Papers

Cultural upheavals impact many aspects of social life, and many studies have investigated their impact on language patterns. However, few investigations have isolated the impact of upheavals on individuals at scale in popular media. The current work evaluated millions of song lyrics spanning more than a century in search of within-artist and between-artist signals of distress from the Vietnam War, the terrorist attacks of 9/11, and COVID-19. Compared to a five-year baseline, rates of self-references - a marker of psychological distancing - were significantly reduced after the Vietnam War and September 11th. Cognitive processing terms were elevated post-upheaval vs. pre-upheaval, which indicated artists' increased attempts to make meaning from such massive disruptions. Content patterns corroborated these findings as artists wrote more about "life and freedom" (societal conditions) and less about "courtship and nightlife" (interpersonal connection) following the upheavals. Cultural upheavals modify individual and collective verbal behavior, demonstrating their far-reaching impact on society.

We study divergence-form elliptic equations with Dini coefficients, extending the frameworks of \cite{NV} for Lipschitz coefficients and \cite{HJ1} for Hölder coefficients. We first establish an almost monotonicity property for the doubling index under merely continuous coefficients. This leads to weak volume estimates for critical sets and uniform volume estimates for nodal sets. The Dini assumption is essential here since we construct an example with continuous coefficients and bounded doubling index whose nodal set has infinite measure. We also prove polynomial growth estimates for sub-level sets. Using a different approach, we establish quantitative uniqueness of tangent maps and a cone-splitting principle, which yield explicit Minkowski-type estimates for critical sets. Finally, combined with the results of Kenig–Zhao \cite{KZ4}, our estimates give measure bounds for boundary critical sets.

Medical AI models hold immense potential to improve patient outcomes, but they are also known to unintentionally memorise individual records from their training datasets. While such memorisation has been linked to targeted privacy attacks, its consequences for clinical deployment, where patients may be assessed by a model that saw their historical data during training, remain poorly understood. Here we show that predictions on a patient's unseen future data can change significantly if a model observed that same patient's anonymised historical data during training, a phenomenon we term "memorisation bias". We demonstrate that this bias exists across diverse data modalities and model architectures, and over prolonged time spans: in some cases, memorisation bias persists on future records acquired decades after the historical records used for training. Moreover, in simulated prospective deployment, memorisation bias has asymmetric effects on the diagnostic accuracy of returning data contributors. When a patient returned with a de novo condition absent from their historical records in the training dataset, diagnostic sensitivity decreased significantly compared to an otherwise identical model not trained on their historical data. Conversely, when their health state was unchanged, both sensitivity and specificity were significantly inflated. Our findings reveal a previously uncharacterised risk in medical AI that arises when a model is deployed on patients who contributed to its training data. This exposes a shortcoming of current model development practice: the de-identification measures designed to protect patients' privacy make it difficult to identify returning contributors and exclude them from the AI-assisted interpretation of their own future data. Mitigating memorisation risks may thus require changes to current model training and deployment protocols.

The COMPASS experiment plays an important role in studies of nucleon structure. Measurements performed in 2016-2017 with an unpolarised liquid hydrogen target and a longitudinally polarised 160 GeV/$c$ muon beam provide a high-statistics data sample for the analysis of semi-inclusive deep-inelastic scattering, giving access to transverse-momentum-dependent parton distribution and fragmentation functions. The 2016 data set was analysed to determine the multiplicities of hadrons produced in DIS differential in $x$, $Q^2$ and $P_\text{T}$, as well as the amplitudes of azimuthal modulations in the hadron azimuthal-angle distributions. In particular, the unpolarised asymmetries $A^{\cos \phi_\text{h}}_\text{UU}$ (related to the Cahn effect), $A^{\cos 2\phi_\text{h}}_\text{UU}$ (sensitive to the Boer–Mulders function), and the beam-spin asymmetry $A^{\sin \phi_\text{h}}_\text{LU}$ were extracted in 4-dimensional bins matching those of the multiplicities, and also integrated over some of the variables.

Autonomous Software Engineering Agents (SWE-Agents) excel in deterministic coding tasks but struggle with Architecture 0, the nascent system design phase plagued by implicit engineering constraints, or Unknown Unknowns (UUs) that are rarely stated explicitly. To investigate how agents navigate UUs, we explore a progressive trajectory across pure-text self-play, tool-augmented feedback, and external physical mapping. Our empirical analysis reveals a cascading chain of failures. Pure-text reasoning inevitably devolves into polite consensus or plausible yet physically impossible fabrications. Attempting to bridge this gap via an early-stage execution sandbox unexpectedly triggers Specification Gaming: agents exploit their autonomy over validation scripts to bypass physical constraints, achieving superficial success without resolving core architectural flaws. To resolve this self-validation trap, we propose the Physical Mapping Guard (PMG). Grounded in the software engineering principle of Separation of Concerns, PMG revokes verification authority from the agent, forcing semantic intents to be evaluated by an external, deterministic Semantic-to-Physical (S2P) mapping engine. Extensive evaluations demonstrate that PMG completely eradicates physical-layer and validation-layer gaming. By precisely isolating residual failures to semantic reinterpretations and auditor overreach, PMG marks a critical step toward genuine affordance grounding in automated architectural design.

We present a novel multifunctional sample-holder concept for compact research-scale vacuum systems. The sample holder is mounted directly on the transfer rod and remains mechanically connected to it throughout loading, transfer, deposition, and ion-beam milling. In contrast to conventional layouts, no handover to a separate substrate stage is required. By combining axial transfer motion, rotation around the transfer-rod axis, and independent substrate rotation, the holder itself defines the relevant process geometries and enables standard deposition, oblique deposition at freely selectable incidence angles, substrate rotation, and co-sputtering from adjacent sources. A shielding plate integrated into the sample holder acts as both a substrate shutter and a source shield. This reduces the need for separate shutter mechanisms and allows a compact radial arrangement of four 2-inch magnetron sputter sources without source-tilting mechanisms. The concept was implemented in a modular vacuum system assembled from standard DN100CF components, combining a load lock, magnetron sputtering, and ion-beam milling. The system reaches a base pressure of $5 \cdot 10^{-8}\,\mathrm{mbar}$ without bakeout. The functionality of the sample-holder concept is validated by oblique deposition of Ta/CoFeB bilayers, which exhibit pronounced uniaxial in-plane magnetic anisotropy, and by co-sputtering of an Au–Ag composition series, whose resistivity follows the expected Nordheim-type composition dependence.

We establish two complementary lower-bound mechanisms for individual eigenvalues of the Dirichlet Laplacian. First, energy orthogonality yields a frequency-dependent cap on the Fourier density of a finite spectral projection. Combining this cap with the standard $L^2$ Bessel estimate and a radial-capacity bathtub principle gives, on every open set of finite positive measure in $\mathbb R^n$ with $n\geq2$, \[ \lambda_k\geq c_n(2\pi)^2\omega_n^{-2/n}|\Omega|^{-2/n}k^{2/n}, \qquad \frac{n}{n+2}<c_n<1. \] The constant $c_n$ is characterized by a scalar equation, with $c_2=0.5383068077\ldots$. This estimate preserves Weyl scaling and strictly improves the individual consequence of the Li-Yau sum inequality, although it does not improve the sharp leading coefficient in that sum inequality. Second, we retain part of the spectral deficit discarded when an eigenvalue sum is bounded by its largest term. A lower bound for the counting function, integrated through the exact first Riesz-mean identity, leads to a strictly monotone scalar equation. Its unique positive root is no weaker than the volume-only bound, and we give necessary and sufficient criteria for strict improvement over both that baseline and any independent lower bound. Quantitative estimates of Jiang-Lin provide an explicit implementation on bounded Lipschitz domains. The final comparisons and numerical example distinguish improvements within this framework from stronger estimates available under additional geometric or spectral assumptions.

Label-free clustering of frozen pretrained visual embeddings offers a scalable route to biodiversity monitoring, but image-only fine-grained taxonomy exhibits a consistent coarse-to-fine failure mode: clusters recover broad taxonomic structure yet plateau at species level. We study this behaviour on BIOSCAN-5M through an information-calibrated clustering analysis. BioCLIP~2 features with UMAP and HDBSCAN reach $0.79$ AMI at family and $0.67$ at genus, substantially improving over the prior image baseline and remaining competitive with oracle-$K$, graph-based, and learned clustering heads on the same frozen features. To diagnose whether the remaining plateau is method-limited or information-limited, we introduce InfoTaxa, which combines clustering efficiency—the fraction of probe-estimated image information recovered by an unsupervised partition—with paired DNA as an audit signal only, not an inference input. The density pipeline recovers approximately $0.90$ and $0.81$ of the image-available information at order and family, respectively. Held-out late-fusion probes show that adding DNA to the image embedding reduces species-level prediction error by approximately two bits. Robustness analyses cover multiple image encoders, described-species and rare-class subsets, probe diagnostics, and held-out-species coarse-rank generalisation and same-species retrieval. Thus, in the tested setting, species-level label-free clustering is both clustering-limited and representation-limited: improved clustering may recover additional image-exposed structure, but cannot close the DNA-audited information gap alone.

We develop an algebraic mechanism based on Laplacian algebras for constructing minimal hypercones and determining their variational properties. Generator counts and degrees organize the constructions; homogeneous multipliers depending on the generators yield subcalibration fields, stability bounds and quantitative area-minimizing inequalities. Two-generator isoparametric algebras give polynomial subcalibrations for their minimizing hypercones. In ambient dimension at least three, strict gradient-square closure forces nonlinear odd degree to be cubic. We then study algebras of degrees $(2,2,g)$ and quadratic compositions, placing OT–FKM splitting quartics and Riedler's pullbacks in a common quadratic-composition framework. It yields two further infinite quartic families with a sharp minimizing threshold, as well as harmonic sextics from complex Gram coordinates. For an irreducible harmonic minimal cubic on its essential space, we prove a sharp bound of five generators for its smallest Laplacian algebra. We determine the minimizing range of Clifford cubics and construct irreducible nonradial harmonic examples in ambient dimensions $8,14,26$; the last is strictly area minimizing. Finally, spectral families whose smallest algebras have arbitrarily many generators provide examples in every degree at least two: real parts of octonionic products, complex Pfaffians and complex determinants. Explicit potentials establish strict area minimality and stability bounds, including across nonisolated singularities. The algebraic identities and certificates are supported by reproducible exact symbolic computations.

Simulated electromyograms are used to understand what an electrode records, to test decomposition and estimation algorithms on signals with known ground truth, and to train learning-based decoders. Most simulators fix the geometry to a cylinder or a slab, or stop at the lead field and leave the rest to the user. We present emgforge, an open pipeline that takes a labelled MRI segmentation of a limb to surface EMG in one command: a tetrahedral mesh with conductivity tensors aligned with each muscle's fibres; one reciprocal finite-element solve per electrode, valid for every fibre of every muscle; fibre beds that are straight or follow the muscle's shape; a motor-unit pool obeying the size principle; motor-unit action potentials on any electrode layout; and a motoneuron-pool and twitch layer that turns a drive or a movement into interference EMG and force. We describe the pipeline stage by stage, and at each stage we show, with an example, why the choice was made. The step that turns a lead field into a single-fibre action potential – direct line-source synthesis – is checked against a closed-form solution ($r = 1.0000$, zero lag), and the whole chain against fifty checks with numeric criteria from the physiological literature. We then use the pipeline for four studies: what an electrode sees as a function of depth, fat, spacing and montage; whether fibre geometry changes the signal; how much crosstalk a grid over one muscle receives from its neighbours; and how interference EMG scales with drive. The code, the validation suite and three datasets with ground truth are released.

We give a computer-assisted classification, up to isomorphism, of all nontrivial finite simply reducible groups of order at most 2000. There are 7889 such groups, all of even order. We provide representatives and a table of their numbers at each order. Order 1024, which is not available as a catalogue of group objects in the SmallGroups library of the computer algebra system GAP, requires a separate construction. Combining descendant generation with a classification of quadratic maps over $\mathbb F_2$, we obtain exactly 803 groups of this order, including 221 of nilpotency class two. We also derive exact counting formulas on several infinite families of orders and explicit bounds from structural subclasses.

This paper presents a sequential analysis of the resolving power of a microparticle as a function of its refractive index and size parameter. We demonstrate that the resolution of a microparticle for incoherent point sources is fundamentally determined by the number of excited Mie modes. Based on this mechanism, we propose a novel quantitative assessment framework that defines the spatial resolution limit via the ratio of the squared field angular momentum of the source to that of the total particle field (comprising the superposition of the source and scattered fields). The analytical results demonstrate good agreement with both numerical modeling and classical limits.

Inferring directed effective interactions from neuronal spike trains is a central inverse problem in statistical physics and computational neuroscience. Kinetic Ising models provide a tractable framework for this task, but their application to neural data typically requires binning spike trains into binary activity variables, discarding within-bin timing and conflating collective network dynamics with single-neuron history effects. We introduce SpiKIsing, a latent-variable model that separates these two levels of description. A discrete-time asymmetric kinetic Ising model describes collective network activity, while continuous-time, history-dependent point processes generate the observed spikes conditional on the latent states, accounting explicitly for refractoriness and post-spike recovery. We derive a variational mean-field expectation-maximization scheme in which the point-process likelihood enters as an effective observation field, enabling joint inference of latent activity, network couplings, and emission parameters. The framework extends naturally to maximum-a-posteriori inference with structured priors, including sparsity and a hierarchical extension favouring Dale-consistent outgoing interactions. We validate parameter recovery on matched synthetic data and test the method on spike trains generated by a recurrent conductance-based leaky integrate-and-fire network. In this setting, SpiKIsing recovers sparse connection structure and correctly classifies all excitatory and inhibitory neurons despite the substantial mismatch between the data-generating dynamics and the SpiKIsing model.

This work characterizes a Gaussian multiuser-channel capacity-region using receiver-subset message atoms, Gaussian single-user equivalents, and successive decoding. A memoryless multiuser-channel model specifies both the channel conditional distribution and the independent-use input distribution. For all linear Gaussian channels, independent Gaussian user signaling and receiver-local worst-case-noise/MMSE-GDFE transformations provide a single-user-equivalent basis for the complete capacity-region construction. Each user distributes its input autocorrelation among a finite set of receiver-subset atoms, whose rate sums satisfy the applicable receiver constraints. Minimum-energy and weighted-rate-sum designs optimize these allocations, while fixed-allocation linear programs determine feasible atomic rates and synchronized time-shared successive-decoding implementations. The resulting framework includes Gaussian multiple-access, broadcast, and interference channels, with numerical examples illustrating their rate regions and receiver designs.

Video anomaly detection (VAD) aims to localize anomalous events in untrimmed videos. Vision-language models (VLMs) provide rich visual understanding for training-free VAD, but existing approaches impose restrictive interfaces between visual understanding and anomaly scoring. Caption-based pipelines compress visual evidence into text, potentially discarding subtle cues, while direct numerical generation forces the model to express its judgment through a small set of predefined scores. Such interfaces can obscure subtle differences in anomaly severity, causing visually distinct clips to receive similar representations or scores and thereby limiting the resolution of anomaly ranking. We propose Probe-VAD, an ordinal binary-probing framework that directly probes severity preferences from a frozen VLM. Given raw video clips, Probe-VAD queries ten ordered severity thresholds and extracts constrained YES/NO continuation likelihoods. Their normalized preferences form a cumulative severity profile, from which tail evidence is aggregated into a continuous anomaly score, with isotonic projection enforcing ordinal consistency. Experiments on public VAD benchmarks demonstrate superior performance with low computational cost. Probe-VAD provides a simple interface for translating frozen VLM visual understanding into continuous, rank-sensitive anomaly scores without task-specific training or caption-based compression. Code is available at: https://github.com/yvestine/COVAS-VAD.

Vision-language-action (VLA) models, world-action models (WAMs), and offline reinforcement learning methods are rapidly expanding the design space of embodied policies, yet turning these algorithms into reliable robot systems remains constrained by fragmented data formats, training stacks, evaluation protocols, inference runtimes, and embodiment-specific interfaces. We present $\mathrm{FluxVLA}$ Engine, an open, configuration-driven platform that turns heterogeneous embodied-policy components into a reproducible data-to-deployment workflow. Rather than introducing another policy model, $\mathrm{FluxVLA}$ standardizes interfaces for datasets, visual-language and world models, action heads, reward- or advantage-weighted learning, distributed training, simulation evaluation, optimized inference, and robot operators. The engine further integrates compositional dual-arm simulation, scalable automatic data generation, and model-decoupled human-in-the-loop rollout, takeover, correction collection, and reward annotation. For responsive physical execution, it combines Real-Time Chunking (RTC) with accelerated inference backends, lightweight remote GPU serving, and configurable trajectory post-processing. Together, these capabilities connect offline learning, simulation validation, online correction, and real-robot execution through shared and auditable contracts. $\mathrm{FluxVLA}$ therefore targets the engineering bottlenecks separating promising embodied-learning algorithms from reproducible evaluation and dependable deployment. Code is available at https://github.com/FluxVLA/FluxVLA

Landau fluid closures are linear in the evolved moments. We examine the consequences of relaxing linearity. As an example, we introduce the nonlinear exact kinetic response closure, exact on an eigenmode but not on superpositions. A counting argument shows that a closure on $N$ instantaneous moments and the field can represent at most $(N+1)/2$ superposed eigenmodes. Guided by this, we train an equivariant neural-network and a learned Padé closure on analytic data. For bump-on-tail and slab ITG instabilities they reduce growth-rate errors by up to three orders of magnitude over Landau closures.

Beam-induced damage fundamentally limits the characterization of beam-sensitive materials by scanning transmission electron microscopy (STEM), since structural information must be recorded before the electron beam irreversibly modifies the specimen. Here, sodium chloride (NaCl) is employed as a model beam-sensitive ionic crystal to investigate beam-induced structural evolution and the low-dose regime in which useful structural information can be recovered prior to significant damage. Four-dimensional STEM (4D-STEM) datasets were acquired at 200 kV using a Timepix3 direct electron detector and reconstructed using real-time integrated centre of mass (riCoM) imaging. We first establish the characteristic damage behavior of NaCl under high electron doses. Across different dwell times and raster scan orientations, damage develops reproducibly into square-faceted voids whose boundaries align with the 100 crystallographic directions of the rock-salt lattice, indicating that the morphology is governed predominantly by the intrinsic crystallography rather than the scan geometry. We then investigate the low-dose imaging regime using dose-fractionated acquisitions. At 130 e-A-2 per frame, normalized cross-correlation with respect to the first frame quantitatively tracks progressive structural degradation and enables the onset of measurable damage to be identified as a function of accumulated dose. A subsequent acquisition at 32 e-A-2 per frame demonstrates that atomic-scale spatial information can still be recovered below this damage threshold. These results demonstrate how dose-efficient 4D-STEM acquisition combined with riCoM imaging can extend the accessible imaging regime of highly beam-sensitive ionic materials while preserving atomic-scale information.

We numerically investigate the gravitational collapse of a charged scalar field coupled to the Einstein and Maxwell equations in spherical symmetry, in 4+1 spacetime dimensions. At the threshold of collapse we find type-II critical phenomena very similar to what is seen in 3+1 dimensions, including self-similarity of the critical solution and power-law scaling of the black hole mass and charge. Well inside the collapse region, we also identify initial data that collapse to an extremal black hole. By varying all parameters of the initial data by up to $\sim0.5\%$, we give evidence that there is a small neighbourhood in the space of initial data where an exactly extremal charged black hole is formed in the evolution of a codimension-1 set of initial data. We believe this is the first such evidence for scalar field collapse from regular initial data.

The mental model construct is widely used in HCI to refer to the knowledge structure people hold in order to reason about and interact with computing systems. Yet it is often operationalized intuitively: the construct is often used interchangeably with related concepts (e.g., folk theories, sensemaking) and methods of studying it (e.g., through elicitation) are many and diverse, with each method resting on distinct assumptions about what counts as a mental model. Generative and agentic AI systems may further complicate mental model formation and elicitation as such systems are opaque by design and increasingly act on users' behalf across files, applications, and on the web. Together, these challenges may hinder the commensurability of research on people's mental models of AI systems. The MM/AI workshop calls for a critical reassessment of how we understand and study mental models in human-AI interaction research. It aims to foster theoretical and methodological exchange on mental models in human-AI interaction, identify open challenges, and develop directions for future research. We invite short papers on users' or stakeholders' mental models of AI systems, particularly contributions that reflect on the conceptual and methodological foundations of the construct. The half-day workshop combines lightning talks, hands-on elicitation exercises, and structured discussions on key questions concerning the future of the mental model for human-AI interaction research.

Much of the ordinary matter in the present-day Universe still escapes direct detection. These missing baryons are thought to reside in a warm-hot intergalactic medium (WHIM) threading the filaments of the cosmic web, whose turbulent and thermal state remains poorly constrained yet underpins any attempt to observe it. Beyond its observational stakes, how this turbulence emerges, as gravitational collapse converts ordered inflow into a disordered cascade, is a question of structure formation in its own right. We characterise the emergence of turbulence in the diffuse gas of a cosmic filament, from its assembly to the present day, in the first simulation of the Web Evolution in Filament Targeted zoom simulations (WEFT) project. The cosmological zoom-in technique is applied to a single filament, evolved from z=63 to z=0 with the moving-mesh code AREPO, reaching a median gas cell size of ~8 kpc. We trace the filament assembly, the thermodynamic state of its diffuse gas, the generation of vorticity at its accretion shocks, and the growth of turbulent motions, then quantify the intermittency of the cascade through high-order velocity structure functions and their relative scaling exponents from extended self-similarity. The filament assembles by the hierarchical merging of several proto-filaments rather than by laminar accretion. Vorticity is seeded baroclinically where the rotating strands meet their accretion shocks obliquely. The flow evolves from a supersonic, shock-dominated state, statistically close to the bifractal Burgers limit, into a developed, mildly supersonic, intermittent cascade whose longitudinal exponents lie closest to the sheet-like She-Lévêque model at z=0. Turbulence is thus an intrinsic, quantifiable property of the diffuse gas of filaments. This pathfinder run provides the turbulent input for forecasts of WHIM observability.

Wi-Fi signal data can be used to compromise the privacy of individuals. While many existing approaches rely on Channel State Information (CSI), collecting this data on typical IoT devices often requires elevated operating system permissions and specialized drivers. Consequently, this paper investigates the feasibility of utilizing Received Signal Strength Indicator (RSSI) data to predict human locations. RSSI was selected because it is accessible even on devices with limited user permissions, and therefore is more applicable to a wider array of IoT devices. To bypass the tedious process of obtaining training data needed to train an RSSI-based model, an existing Wi-Fi pose prediction project was used in this research. However, that project assumed CSI data as input. Therefore, we investigate the feasibility of cross-domain inference, i.e., feeding RSSI data into that existing CSI-based model. We collected an RSSI dataset, synchronized with video ground-truth of a person moving within a room, to evaluate the model's performance. This evaluation confirmed that RSSI data can predict locations with approximately 80% confidence when human movement is present. This demonstrates that a model trained on CSI data can be used to evaluate low-granularity RSSI data consisting of decibel-milliwatt (dBm) values to roughly locate people in the collection space. These results imply that a wide range of IoT devices can be used for privacy invasion in Wi-Fi-dense environments.

For integers $1\le k < n$ and real numbers $c_1, \ldots, c_k>0$ and $d_1, \ldots, d_n\ge 0$, we investigate the space of all $k\times n$ matrices $F$ such that the product $FF^*$ is equal to the diagonal matrix ${\rm Diag}(c_1, \ldots, c_k)$ and the squared norms of the columns of $F$ are equal to $d_1, \ldots, d_n$ respectively. Depending on the field where the coefficients of $F$ are taken from, which can be of real or of complex numbers, we are mainly interested in determining whether the resulting space is path-connected or even simply connected relative to the subspace topology in the space of all $k \times n$ matrices. The criteria presented are closely related to results previously obtained by Cahill, Mixon, and Strawn (2017), Needham and Shonkwiler (2021), the last two authors together with Caine (2026), and the author of this work (2024 and 2026). Flag manifolds, namely orbits of the canonical conjugation actions of ${\rm O}(n)$ and ${\rm U}(n)$ on the spaces of symmetric real and Hermitian $n\times n$ matrices, respectively, play a central role in our development.

We study the structure and distribution of atoms in the monoid $\mathcal{M}{\rm on}(R)$ of nonzero monomial ideals of the polynomial ring $R=K[X_1,\ldots, X_N]$, with $N\ge 2$. We characterize the atoms with at most four minimal generators and introduce the density $d(N,\mu)$ of atoms among monomial ideals with $\mu$ minimal generators. For $\mu\le 4$, we prove the existence of this density and determine its asymptotic behavior as $N\to\infty$. In the bivariate case, we also obtain a uniform lower bound for the density of atoms in a divisor-closed submonoid of $\mathcal{M}{\rm on}(R)$ generated by equigenerated ideals.

Wavelets and frames that provide strong guarantees for signal representations are a cornerstone in signal processing theory, but have long been restricted to non-causal settings. Recent work extended wavelet analysis to time-causal systems that operate on streaming signals, with exact reconstruction and time-recursive implementations. However, the frame guarantees that make such representations reliable under noise and quantization are uncharacterized. We derive closed-form frame bounds and conditioning on band-limited domains, together with peak frequencies, constant-Q bandwidth tiling, and spectral decay rates for time-causal bandpass wavelets. Our work provides design rules for the scale ratio and channel count, which we validate numerically against discrete implementations of the causal wavelets in terms of recursive filters.

Green economic complexity provides a generalizable framework for examining countries' productive capabilities in a defined product set. We apply this framework to AI-enabling goods within the full product space, linking current specialization with adjacent diversification opportunities. Using BACI exports for 2007-2023 and 103 AI-enabling goods, we measure complexity-weighted specialization (AECI), product-level adjacent opportunities (AIAP), and average complexity-weighted relatedness of remaining candidates (AECP). In 2023, Japan leads AECI, while China leads AECP; portfolio breadth accounts for much of the variation in raw AECI. Initial raw potential is positively associated with subsequent changes in the AI-enabling export share, but its associations with changes in AECI and specialization counts are not statistically significant at the 5% level. Our contribution is a trade-based assessment of AI-enabling productive capabilities and related opportunities. The results and public dashboard provide a preliminary complement to publication and patent indicators, not a comprehensive measure of national AI performance or a validated forecast of diversification.

A skew morphism on a finite group $A$ is a permutation $\varphi$ on $A$ that fixes the identity element of $A$ and for which there exists an integer-valued function $\pi:A\to\mathbb{Z}_{|\varphi|}$ such that $\varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y)$ for all $x,y\in A$. The kernel of $\varphi$ is the subgroup $\Ker\varphi=\{x\in A\mid \pi(x)=1\}$, and the index $[A:\Ker\varphi]$ is called the skew-type of $\varphi$. In this paper we construct, classify and enumerate the skew morphisms of skew-type four on cyclic $2$-groups. Our main results give explicit formulas for all such skew morphisms and closed-form expressions for their numbers.

Autonomous nano-UAV navigation requires accurate ego-motion estimation under stringent size, weight, power, and computing (SWaP-C) constraints, where visual sensors and LiDARs exceed payload limits, optical flow degrades in low-texture scenes, and inertial-only state estimation is susceptible to accumulated drift. While multi-zone time-of-flight (ToF) arrays provide a lightweight metric complement, 6-DoF estimation from merely 384 ranges per frame is challenged by invalid returns, anisotropic observability, and temporal computational scaling. We propose TIO-FORMER, a camera-free, optical-flow-free, and mapless range-inertial odometry framework driven by an IMU and an ultra-lightweight (15 g) payload of six orthogonal 8 x 8 ToF arrays. Our frontend pairs consecutive range grids with a bilateral gated difference, while IMU-guided cross-attention dynamically routes directional features conditioned on platform kinematics. A Streaming Causal Transformer couples an uncompressed Local KV cache with compressed Chunk-FIFO memory, maintaining bounded inference cost and memory footprint independent of flight duration. In real-flight evaluations, TIO-FORMER reduces open-loop position error by 54.4% compared to nano-UAV optical flow and by 66.4%-89.1% over learned inertial baselines. We also evaluate performance across multiple environments and robustness under severe sensing degradation. Deployed on an edge RISC-V companion computer, TIO-FORMER achieves a P95 latency of 10.466 ms and peak resident memory of 6.324 MiB (less than 5 percent system RAM), demonstrating that sparse range sensing provides practical geometric anchoring for resource-constrained micro-aerial robots. Code is available at https://github.com/Ly041021/TIO-Former.

We study a state-constrained Bolza optimal control problem governed by a non-local continuity equation in the Wasserstein space $\sP_2(\R^d)$. We develop a Pontryagin maximum principle for these problems in which both the cost functionals and the constraints are only locally Lipschitz, and the initial measure does not necessarily have compact support. To derive the main result, we introduce a notion of a Clarke-type deterministic subdifferential over $\sP_2(\R^d)$. The proof of the main result combines a careful adaptation of the Lasry-Lions regularization to the Wasserstein space coupled with stability results of the Clarke subdifferential that allow us to recover the first-order information. We also show that, for functionals convex along plans, this subdifferential admits a global supporting characterization and provides a first-order characterization of global minimizers.

It is tantalizing to consider the recent observation of the LUX-ZEPLIN (LZ) experiment of a high energy nuclear recoil candidate at $E_{\rm Recoil} \simeq 248$ keV as the long-awaited signal of a weakly interacting massive Dark Matter (DM) particle. Although this signal is still weak and needs to be confirmed by further data and inspection, we attempt to interpret it in the context of the 2HD+a model in which a two-Higgs doublet model (2HDM) is supplemented by a light pseudoscalar Higgs boson $a$ and an isosinglet fermionic DM particle $\chi$. The model has the virtue of reproducing the correct cosmological density and evading the previous limits from direct and indirect detection of DM particles, while passing all constraints from colliders searches and high-precision measurements in the Higgs, electroweak boson and heavy-flavor sectors. We indeed find regions of the parameter space of the model, with a rather heavy 2HDM spectrum but a very light pseudoscalar $a$ boson, $m_a \approx 1-10$ GeV, as well as a DM fermion with a mass of a few hundred GeV, which are compatible with the LZ recoil event. The related extensive investigation of the parameter space of the 2HD+a model with fermionic DM, including the wide range of complementary constraints from both DM phenomenology and collider searches as well as precision measurements are presented.