systems has introduced computational demands whose environmental consequences are substantial yet underexamined. This paper examines the environmental footprint of modern AI systems across energy consumption, carbon emissions, water usage, and electronic waste over the full lifecycle of large language models, multimodal foundation models, and agentic workflows, from hardware fabrication and training through fine-tuning and inference to end-of-life disposal. This work provides a conceptual analysis, utilizing order-of-magnitude estimations based on published data, without conducting original physical measurements. We contribute a lifecycle taxonomy that crosses lifecycle phases with five impact dimensions and emission scopes; a Sustainability Assessment Framework for AI Systems (SAFIA) comprising nine indicators; a comparative analysis of traditional, generative, and agentic AI; seven open challenges; policy recommendations for regulators, cloud providers, hardware manufacturers, and AI developers; and a research roadmap to 2035. The analysis indicates that inference can rival or exceed training energy over a deployment lifetime, that agentic workflows can multiply the energy of equivalent single-pass inference by one to several orders of magnitude depending on the number of model and tool calls, that indirect water use and embodied carbon are systematically underreported, and that measurement tools, disclosure practices, and regulation have not kept pace with agentic deployment. These findings call for agent-aware energy measurement, lifecycle-based carbon and water accounting, and mandatory disclosure for large-scale AI training and deployment.

We observe that the classical $n\log n$ time threshold for one-tape Turing machines is also a threshold for their accepting-path counts. Below it, every nondeterministic one-tape machine running in strong $o(n\log n)$ time has a rational ordinary generating function of accepting-path counts. At strong $O(n\log n)$ time, the situation changes completely: there is a fixed one-tape machine whose accepting-path function is complete for $\#\mathsf P_1$, the tally analogue of $\#\mathsf P$, under parsimonious polynomial-time tally reductions. A second construction within the same time bound gives positive accepting-path counts with a noncomputable exponential growth rate. The rationality result combines the one-tape time gap with the linear-time counting theorem of Tadaki, Yamakami and Lin. The completeness proof adapts the linear-time universal counting machine of Beame et al. to the one-tape setting.

In many teleoperation applications, collecting a large number of demonstrations as required for traditional probabilistic learning from demonstration (LfD) approaches may not be feasible. To still give operators the ability to intuitively create trajectories as Virtual Fixtures (VFs), we propose to leverage a motion prior in the learning process. Particularly, by using Linear Quadratic Tracking (LQT), users are able to define guiding trajectories from the demonstration of just a few via points. To account for orientation guidance, we further reformulate classical LQT on Riemannian manifolds, introducing an additional geometric prior. Through a probabilistic interpretation of the LQT solution, we derive a covariance estimate at each trajectory point which we use to modulate the stiffness of the resulting fixture, resulting in strong guidance around the via points and softer guidance when far away. The covariance information is also used to define a validity region of the fixture, allowing the operator to leave its influence area and conduct unmodeled tasks. We evaluate the proposed Riemannian LQT formulation in a set of toy examples and the full framework on a cutting task requiring high precision in a minimally invasive surgery setting on the da Vinci Research Kit (dVRK).

Diagnosing a patient from video requires more than recognizing the sign: a vision-language model must turn what it sees into hypotheses, questions and tests. DynamicDx evaluates each step in 71 neurological consultations across 11 sign categories, linking authentic patient videos to confirmed diagnoses and fixed charts built from the same case reports, so that every model queries the same evidence. Across five such models, video improves accuracy by 9.9-22.5 percentage points over blind input, but neither recognition alone nor temporal order explains the gain: the cause is usually missing from the model's video-only differential diagnosis even when the sign is recognized, and shuffling the frames produces no reliable accuracy loss. Instead, a trajectory replay traces most of the gain to the investigation results the video prompts. Evidence acquisition is the bottleneck: supplying the decisive investigations raises accuracy to 73.2-93.0%. Two interventions act on it. A post-trained 4B video describer improves sign descriptions, especially from a short, densely sampled segment, and source-clean literature retrieval expands initial hypotheses; both bring the tests a model orders closer to those the treating clinicians documented and, through them, raise accuracy. For video-based diagnosis, seeing better helps when it leads to asking better.

Prior information for real-world physical quantities is most elegantly expressed via partial differential equations (PDEs). In this paper, we propose a novel way to solve PDEs using probabilistic inference on a factor graph. In general, factor graphs provide a natural way to encode prior knowledge into a model as explicit factors; here, this knowledge is provided by a governing PDE, which narrows the solution space, while observed data further shape the posterior over the parameters. The approximate parameter posterior is inferred using message passing based on moment matching, without posterior sampling or global gradient-based optimization. We demonstrate our approach on the first-order advection and the second-order semi-linear Fisher-KPP equations, where it achieves predictive accuracy comparable to a standard baseline while providing structured predictive uncertainty. Moreover, the inferred posterior marginal means and uncertainty structure match more closely those obtained using Hamiltonian Monte Carlo than the evaluated mean-field variational inference baseline, while requiring up to 10x less training time in our experiments, with inference speed comparable to variational inference.

Let $R_{n,p}$ be the determinantal hypersurface ring defined by the determinant of a generic $n \times n$ matrix in characteristic $p$ where $n \geq 2$. In this paper, we obtain explicit bounds for the $F$-signature of $R_{n,p}$. For the upper bound, we prove that this $F$-signature is decreasing in $n$, so the $F$-signature of $R_{2,p}$ serves as an upper bound, which is $2/3$. For the lower bound, we find a toric degeneration $B_n$ of $R_{n,p}$, so the $F$-signature of $B_n$ serves as a lower bound. This $F$-signature can be computed using either Gröbner basis or Han-Monsky machinery, and its value is $\frac{(n!)^2}{(2n-1)!}$.

Phonon–magnon coupling has been extensively studied in ferromagnets, whereas its microscopic mechanisms in antiferromagnets remain less understood. Here, we combine first-principles calculations with spin–lattice dynamics to investigate phonon–magnon interactions and their impact on thermal transport in antiferromagnetic NiO and MnO, which are put in contrast to the ferromagnetic EuO with an identical crystal structure. Green–Kubo and spectral energy density analyses show that spin dynamics reduce phonon thermal conductivity and lifetimes, with the strongest effects in MnO. Comparison of the excitation spectra indicates that spin-induced phonon scattering depends sensitively on the relative phonon and magnon energy scales, while the contrasting behavior of MnO and EuO further highlights the role of magnetic order. A simplified phase-space model further illustrates that, for comparable phonon and magnon energy scales, the antiferromagnetic case can support a larger phonon–magnon scattering phase space than the ferromagnetic case, suggesting a greater number of kinematically allowed scattering channels. These results identify excitation energy scales and magnetic order as key factors governing phonon–magnon scattering in magnetic materials.

For planar convex bodies $A_0,A_1,A_2$ satisfying $\frac12(A_0+A_2)\subseteq A_1$, we prove that the union of the three slices $\{i\}\times A_i\subseteq\mathbb{R}^3$, $i=0,1,2$, contains a point such that every closed halfspace containing it captures at least $2/9$ of their total area. This establishes the three-slice case of Oertel's mixed-integer centerpoint conjecture in $\mathbb{Z}\times\mathbb{R}^2$ with the best possible constant.

Online safe reinforcement learning (RL) seeks policies that maximize reward while satisfying safety constraints. Reward and safety can induce multimodal action distributions, challenging the prevailing primal-dual methods: Gaussian actors may collapse onto a single suboptimal mode, and optimization over the nonconvex Lagrangian landscape can be unstable. Diffusion and flow policies can represent such distributions, but recent work with a diffusion actor relies on estimating and matching the score of an augmented-Lagrangian target policy. Instead, we differentiate the augmented objective directly through the generation path of a flow policy, so no score needs to be estimated. Because a flow policy lacks a readily available action log-density for entropy regularization, we build on the density-free kinetic-energy regularizer of FLAC, a recent reward-only method, and propose Reparameterized Augmented-Lagrangian Flow Actor with Least Energy (RAFALE), an off-policy actor-critic method for safe RL. We formulate its update as a constrained one-ended generalized Schrödinger bridge and show that, for each source draw, this path-space problem is exactly an entropy-regularized problem in action space. At positive noise, its solution reweights the reward-only action distribution only where the estimated cost exceeds a threshold set by the Lagrange multiplier. As the noise vanishes, the optimal value converges to that of a least-energy map objective that the flow policy optimizes directly. Across seven Safety-Gymnasium tasks, RAFALE achieves competitive reward with mean final cost within budget on every task, whereas strong baselines trade one for the other; ablations support the necessity of both its augmented objective and its flow actor.

We investigate the growth of a circular domain in a phase-separating lipid membrane and its relation to the budding instability. We describe the in-plane dynamics with a conserved, time-dependent Ginzburg-Landau model under radial symmetry. Numerical solutions show a crossover of the domain size $D$ as a function of time $t$ from $D\sim t^{1/3}$ at early times to $D\sim t^{1/2}$ at later times, followed by saturation due to finite system size. The time-dependent line tension $\sigma(t)$, evaluated from the evolving concentration profile, rises rapidly before approaching the planar-interface value. This behavior distinguishes an early line-tension-dominated regime from a later domain-size-dominated regime. To estimate the budding instability, we combine $D(t)$ and $\sigma(t)$ with a quasistatic criterion for the loss of stability of a partially budded domain. The budding-instability time decreases with increasing membrane spontaneous curvature and increases near the critical point. Thus, the evolution of both domain size and line tension is essential for determining the time required for the budding instability.

Santos asked when intersections of dilated Hadamard simplices with cubes are integral, smooth, or normal, in a prescribed affine lattice. We construct a nonintegral example in dimension eleven and prove that no smaller-dimensional example exists. We characterize smoothness completely and show that every smooth member of this family is normal. An explicit example in dimension fifteen shows that integrality alone does not imply normality. For Sylvester simplices of order at least sixteen, we establish a sharp uniform integrality bound and construct counterexamples immediately below it. We also obtain sufficient normality bounds for general Hadamard simplices and stronger bounds for the Sylvester family. The proofs use integer decomposition for boxes with separated corner cuts and rounding under three signed slab constraints. All numbered results have formal counterparts verified in Lean.

We study online dynamic pricing with censored demand, where an arbitrary inventory level is revealed before pricing and may adapt to past observations, while demand follows an unknown, price-dependent distribution that is stationary over time. For a horizon of $T$ rounds, Xu et al. [2026] achieved $\widetilde{\mathcal{O}}(\sqrt{T})$ regret under restrictive structural assumptions including linear demand, price-independent additive noise, and conditions relating inventory levels to the noise support. Our first contribution is to extend this framework to a substantially more general and statistically harder nonparametric setting, requiring only the natural assumption that expected sales are nonincreasing in price and allowing nonlinear demand curves and price-dependent noise. For this model, we first propose a simple baseline, Double-Grid-UCB, which discretizes both price and inventory and achieves $\widetilde{\mathcal{O}}(T^{3/4})$ expected regret using separate revenue estimates for each price-inventory grid pair. Then, we develop Threshold-UCB, which improves the expected regret to $\widetilde{\mathcal{O}}(T^{2/3})$. Unlike Double-Grid-UCB, Threshold-UCB reuses sales observations across inventory levels through shared estimates of demand-tail probabilities, allowing the same data to support revenue upper bounds for multiple inventories rather than a single inventory bin. We also complement this upper bound with an $\Omega(T^{2/3})$ lower bound via a reduction from stochastic posted pricing, establishing its minimax optimality. Finally, extensive experiments across inventory processes, demand functions, and noise models demonstrate consistently superior performance of Threshold-UCB over benchmark algorithms.

We aim to derive convenient analytic estimations of magnetic inference errors, which can be used to inform and facilitate the creation of the science-traceability matrix of a polarimetric instrument. In order to do this, we study the general problem of the propagation of Poissonian noise in polarized light signals to derived data products of the Stokes profiles, namely integral moments of arbitrary orders and spectral derivatives of the intensity. In particular, we derive the errors on the longitudinal and transversal projections of the magnetic field inferred from the weak-field approximation (WFA) of the Zeeman effect. The propagated errors on magnetic inference are traced back to the signal- to-noise ratio (SNR) of the observations. The results can be used to quantify the contributions of different environmental and instrumental conditions (spectral line width, spectral resolution, line spread function, stray light) to the overall error on the inferred quantities. Our tests indicate that the integral-moment method of inference is comparable to the local derivative in a predictable way.

Spin pumping into superconductors is generally expected to become less efficient below the critical temperature $T_\textrm{c}$ because quasiparticle transport freezes out. Here we report a pronounced enhancement of the spin pumping-induced magnetic damping in Py/Nb heterostructures, confined to a narrow temperature interval immediately below the superconducting transition. The damping exceeds its normal-state value and therefore cannot be explained within the conventional quasiparticle picture of spin transport. The enhancement coincides with the finite-resistance vortex-creep regime of the Nb layers and disappears upon cooling into the pinned vortex state, indicating that mobile Abrikosov vortices provide an additional channel for spin-angular-momentum dissipation. These results establish ferromagnetic resonance as a sensitive probe of dissipative vortex dynamics in superconductors.

We calculate the exact values of the relative isoperimetric profile for a unit square with a central square removed. In other words, given a removed central square of a fixed size, we provide a function which produces the smallest relative perimeter which bounds any possible area within this shape.