Papers

Characterizing intermediate quantum chaos in systems with mixed phase spaces requires probing spectral correlations across multiple scales. Here, we present a multi-scale statistical analysis of the resonance spectra of ultracold 166Er and 168Er atoms using higher-order spacing ratios, spacing increments, and the accumulated power spectral density of decimated level sequences. Our analysis reveals that while the spectra exhibit clear level repulsion, they are consistently better described by semi-Poisson than by standard Wigner-Dyson ensembles, with this intermediate character persisting across higher-order correlations. The accumulated power spectrum reveals an intermediate 1/f^alpha regime, with alpha approximately 1.5 at full spectral resolution and a tendency toward the integrable random-walk limit alpha = 2 at intermediate decimation scales, indicating a scale-dependent loss of spectral rigidity. Furthermore, the spacing-increment distributions independently reveal statistics intermediate between Laplace and Gaussian limits. Together, these complementary diagnostics show that the semi-Poisson character reflects persistent non-Wigner-Dyson correlations beyond the nearest-neighbor scale, providing a consistent picture of intermediate quantum chaos and a possible connection to hierarchical trapping in the underlying collision dynamics.

For any non-zero periodic function f\,: Z $\rightarrow$ C of period N ___ 1 and any non-zero algebraic number z\_0 that doesn't lie on a half-line [e^2i${\ell}$$\pi$/N , e^2i${\ell}$$\pi$/N $\infty$[, 0 ___ ${\ell}$ ___ N -1, we give a lower bound of order sqrt{s/log(s)} on the dimension of the Q(z\_0 )-vector space spanned by the numbers L(f, i, z\_0 )\,: sum\_{m=1}^$\infty$ f(m)z\_0^m/m^i. This generalizes a result Fischler proved in 2026, corresponding to f identically equal to 1 and |z\_0| ___ 1: in this case, the numbers L(f, i, z\_0 ) = Li\_i (z\_0 ) are polylogarithm values. Except for a finite number of cuts in the complex plane, our result still holds when |z\_0 | > 1, that is in a domain where the series definition above for the numbers L(f, i, z\_0 ) doesn't converge anymore, and we make sense of these numbers through analytic continuation. To obtain this result, we construct linear combinations of the numbers L(f, i, z\_0 ) using a refined version of Siegel's lemma, and we apply to them a linear independence criterion generalizing the one used by Fischler. To check the assumptions of this criterion, we rely on an integral representation of the polylogarithm functions and on a ”Shidlovskii lemma”.

We prove that every complete, connected, noncompact Riemannian three-manifold without boundary with scalar curvature at least $6$ has conjugate radius at most $2\pi/3$. This resolves Shen's conjecture on the strict conjugate-radius bound $\operatorname{conj}(M,g)<\pi$ in dimension three.

Edge language-model agents must hold a persona and reason correctly at once, in one context window that fills with history and persona instructions. We study what happens to the logical part of such an agent when that history is long, misleading and persona-heavy (persona-logic interference), and present a Decoupling Architecture (AO-DA) that separates logical inference ("What") from persona expression ("How") into two inference paths on one INT4 base model with hot-swappable LoRA adapters. The logic path receives only the core turn and emits a verifiable structured state (Micro-State); the persona path renders it in character with the full history. In same-base-model ablations on an Apple M2 laptop (Llama-3.1-8B-Instruct and Gemma-3-4B-it, 4-bit; 480 runs: 2 bases x 4 pollution levels x 3 arms x 2 tasks x 2 personas x 5 seeds) we find: (i) the decoupled logic path is structurally invariant to pollution: its prompt stays at 180 (Llama) or 167 (Gemma) tokens while the mixed single-pass prompt grows from 242 to 1,203 on Llama, and its outputs are byte-identical across levels (40/40); (ii) the mixed single pass degrades monotonically (composite logic score 0.669 to 0.150 on Llama, 0.487 to 0.150 on Gemma), mostly by failing to emit the required structured output (80-95% of runs on Llama, 100% on Gemma at the two highest levels); (iii) with the same pollution fed into the logic path, the dedicated-adapter, dedicated-format path is still more robust than the single pass on the 8B model (failure 0-20% vs 25-95% at L2-L4; paired $\Delta$ +0.30 to +0.50, Cliff's $\delta$ 0.50-0.85, Holm-adjusted $p \le 0.03$) but not on the 4B model, where both collapse. Separation costs one extra decode on a topic's first turn (28.2 s vs 18.2 s on Llama) and buys persona hot-swapping in 1.7 ms (warm median) without re-running the logic path. Code, logic-path adapters, logs and analysis scripts are released.

We develop a sparse domination theory that captures both local polynomial approximation and cancellation of the input below the scale of each sparse cube. Its coefficients are percentiles of localized smooth maximal functions of the input minus its local polynomial approximation, combining features of mean-oscillation sparse bounds and of the cancellative sparse bounds of Conde-Alonso, Lorist and Rey. Using wavelet representations, we characterize the Calderón-Zygmund operators whose derivatives admit these bounds by explicit polynomial testing conditions. In the homogeneous setting, the same conditions characterize weighted Hardy-Sobolev inequalities with linear dependence on the $A_\infty$ characteristic. This quantitative dependence detects the transition from BMO to $L^\infty$ testing conditions that Lerner found for pointwise bounds by Riesz potentials, a distinction that qualitative weighted estimates cannot recover. In the inhomogeneous setting, we prove corresponding weighted inequalities and show that they are strictly weaker than pointwise sparse domination from the second derivative order onward. Consequences include Hardy-Sobolev estimates below the Banach range, sharp weighted Sobolev inequalities, and pointwise bounds by Riesz potentials.

Deep learning has made rapid advances in weather forecasting: autoregressive models trained on atmospheric reanalyses now rival dynamical models across nowcasting, medium-range, and subseasonal-to-seasonal lead times, producing well-calibrated ensemble forecasts at reduced cost. We review these advances and consider their extension to climate horizons, where the challenge shifts from initial-condition skill to producing reliable statistical responses under altered forcings. AI-powered climate prediction systems must produce credible forced responses to drivers (e.g., greenhouse gases, land-use change) typically outside the observed record. We propose two minimum requirements for AI in climate modeling: (i) external forcing agents must enter explicitly enough to support interventions in which they vary independently; and (ii) robustness must be stress-tested in out-of-distribution regimes, including extremes and counterfactual trajectories. Using leading AI autoregressive emulators and hybrid physics-AI models, we identify development and coupling challenges. Comparing the reported throughput of these models with that of GPU-ported dynamical models highlights how AI can reduce time-to-solution by advancing only the target variables at the required resolution and using longer time steps, rather than integrating a full high-frequency, multivariate state. Diverse AI downscaling strategies can partially substitute for explicit fine-scale resolution, paving the way toward inexpensive local hazard assessment across prediction horizons.

Large language models are increasingly contributing to mathematical research, where progress often depends on efficient proof search, incremental improvements and careful verification. We describe Bolzano, a multi-agent open-source system that uses parallel prover agents with a verifier agent and maintains a human-readable research state. Initial manual use on expert-selected problems yielded 8 results whose proofs were checked by domain experts. Motivated by these case studies, we ran Bolzano without problem-specific human guidance on about 3,800 open problems extracted from four sets of papers, solving about 200 open problems. One experiment used papers accepted to STOC 2026, a top conference in theoretical computer science. There, we answered four questions raised in the papers, as confirmed by their authors.

Mean field limits describe the training dynamics of wide neural networks through the evolution of the empirical distribution of their parameters. Although functional central limit theorems characterize the asymptotic fluctuations of this distribution, quantities of practical interest are typically nonlinear observables of the parameter distribution rather than the distribution itself. In this work, we show how these mean field fluctuations propagate to finite dimensional nonlinear observables for shallow neural networks trained by stochastic gradient descent. Working in the weighted Sobolev space in which the limiting fluctuation process is constructed, we apply a functional Delta method under ordinary Fréchet differentiability, without requiring Lions derivatives with respect to the measure variable. We obtain a central limit theorem for the observables and, under a suitable representation of their differentials, an explicit covariance formula inherited from the underlying mean field fluctuation theory. We also study whether prescribed quantities of interest can be recovered from the selected observations. Under a constant rank assumption, we prove that a quantity of interest factors locally through the observation functional if and only if, throughout a neighborhood, the kernel of the differential of the observation is contained in that of the quantity of interest. Thus, a differential condition expressed directly in the ambient Sobolev space yields an exact nonlinear local factorization. These results provide a framework both for quantifying finite-width uncertainty on observable, statistically or physically meaningful quantities and for assessing whether the chosen observations contain the information required to identify them.

The Polynomial Modular Number Systems (PMNS) aim to represent elements of fields or rings of large characteristics using polynomials satisfying bounds on some parameters (degree, absolute values of the coefficients). Those PMNS, while some conditions are fulfilled, using convenient parameters and implementation features, allow some speed-ups in cryptographic computations. Recent works (Meloni et al. \cite{MeloniPV25}) propose better speed-ups by improving the parameter generation of the system, and by using multi-precision polynomial coefficients, i.e. coefficients stored using several machine words. In this work, we first present PMNS schoolbook software implementation better in some context than the Toeplitz state-of-the-art counterpart of \cite{MeloniPV25}, taking advantage of smaller memory cost by being free to choose a smaller $n$ parameter, minimizing at the same time the complexity of the multiplication. This implementation for 4096 bit modulo size shows element size smaller by 11% and 20 % speed-up. We thus present a new improvement on the PMNS, applying to the internal reduction an approach similar to the truncated Montgomery reduction technique presented by Didier et al. in \cite{DidierEGR24}. In the context of software implementations using AVX512 instruction set extension, and modulo size up to 8192 bits, this new approach allows speed-ups up to 15% in modular multiplication computation, in comparison with conventional approaches.

The increasing diversity of high performance computing systems makes separate, architecture specific implementations of lattice gauge theory algorithms costly to maintain. We present kwqft, a performance portable Kokkos implementation of Wilson pure gauge Monte Carlo simulation for $\mathrm{SU}(N)$ Yang-Mills theory in an arbitrary number of space-time dimensions. The gauge group order $N$ and the dimension $D$ are compile time parameters. A single source targets the Serial, OpenMP, CUDA, HIP, and SYCL execution spaces, with MPI halo exchange overlapped with interior updates. The implementation reproduces the exact two-dimensional plaquette and published three and four dimensional values for gauge groups up to $\mathrm{SU}(17)$. On an NVIDIA A100 the Kokkos CUDA backend is competitive with a native CUDA code, SIMD acceleration improves the OpenMP path on Armv9 processors, and a large scale speedup is demonstrated for an $\mathrm{SU}(4)$ lattice on the LineShine supercomputer, currently ranked first on the TOP500 list.

This paper derives an equivalent formulation of the Costabel FEM-BEM coupling for the time-harmonic Maxwell transmission problem with a Lipschitz interface, and constructs a block-diagonal preconditioner for the resulting discrete system. The reformulated coupling is posed on a product of trace spaces and is obtained by introducing a trace lifting operator and the Steklov–Poincaré operator. At the algebraic level, it corresponds to eliminating the interior FEM unknowns, resulting in a discrete system that involves the Schur complement of the interior FEM block. Assuming that the frequency lies outside the resonance sets, we prove that the reformulated coupling is equivalent to the Costabel coupling at both the continuous and discrete levels. Using the operator preconditioning framework, we build a preconditioner from the Galerkin matrix induced by the Maxwell single layer boundary integral operator. The spectral condition number of the preconditioned matrix is shown to be uniformly bounded. Numerical experiments illustrate the practical effectiveness of the proposed approach.

Large Language Models (LLMs) can generate drone programs from natural-language mission descriptions, but syntactically valid programs may still violate user intent, environmental constraints, and mission-level behavior. This problem is pronounced in cyber-physical applications, where correctness depends on the interaction among generated code, mobile sensing, environmental geometry, event-driven analytics, and physical execution. Existing drone code-generation systems primarily use prompt guardrails or simulator outcomes and provide limited failure localization. We present AeroEval, an agent-assisted middleware for staged validation of AI-generated drone missions. AeroEval combines deterministic program analysis with context-grounded LLM agents. It first validates program syntax, platform API usage, and mission intent, and then evaluates the realized behavior using execution trajectories, mission requirements, and environmental context. Each stage returns structured failure information for iterative regeneration. In our evaluation using 20 navigation tasks and five analytical mission types over AirSim and Gazebo simulators, AeroEval improves navigation success from 55% to 95%. In a stagewise ablation study, our Code and Trajectory Validators by themselves achieve mean run-level success rates of 44% and 56%, respectively, while the full AeroEval pipeline achieves 88%; the stages detect complementary failures in program structure, API usage, mission intent, obstacle avoidance, altitude, coverage, and event-driven transitions and the guided regeneration corrects for them. Across the main analytics missions, AeroEval increases aggregate run-level success from 34% for one-shot AeroGen to 88% within the regeneration budget. These results demonstrate the benefit of combining program-level and execution-grounded agentic validation for AI-generated drone applications in the evaluated environment.

Offline reinforcement learning enables reward-driven policy improvement from fixed datasets without requiring online exploration, making it particularly attractive in safety-critical domains. A central challenge, however, is distribution shift: policy optimization may favor actions that are weakly supported by the offline data, rendering value estimates unreliable. Existing approaches primarily control this shift in the policy's own action space. In interactive environments such as autonomous driving, this can be insufficient: a candidate ego trajectory may remain well supported under the marginal behavior distribution while being poorly supported jointly with the surrounding-agent behavior observed in the logged interaction. We refer to this degradation in interaction support as interaction distribution shift (IDS), and introduce Interaction-Constrained Drive Policy (ICDP), an offline reinforcement learning framework that explicitly controls interaction-level distribution shift. Starting from the joint data distribution over ego and surrounding-agent futures, we show that joint-support degradation decomposes exactly into an ego-support component and a residual interaction-support component. We recover the latter through contrastive density-ratio estimation, isolating interaction compatibility without explicit joint-density modeling, surrounding-agent prediction, or rollouts in reactive simulators or learned world models during policy optimization. Closed-loop evaluations on nuPlan, Interplan and real-world truck experiments show that ICDP suppresses high-value yet interaction-unsupported trajectory selections and improves performance in interaction-critical driving scenarios. Project webpage: https://mahmoud-selim.github.io/ICDP/

In the analysis of multivariate data, factor models represent a powerful technique for both reducing dimensionality and facilitating qualitative understanding of the latent determinants governing the observed data. Interpretability, however, is often hindered by the non-identifiability of factor loading matrices due to rotational invariance. A prevailing strategy to address this issue is to consider positive lower triangular structures. A relaxation of the latter condition has been recently proposed in the literature with the so called generalized lower triangular structure. However, its Bayesian implementation presents substantial challenges, requiring complex reversible-jump algorithms and making prior elicitation difficult because of the limited interpretability of the model parameters. In this paper, we introduce a generalized lower triangular process prior that allows both global and within-component sparsity structures for learning both the number of factors and possible sparsity structures within the vector of observations. The proposed approach provides straightforward prior parameters elicitation exploiting possibly different prior information on the rank and sparsity characteristics. We also explore connections with the Indian buffet process, providing further insight into the sparsity structure induced by the proposed prior. Posterior computation can be performed resorting to a Gibbs sampler with Metropolis-Hastings moves. The efficacy of the proposed method is demonstrated through comprehensive simulations and the analysis of the Big Five Personality Test data.

Text-to-point-cloud localization estimates a position in a city-scale 3D map from descriptions of surrounding objects. Existing coarse-to-fine methods retrieve submaps using aggregate learned compatibility and then localize within a selected submap. However, repetitive or similar urban objects can inflate the embedding similarity between the query and multiple submaps, even when the instance layout within a submap violates the query description. Meanwhile, query-relevant instances often span submap boundaries, leaving the retrieved submap with incomplete contextual evidence. We term these failure modes layout-inconsistent aliasing and boundary evidence incompleteness, respectively. To address them, we propose PARC-Loc, a coarse-to-fine localization framework built on Partial Assignment with Relational Consistency (PARC). PARC jointly models hint-object compatibility and pairwise spatial relations, allowing unmatched elements while favoring assignments consistent with the queried layout. At the coarse stage, its candidate-level assessment complements neural similarity for layout-consistent submap selection. At the fine stage, the context is expanded with query-relevant instances from adjacent submaps, while PARC yields object-level matching weights that guide cross-modal attention. Extensive experiments on KITTI360Pose and CityLoc show that PARC-Loc outperforms conventional coarse-to-fine baselines. On KITTI360Pose, our method improves Top-1 localization recall at 5 m from 0.50 to 0.67, achieving a 34% relative gain over the strongest baseline.

Transformers have in-context learning capabilities, where some known learning algorithms can be executed in the forward pass through the model. Recent work shows that transformers can exactly perform Lloyd's algorithm for $k$-means clustering with $n$ points in $d$ dimensions with an embedding size $d_{\textsf{emb}} = d+k$ (thus, requiring attention projection matrices of size $(d+k)^2$). In this work, we build upon this result in the following ways: First, we present an equally expressive but smaller transformer that executes Lloyd's algorithm with embedding size $d_{\textsf{emb}} = (d + \lceil \log_2 k \rceil)$. Next, we train these transformers to learn the clustering algorithms given a distribution of clustering tasks, and theoretically characterize and empirically validate the factors affecting the convergence and in-distribution generalization of learning algorithms based on stochastic gradients. Finally, we probe the general clustering abilities of these learned algorithms (in the form of transformers), and try to understand situations where they succeed and fail.

Flow matching enables language generation in few steps, but whether additional integration steps improve reasoning remains unclear. We prove that a flow parameterized by a two-layer Transformer can solve graph reachability, with the required number of integration steps increasing with the target's distance from the root. Yet, standard flow language models can fail to benefit from additional steps on reasoning tasks. We attribute this limitation to objectives that supervise each time point independently, without explicitly training successive steps to build on one another. To address this, we instead train through the model's own latent rollout over a randomly sampled subinterval of [0, 1], decoding only at the endpoint. On ProsQA, this raises accuracy to 97% and enables performance to improve with additional integration steps. For the longer rollouts required by reasoning tasks such as Sudoku and Maze, retracting the latent state onto a sphere stabilizes the dynamics and yields substantial gains over baselines with more than three times as many parameters. Sampling multiple rollouts further improves performance when paired with a parameter-free selection score, although reliable selection remains challenging for longer answers. Together, these results establish a theoretical basis for reasoning with flows and show how rollout training, stable latent dynamics, and rollout selection help realize this capacity in practice.

We study two-variable first-order logic with a finite, input-dependent number of distinguished successor relations and arbitrary additional unary and binary predicates. Each distinguished relation must be the exact immediate-successor relation of some linear order on the common domain; the orders themselves are not available in the language and may have arbitrary order types. We prove that satisfiability belongs to 2NEXPTIME, uniformly in the number of successors. The proof gives finite certificates for possibly infinite models. A closure operation separates local neighbourhood descriptions, called star types, into those of bounded multiplicity and those that can be realized infinitely often. The bounded part is represented explicitly. Outside it, integer height vectors allow overlapping successor requirements to be matched without creating cycles or unintended identifications. Ordering the resulting path components densely then recovers exact successor relations. Consistent assignments of the additional binary predicates handle witnesses involving the bounded part. The same certificates decide infinite satisfiability in 2NEXPTIME and give a doubly exponential threshold above which a finite model guarantees an infinite model. A doubly exponentially large finite core can be forced with only two successors and unary predicates. For finite models, we prove that satisfiability subject to a bound on the total number of reference adjacencies lost by the other orders is NEXPTIME-complete, even when the budget is encoded in binary and the number of successors is part of the input.

Mid-prefill pruning can reduce the sequence processed by deeper transformer layers, but attention concentration alone does not certify that discarded context is dispensable. We formulate EntroPrefill as a Renyi-guided proposal mechanism coupled to explicit constraints on discarded attention mass. Sink-isolated, regularized head pooling respects grouped-query attention while exposing a quantitative trade-off between specialization and worst-head coverage. We derive a mixture-to-head deletion envelope, a computable upper bound on feasible token removal, and a finite-sample observer guarantee that remains valid when the pruning layer is selected adaptively. We then establish a conditional transformer perturbation bound with explicit sufficient Lipschitz constants and a first-token decision-margin corollary. A counterexample shows why shallow observations alone cannot imply an unconditional future-output guarantee. The systems analysis distinguishes query-head unions, physical page allocation, and KV-transfer payload, and gives an arithmetic break-even condition for pruning. This manuscript is theoretical in scope: it defines the procedure, its assumptions, and its formal limits, but does not report measured acceleration or task-accuracy preservation. Experiments are reserved for subsequent validation of the assumptions, approximation tightness, and end-to-end resource trade-offs.

Classical Arabic poetry generation requires simultaneously satisfying semantic, linguistic, and fine-grained prosodic constraints. Existing systems typically control broad poetic attributes but do not jointly model semantic intent, meter subform, and poem length. We present Shaer, a controllable Classical Arabic poetry generation framework jointly conditioned on natural-language descriptions, meter subforms, and target hemistich counts. To support this task, we construct an enriched corpus of 116,032 classical Arabic poems derived from Ashaar, containing normalized meter-subform labels and automatically generated, validated semantic descriptions. We then adapt Yehia-7B using QLoRA-based supervised fine-tuning with a completion-only objective. Our evaluation combines automatic assessment of base-meter conformity, requested-subform adherence, and length control with three LLM judges, blinded human evaluation, and memorization analysis. Shaer achieves 95.17% base-meter accuracy, 91.75% poem-level meter-subform accuracy, and 83.40% exact count accuracy. Relative to its untuned foundation model, these results represent gains of 68.68, 57.77, and 38.93 percentage points, respectively; Shaer also attains the highest base-meter accuracy among all evaluated systems. Multi-LLM evaluation and a blinded human assessment of top-ranked outputs further indicate competitive semantic and literary quality. Finally, analysis of all 3,481 test generations finds no exact copies from the training corpus or paired source poems. Code, models, and datasets are publicly available.

Watermarking diffusion-generated images requires balancing provenance signals with image quality, robustness, and computational cost. This work organizes methods along two axes: insertion mechanism and primary signal-bearing representation, and formalizes a representative $z_T$-Fourier pipeline for verification and identification. We then use the taxonomy to structure three protocol-bounded case studies. The first examines associations among frequency integrity, detection, quality, and cropping behavior. The second revisits persistence under seed-linked and seed-independent editing and formulates a scoped Semantic Imprinting Hypothesis without claiming a localized carrier or causal mechanism. The third studies single-shot VAE-latent phase modulation, including its efficiency, regeneration robustness, and robustness–quality operating points. Finally, we separate four content-level attack families from model/pipeline adaptation, propose corresponding evaluation protocols and testable conjectures for parameter-tuning threats, and identify additional temporal extensions for video. These analyses do not establish a universal ranking; instead, they provide a framework for matched, protocol-aware comparisons of watermarking systems for diffusion-generated images.

We construct Dirac-harmonic maps from closed spin tori whose map components are not harmonic. For a closed Riemannian surface as target, we prove that such solutions exist for every source metric and every spin structure whenever the target metric is nonflat. The maps can be chosen null-homotopic, of rank one everywhere, with nowhere-vanishing tension and unbounded energy. For a strictly negatively curved closed oriented target surface, every homotopy class contains such a sequence when the source has the trivial spin structure. For the other spin structures we give a compatibility condition for the same construction. Adding a harmonic circle component yields coupled immersions into the product of any such surface with a circle. The construction combines a spinor phase that cancels the rotation of a moving target frame with a curvature balance along a closed curve. Minimizing the energy of short loops with prescribed signed curvature area produces the required curves without any symmetry assumption on the target. Their total geodesic curvature determines the spinor's periodicity. We also give a curve criterion in arbitrary target dimension, applications to totally geodesic surfaces and warped products, and a local choice of target metric that works on every closed manifold of dimension at least two.

A nuclear recoil measures dark matter (DM) scattering on nucleons, but usually cannot reveal the nature of the halo DM. An interchange of the ground and excited states of the DM can preserve an inelastic recoil spectrum while changing ground-state annihilation by several orders of magnitude. Solar neutrinos can then provide information that nuclear recoils leave unresolved. Motivated by the high-energy LUX-ZEPLIN candidate, we investigate a possible way to resolve the composition of singlino-Higgsino DM in the next-to-minimal supersymmetric standard model (NMSSM) by using nuclear recoils and solar neutrinos. Our analysis identifies solar-compatible singlino ground states and Higgsino ground states with weak inelastic transitions, whereas Higgsino-pair inelastic LZ fits predict excessive solar signals. An elastic Higgsino scattering alternative can suppress solar capture by closing the inelastic transition. Recoil spectra, solar evolution and target complementarity can therefore probe distinct aspects of the singlino-Higgsino DM composition, with residual degeneracies set by annihilation, halo and detector assumptions.

In this paper we have developed a differentiable approximation of the well-known SEEPS score, which we name SoftSEEPS. This allows the training of a Machine Learning model to forecast precipitation directly. We test SoftSEEPS on the IMERG dataset (0.1 degree resolution) by training a decoder for precipitation on the latent space of a pre-trained low-resolution forecasting model. Combining SoftSEEPS and RMSE in a joint objective is possible with marginal trade-offs in either metric.

We study Standard Model Effective Field Theory (SMEFT) extensions in portal-mediated scattering processes from the perspective of quantum entanglement. Quantum information metrics maintain phase-sensitive spin and momentum correlations, whereas conventional collider and direct detection observables mainly depend on unpolarized cross-sections and event rates, which often suppress dimension-six interference terms or average over internal degrees of freedom. We assess linear and Von Neumann entropy fluctuations induced by higher-dimensional operator insertions by building final-state density matrices using helicity amplitudes. By avoiding conventional kinematic degeneracies, our formulation shows that entanglement measures capture interference contributions linearly in $1/\Lambda^2$, offering improved sensitivity to new physics scales. A theoretical framework for SMEFT Wilson coefficients is established by this information-theoretic method, creating new opportunities for accurate tests of fundamental interactions in high-energy and astroparticle physics.

This paper derives necessary optimality conditions for free end-time optimal control problems governed by sweeping process dynamics. In contrast to classical optimal control problems, the presence of the normal cone term in the state equation introduces discontinuities with respect to the state variable and prevents the standard Lipschitz regularity assumptions typically used in optimal control theory. As a result, both the analysis of trajectories and the formulation of optimality conditions require refined tools. We address problems with general endpoint constraints and time-dependent data, considering both the case in which the dynamics are Lipschitz continuous in time and the more challenging setting of merely measurable time dependence. Special attention is devoted to the additional transversality conditions associated with the free end-time variable. In the Lipschitz case, these conditions are expressed in terms of a function of bounded variation that coincides almost everywhere with the maximized Hamiltonian. In the measurable case, we show that a suitable interpretation can be obtained via the notions of sub- and super-essential values of the maximized Hamiltonian, recently introduced in the literature, leading to strengthened transversality conditions. These conditions also involve an additional term reflecting the interaction between the costate arc and the normal cone to the moving set at the optimal endpoints. Our approach combines suitable perturbation techniques with a penalization method tailored to sweeping processes. The moving set is modelled as a finite intersection of inequality-defined sets satisfying suitable constraint qualifications, including a positive linear independence condition and a diagonal dominance property of the associated Gramian matrix. We also introduce a local version of the constraint qualification condition. Our results apply to a broad class of problems, including those involving unbounded moving sets such as polyhedra. The resulting optimality system extends and sharpens recent results for classical free end-time problems to the non-Lipschitz, discontinuous framework of sweeping processes. The relevance of the transversality conditions obtained in this article is illustrated through two simple examples.

We present an automated method for reducing fault-tolerant circuits through fault-equivalent rewrites. Starting from a known fault-tolerant circuit, the search applies non-reducing enabling rules to expose Bell-pair reductions, each of which removes an ancilla preparation and a CNOT gate. Because every search transition preserves fault equivalence, the resulting circuits inherit the fault-tolerance properties of the input circuit. Candidate circuits are evaluated using circuit-level Monte Carlo simulation. For Shor-style syndrome extraction with the $[[7,1,3]]$ code, our method reduces one syndrome-measurement round from 30 to 18 ancilla preparations and from 54 to 42 CNOT gates. At a physical two-qubit error rate of $p = 10^{-3}$, the optimized circuit lowers the logical error rate by approximately 21% for both logical basis states. The reduction ranges from 13% to 23% over a range of $p$ spanning two orders of magnitude. We also apply the method to Steane-based dynamic syndrome extraction constructed from Goto's verified logical-$\lvert 0 \rangle$ preparation, in which the verification qubit serves as a flag. The search selects a circuit using four ancillas and 14 CNOT gates, matching the resource counts of the previous design but with an improved CNOT depth. Under depolarizing idle noise at $3p/10$ the selected circuit lowers the logical error rate by approximately 15% for both logical basis states, and by approximately 10% at $p/10$. These results demonstrate that automated fault-equivalent rewriting can identify circuits with lower resource costs or improved logical performance without separately verifying the fault tolerance of every candidate.

Cosmic birefringence, the rotation of the polarization plane of cosmic microwave background (CMB) photons, provides an intriguing probe of physics beyond the Standard Model. In this paper, we investigate a vector Chern-Simons coupling between the neutrino current and photons as a possible origin of isotropic cosmic birefringence. Firstly, we perform the first analysis of anisotropic cosmic birefringence induced by the neutrino current. We find that the anisotropic signal sourced by lepton-number isocurvature fluctuations can be important on large scales, whereas on small scales, the anisotropic signal induced by gravitational effects becomes dominant comparing with the axion-like particle (ALP) scenario. Secondly, we show that a large lepton asymmetry generated through the Affleck-Dine mechanism can successfully account for the observed isotropic birefringence, and discuss its possible connection to the recently reported low helium-4 abundances in Subaru EMPRESS and Atacama Cosmology Telescope (ACT).

Standard quantum mechanics takes the complex numbers as its scalar algebra. We ask whether this complex structure is algebraically fundamental or may instead form a distinguished embedded sector of a larger commutative and associative scalar algebra. Requiring the ordinary complex sector to remain intact while admitting an additional stable complex-like analytic sector turns the latter into a proper ideal, makes zero divisors unavoidable in finite dimension, and implies a lower bound of four real dimensions. The bicomplex algebra realizes this minimum, and under an additional compatibility assumption the four-dimensional realization is unique up to isomorphism. The resulting algebra exhibits two distinct decompositions: the canonical decomposition into orthogonal idempotent ideals and a decomposition adapted to the embedded complex sector and the additional ideal-valued sector. The ordinary complex scalars therefore lie diagonally across the canonical idempotent decomposition. The ideal sector supports Taylor series, oscillatory exponentials, Fourier-type kernels, and Schrödinger-type expressions, and carries a formal ideal-valued eigenvalue structure. Restricting the Born rule to the embedded complex sector recovers its standard form. Whether this dual scalar architecture has physical significance beyond the algebraic framework remains an open question.

Mental imagery, “seeing with the mind's eye” is an essential aspect of human cognition. Despite rapid progress Large Language Models (LLMs) and Vision Transformers (ViTs) still underperform on tasks requiring spatial understanding. To address this, we introduce Flow-of-Thought (FoT), a framework that integrates the generation of visual sketches as intermediate reasoning steps, mimicking mental imagery in humans. We train coordinate-aware trajectory flow fields on $SO(2)$ group orbits and cumulative shortest paths, then freeze the learned dynamics; same vs. different decisions compare competing generative hypotheses using foreground-weighted reconstruction energy. On locked tests FoT reaches 100.0% accuracy on Tetris and 99.0% on colored shapes. Under frozen transfer, the orbit-trained 2D flow improves over its endpoint-only control on BLINK Multi-view (72.2% vs. 63.9% on 133 public validation pairs), supporting continuous visual traces as an effective and interpretable representation for spatial reasoning in some out-of-distribution settings.