Papers

Neural operators provide fast surrogates for time-dependent PDEs, but autoregressive deployment creates a refinement-allocation problem: prediction errors vary over space and time, while only a finite number of local corrections can be committed along a trajectory. We formulate this as budgeted adaptive neural-operator solving. A global Fourier neural operator advances the full field, a local operator proposes patch-wise residual corrections, and a set-aware selector chooses where to refine. A macro policy decides when and how much of the remaining refinement budget to spend. We introduce rollout-verified policy improvement (RV-PI), which evaluates feasible refinement counts through actual continuation rollouts of the learned PDE solver, converts long-horizon advantages into conservative policy targets, and accepts an update only when held-out trajectory error improves. On the shallow-water benchmark with a 32-intervention budget, RV-PI achieves a three-seed mean trajectory relative L2 error of 0.6910, improving over immediate-only policy improvement by 5.37% and RandomMacro by 2.41%. On the forcing-driven Brusselator benchmark with a 76-intervention budget, RV-PI attains 0.09954, improving over immediate-only policy improvement by 2.31% and RandomMacro by 5.32%. These results show that, under a fixed refinement budget, the value of a local correction depends on its downstream effect on the autoregressive trajectory, not only on its immediate error reduction.

We study assignment quality in 3D heterogeneous multi-agent reach-avoid games and identify a recurring failure mode of cardinality-only matching in geometrically structured scenarios, which we term Geometric Sprawl. In these cases, multiple maximum-cardinality assignments are available, but some induce spatially incoherent pairings and inefficient pursuit trajectories. Building on the evasion-space framework of Yan et al.~\cite{yan2022}, we introduce a cardinality-first weighted sequential matching method in which the Hamilton–Jacobi–Isaacs interception value $z_I(s,j)$ is used as a secondary assignment weight. Each sequential stage is solved with a min-cost max-flow backend, while the unweighted baseline uses the same solver with the weight term removed. We evaluate both methods on a deterministic 35-scenario benchmark (7 families & 5 initialization variants) under two regimes: a diagnostic stationary-unmatched setting and a hybrid saddle-point setting with goal-directed unmatched evaders. On this benchmark, the weighted method resolves 13 of 15 geometric stress-test instances that cause repeated timeouts for the unweighted baseline in the diagnostic regime, and under the hybrid regime improves mean captures from $3.20$ to $3.91$ (22% increase) and mean interception height from $3.87$ to $5.36$ (40% increase). We also report lower path tortuosity and lower angular-effort proxy values, suggesting smoother pursuit trajectories in this first-order simulation model. We release the simulator and benchmark suite at \href{https://github.com/Prajwal-Vijay/geometric-coherence-weighted-matching}{github.com/Prajwal-Vijay/geometric-coherence-weighted-matching} to support reproducible evaluation of assignment strategies for 3D reach-avoid games.

In this paper, a comparative review of different hybrid models for short-term forecasting of building thermal demand is carried out. Particularly, the assessment tackles the comparison of data-driven models enhanced with other state-of-the-art techniques. At the first step, the existing techniques reported in the literature are analysed. It is concluded that Metaheuristics or a data-driven model are used to identify the parameters of the basic model. The qualitative evaluation includes for each method the input and output features, main advantages and drawbacks. At the second step, an existing dataset of historical thermal demand from Scottish households, as well as historical weather forecasts are utilized to assess additionally the performance of existing hybrid methods. From the assessment of 13 hybrid methods, the Empirical Modal Decomposition - long short-term memory - Markov (EMD-LSTM-Markov) model can predict with the highest accuracy the day-ahead power pattern of heating and domestic hot water (DHW) demands. Though local power peaks are also accurately predicted, high power swells and spikes are underestimated. Other methods, such as Support Vector Machine - Simulated Annealing (SVM-SA) and Random Forest - Improved Sparrow Search Algorithm - LSTM (RF-ISSA-LSTM) predict a smooth pattern of heating and DHW demand profiles with rapid changes underestimating most power peaks.

While corporate sustainability mandates are expanding, the systemic reliance on self-reported emissions data exposes financial markets to pervasive greenwashing. Current literature relies heavily on subjective ESG ratings or textual sentiment analysis, leaving a critical econometric gap in objectively quantifying physical climate realities. To resolve this information asymmetry, we fuse U.S. SEC financial fundamentals with facility-level EPA greenhouse gas registries to establish a mathematically guaranteed baseline of physical corporate emissions. Leveraging a gradient boosting architecture and Mondrian Conformal Prediction, we quantify the shortfall between self-reported data and this algorithmic baseline into a novel Conformal-Weighted Continuous Divergence (CWCD) metric. Evaluating this divergence via a cross-sectional lead-lag econometric design, we uncover a robust mechanism of market discipline: algorithmic emissions divergence exhibits a severe, statistically significant negative relationship with subsequent market valuation (Tobin's Q) and operational profitability (ROA). Providing definitive evidence against the market blindness hypothesis, this study proves that institutional capital actively prices environmental deception not merely as an ethical lapse, but as a leading indicator of fundamental corporate mismanagement. Ultimately, these findings provide the quantitative justification necessary for asset managers and regulators to deploy algorithmic auditing infrastructure at scale.

We generalize de Rham's decomposition theorem to proper metric spaces: every proper metric space has a unique decomposition as the product of a Euclidean space and a finite or countable pointed $\ell^2$-product of nontrivial irreducible non-Euclidean factors. More generally, every complete metric space splits canonically into a Hilbert factor, a pointed $\ell^2$-product of irreducible non-Euclidean factors, and a factor with no nontrivial irreducible factors. These results partially answer a question of Ulam.

Feasibility of a Signal Temporal Logic (STL) specification asks whether, from a given initial state, an admissible control input can satisfy its continuous-time requirements under actuator limits. Establishing feasibility is essential for detecting unrealizable tasks and repairing specifications before execution. State-of-the-art Mixed-Integer Linear Programming (MILP) methods face growing model sizes as temporal horizons and formula complexity increase, and can accept control witnesses that violate continuous-time STL semantics between samples. We propose a geometric approach to STL feasibility and temporal repair that translates temporal requirements into spatial constraints evaluated at the initial state. Its compiled feasibility check is independent of horizon length for fixed compiled dimensions. We prove nonnegative continuous robustness under a joint controller assumption. On 6D UAV benchmarks, median geometric repair times are 0.265–1.510 ms; we show up to 1.68x10^4 speedup over MILP feasibility checker. All geometric runs pass continuous STL validation, whereas majority of completed MILP control witnesses violate continuous-time STL.

This work continues the study of the real vector field theory.It shows how the potentials can be used to derive the field and dynamical variables of the wave electrojeitonic field generated by an electrically charged point particle.The derived expressions provide the angular distributions of the instantaneous electrojeitonic radiated power emitted by an charged particle in arbitrary motion. The results predict the dominance of longitudinal electrojeitonic radiation from ultrarelativistic charged particles.Keywords: electrojeitonic field, longitudinal electrojeitonic waves, electrojeitonic radiation.

LLM agents can make unsafe tool calls even when instructed to behave safely. Existing defenses constrain agents before execution, modify tool inputs/outputs, or rely on LLM judges; these approaches may depend on model behavior or block unsafe actions without helping the agent recover. We argue that the execution environment should instead enforce safety as the agent runs and steer it toward safe alternatives when violations occur—we call this Environment Steering. We implement this by modeling the agent and harness execution state as database tables, track the record-level data flows, and check these data flows against declarative policies during runtime. When violations are detected, policy- and context-specific feedback steers the agent toward safe trajectories. On AgentDyn, this enables the agent to improve task success rate over no-defense while achieving 0% attack success rate.

Automated skill extraction underpins workforce planning, yet most systems represent skills as flat labels with no notion of the responsibility level at which a skill is practiced. The Skills Framework for the Information Age (SFIA) captures exactly this dimension, defining 147 professional skills across seven responsibility levels, but no automated LLM-based extraction targeting SFIA has been reported. We formalize the task as structured prediction of (skill, level) pairs from free text and ask three questions: how accurately can text be mapped onto SFIA's closed vocabulary, which strategies reliably predict the level alongside the skill, and do agentic designs improve on simpler retrieval and prompting? We evaluate five strategies (a lexical baseline, dense retrieval with LLM reranking, a zero-shot schema-constrained LLM, single-agent agentic RAG, and a three-agent retriever–matcher–verifier crew) against expert-mapped European ICT role profiles, all drawing on an SFIA~9 corpus built by a fully automated agentic pipeline that we release. Retrieval-based matching identifies the most skills while generative strategies are markedly more precise; only strategies assigning the level as an explicit decision predict it reliably, with similarity-based selection more than twice as inaccurate; and the crew doubles latency without improving accuracy, so added agent roles do not automatically benefit closed-taxonomy matching. These results provide the first reproducible baseline for structured, level-aware skill extraction against SFIA.

Training a language model on data with a narrow flaw can sometimes make the model broadly misaligned. Inspecting the data at face value often does not settle whether it will emerge, and today it is caught only after training, by auditing the resulting model. To complement post-hoc audits, we introduce Alignment Forecasting: the task of predicting alignment failures before training. Given a target model, a fine-tuning dataset, and a failure mode such as deception or sycophancy, a forecaster outputs the probability that fine-tuning would meaningfully increase that failure mode. To measure progress on alignment forecasting, we introduce ALIGNMENTFORECASTBENCH, a benchmark of over 5,000 forecasting questions spanning 17 target models, 32 datasets, and 16 failure modes. Frontier models prompted directly perform poorly on ALIGNMENTFORECASTBENCH. We therefore propose a forecasting scaffold in which an LLM reads the dataset and rates how strongly and broadly it pushes the model toward misbehavior, and a simple learned model combines that rating with the failure mode's base rate and the target model's prior tendency. This forecasts well above chance, and beats a model fine-tuned on the task and a simple forecaster allowed to see how weaker models behaved after fine-tuning on the same data. Its signals also flag problematic training examples that a frontier-model classifier misses. Filtering those examples out from real post-training data such as UltraChat results in more aligned models on our multiple-choice evaluation in most cases, though the benefit in open-ended conversations is unclear. More progress is needed before forecasts can reliably guide training data curation in practice, but our results suggest that forecasting many alignment failures before training can be tractable in the SFT setting.

Large language models are increasingly used as interacting agents, but it remains unclear how robust their coordination is when public communication is unreliable. We study this question in iterated $N$-player Stag Hunt games played by homogeneous LLM groups under controlled programmatic action inversion, which changes both the public transcript and the actions used for execution. Across an experimental grid spanning group sizes, coordination thresholds, corruption levels, and seven LLMs, we observe three main patterns. First, honest agents' pre-flip Stag choices decline as corruption increases, but the sharp fall in public success is primarily mechanical. In the focal $N=5,M=3$ setting, pre-flip success remains 78% at 80% corruption, while public success falls to 12%. Second, honest choices are associated with the public history available at decision time, particularly under high corruption. Third, three threshold-style public-report benchmarks yield similar action-match rates to the LLM agents, showing substantial descriptive agreement between LLM decisions and these benchmarks. Overall, our results show that original choices, public actions, and executed outcomes must be separated when evaluating multi-agent robustness, as corrupted communication can severely and predictably degrade mutually beneficial cooperation.

Hands-free communication devices and speakerphones are inherently affected by acoustic echo and background noise. To mitigate these impairments, end-to-end discriminatively trained neural networks have emerged as the best-performing approach in research and deployment. While recent advancements in generative methods have provided remarkable results for various speech enhancement tasks, diffusion-based acoustic echo control (AEC) research is still restricted to non-causal, utterance-level processing, thereby not widely applicable in practice. With this work, we are the first to propose low-delay (i.e., causal) diffusion-based joint AEC and noise control models DiffVQE2 / DiffVQE2-S, excelling the so-far state of the art DeepVQE / DeepVQE-S models in multiple objective metrics, and, most importantly, in subjective MOS, respectively. In addition, our models are less complex. Furthermore, we show that a limited lookahead applied to the efficient DiffVQE2-S model allows for an even higher performance. These results have been obtained on the ICASSP 2023 AEC Challenge blind test set. We claim the first streaming-capable, diffusion-based acoustic echo and noise control that excels state-of-the-art discriminative approaches.

Reliable breast ultrasound lesion segmentation requires accurate boundaries and evaluation that prevents patients or duplicate images from crossing data splits. We propose Channel Local Contrast (CLC), a compact refinement of the YOLO26 segmentation prototype head. CLC adds a fixed local high-pass residual controlled by 64 zero-initialized, bounded channel gates. Baseline and CLC were compared in five matched folds on each of four breast ultrasound datasets. BUS-BRA used patient-disjoint outer tests with separate inner validation. BUS-UCLM and BrEaST used patient-grouped validation folds; BUSI used duplicate-component groups because patient identifiers are unavailable. Group-macro Dice increased by 1.68, 3.11, 1.12, and 2.45 percentage points on BUS-BRA, BUS-UCLM, BUSI, and BrEaST, respectively. Only the BUS-BRA paired 95% confidence interval excluded zero. CLC adds 64 parameters and 0.0049 giga floating-point operations (GFLOPs). At 640 pixels, single-T4, batch-one, 16-bit floating-point (FP16) TensorRT graph times were 2.1478 ms for CLC and 2.0512 ms for baseline, excluding preprocessing and postprocessing. CLC increased group-macro Dice across all four datasets with a measured T4 forward-pass overhead of 0.0966 ms. Code: https://github.com/mfazrinizar/CLC-YOLO

A Hybrid Residual Attention Network is proposed for accurately classifying silkworm images into six different classes, including healthy and diseased states. It uses residual blocks for deep feature extraction and attention to focus on disease related features. A novel Integrated Adaptive Momentum Optimizer was introduced to enhance convergence and improve training efficiency. The dataset of silkworm images underwent preprocessing techniques such as normalization, resizing, and noise reduction, along with augmentation strategies to improve data quality and diversity. It is optimized using IAMO, achieved an accuracy of 98.67%.The integration of spatial and channel wise attention mechanisms, coupled with IAMO, significantly enhanced the model ability to recognize subtle differences between classes. Results indicate that HRAN can be used to detect disease at an early stage in sericulture, and future work will enhance scalability and efficiency in different environments.

Compressed-domain video captioning avoids full video decoding by operating directly on I-frames, motion vectors and residuals, trading a small amount of accuracy for a large gain in inference speed. CoCap established this pipeline using a CLIP vision encoder and a shallow BERT-style multimodal decoder. Both components predate substantially stronger alternatives. We ask a narrow, controlled question: how much of CoCap's accuracy is limited by these two components, and which of the two is the binding constraint? We replace the CLIP I-frame encoder with SigLIP2 and the BERT-style decoder with GPT-2, and evaluate three configurations (the original pairing, the encoder substitution alone, and both substitutions together) under identical data, sampling budget and optimisation schedule. All comparisons are made against our own reproduction of CoCap rather than its published numbers, because we train on a 4,999-clip subset of VATEX at a reduced sampling budget; absolute values are therefore not comparable with the original work. Our reproduction tracks the published result closely: CIDEr and METEOR run slightly above it (54.9 against 52.7; 23.4 against 23.2), BLEU-4 and ROUGE-L slightly below (29.7 against 31.4; 48.9 against 49.4). We attribute the differences to our evaluation subset rather than to any improvement in either direction. We find the two substitutions pull in opposite directions: SigLIP2 alone improves every metric (+4.5 CIDEr), while adding GPT-2 on top erodes that gain, because a pretrained decoder overfits 4,999 clips within two epochs. We additionally report inference latency for each configuration, since speed is the property that motivates compressed-domain captioning in the first place, and an accuracy gain purchased at a latency cost should be reported as such.

A microphone on the airframe of a small multi-rotor UAV is dominated by rotor ego-noise, so spoken flight commands arrive at negative signal-to-noise ratio (SNR). We study small-footprint keyword spotting (KWS) for a ten-word command vocabulary under real ego-noise, training on one quadrotor and testing on another. Besides per-clip accuracy we measure the streaming false-alarm rate on 4.4 h of continuous rotor noise. We compare classical noise-robust front-ends (CMN, PCEN, spectral subtraction), test-time adaptation, and two front-ends that track the per-band ego-noise floor over the two seconds preceding the decision window and either subtract it (normalisation) or feed it to the network as a second input channel (conditioning). Per clip, all front-ends look alike: +2-3 points on average, up to +14 at -15 dB. On continuous rotor noise they differ sharply. Normalising front-ends fire about ten times more often than plain log-mel at the same threshold and end up below it at a budget of one false alarm per hour (-9 points at 0 dB). Conditioning keeps the baseline's false-alarm rate and turns its gain into detections (+8 points at -10 dB over three seeds); on top of PCEN it gives the best per-clip accuracy and false-alarm rate, and a level-anchored variant is also invariant to the microphone gain. Real drone+interferer recordings expose the remaining failure mode, environmental sounds and bystander speech, which training negatives halve. A single script reproduces all on-device numbers on the NVIDIA Jetson Orin NX flight computer, where the complete pipeline costs 3 ms per 100 ms hop on the CPU.

Most existing MEG and EEG (M/EEG) visual decoding methods align brain signals with a single global embedding extracted from a pretrained visual encoder, leaving open whether intermediate patch representations, which preserve richer and more granular rich visual information, can improve representation learning. To address this question, we introduce the Residual Patch Adapter (RPA), a lightweight, modular adapter that leverages all patch tokens from an intermediate layer of a ViT visual encoder for alignment. Through extensive ablation analyses, we first show that pooling or masking patch tokens degrades the learned representation, demonstrating that retaining the full set of patch tokens is important for EEG alignment, while the CLS token provides little unique information. We then use a series of six quantitative feature analyses to show that both higher-level semantics and lower-level visual features, including color and texture, are essential for this EEG-to-image alignment. Under current protocols, our system achieves Top-1 accuracies of 95.4% within-subject and 35.5% cross-subject on THINGS-EEG2, and 65.2% and 6.7%, respectively, on THINGS-MEG, achieving state-of-the-art (SOTA) performance across both datasets. Evaluations with alternative brain encoders, including pretrained EEG foundation models, demonstrate that the approach extends beyond the projection-based EEG encoder. Furthermore, we provide a plug-and-play interface that allows RPA to be replaced by convolution, attention, or ConvNeXt alternatives. Together, these findings provide significant insight into M/EEG-to-image representation learning by establishing design principles for leveraging the latent space of visual encoders, and open new directions for brain–image alignment and non-invasive brain–computer interface (BCI).

Given a finite preorder $\tau$, we study how its order relation determines the $h^*$-polynomial of the associated polar preorder polytope. Let $\mathcal R_{\tau}^{\vee}$ be the convex hull of the negative standard basis vectors and the indicator vectors of nonempty order ideals, and write $h_\tau^*(t)=h^*(\mathcal R_{\tau}^{\vee},t)$. Athanasiadis and Chapoton conjectured that this enumerative invariant takes ordinal sums to products: $$h_{\tau_1\oplus\tau_2}^*(t)=h_{\tau_1}^*(t)\,h_{\tau_2}^*(t).$$ We prove the conjecture for arbitrary finite preorders, including those with nontrivial equivalence classes. More precisely, we construct a positively homogeneous piecewise unimodular shear from the free sum $\mathcal R_{\tau_1}^{\vee}\oplus\mathcal R_{\tau_2}^{\vee}$ onto $\mathcal R_{\tau_1\oplus\tau_2}^{\vee}$, giving lattice-point bijections at every nonnegative real dilation scale. The key is a formula for the Minkowski functional in terms of the least nonnegative order-reversing majorant: after the shear, the functional becomes the sum of the two factor functionals. Together with the Ehrhart product formula for free sums, this proves the conjecture and the corresponding product formula for normalized volume.

Gravitational generation of quantum entanglement on squeezed coherent states in a system of two quantum mechanical particles is explored. The particles are modeled as harmonic oscillators, and their gravitational interaction is described by an interaction potential. Dynamics of the gravi- tationally induced entanglement is explored using the linear entropy of entanglement. An analytical expression for the linear entropy is obtained via Gaussian integration and covariance method. In the short-time weakly coupled regime, it is observed that the entanglement is proportional to the square of the time interval, square of the interaction strength, and proportional to the squeezing parameters of the modes. These results provide insights into the effects of quantum squeezing on entanglement generation in systems with gravitational interactions. Analytically and numerically it is shown that momentum squeezing can enhance gravitationally induced quantum entanglement.

We extend the Polyakov-loop-enhanced linear-sigma model to encompass four flavors and utilize it to analyze the light, strange, and charmed meson mass spectrum as it transitions from the vacuum into a hot and dense medium. Within the mean-field approximation, we determine the masses of scalar ($0^{++}$), pseudoscalar ($0^{-+}$), vector ($1^{--}$), and axial-vector ($1^{++}$) meson states, encompassing both open- and hidden-charm constituents, as functions of temperature $T$ and baryon chemical potential $\mu_B$. With parameters calibrated to the vacuum spectrum, the charm degree of freedom proves essential for an accurate description of observed masses, and charmed states acquire their in-medium modifications from the light and strange condensates that modify their valence quarks. Each species seems to undergo melting along its distinct trajectory, yet all transitions occur within a narrow band surrounding the chiral transition. The open-charm $D$-meson functions as a precise indicator of chiral restoration: its mass increases substantially across the transition and reflects the non-strange condensate, whereas hidden-charm states remain largely unaffected and serve as reference standards for the surrounding matter. We establish that transition points from three independent measurements delineate the chiral phase boundary ($T_c$, $\mu_B$), whose curvature matches lattice-QCD predictions and which persists as a crossover throughout the examined range, exhibiting no critical endpoint.

This paper develops a data-driven framework for long-term prediction of fluid–structure interaction (FSI) dynamics, focusing on the flow-induced vibration (FIV) of a flexible plate. A stiffness-conditioned neural evolution operator jointly represents the Eulerian flow field and Lagrangian structural state. The plate is represented by 101 ordered structural tokens carrying nodal coordinates and velocities, with nondimensional bending stiffness as a global conditioning variable. Bidirectional cross-attention couples fluid and structural representations within a hybrid CNN-Transformer architecture. Trained with staged multi-step autoregressive rollouts and symmetry-reflected trajectories, a single operator captures three stiffness-dependent response regimes: deflected–flapping, deflected, and flapping. The predicted trajectories preserve the principal flow structures, structural oscillations, and dominant frequencies, while blind 1000-step rollouts remain bounded. The operator also interpolates to stiffness values excluded from training. To reduce sensitivity to under-resolved near-wall gradients in force reconstruction, we develop a differentiable aerodynamic-force module based on the derivative-moment transformation (DMT). Conventional wall-stress surface integrals are replaced by an enclosed 2D curve integral around the core vortex region, enabling accurate reconstruction of lift and drag. A Signed Distance Function (SDF) and smoothed Dirac-delta formulation make the integration fully differentiable while preserving gradient flow. The proposed framework provides an accurate and differentiable surrogate for stiffness-dependent FSI dynamics, enabling efficient parameter studies and future stiffness optimization for flow-energy-harvesting applications.

Compact models of titanium-dioxide memristors used in circuit simulation commonly follow the drift formulation of Strukov et al. and assume a constant ionic mobility, although oxygen-vacancy migration is thermally activated and Joule self-heating is unavoidable. We present ATDM (Arrhenius Thermally Activated Drift Model), a minimal electrothermal compact model that couples the drift equation to a lumped heat balance through an Arrhenius mobility. It adds one thermal state while preserving the electrical state variable, the relation $v=iR(x)$, and the isothermal limit. The model is implemented in Verilog-A, compiled with OpenVAF, and simulated as a device in ngspice, where it reproduces an independent reference implementation within $0.009\,\%$ of the peak voltage and recovers the isothermal excursion at zero activation energy. A dimensionless formulation introduces a thermal lag $\varepsilon$ and an effective switching number $\Theta$. Across $2.5\times10^{5}$ simulations, $\Theta$ orders the state-variable excursion over the tested quasi-static domain with a robust relative scatter of $4\,\%$ and no fitted constant, and the $(\varepsilon,\Theta)$ regime map quantifies when the quasi-static thermal reduction remains valid. Under current drive, the stroboscopic map of the reduced model is proved to be strictly increasing, which excludes period-doubling and chaos in that reduction. Within the sampled ranges, a variance-based sensitivity analysis identifies the effective thermal resistance as a first-order contributor to self-heating, while separate capacitance sweeps show a weak influence of the thermal capacitance in the quasi-static regime. The results characterize the specified model with representative, uncalibrated parameters.

We disprove a weighted generalization of the union-set conjecture [Fra95] raised in [Gow16]. We construct nonnegative weights on subsets of a finite ground set satisfying $w(\varnothing)=0$ and $w(A\cup B)\ge\min\{w(A),w(B)\}$, while every coordinate belongs to an arbitrarily small fraction of the total weight.

We introduce Latin Eulerian numbers $\LE{n\atop k_1,\dots,k_n}$, a multivariate refinement of classical Eulerian numbers counting order-$n$ Latin squares by column ascents. We establish their fundamental symmetries, univariate marginals, and an exact multiplicity divisibility property. For the total ascent statistic $\Sigma(L)=\sum_i k_i(L)$, we prove the sharp, isolated bounds $n-1 \le \Sigma(L) \le (n-1)^2$, demonstrating that the adjacent values $n$ and $(n-1)^2-1$ are strictly unattainable. To analyze intermediate values, we show that symbol permutations typically ignored in classical enumeration directly govern $\Sigma$ via an exact formula. This insight yields explicit constructions for the interior range, motivates a unimodality conjecture for the total ascent distribution.

We propose a new model for describing the excitation of atoms by short symmetric pulses. The theory is based on the impulse approximation and incorporates a confining potential approximated by a harmonic oscillator. Results are presented for a wide variety of parameters, including field intensity and laser frequency. Permitted and forbidden transitions are analyzed in detail. The photon energy spectrum presents peaks attributed to multiphoton absorption. Our model demonstrates robustness and reliability, paving the way for addressing more complex scenarios.

Inspired by the polymath Abraham Ibn Ezra (1089-1167) who approximated {\pi} by 20/9 times the square-root of 2, and contemporary scholar, RSJ Reddy, who gave (14-sqrt(2))/4, we point out that both of these approximations are optimal in some sense, and we generate many other ones that are even more optimal, albeit not as nice.

The Van der Waals black hole (BH) is a non-Kerr model in Anti-de Sitter (AdS) spacetime that exhibits characteristic thermodynamic phase transitions. Whether the physical validity of parameters such as the BH molecular volume $b$ and pressure $P$ is feasible still requires observational verification. As a sensitive probe of strong gravitational fields, the BH photon ring directly carries spacetime geometric information, making it an ideal object for model testing. In accordance with the spacetime metric associated with this BH, this study obtains the null geodesic equations for photons and conserved quantities, determines the photon sphere conditions and radii via effective potential analysis, investigates the photon ring classification and radiative properties, and employs measurements from the Event Horizon Telescope (EHT) to place constraints on parameters and simulate the optical appearance. The results show that the molecular volume parameter $b$ significantly regulates the radius of the photon sphere radius, photon ring structure, and the luminosity. Within a specific interval, the model exhibits a high degree of agreement with the EHT measurements for M87* and Sgr A*. This interval not only satisfies the energy conditions (weak, strong, and dominant) but also corresponds to a stable Van der Waals-type phase transition region. Furthermore, the photon ring can distinguish between the Van der Waals BH and the Schwarzschild BH: due to the small-black-hole-large-black-hole (SBH-LBH) phase transition and microstructural discontinuities, the photon ring of the Van der Waals BH is particularly sensitive to the parameter $b$, whereas the Schwarzschild BH lacks these features. This work uses the photon ring to probe BH molecular models, linking its microstructure, spacetime geometry and observational signatures, and provides a new way to derive BH microphysics from observations.

In this short note, we provide a simple proof of the irrationality of Euler's number $e$, without using the classical estimates based on continued fractions or Taylor series expansions.

We revisit the combinatorial loop-equation method for computing planar disc amplitudes in multi-matrix models with polynomial potentials. We develop a procedure which organises the Schwinger-Dyson constraints by the level of their boundary insertions and, when the resulting system closes, produces an algebraic equation for the planar disc function. Using this method we recover the disc partition functions associated with fixed, mixed, and free boundary conditions in the three-state Potts model, previously obtained by saddle-point methods. As a novelty we derive an algebraic equation for the fixed-boundary resolvent of the three-state Potts model with unequal quadratic and cubic couplings. We further show one can compute the disc partition function for several unsolved two- and three-matrix models. These examples demonstrate that loop equations provide a practical route to identifying and solving sectors of multi-matrix models beyond the standard one- and two-matrix cases.

This paper studies disjointness and \(\mathscr{F}\)-product recurrence with respect to zero-entropy systems. First, we prove that, for a point whose orbit closure has zero topological entropy, \[ \text{distality}\rightleftharpoons \Finf\PRzero\rightleftharpoons \Fpubd\PRzero \rightleftharpoons \Fps\PRzero \rightovernotleft \Fs\PRzero. \] We also construct a minimal topological dynamical system with uniform positive entropy which is disjoint from all zero-entropy \(M\)-systems but is not disjoint from some zero-entropy \(E\)-system, i.e., \(\Ezero^{\perp}\subsetneq \Mzero^{\perp}\), giving an affirmative answer to a question of \cite[W.~Huang, K.~K. Park and X.~Ye, Topological disjointness from entropy zero systems, Bull. Soc. Math. France 135 (2007), 259–282]. Moreover, the same construction shows that there exists an \(\Fps\PRzero\) point which is not \(\Fpubd\PRzero\), i.e., $\Fps\PRzero$ $\nRightarrow \Fpubd\PRzero$, giving a negative answer to a question of \cite[P.~Oprocha and G.~H. Zhang, On weak product recurrence and synchronization of return times, Adv. Math. 244 (2013), 395–412].