Papers

A program for fluctuating kinetic theory is proposed in this paper to study nonlinear Lévy-type fluctuation corrections to kinetic PDEs in a unified way. The Vlasov–Fokker–Planck (VFP), Landau, and Boltzmann equations can each be decomposed into a kinetic transport term and a generalized gradient structure generated by a nonlinear dual pair of dissipation potentials. Going beyond the linear Onsager structure and the classical fluctuation–dissipation relation, we propose a new nonlinear Lévy-type fluctuation–dissipation relation that identifies the thermal fluctuations associated with this generalized gradient structure. On a regular tilted class, the canonical action of the generalized gradient structure agrees with the Freidlin–Wentzell-type action predicted by the resulting SPDE. This consistency gives thermodynamic support for the new nonlinear fluctuation–dissipation relation and leads to a master fluctuating kinetic equation. We further establish a sufficient condition on the nonlinear dual dissipation potential under which its centered cumulant admits a Lévy–Khintchine representation, and show that the resulting Lévy current can be realized through Gaussian white noise and a compensated Poisson random measure. As an application of this framework, an \(\alpha\)-stable Lévy-type Dean-Kawasaki equation is derived. Furthermore, by rescaling the fluctuating Boltzmann equation under a distinguished relation between the noise intensity and the hydrodynamic scaling parameter, we prove that its Hamiltonian converges to the Hamiltonian of the Landau–Lifshitz–Navier–Stokes equations. This reveals a scaling relation between kinetic fluctuations and fluctuating hydrodynamics.

Frontier large language models (LLMs) can generate heuristic functions that guide search to achieve state-of-the-art performance in satisficing planning, where any plan is acceptable. However, these heuristics are not guaranteed to be admissible and can lead to suboptimal plans. We introduce LeanPlan, the first planning system that finds optimal plans with LLM-generated heuristics whose admissibility is machine-checked. Given a domain description and training tasks, an agentic loop uses planner feedback to iteratively improve a reusable domain-specific heuristic, its admissibility proof and the required domain assumptions. LeanPlan implements the heuristic, its proof and an efficient planner with machine-checked grounding and search in Lean 4. We evaluate LeanPlan on ten domains from the International Planning Competition and three new domains, using test tasks with up to 57 times as many objects as the training tasks. With GPT-5.6 Sol in the agentic loop, we successfully generate heuristics and admissibility proofs for all these domains. With the resulting heuristics, LeanPlan usually expands fewer states than the state-of-the-art Scorpion planner and solves more tasks overall.

Existing research on user fairness in recommender systems has developed diverse objectives. However, it has paid limited attention to a distinct distributive perspective: whether users' contributions to model learning should be reflected in the recommendation benefits they receive. We argue that, in addition to existing fairness protections, a fair system may account for the alignment between users' estimated contributions and the recommendation performance they receive. Such alignment can incentivize sustained and informative engagement, thereby supporting a sustainable recommendation ecosystem. To this end, we propose Contribution-Performance Fairness, a novel fairness perspective which requires recommendation performance to be aligned with estimated contribution across user groups and to remain equitable among users with comparable contributions within a same group. To instantiate this perspective, we introduce the Contribution-Performance Fair Recommender (CPFR), a framework applicable to different backbone recommenders. CPFR constructs ordered user groups from a training-dependent contribution considering interaction volume, loss alignment, and optimization intensity, and jointly optimizes recommendation accuracy with the two fairness requirements. A game-theoretic analysis shows that such alignment can strengthen contribution incentives and improve system-level recommendation accuracy under voluntary contribution. Experiments on three datasets and three backbone models demonstrate that CPFR achieves a strong accuracy–fairness trade-off under the proposed operational metric.

Sensors are useful not only for understanding the world but also for deciding what to do next. Existing sensor models however largely stop at perception: they recognize states or predict outcomes, leaving actions modeled separately through task-specific and often closed label spaces. We introduce Sensor-Language-Action (SLA) modeling, a framework that connects multimodal sensor observations, natural language, and actions within a unified model. SLA uses language as a semantic interface between sensing and acting, allowing heterogeneous actions to be represented, predicted, and explained while remaining grounded in the underlying sensor evidence. We build a large-scale SLA benchmark consisting of datasets that span more than 116,000 individuals, 79 sensor modalities, and 60 action groups, together with a multi-faceted captioning pipeline that aligns user context, sensor dynamics, and action evidence. Building on this framework, we present OpenSLA, a unified SLA model for hierarchical action prediction, state understanding, and action explanation. Extensive experiments on real-world tasks in clinical prediction, operating rooms, and metabolic health verify its superior performance over the state-of-the-art. OpenSLA also demonstrates intriguing capabilities including language-guided evidence grounding and zero-shot generalization to unseen actions and cohorts.

We study the Iwahori Gaiotto conjecture for cotangent types and its application to the representation theory of the (mixed, small, and Lusztig) quantum supergroups. Using local and global models and SW-Zastava spaces, we construct factorization functors and compare the Iwahori Gaiotto category with the category $O$ of the mixed quantum supergroup. We then study the images of intersection cohomology sheaves and the metaplectic Hecke action. In type A, we describe the finite and affine monodromic categories, the corresponding Yokonuma–Hecke actions, and their role in the Kazhdan–Lusztig algorithm. The last section treats the pointwise purity.

HOMFLY-PT polynomials describe analytic continuation of Wilson averages in Chern-Simons theory to arbitrary complex values of two independent parameters $q$ and $A$. They also depend on the knot and representation of the gauge group. However, when $q^2$ is a primitive $m$-th root of unity, e.g. $q=\pm e^{i\pi/m}$, these polynomials exhibit a universal (knot-independent) factorization: $H_R$ becomes the product of the polynomials for the $m$-core of the Young diagram $R$ and of one and the same factor $H_{[m]}$ for every $m$-ribbon of $R$. In all the examples which we computed this factor is just the special polynomial at $A^m$. At $q=\pm1$ factorization follows from the singularity of the cabled HOMFLY, which is the same for all representations. At $m>1$ the relevant singularity is in the projector, and what survives of it is a finite sum of braids $X_m$ – the $m$-th power sum inside the cable, which can be freely moved through the other strands. For the proof we use the Murnaghan-Nakayama rule and the Adams operation. Discovery of this hidden structure explains the old factorization puzzle.

Non-classical dynamics in open quantum systems can be hidden in temporal correlations that are invisible to standard state- and channel-based tests. We define coherence for multi-time quantum processes and show that access to intermediate times can reveal coherence absent from all corresponding pairwise channels. Incoherent processes are fixed points of dephasing on all input and output spaces, and their coherence is quantified by relative entropy. As a proof of principle, we use an Ising model in which all three pairwise channels are incoherent while the full three-time process remains coherent. We observe this multi-time coherence on a superconducting quantum processor using a coherence witness and full process tomography.

Large Language Models (LLMs) are widely used to generate code. Although their functional plausibility keeps improving, the generated code often contains security vulnerabilities. The functionality-security gap captures code that passes functional tests but fails security tests. A recent longitudinal study of three model families concluded that LLMs become smarter but not safer, with the only considered open-weight family stagnating. Whether this holds for other (open-weight) families and particularly for compact models remains open. We present a longitudinal study of the gap across 32 LLMs from seven model families (five open-weight), covering three successive releases per family in flagship and compact variants. Using CWEval with 119 tasks in five programming languages and 31 CWEs, we compare trajectories across families, model sizes, and languages. Newer models do become safer in absolute terms, although no family closes the gap. Unlike prior work, we find that openness does not separate the families: every considered open-weight family narrows the gap significantly, while Gemini 3.1 Pro keeps a gap as wide as the one reported for Llama. Compact models usually produce less secure code than their flagship counterparts, with notable exceptions (e.g., Gemini 3.7 Flash). At the CWE level, we confirm persistent weaknesses such as log injection (CWE-117) and HTTP response splitting (CWE-113) and regressions in the newest proprietary models on memory and integer weaknesses, and show that the same CWE carries very different risk across languages. From these results, we derive implications for LLM vendors, researchers, and developers. In particular, developers should assume neither that upgrades improve security nor that proprietary models are more secure; they should rerun security checks after each model change and provide secure APIs in the model's context.

We show that linear-growth-rate heterogeneity combined with complex global coupling can generate quasiperiodicity and chaos in a finite population of Stuart-Landau oscillators with identical natural frequencies and no Kerr-type nonlinear frequency shift. Lyapunov spectra identify limit cycles, quasiperiodic tori, and chaotic attractors, while the order-parameter amplitude exhibits signatures consistent with period-doubling-like transitions towards chaos. We further derive a finite-size invariant manifold of vanishing-order-parameter phase-locked solutions represented by closed polygons with fixed side lengths and demonstrate their configuration-dependent transverse stability. Ensemble sampling reveals pronounced coexistence among polygonal and ordinary phase-locked cycles, quasiperiodic tori, and chaotic attractors. An amplitude-time rescaling identifies the leading parameter approximately organizing the regime boundaries and the similar bifurcation and multistability patterns. These results advance our understanding of collective dynamics in amplitude-inclusive oscillator networks by revealing how heterogeneity and complex coupling jointly shape dynamical complexity, bifurcation structure, and multistability.

Awkward Array is a widely used library in high-energy physics (HEP) for representing and manipulating nested, variable-length data in Python. Previous CHEP contributions have explored GPU acceleration for Awkward Array, demonstrating the feasibility and performance benefits of CUDA-based backend while also identifying limitations related to irregular data access, fine-grained kernel launches, and composability of operations. In this contribution, we present recent developments that build directly on these earlier efforts by introducing a CUDA execution model for Awkward Array based on the Python CUDA Core Compute Libraries (CCCL). Using CCCL, we eliminate the need for custom CUDA kernels and can instead use a high-level Python interface. The CCCL-based approach also enables fusion of multiple Awkward operations into a reduced number of CUDA kernels, addressing kernel launch overhead observed in earlier GPU implementations. Lazy execution allows expression graphs to be constructed and optimized prior to kernel generation, improving performance for analysis workflows involving jagged arrays, combinatorial operations, and reductions. In contrast to earlier approaches, this design also emphasizes extensibility, allowing user-defined Python code to be incorporated into GPU execution paths with minimal boilerplate and without breaking existing analysis semantics. We present performance studies that demonstrate improvements over previously reported eager GPU execution strategies for representative HEP analysis patterns. These developments extend the GPU capabilities of Awkward Array toward a more composable and sustainable backend, aligned with the needs of Python-based analysis at the HL-LHC and beyond.

We prove that for every prime power $q$ and every integer $r\geq 3$ there exists a maximum $2$-scattered $\mathbb{F}_q$-subspace of $V(r,q^6)$, that is, a $2r$-dimensional $\mathbb{F}_q$-subspace meeting every $2$-dimensional $\mathbb{F}_{q^6}$-subspace in dimension at most $2$. Since an example in dimension three is known and direct sums preserve the property, it suffices to treat $r=4$ and $r=5$. For $r=4$ we study the subspaces $U_b=\{(x,x^q+bx^{q^5}):\mathrm{Tr}_{q^{12}/q^4}(x)=0\}$ of $\mathbb{F}_{q^{12}}^2$, $b\in\mathbb{F}_{q^{12}}$. We describe the parameters $b$ for which $U_b$ is not maximum $2$-scattered in terms of trace conditions and Dickson determinants, and deduce that at least $\frac{1}{2}q^{12}-q^{11}+O(q^{10})$ parameters work; this number is positive for $q\geq 3$, and a computer search settles $q=2$. For every $r\geq 5$ coprime to $6$ we show that $U_s=\{x+\varepsilon s\,x^{q^r}:x\in\mathbb{F}_{q^{2r}}\}\subseteq\mathbb{F}_{q^{6r}}$ is maximum $2$-scattered for all $\varepsilon\in\mathbb{F}_{q^6}\setminus\mathbb{F}_{q^2}$ and $s\in\mathbb{F}_{q^r}\setminus\mathbb{F}_q$. Consequently, $\mathbb{F}_{q^6}$-linear $[2r,r,4]_{q^6/q}$ MRD codes exist for every $r\geq 3$; for $r$ coprime to $6$, the codes obtained from $U_s$ are equivalent to their duals.

We review the notion of representing music using point sets and argue that such representations are better adapted than sequential representations for matching patterns in unvoiced, polyphonic music, such as keyboard music. Musical transformations such as transposition, inversion, diminution, augmentation and retrograde can be modelled by geometric transformations in pitch-time representations that combine translation with scaling parallel to and reflection in the time axis. We identify eight types of geometric pitch-time representation that use chromatic pitch, morphetic pitch, morph or chroma to represent pitch and either onset time or midtime to represent time. We illustrate how these types of representation allow us to characterise different types of musical transformation. For example, by using midtime instead of onset time, we can precisely characterise certain retrograde relationships; and by using morph and chroma pitch representations we can characterise transformations involving octave displacements and duplications. We present the concept of a transformation class and consider the three specific classes, $F_{\mathrm{2STR}}$, $F_{\mathrm{2STRMod7}}$ and $F_{\mathrm{2STRMod12}}$. We introduce the notion of an inter-pattern transformation graph for a set of patterns, $S$, and a transformation class, $F$. Each vertex in such a graph represents a pattern in $S$ and there is an edge in the graph from pattern $P_1$ to pattern $P_2$ if and only if $P_1$ can be mapped onto $P_2$ by a transformation in $F$. We show, with the aid of such graphs, that the musical relationships between the occurrences of the HAYDN theme in Ravel's Menuet sur le nom d'Haydn can be precisely described in terms of transformations in $F_{\mathrm{2STR}}$, $F_{\mathrm{2STRMod7}}$ and $F_{\mathrm{2STRMod12}}$ within the pitch-time representations considered.

We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.

Conventional compressed sensing (CS) has a measurement lower bound of M = {\Omega}(K log(N/K)) under non-adaptive measurements. Recent experiments on quantum compressed sensing (QCS) have reported numbers of measurements below this classical lower bound. In this work, we establish lower bounds on the measurement complexity of QCS from an information-theoretic and quantum-physical perspective. QCS exploits quantum parallelism, enabling a unitary domain-alignment evolution to act on a superposition of all N basis states and map the sparse basis onto the measurement basis in a one-to-one manner. Consequently, the locations of nonzero components are explicitly carried by measurement-index labels. If only basic statistical information about the K nonzero components is required, the total number of effective index samples satisfies the coarse necessary condition Ms = {\Omega}(K). Under independent single-index projective measurements, when the support is unknown, the nonzero probabilities satisfy pn = {\Theta}(1/K), and exact support recovery is required with a fixed success probability, the sampling-coverage requirement leads to Ms = {\Theta}(K ln K). If each nonzero amplitude coefficient is further required to achieve a coordinate-wise relative root-mean-square error {\epsilon}, the optimal effective index sample complexity is Ms = {\Theta}(K ln K + K/{\epsilon}2), which reduces to {\Theta}(K ln K) for fixed {\epsilon}. Multimode photon-number-resolving detection can reduce the number of experimental rounds but not the total effective index sample complexity. These results show that quantum parallelism is not only a core resource for quantum computing but can also play a transformative role in measurement science.

In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on $\mathbb{C}^n$ and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.

Since the early adoption of e-commerce, travel and tourism has been a lab for the design of recommender systems: tools that help travelers choose destinations, flights, accommodations, and combine them into itineraries. Data-driven recommendation techniques, ranging from case-based reasoning to reinforcement learning, have been adapted to travelers' needs. The research community has produced multifaceted prototypes of travel and tourism recommender systems (TTRSs), which are context-dependent, multistakeholder-oriented, and more recently, addressing sustainability issues, such as overtourism. Despite this enduring work, TTRSs are not widespread yet. We argue that three limitations can explain this: outdated and sparse data sets used to train and validate TTRSs, algorithms that prioritize prediction accuracy over domain-specific dimensions such as novelty and contextual relevance, and a failure to address the specific needs of travelers. Targeted incremental research could address these limitations, but a disruptive factor has meanwhile entered the ecosystem of tourism information and commercialization platforms: generative artificial intelligence. According to market research, GenAI applications are becoming the primary entry point for travelers planning their trips. This forces research to rethink how TTRSs should be designed and which core techniques should be integrated. We claim that future TTRSs, in addition to offering personalized information filtering, should become more flexible advisors that support decision making, integrating multiple data types and AI techniques, from data mining to natural language processing. Moreover, they must transparently balance the conflicting goals of travelers, service suppliers, platform owners, and local communities. We then outline research targets for building more effective TTRSs, fruitfully combining old and new recommendation techniques.

NVFP4 is an attractive datatype for large language model (LLM) inference, offering compact storage and native tensor-core acceleration. However, preserving accuracy using NVFP4 requires careful quantization. In this work we develop a novel quantization scheme called Optimized Smoothing and Scaling for NVFP4 (OSFP4). For each linear projection it uses a diagonal smoothing matrix whose entries are optimized to minimize the squared matrix-product quantization error under NVFP4, taking into account the rounding procedure that is used (either round-to-nearest, or GPTQ-style successive interference cancellation). This requires performing joint optimization on the smoothing entries as well as the block scales, which is facilitated by analyzing a multiplicative-dither FP4 quantizer instead of the fixed deterministic one. Experiments show that OSFP4 achieves the highest average accuracy among the evaluated competitors in the corresponding quantization settings, while retaining approximately 94-97% of vendor NVFP4 prefill throughput on the measured workloads. Our code is available in https://github.com/neriahbd/OSFP4

As video capture moves to handheld and edge devices, motion blur from camera shake has become a pervasive degradation that lowers perceptual quality and harms downstream vision tasks. The strongest deblurring networks recover impressive detail, yet they remain computationally heavy and overwhelmingly complex, so their quality comes at a cost that consumer hardware cannot pay in real time. This gap between restoration quality and on-device speed is exactly what makes real-time deblurring difficult. We developed and implemented TSRN-RTVD, an efficient video deblurring system that explicitly reconstructs the underlying camera trajectory during exposure and uses the recovered motion to guide restoration. This approach turns the physical cause of blur into a signal that drives sharpening. Our system runs on a single consumer GPU and restores the video at 30 FPS while reaching 30.08 dB PSNR on the GoPro dataset. We demonstrate TSRN-RTVD on consumer devices with interactive side-by-side visualization of the blurry input and the deblurred output, live throughput, and an on-screen view of the recovered camera trajectory. Demo video is available at https://youtu.be/3alMwVrVALU.

Contextual priors improve neural-to-language decoding by reshaping candidate scores. However, confidence is read from the same reshaped scores, so the errors a prior leaves behind can become more confident with no change in accuracy to reveal it. We study how a prior shapes confidence in speech retrieval on MEG-MASC and MOUS using local decoding scores, a contextual prior combined by additive shallow fusion, and the fused top-two margin as confidence. Among initially incorrect predictions, we find a confidence-ordering reversal: a larger margin makes a repair more likely when the correct candidate starts near the top of the local ranking, but less likely when it starts lower. On MEG-MASC, pooled correctness AUROC is 0.87, yet AUROC separating repairs from residual errors falls from 0.70 at initial ranks 2-3 to 0.39 at ranks 21-50. Errors starting beyond rank 20, inside the reversed region, make up 46.6% of all post-fusion errors. We propose a score-level account: a repair must first close the correct candidate's initial deficit, limiting its final margin, whereas a residual error can build a large margin between two incorrect candidates. A causal intervention that changes only the fusion weight moves the reversal to deeper ranks as predicted. Under a word-level LM prior, it keeps moving after accuracy gain peaks, so a weight chosen for accuracy does not settle confidence. Reading local and prior scores separately improves selective decoding: the decoder answers on 74.5% of windows instead of 56.7%, while 92% of output sets still contain the correct candidate. Confidence after contextual fusion should retain the local and contextual evidence behind each prediction, not just the fused scores. Project website: https://confidencereversal.github.io/; Code: https://github.com/AmadeusFake/NeuDecodingConfReversal

Nonlinear neural networks develop structured internal representations, yet how their geometry is determined by the tasks being learned remains poorly understood. Here, we develop an analytical framework for piecewise-linear feedforward and recurrent networks that links learning, activation-region structure, and neural selectivity. We show that, at any stationary point of gradient-aligned learning, a nonlinear network decomposes into local linear regressions over its activation regions. Deviations from the corresponding least-squares solutions are jointly constrained by network weights shared across regions and vanish in the low-error regime, yielding an approximate piecewise least-squares decomposition of the task. This structure admits a decision-tree interpretation, which we recover numerically by fitting trees to predict network activation patterns from the input. We further derive how the regions in which neurons are active determine the task statistics they capture, thereby organizing neural selectivity into distinct subpopulations. The resulting predictions closely match the selectivity geometry observed in simulated networks and two empirical neural datasets. Finally, we show that neural baseline regulates activation pattern diversity, placing networks along a continuum between coarse, generalizing representations and fine-grained, expressive representations. Together, these results establish activation regions as a unifying framework for describing how nonlinear networks decompose task structure into local computations and how those computations can be revealed through neural activity.

Machine learning classifiers for remote sensing imagery are typically evaluated as though every pixel were an independent sample. Spatial autocorrelation violates this assumption, since neighboring pixels carry redundant information which inflates sample sizes. How many independent samples does a satellite image actually contain? For an $n \times n$ image whose spatial correlation persists over a range of $r$ pixels, the effective sample size is $\Theta(n^2/r^2)$, not $n^2$. We prove this as a finite-sample upper bound for classifiers on spatially correlated data, and show via a matching lower bound that the rate is tight, and no algorithm can do better. We extend the results to images with directional correlation and spatially varying correlation structure. Our result justifies spatial cross-validation since block holdout with separation proportional to the correlation range achieves optimal generalization guarantees, while random holdout can underestimate confidence interval widths by a factor proportional to $r$. We validate the theory on synthetic data and satellite image tiles from three sensors (Landsat 8, Sentinel-2, and Sentinel-1).

We show that any integral cubic form in ten or more variables has a nontrivial integer zero. Like earlier authors on this topic, we use geometric methods to produce a zero in some cases, and the circle method in all other cases. New ingredients are required on both fronts: in the first case, bounds on the dimension of singular loci and incidence varieties, and in the second case, a stratified geometric sieve, together with stratification results for point counts over finite fields and a cube-root Hensel lifting analysis.

In this work, we introduce Crazyflow, an accurate, differentiable simulator built on JAX. By leveraging jit compilation via XLA, Crazyflow unifies physics and control into a single differentiable computation graph, enabling massive parallelization on accelerated hardware without sacrificing modeling accuracy. This architecture achieves order-of-magnitude speedups over existing baselines, capable of training deployable reinforcement learning agents in seconds. To highlight its highly modular design, we demonstrate how easily Crazyflow can be extended by integrating a complete, high-fidelity Ultra-Wideband (UWB) and Inertial Measurement Unit (IMU) simulation pipeline coupled with a full-state Extended Kalman Filter (EKF). This capability allows for massive parallel controller evaluation under realistic, degraded state feedback with minimal impact on GPU throughput. By combining speed, accuracy, and extensibility, Crazyflow serves as a foundational tool for the next generation of aerial robotics research.

We consider a Bardeen black hole (BBH) with variable mass and magnetic charge within the framework of an extended model of gravity and electrodynamics, where the boundary terms in the varied action are treated as geometric quantum fluctuations of spacetime. We propose that the extended Riemann manifold is generated by a new connection, $\hat{\delta\Gamma}^{\mu}_{\alpha\beta}$. These connection components contain geometric information regarding both gravitational and electromagnetic fluctuations on the background curved metric described by a Riemann manifold. Furthermore, we calculate the expectation values for the magnetic field components using a nonlinear and non-commutative quantum algebra for the gravitational and electromagnetic potentials. Our results are consistent with a radiating massive magnetic monopole that produces a radial component of the magnetic field confined to distances $r<\sqrt{3/\lambda_0}$, which are restricted by the vacuum energy density. The field $\hat{A}^{\mu}$ describes massive photons found in the vicinity of a BBH, forming a gravito-electromagnetic structure analogous to that of an atom, which could be a candidate for dark matter in the early universe.

Dispersion is a key limiting factor in ultrafast systems as it modifies the temporal structure of ultrashort optical pulses. Conventional dispersion compensation techniques, though widely used, rely on a combination of several bulky optical components and complex, long propagation paths, posing challenges for integration into compact photonic platforms. All-dielectric resonant metasurfaces operating in the Huygens' regime of spectrally overlapping electric and magnetic dipolar resonances offer a promising route to low-loss dispersion control at the sub-wavelength scale; however, the achievable dispersion from a single layer remains fundamentally limited by its phase gradient and spectral bandwidth. Here, we experimentally demonstrate in-line dispersion control of femtosecond laser pulses using a multilayer architecture of dielectric Huygens' metasurfaces, without requiring spatial separation of their spectral components, as typically employed in Fourier-plane dispersion compensation schemes. The phase dispersion accumulates across stacked layers approaching a total of 8pi, corresponding to a maximum group delay dispersion of around 3969 fs2. This enables efficient compensation of the input chirp and results in a significant compression of femtosecond laser pulses in the telecom wavelength range. Importantly, the metasurface stack functions as a single compact transmissive element, which is simply inserted into the beam path. Overall, our results establish a compact, scalable platform for integrated pulse compression and ultrafast dispersion engineering.

The mean exit time of a Brownian motion from a tube around a closed, minimal embedded \(n\)-dimen\-sional submanifold of the \((n+m)\)-dimen\-sional sphere is studied, establishing two-sided bounds via radial transplant. In accordance with known results when \(n = 0\) or \(m = 1,\) the mean exit time goes to infinity as \(n \to \infty\) and to \(0\) as \(m \to \infty.\) Simultaneously, bounds for the volume of such tubes are derived and compared to Weyl's tube formula.

In this study, we address the seemingly open question of disparity between the experimentally and theoretically observed Raman spectra for the altermagnetic $\alpha$-MnTe. We establish that the consideration of long range (LR) dipole-dipole interaction is crucial to accurately estimate the phonon band structure and thereby capturing each of the experimentally observed Raman signatures. The LR correction brings about substantial changes to the high-frequency optical modes and their group-theoretical representations. Specifically, for the highly debated Raman peak around 175 cm$^{-1}$, alongside the Raman silent B$_{1u}$ mode, the LR corrections introduce Raman-active longitudinal optical A$^{\prime}$ and A$_1$, and transverse optical A$_1$ modes. Overall, the calculated Raman spectra suggest that the intensity of these modes is weak in the pristine system, while certain prescribed distortions can increase their intensity. The Raman peak around 140 cm$^{-1}$, as observed experimentally, is identified to be emerging from a higher-order Raman process due to zone off-center contributions, while the other debated 120 cm$^{-1}$ peak has both the zone center and off-center contributions.

Portable mobile-manipulation demonstrations can help alleviate data scarcity for embodied intelligence, but obtaining reliable, low-cost, and robot-free motion supervision from RGB observations remains challenging. Existing approaches often rely on teleoperation or specialized devices equipped with additional sensing hardware, while directly using estimated visual odometry (VO) trajectories can introduce inconsistencies due to accumulated drift and imperfect motion supervision. We present the Visual-Odometry-Conditioned Mobile Manipulation Interface (VOMMI), a portable demonstration collection and learning framework that connects portable RGB demonstrations to vision-language-action (VLA) post-training through offline trajectory reconstruction and online visual-motion conditioning. VOMMI synchronizes body and hand views to capture navigation context and local object interactions without requiring human-robot kinematic correspondence calibration. R2-VO refines offline demonstration trajectories using sparse geometric anchors and produces causal local-motion tokens over multiple prediction horizons for online policy conditioning. An action-group residual adapter incorporates these tokens only into the base branch. Experiments use a 500-trajectory portable for each task, with 75 trajectories held out for RGB-VO evaluation, and 200 robot demonstrations as references. Our policy, post-trained only on portable demonstrations, achieves 18.2% lower base-velocity error than a policy trained with robot-collected demonstrations, while maintaining comparable end-effector translation accuracy. Offline reconstruction reduces absolute trajectory errors for the body and hand streams by 24.6% on average relative to the best evaluated baseline for each stream. The complete system improves the mean success rate by 8.3 percentage points over OpenPI 0.5 across three real-robot tasks.

Quantum automated learning (QAL) trains quantum models by directly updating quantum states, offering an approach to quantum machine learning that avoids optimizing variational circuit parameters. However, post-selection constrains the probability of obtaining the final learned model. We develop a post-selection-free QAL algorithm that organizes a complete training path into a coherent quantum circuit and uses fixed-point amplitude amplification to increase the probability of obtaining the learned model. We provide theoretical guarantees on output error and learning loss, and identify conditions under which additional coherent resources reduce the cost of restarting failed trajectories. The construction gives QAL a coherent implementation with explicit learning guarantees and resource costs, enabling a model with certified learning quality and controlled output error to be obtained with high probability.

We study the truncation $(-)^{\leq0}$ of dg categories. We first show that given a dg category $\mathscr{C}$ with shifts, for example a pretriangulated dg category, the canonical functor $\mathscr{C}^{\leq0}\to\mathscr{C}$ is a localization whose kernel is compactly generated by the $0$-th cohomology. Next we demonstrate that the derived category of the truncation serves as a triangulated analogue of the Auslander's category of coherent functors over abelian categories. We give a description of the Auslander-Reiten-Serre duality in terms of the inverse dualizing bimodule of the truncation. Building on truncations, we introduce the notion of connective resolutions of dg categories, defined as a localization functor from a connective dg category. This notion encompasses non-commutative resolutions of algebras in module categories, cluster tilting objects in triangulated categories, and also the truncation as the universal connective resolution. We give a sufficient condition for an object in a triangulated category to give a connective resolution of its enhancement in terms of finiteness of resolution dimension. Furthermore, we show that every proper dg module over a connective dg algebra is a direct summand of a dg module giving a connective resolution. Consequently, for every proper connective dg algebra, its bounded dg derived category has a connective resolution. Finally, we give some explicit description of the truncation for some categories including the derived and cluster categories of a Dynkin quiver, and the Yoneda category of a finite dimensional algebra.