Papers

Moiré patterns in twisted bilayer materials exhibit long-range periodic order that is highly sensitive to twist angle. Identifying commensurate angles from real-space atomic structures remains challenging, as spectral and geometric methods emphasize global periodicity and are sensitive to disorder and finite-size effects. Here, we introduce a data-driven topological framework that quantifies moiré periodicity by treating atomic configurations as point-cloud data and extracting multiscale signatures using persistent homology. At the core of our approach is a small-neighborhood separation filter that removes redundant local motifs in persistence diagrams while preserving key structural features, enabling sharp minima in Wasserstein distances between twisted and untwisted reference configurations that accurately recover commensurate angles. We benchmark this framework against geometric and spectral similarity measures and show that the resulting topological descriptors remain stable under positional disorder ranging from weak to strong perturbations in the bond length. We further transfer these descriptors using a constrained Gaussian process surrogate to sparsely sampled configurations of a twisted MoTe$_2$ dichalcogenide bilayer. These results establish topological descriptors with neighborhood separation as a robust framework for identifying commensurate order in moiré systems and tracking commensurate structural similarity under disorder, sparsity, and finite-size effects.

Extreme emission metal-poor galaxies (EEMPGs) are excellent local laboratories for understanding the extreme physical conditions and ionizing radiation fields in the early Universe. However, the exact source of high-ionization emission lines in them, whether from intermediate-mass black holes (IMBHs), ultra-luminous X-ray sources (ULXs), or radiative shocks, remains debated. We characterize the fundamental properties and ionizing radiation field on metal-poor EEMPGs, aiming to identify the dominant sources of the highly ionizing photons that drive these lines. We selected a sample of 11 EEMPGs, among the most metal-poor galaxies with JWST/MIRI observations known so far (12+log(O/H) < 8.0, or Z/Z$_\odot$ < 20%). Using optical and IR diagnostic diagrams for ions of both high and low ionization potential, we constrain the ionization source dominating their spectral features. We detect high-ionization lines, notably He II$\lambda$4686 in all galaxies and [Ne V] 14.3 $\mu$m in 42% of a broader sample of local EEMPGs. The multi-wavelength diagnostic diagrams reveal that our EEMPGs are located in areas that normally are occupied by active galactic nuclei (AGNs) or between the star-formation and AGN sequences. Evaluating the energetics required to produce these lines, we find that radiative shocks and ULXs are not sufficient. Instead, our analysis suggests that a combination of sources with star-formation and a small contribution from an IMBH provide enough high-energy photon budget to explain the emission lines of ions with high-ionization potentials (> 54 eV). Our EEMPG sample, covering various properties, is ideal for studying the first galaxies. Their flux ratios of low- and high-ionization lines suggest stellar radiation as the likely ionization source, with a small contribution from an IMBH (4-8%). Pure shocks fail to explain the observed emission line ratios and ionizing photon budget.

Accurate localization of the bronchoscope within the bronchial tree is essential for clinicians to be able to reach target lesions, perform biopsies and avoid misidentification of airway segments during diagnostic and therapeutic procedures. However, existing navigation systems typically rely on patient-specific CT scans or additional external sensors, increasing cost, setup time and patient radiation exposure. This work presents BronchoTop, a real-time, RGB-only framework for topological bronchoscopy localization that eliminates the need for patient-specific data. BronchoTop estimates scope location relative to a generic airway model through four modules: lumen detection and tracking, lumen-branch label association, probabilistic scope location estimation, and switch verification. By using only standard bronchoscopy video input, BronchoTop provides practical, real-time navigational assistance to physicians. Evaluation on phantom, simulated and real data demonstrates state-of-the-art accuracy, improving existing approaches performance by over 20% on real bronchoscopy sequences. BronchoTop is the first published framework including both the localization algorithms as well as all the real data used, together with code to generate additional simulations, encouraging and facilitating further developments and benchmarking. The results highlight BronchoTop's potential to enhance procedural safety, efficiency and accessibility in clinical and robotic bronchoscopy.

We present LightMIS, a scalable family of ultra-lightweight convolutional networks for 2D binary medical image segmentation without a learned stage-wise decoder. LightMIS aligns the outputs of a five-level encoder to a common resolution using Scale-Aligned Projection blocks, aggregates them once, and refines the fused representation with an Adaptive Fusion Cascade. The cascade combines Adaptive Kernel Fusion with the proposed Progressive Receptive Fusion module, which uses temporary channel expansion, complementary depthwise receptive fields, and progressive cross-branch information transfer. We evaluate LightMIS-T, LightMIS-S, and LightMIS using five-fold cross-validation under a common nnU-Net v2.3.1 protocol on DRIVE, Kvasir-SEG, DSB18, BUSI, ISIC-2017, and ISIC-2018. Full LightMIS contains 0.131 M parameters and requires 0.575 GFLOPs for a $3\times256\times256$ input, achieving modality-macro Dice and IoU scores of 86.71% and 78.99%, respectively. Mobile U-ViT obtains 86.75% Dice and 79.07% IoU, so the observed differences are 0.04 and 0.08 percentage points. Relative to Mobile U-ViT, nnWNet, and nnU-Net, LightMIS reduces parameter count by 90.58$-$99.61% and GFLOPs by 82.54$-$96.14%. On an Arm Mali-G52 MC2 GPU, all LightMIS variants achieve full GPU delegation, with median delegated latency ranging from 53.31 ms for LightMIS-T to 138.31 ms for LightMIS. These results demonstrate a favorable accuracy-complexity trade-off and on-device execution feasibility for the evaluated tasks. The code is publicly available at https://github.com/AndreiiArhire/LightMIS.

Two types of non-Hermiticity found in physical systems, i.e., non-reciprocal couplings and complex potentials, have gained considerable interest recently. The former leads to the non-Hermitian skin effect, while the latter gives rise to a range of non-Hermitian symmetries such as parity-time ($PT$) and particle-hole symmetries. Although these two non-Hermitian forms have been incorporated in the same models, so far they have been treated as distinct families of non-Hermiticity. In this work, we establish an isospectral mapping between them using the Lanczos transformation. More specifically, we show that a generalized Hatano-Nelson model $H$ with non-reciprocal and spatially varying couplings can be mapped to a tight-binding model $H_L$ with real symmetric couplings and an imaginary on-site potential. This result holds even when the original $H$ already has an imaginary potential and exceptional points. Our work provides a refreshed understanding of the connection between different forms of non-Hermiticity. It also offers an approach to obtaining an intuitive physical understanding of exceptional points in $H_L$ that are elusive in $H$. Finally, our findings also warrant a versatile approach to constructing non-Hermitian systems with a complex potential and a real spectrum, without $PT$ symmetry.

Model Predictive Path Integral (MPPI) control relies on stochastic trajectory sampling, and its performance under limited rollout budgets depends strongly on the structure of the proposal distribution. Conventional Gaussian perturbations, even when temporally correlated, transmit high-frequency jitter to the executed commands when only a few rollouts are available. We introduce Spike-MPPI, a motoneuron-inspired proposal in which a common stochastic drive recruits pools of motor units whose discharges are filtered by twitch kernels, yielding sparse, temporally coherent perturbations. We evaluate Spike-MPPI on legged locomotion and manipulation tasks with a Franka FR3 arm in simulation, as well as on a physical robot. Spike consistently produces the smoothest executed commands across all tasks, including against spectrum-matched Gaussian proposals, and a planar ablation identifies the common drive as the largest contributor to this smoothness among the tested motor-pool mechanisms. In manipulation, this smoothness is also accompanied by improved task performance and success, such as in ball balancing, where Gaussian, pink-noise, and spectrum-matched proposals largely fail. On hardware, Spike also yields the shortest task completion times and the smoothest commands. These results show that, beyond its power spectrum, the statistical structure of the sampling is a key design factor for finite-budget MPPI control.

Comparison of predictive values of diagnostic tests is a topic of interest in Medical Statistics, and has been the subject of different studies. In clinical practice, it is frequent to observe categorical covariates when comparing diagnostic tests. In this framework, a global hypothesis test is proposed to simultaneously compare the predictive values of two diagnostic tests when in all of the individuals categorical covariates are observed. This hypothesis test is solved through regression models and also by weighted least squares method for the analysis of categorical data. Simulation experiments were carried out to study the asymptotic behavior of these methods when a binary covariate is observed and when a covariate with three categories is observed, and these were compared to the behavior of the global test when the covariate is ignored. In general, the method based on regression models has shown to have better asymptotic behavior than the other methods. Furthermore, we studied the application of the method based on the regression models when no covariate is observed, for which the individuals in the sample are randomly assigned to a binary dummy random variable. Simulation experiments carried out showed that this method has greater power than the method without the covariate. The results were applied to two examples.

We complete, in the general Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for dimensions \(3\le n\le29\), initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or the solution is asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for every dimension \(n\ge30\) in our companion paper.

Benchmarking and routing platforms increasingly act as intermediaries connecting large language model providers with end-users. However, providers on these platforms typically use a fixed price per token, preventing users from achieving the most competitive price for their tasks. In this work, we design a procurement platform where token prices for each task are driven by provider competition, enabling users to secure competitive pricing for guaranteed quality levels. To this end, the platform sequentially routes queries via a reverse second-price auction that incentivizes model providers to truthfully bid their best estimate of the average cost to serve a user's query. As it routes queries, the platform learns the quality offered by each provider and progressively routes queries to the most cost-competitive provider among those meeting a desired quality threshold. To validate our design, we conduct experiments with multiple LLMs from the Llama and Qwen families on popular mathematical reasoning and question-answering benchmarks. The results show that the pricing margin of the most cost-competitive provider on our platform varies significantly—from $10\%$ to $71\%$—depending on the task and quality threshold. This suggests a substantial inefficiency in the current fixed-price market, and it demonstrates that our platform may enable users to capture maximum savings whenever competitive market conditions permit.

We propose a class of extended generalized Pareto models for right-censored survival data, with particular emphasis on tail inference and long-term extrapolation. Our framework integrates extreme value theory and survival analysis, combining a generalized Pareto distribution with a flexible perturbation distribution on the unit interval. We consider three perturbation specifications: a parametric Beta model, a Bernstein polynomial estimator, and a histogram-based estimator. To facilitate direct comparison, all three models are fitted using a unified iterative procedure adapted to right censoring through Kaplan-Meier-based pseudo-observations. A Monte Carlo study evaluates finite-sample performance across different tail indices, censoring levels, sample sizes, and model complexities. The results reveal a trade-off between flexibility and stability: the Beta specification generally performs best for tail-index estimation, whereas the histogram estimator performs particularly well for scale estimation under low censoring. The Bernstein estimator shows intermediate performance and greater sensitivity to sample size and censoring. Applications to bladder cancer recurrence and heart-failure survival data show that models with very similar in-sample fits can nevertheless produce markedly different tail-index estimates and long-term extrapolations. These findings emphasize the importance of perturbation specification when extended generalized Pareto models are used for survival extrapolation under censoring.

The ResNet-18 image classification model is employed to determine the physical parameters of a plate reverb from a recording of the impulse response. The model is adapted to derive parameters using normalized and downsampled multi-resolution spectrograms computed from the provided impulse responses (IRs). To refine the prediction of the output location, the spectral phase response is also included as an additional input channel to the network since multiple output locations can give the same magnitude response for high-order resonant modes. On a 5000 IR validation set, our model achieves an average normalized mean squared error (NMSE) of 0.02920 across all parameters, with the lowest average NMSE occurring for parameters yo (0.00228), Ly (0.00347), and xo (0.00574).

We study how Difference of Convex (DC) decomposition affects cutting-plane approximation in global optimization. For a smooth decomposition $f = g-h$, let $d$ be the dimension of the span of all Hessian ranges of $g$ over the convex hull of a compact feasible set. The smallest attainable dimension equals the minimum rank of a constant positive semidefinite matrix majorizing the Hessians of $f$ on that convex hull, and is attained by a quadratic first component. Retaining earlier gradient cuts and accepting new cuts only when the model error exceeds $\epsilon$ gives an $O(\epsilon^{-d/2})$ bound on accepted cuts. For an adaptive global DC method, this also bounds the number of subproblems solved exactly and globally. Under nondegeneracy, the exponent is sharp for uniform cutting-plane approximation of quadratic first components. A structured example reduces the certified exponent from $n/2$ to $1/2$ and the global subproblem to one variable.

Accurate simulations of non-Markovian quantum transport remain limited to small systems, and a key bottleneck is that each system site requires an independent set of quantum bath orbitals. We introduce the Stochastic Phase Algorithm (SPA), which replaces the independent local Gaussian baths in single-quasiparticle Holstein models by $R$ shared quantum baths with stochastic site-dependent phases. We prove that phase averaging reproduces the target two-point bath correlation matrix for every $R$, while increasing $R$ systematically suppresses errors from higher-order cross-site correlations. We obtain a fixed-time $O(R^{-1})$ trace-norm error bound with a prefactor independent of system size and connectivity. This spatial compression applies directly to unitary baths and can be combined with coupled-Lindblad spectral compression [Phys. Rev. Lett. 136, 090403 (2026)], which represents each shared environment by a very small number of coupled, damped quantum modes fitted to its thermal bath correlation over the simulation window. Numerically, SPA converges against direct unitary benchmarks on a $3\times3$ lattice, enables full-state-vector quantum-bath dynamics on a $100\times100$ lattice, and, with $R=1$, closely reproduces near exact benchmarks for exciton populations in bacteriochlorophyll aggregates and carrier mobility in rubrene.

Turn-taking prediction is especially relevant for social robots that act as mediators in human-human interaction, where the expected action is often not to speak, but to orient, wait, avoid interruption, or prepare a balanced intervention. This paper presents Multimodal Voice Activity Projection (MM-VAP) as a human state-aware perception layer for future robot mediation behavior. The model estimates the future evolution of the conversational floor from synchronized audio-visual evidence and derives turn-taking events such as Hold, Shift, Shift prediction, Backchannel prediction, and overlap-related states. The approach uses VA-related pretrained audio-visual encoders, LoRA adaptation, inter-speaker attention, and zero-shot event inference from future voice activity projections. Experiments on NoXi, NoXi+J, and Haru EDR support the feasibility of this formulation, especially for floor management events that can be connected to gaze preparation, active listening, and conservative intervention. Finally, the paper defines the expected robot output interface and discusses the main deployment constraints, including real-time inference, preprocessing latency, multimodal synchronization, and input-quality monitoring.

Time-frequency methods are well suited to the analysis of data from the Laser Interferometer Space Antenna (LISA), including nonstationary noise and data gaps. Another motivation is that the sparse time-frequency support of binary signals allows for fast waveform generation, which is the focus of this work. Amongst the many possible time-frequency representations, the orthogonal Wilson-Daubechies-Meyer transformation has a frequency translation symmetry that allows for a banded heterodyne transformation of chirping signals. When combined with the sparse evaluation of the LISA time-delay-interferometry (TDI) response using “TDI on the fly,” the time-frequency representation has a small memory footprint and highly parallel operations. Full-observation, full-cadence waveforms are avoided: templates are assembled from sparse carrier tracks and local packet calculations, with short direct endpoint segments where the slow-track approximation fails. A family of fast template-generation algorithms is described for three important source classes: galactic binaries, massive black-hole binaries, and extreme mass-ratio inspirals (EMRIs). The same construction applies to the slowly evolving portions of all three signals; the principal differences arise at frequency turnovers, merger, and plunge. The calculation may be organized carrier by carrier, or the polarization waveforms may be transformed first and the detector response applied to their combined time-frequency representation. The latter construction is referred to as “TDI Tapestry.”

We establish a Petersson-Rankin-Selberg identity for Hilbert Rankin-Cohen brackets over totally real fields of degree greater than one and arbitrary narrow class number. This extends results of Zhang-Zhang and Zhang-Zhou. For even $k,\ell\ge 2$, $r\in\mathbb{Z}_{\ge 0}$, $K=k+\ell+2r$, and normalized full-level cuspidal Hecke eigentuples $f\in S_K(\omega_f)$ and $h\in S_\ell(\omega_h)$, we show $\langle f,[E_k,h]_r\rangle=C_{F,k,\ell,r}L^S(k/2,\Pi(f)\times\Pi(h)^\vee)/L_F(k,\omega_f\omega_h^{-1})\ne 0$, where $C_{F,k,\ell,r}>0$. Specializing to $k=2$, we remove the remaining GRH assumption in the product classification of Hao-Qin-Zhou. Hence, over real quadratic fields of narrow class number one, the only full-level product identities among Hecke eigenforms of even parallel weights at least two, up to interchanging the factors, are $E_4^{\mathrm{eig}}=60(E_2^{\mathrm{eig}})^2$ and $h_8=120E_2^{\mathrm{eig}}h_6$ over $\mathbb{Q}(\sqrt{5})$.

Human teleoperators spend substantial time demonstrating behaviors that robots can already perform autonomously, limiting the scalability of data collection for robot foundation models. Task and motion planning (TAMP) can automate many of these behaviors, but a fixed planning domain may not support every stage of a long-horizon manipulation task. We present TANDEM (Tamp with As-Needed Demonstrations for Efficient Model fine-tuning), a system that combines TAMP with selective human teleoperation to collect demonstrations for tasks beyond the planner's capabilities. Our key idea is to represent human assistance as an on-demand planning capability. Given a language instruction and visual observation, TANDEM uses pretrained vision-language models to extend the planning domain with missing predicates and human-executed magic operators. This allows the planner to interleave autonomous and human-executed stages without task-specific intervention points. After each human stage, TANDEM re-perceives the scene and checks whether the intended effects hold before resuming autonomous planning. To support fine-tuning vision-language-action (VLA) models, TANDEM also uses example pretraining trajectories to align planner-generated motions with the target model's pretraining distribution. We evaluate TANDEM on five long-horizon manipulation tasks beyond the TAMP domain's capabilities. On a representative long-horizon task, TANDEM collects 2.9x as many demonstrations as full-task teleoperation at the same human intervention time. Fine-tuning a pretrained \pi_{0.5}-DROID model on 20 TANDEM demonstrations per task increases average task success from 0% to 60% across the five tasks.

We extend the phi-FD finite-difference scheme, which handles domains described by a level-set function on a Cartesian grid, to Neumann boundary conditions. The condition is relaxed near the boundary through the level-set and an auxiliary field, which is eliminated by writing the relaxed condition at a boundary node and at its nearest interior node. The scheme uses only interior nodes and the level-set: no ghost values, flux reconstruction or cut-cell volumes. We prove optimal consistency and show second-order convergence in the L2, H1 and Linf norms on a non-convex domain. Two elementary precautions, an individual normalization of the boundary equations and a rule for the choice of the coupled interior node, make the condition number O(h^-2) and independent of the smallest cut cell, without any stabilization term.

We present VGM-VS, a visual servoing method built on a pretrained feed-forward visual geometry model. Given the current view and a reference image captured at the target configuration, we estimate the relative camera pose with a visual geometry model and apply it iteratively as the pose increment of a closed-loop pose-based visual servoing (PBVS) scheme. The geometry-aware representation acquired from large-scale pretraining keeps this estimate reliable when the target is occluded, weakly textured, or covers only a small part of the image. However, the scale ambiguity inherent to these models leaves the predicted translation defined up to an unknown scale, while the pose increment must be metric for robot control. We close this gap with a scene-specific metric adaptation: the robot autonomously records image–pose pairs along a predefined motion starting from the target pose, and we fine-tune the camera head on these data, jointly learning the hand–eye transform and thus removing the need for a dedicated calibration process. We evaluate our method on three real-world assembly tasks with demanding tolerances: USB-C cable picking, cable insertion, and RAM insertion. Running in real time at 30Hz, VGM-VS converges to submillimeter terminal accuracy on the cable tasks, and reaches success rates of 90–100% when the target is moved during servoing. It converges in all trials under initial displacements of up to 30cm from the reference pose and with 50% of the target object occluded, outperforming the compared visual servoing baselines.

We confirm a conjecture posed by T. Iwaniec in 1982: the $L^p$ norm of the Beurling–Ahlfors transform is $p-1$ if $p\geq 2$, and $(p-1)^{-1}$ if $1<p\leq 2$.

We show that a Riemannian metric on $RP^3$ is a surface Zoll metric if and only if its four projective area widths are equal. We also establish a weighted Crofton formula on $RP^3$ under surface Zoll metrics, from which we derive an inequality relating the systole, the volume, and the common value of the projective area widths.

For a subset $S$ of a finite group $G$, let $I_G(S)$ denote the set of commutators $[g,x]=g^{-1}g^x$, where $g\in G$ and $x\in S$. Suppose that a finite group $G$ has a Carter subgroup $C$, that is, a nilpotent subgroup containing its normalizer. Suppose that any subgroup generated by a subset of $I_G(C)$ is $r$-generated. We prove that if $G$ is soluble, then the derived subgroup $G'$ has $r$-bounded rank. We produce examples showing that the solubility condition cannot be dropped. For any finite group, we prove that the rank of $G'$ is $(r,l)$-bounded, where $l$ is the maximum rank of composition factors of $G$ isomorphic to $PSL_2(q)$ for $q\equiv 7\,(\operatorname{mod}8)$. We also prove in the general case that $G'$ has $r$-bounded rank under the additional condition that for any $x\in I_G(C)$, any subgroup generated by a subset of $I_G(x)$ is $r$-generated. The proofs rely on the classification of finite simple groups, using which we prove that if a finite simple group $G$ has an element $x$ of prime order $p$ such that any subgroup generated by a subset of $I_G(x)$ is $r$-generated, then $G$ has $r$-bounded (Prüfer) rank or is isomorphic to $PSL_2(q)$ with $q \equiv 3\,(\operatorname{mod}4)$ when $p=2$, or to $PSL_2(q)$ with $q \equiv -1\,(\operatorname{mod} p)$ when $p\ne 2$.

Envy-freeness is a fundamental notion of fairness in the allocation of indivisible goods. In this paper, we study envy-free allocation under Leontief preferences, which model perfect complements. Although Leontief preferences have been extensively studied in the context of allocating divisible goods and market equilibria, they have received comparatively little attention for the allocation of indivisible goods. We show that, unlike additive valuations in cardinal preferences, an envy-free allocation always exists for Leontief preferences when there are at least two goods. In contrast, envy-free allocations may fail to exist when there is a single good, however it can be decided in polynomial time. We next study the problem of computing a welfare-maximizing envy-free allocation. We prove that this problem is NP-hard in general, whereas it is polynomial-time solvable when there is only a single good or agents have identical demands. Finally, we investigate the parameterized complexity of this problem.

We compute contours of the enhanced quark number susceptibility ratio $R_q$, normalized by the free quark gas susceptibility, around the critical end point (CEP) using the on-shell renormalized two-flavor quark-meson (RQM) model and its two Polyakov-loop-extended variants: the Log RPQM and PolyLog-glue RPQM models, employing logarithmic and PolyLog-glue forms of the Polyakov-loop potential without and with quark back-reaction, respectively. These contours are compared with those from the curvature-mass parametrized quark-meson-with-vacuum-term (QMVT) model and its logarithmic Polyakov-loop extension (Log PQMVT) [117], to assess how different treatments of quark one-loop vacuum fluctuations affect the critical region. Although the critical fluctuation regions near the RQM/Log RPQM CEP are reduced in $T$-$\mu$ extent relative to the QMVT/Log PQMVT case, the higher-$T$, lower-$\mu$ CEP location shifts its enhanced-susceptibility domain toward higher $T$ and lower $\mu$. Since the $\sigma$ and $\pi$ curvature and pole masses differ in the RQM/Log RPQM model but coincide in QMVT/Log PQMVT, we also compare contours of the enhanced scalar susceptibility ($\sim 1/m_\sigma^2$) around the respective CEPs. To isolate the roles of strange flavor and the $U_A(1)$ anomaly, we compare $R_q = 2, 3, 5$ contours from our two-flavor RQM/Log RPQM/PolyLog-glue RPQM model calculations with the corresponding 2+1 flavor RQM/RPQM model very recent results in Ref [146].

We establish whole-sequence convergence of the primal iterates of the smoothing-based full-splitting proximal subgradient method (S-FSPS) of Boţ, Li, and Tao (SIAM J. Optim., 35 (2025), pp.~2623–2653) with a prescribed, nonsummable sequence of vanishing smoothing parameters. The challenge is that each iteration uses a different smoothed model. We address this by constructing fixed lifted potentials, deriving compatible sufficient-decrease and relative-error estimates, and applying a scaled Kurdyka–Łojasiewicz (KL) finite-length argument that controls the residuals caused by changes in the smoothing parameter. Under a KL assumption on the corresponding fixed lifted potential and a weighted summability condition on these residuals, the primal trajectory has finite length. For power schedules $\gamma_k=(k+k_0)^{-\beta}$, with $k_0\geq1$ and $1/2<\beta\leq1$, the summability condition holds when the lift exponent is sufficiently large. Consequently, the primal sequence converges to an exact limiting lifted stationary point without imposing full-row-rank assumptions on the linear operators. As a corollary, we establish whole-sequence convergence for a variable-smoothing full-splitting projected-gradient method in nonconvex nonsmooth composite optimization. Examples distinguish primal convergence from convergence of the auxiliary dual variables and illustrate the role of nonsummability in guaranteeing exact stationarity.

Phishing emails that impersonate Nigerian fintech providers can combine deceptive sender addresses, lookalike links, and locally familiar language. This study presents a Gmail browser extension that integrates sender-domain and URL checks with a bidirectional long short-term memory (BiLSTM) classifier. The extension compares visible sender addresses and links with profiles for eight fintech platforms, obtains a phishing probability from a locally hosted Flask service, and displays a legitimate, warning, or phishing verdict when an email is opened. The BiLSTM classifier was evaluated on 8,943 test messages from a cleaned dataset of 59,622 phishing and legitimate emails. The test confusion matrix recorded 4,308 true negatives, no false positives, one false negative, and 4,634 true positives. These counts correspond to 99.99% accuracy, 100.00% precision, 99.98% recall, and 99.99% F1 score. Tokenized sequence analysis identified 5.79% overlap between the training and test sets, which may inflate performance estimates for independent messages. A Gmail demonstration showed the integrated extension producing user-visible verdicts, although the complete system was not evaluated on a labeled test set. The findings establish the feasibility of the implemented prototype while leaving its end-to-end detection performance and generalization to unseen attacks open for further evaluation.

We study braidings and infinitesimal braidings on categories of bi(co)modules and tetramodules, and their compatibility with duoidal structures. For an arbitrary coalgebra, we classify braidings on its category of bicomodules with the cotensor product in terms of canonical $R$-forms, dualizing the classification for bimodules obtained by Agore, Caenepeel, and Militaru. Every such braiding is a symmetry and admits only the zero infinitesimal braiding. We construct duoidal structures on categories of bi(co)modules and tetramodules over bimonoids in braided monoidal categories under suitable assumptions on equalizers and coequalizers. We then introduce pre-Cartier duoidal categories and their one-sided variants. We establish obstructions to compatible braidings for tetramodules, construct nonzero one-sided pre-Cartier structures on bi(co)modules, and give a pre-Cartier duoidal example with distinct monoidal products and a nonzero infinitesimal braiding.

We report the detection of a tentative, narrow spectral feature in the GeV gamma-ray spectrum of the blazar 4FGL J1754.2$+$3212, using approximately 16.5 years of observations from the Fermi Large Area Telescope. A detailed likelihood analysis of the time-averaged spectrum reveals a localized, line-like excess at an energy of $\sim$31 GeV, with a local statistical significance of $\sim$3$\sigma$ (3 degrees of freedom), without corrections for multiple trials and the look-elsewhere effect. This feature is not well described by standard smooth continuum models such as a single log-parabola. The addition of a Gaussian component significantly improves the spectral fit. If confirmed by future observations with higher sensitivity, this feature would represent a novel phenomenon in blazar astrophysics. We explore its potential physical origins, which could involve exotic processes such as dark matter annihilation or photon-axion-like-particle oscillations, or extreme astrophysical mechanisms within a structured jet. Regardless of its ultimate nature, this finding highlights the potential of deep spectral studies of blazars to reveal non-standard physics and challenges conventional one-zone emission models. Definitive verification awaits observations by next-generation instruments, particularly the Very Large Area $\gamma$-ray Space Telescope (VLAST).

The Dyson series expands the propagator of a time-dependent Hamiltonian in powers of the Hamiltonian, but its truncations are in general not unitary. The Fer expansion writes the same propagator as an infinite product of matrix exponentials, each of them unitary, and its remainder decays doubly exponentially with the number of factors. Convergence, however, is guaranteed only within a finite radius: the time integral of the norm of the Hamiltonian must be smaller than $2$. This is the best value known to date. Here we improve it by about $30\%$, raising it to about $2.6058$. The result also holds for non-Hermitian Hamiltonians that are Hermitian with respect to a fixed metric.

The objective of this paper is to identify a finite group based on the orbit of a vector under its action. When a finite group acts unitarily on a Hilbert space, the associated Gram matrix lies in the group algebra and satisfies identities that encode the algebraic group structure. We ask about the converse: Given a Gram matrix obtained from the orbit of a vector under the group action, can one recover the underlying abstract group structure? Our main result identifies a short list of conditions on a family of orthogonal matrices that force the family to be the right regular representation of a finite group. Building on this characterization, we develop a staged optimization framework that enforces these conditions progressively. Numerical experiments on the dihedral group $D_4$ and the tetrahedral rotation group $A_4$ recover $D_4$ exactly and all twelve $A_4$ matrices up to modest precision.