Papers

Actual quantum key distribution network nodes may be vulnerable to side-channel attacks such as electromagnetic leakage. In this study, we measured electromagnetic emissions from a prototype quantum key distribution device implementing a time-bin decoy-state BB84 protocol with Y and Z bases. We measured the electromagnetic spectra and waveforms at distances of 0 m and 3 m from the transmitter and receiver inside an anechoic chamber. The results showed that the transmitter was the primary source of electromagnetic leakage, and distinct differences were observed between the quantum states generated at the third harmonic of the 1241.6 MHz clock.

We prove new structural results for algebraic generalized Ricci solitons on solvable Lie algebras and we discuss the existence of examples in low dimensions. We establish that all non-trivial solvable algebraic generalized Ricci solitons must be expanding and give necessary conditions for the existence of such solitons on one-dimensional extensions of abelian Lie algebras. Finally, we classify algebraic generalized Ricci solitons on three-dimensional Lie algebras, and algebraic generalized Ricci solitons on four-dimensional solvable unimodular Lie algebras, up to isometry and scaling.

Structural system theory studies which network topologies can sustain a prescribed system property such as controllability or stability. When the topology is itself random, the relevant question becomes probabilistic: how likely is a graph drawn from a stochastic model to sustain the property? Such probabilities measure the abundance and robustness of the property across topologies, and indicate whether systems requiring it can be reliably deployed in uncertain environments. We address this question for asymptotic stability of linear systems in the directed graphon setting. We consider two graph-theoretic properties. The first is $\mathcal N$, and it requires that for every $k\leq n$ some $k$-vertex induced subdigraph of $D$ admits a cycle cover, and the second is $\mathcal S$, which requires that these subdigraphs can be chosen so that their node sets form a nested sequence $V_1\subset\cdots\subset V_n=V(D)$ starting from a single vertex with a loop. We have shown that $\mathcal N$ is necessary and $\mathcal S$ is sufficient for structural stability. We sample $D$ from a directed step-graphon $W$. Our main results give necessary and sufficient conditions for $\Pr(\mathcal N)\to 1$ and $\Pr(\mathcal S)\to 1$ as $n\to\infty$. In more detail, to a step-graphon $W$ with skeleton digraph $S$ on $q$ nodes and concentration vector $x^*$ we associate a cycle polytope $\vec{\mathcal X}(S)\subseteq\Delta_q$. The conditions are then formulated in terms of the position of $x^*$ within $\vec{\mathcal X}(S)$, the dimension of the polytope, the loop density of $W$ and, for $\mathcal S$, an ordering condition on the cycles of the skeleton. Together these results identify, for directed step-graphons, the regime in which a sampled topology is overwhelmingly likely or unlikely to sustain stable dynamics.

A crystalline undulator is a crystal exhibiting periodic deformations that cause channeled particles to oscillate, generating coherent electromagnetic waves. In this study, stressor layer patterning has been employed to induce the desired deformations on a silicon substrate. Finite element method simulations were performed to optimize the geometric parameters of the undulator. The primary focus was on achieving sinusoidal deformation with sub-millimeter period and amplitude exceeding 1~nm, utilizing the silicon (110) plane for its superior channeling properties. Key parameters, such as substrate thickness and undulator period, were meticulously refined to ensure uniform deformation while minimizing the impact of higher harmonics, which could degrade performance. Based on the simulation results, a crystalline undulator, 160 $\mu$m thick and consisting of 10 periods with a period length of 334 $\mu$m, has been successfully fabricated. The final device demonstrates structural integrity and a uniform deformation extending up to 20 $\mu$m from the surface. Specifically designed for use with 5-30 GeV particle beams, the undulator is capable of generating gamma photons in the 5-15 MeV range. This work effectively integrates advanced simulation techniques with precise fabrication methods, demonstrating the feasibility of crystalline undulators as high-performance devices for generating gamma radiation.

Reliable visual reasoning requires composing multiple visual observations and returning consistent answers to logically equivalent questions. We introduce Hob-VL, a benchmark for visually grounded Boolean reasoning. Hob-VL comprises two tasks: (1) evaluating whether a Boolean rule holds in an image, and (2) identifying the (unique) object satisfying a Boolean description. Hob-VL contains 6,000 human-verified balanced Yes/No questions, each defined by a Boolean combination of ten visual statements, across 1,000 generated scenes and 46 diverse labeled photographs, along with 1,000 object-identification questions over the same photographs. Our question families are deliberately constructed to challenge reasoning through misleading local cues and nested logical operations, and include symbolic and structured natural-language presentations. Across eight model configurations with thinking disabled or minimized, Boolean accuracy ranges from 48.52% to 50.57%, while the identification accuracy reaches at most 43.0%. A thinking-enabled GLM configuration achieves uneven gains while retaining substantial errors and inconsistencies. Hob-VL exposes these failures through executable reference answers and matched evaluations.

A long-time Poincaré section flattens a chaotic orbit into one static blur, erasing the order in which the orbit visits its own local structures. We introduce the sliding-window frequency ratio (SWFR), built from nothing but radial and polar turning events, to recover that order along individual relativistic orbits. Each window spans a fixed number of radial cycles and simply counts the polar events inside it; because event times are kept, any candidate interval can be sliced out and replotted as its own Poincaré section. No spectrum, no reference center, no basis functions. Integrable Kerr benchmarks recover the known frequency ratios, and for regular motion with uniformly bounded count deviations the counting-error bound falls off as $O(W^{-1})$. The same counts then pay off in chaos. In magnetized Kerr spacetime a single charged orbit dwells near $3/5$ and later near $4/7$, and exactly those intervals open into fivefold and sevenfold section structures; a second orbit dwells near $1/2$ with two lobes. In Schwarzschild–Melvin spacetime a photon holds $4/5$ across a fivefold pattern. In every case the section covers exactly the interval SWFR selected: integer counts and phase-space geometry agree that a globally chaotic orbit is paying a temporary visit to a resonance.

Miniaturized ultrasound (US) probes require programmable and synchronized transmit (TX) excitation across multiple elements, while existing compact platforms often rely on limited microcontroller (MCU) pulse generators or closed-source fixed-function pulser devices. We present U-Sonic, an open-source digital US TX peripheral integrated into a 32-bit RISC-V system-on-chip (SoC). The implemented SoC integrates 8 pulser cores, while the parameterized architecture supports up to 16 channels. Each core generates single- or dual-tone bursts with programmable period, duty cycle, pulse count, polarity, and idle level, together with optional inverted stop pulses for active damping. A shared memory-mapped Open Bus Interface (OBI) enables synchronous start and stop of arbitrary channel subsets and supports composite bipolar, gated, and three-level excitation schemes. Functional correctness was verified in Verilator against a Python golden model over 4379 checked cycles across directed and randomized configurations, and confirmed on a Terasic DE10-Lite field-programmable gate array (FPGA). The design was synthesized and placed-and-routed in IHP 130 nm. The post-layout area in kilo gate equivalents (kGE), scales as 1.65 kGE plus 1.66 kGE per channel. The 8-channel instance occupies 14.9 kGE, corresponding to approximately 14.3% of the 104 kGE SoC. The register-transfer level (RTL), register descriptions, verification collateral, and software support are released as open source.

Wearable ultrasound enables continuous deep-tissue monitoring, and a single programmable probe can operate in multiple complementary modes, such as structural A-mode and Doppler flow measurement. However, each operating mode requires dedicated measurement parameters and peripheral states, with no single configuration serving all modes on resource-constrained devices. Time multiplexing of operating modes introduces reconfiguration latency that lowers the effective mode repetition rate. To address this limitation, we present an open-source, transition-aware control stack for low-latency, in-session reconfiguration of the 32-channel TinyProbe wearable platform. Operating modes are described as hardware configurations, and host-side shadow registers track the peripheral states, enabling transition-specific register updates. Transition sequences are executed either by the host (over Wi-Fi 6) or by a firmware loop on the probe MCU. We validate the stack on a pulsatile-flow phantom by interleaving blocks of 25 to 100 pulsed-wave Doppler shots at 1.43 kHz PRF with single 16-channel A-mode acquisitions, changing channel configurations at every transition. Compared to full reconfiguration, the overhead per transition decreases from 30.2 ms to 11.6 ms (host-scheduled) and 3.1 ms (MCU-scheduled). For 75-shot Doppler blocks, the multi-mode repetition rate reaches 16.0 Hz (MCU-scheduled), 90.1% of the theoretical maximum of 17.7 Hz. Concurrent reconstruction of a Doppler spectrogram and a lumen-diameter trace demonstrates the functionality of time-multiplexed flow and structural monitoring.

Decision models often score a variable-sized set of candidate actions encoded in a single sequence. This setting is increasingly relevant for System 1 components inside generative systems, where candidates may be proposed or ordered differently across runs. Standard causal cross-encoding is expressive, but it can make a candidate's score depend on serialization order rather than on the underlying decision problem. We introduce candidate-independent block-causal attention, which preserves causal computation within the shared context and each candidate while blocking cross-candidate information flow and resetting candidate positions. We compare this architecture with standard causal attention and complementary invariant baselines across Gemma 3 1B, Qwen3 1.7B, and Qwen3 4B backbones. Candidate-independent attention consistently reduces permutation sensitivity while retaining competitive decision quality; ablations indicate that candidate isolation is the primary source of the effect, with position resetting completing the intended symmetry. A larger Qwen3-4B study further examines the behavior of the proposed architecture with substantially more training data. Code is available at the \href{https://github.com/guyAmit/ci-decision-models}{\textcolor{blue}{project repository}}, and the \href{https://huggingface.co/Guy-Amit/qwen3-4b-ci-decision-4096-poc}{\textcolor{blue}{Qwen3-4B model artifact}} is available on Hugging Face.

In polar semiconductors the Fröhlich interaction is the dominant electron–phonon coupling, yet excitonic resonances in materials such as halide perovskites remain anomalously sharp. We show that standard frozen-center-of-mass treatments of the exciton–phonon problem miss the decisive kinematic degree of freedom: restoring the exact center-of-mass (COM) recoil reveals a universally open, parameter-free $1s\to1s$ absorption channel at recoil momentum $q_*=\sqrt{2M_{\rm ex}\hbar\omega_{\rm LO}}/\hbar$, whose rate scales as $N_{\rm LO}(T)$. We prove that this recoil channel is controlled by destructive electron–hole interference: the recoil linewidth vanishes with the mass asymmetry as $\gamma_{\rm LO}^{\rm recoil}\propto\mathcal{F}_{1s,1s}(q_*)^2$, and the elastic dressing obeys the exact suppression law $S_X/S_{\rm ind}=\eta^2(6-\eta^2)/5$ within the hydrogenic Fröhlich model. The theory establishes a hierarchy of scattering regimes. In mass-asymmetric materials (GaAs, $\eta=-0.74$) the recoil channel is active ($\gamma_{\rm LO}^{\rm recoil}=2.2$~meV); in mass-symmetric materials (FAPbI$_3$, $\eta=0$; MAPbI$_3$, $\eta=-0.11$) it is killed by interference (0.00 and 0.12 meV), showing that the observed 27–40 meV perovskite linewidths cannot be accounted for by COM recoil and therefore require internal-state-changing and other inelastic channels, of which the constructive, $\eta$-robust $1s\to np$ resonance is the leading candidate within the present model. The Fröhlich constant $\alpha$ alone is therefore insufficient as a figure of merit: after projection onto the correlated exciton, the controlling parameters are $\eta$, $q_*a_X$, and the Rydberg detuning.

Stochastic recursive momentum (STORM) achieves fast convergence for nonconvex optimization via the variance reduction effect, but existing analyses rely on the strong average smoothness assumption. In this paper, we study the convergence of STORM for different objectives without average smoothness. We first revisit the results under average smoothness, obtaining the $O(T^{-1/3})$ bound for nonconvex objectives and the $O(\sigma^2/(\mu T))$ bound for last-iterate output under the $\mu$-Polyak–Łojasiewicz~(PL) condition. Without average smoothness, we design an auxiliary sequence and compare the STORM update with it in the analysis. With the help of this sequence, we prove that STORM still attains an $O(T^{-1/4})$ rate for nonconvex objectives, which is optimal under standard smoothness. For convex and $\lambda$-strongly convex objectives, we further prove averaged and last-iterate bounds with optimal rates of $O(\sigma R/\sqrt T)$ and $O(\sigma^2/(\lambda T))$, respectively. All the obtained results use the same STORM recursion with different hyperparameter choices.

Intracule pair densities provide insight into electron correlation, but their routine analysis in extended systems is limited by the cost of numerical integration and the restriction of analytical methods to Gaussian basis functions. We present an efficient multicenter integration scheme for intracule densities and their moments. By adapting the topological fuzzy Voronoi cell formalism, we partition intracule space around interatomic displacement vectors, concentrating quadrature points near secondary density maxima that standard single-center grids poorly resolve. Benchmarks on linear alkanes show improved convergence with increasing molecular size, achieving relative errors below 0.02% in electron-electron repulsion energies with fewer quadrature points than single-center methods. The partitioning also enables the decomposition of global two-electron properties into spatial contributions associated with short- and long-range electron-pair separations. Coupling the multicenter grid with kernel density estimation reconstructs smooth radial intracule distributions at large interelectronic distances without the dense angular grids required by conventional surface integration. Validation on the S22 dataset supports the reliability of the method across diverse molecular systems. These developments facilitate intracule analysis in polyatomic systems and the investigation of electron correlation and dispersion interactions.

The Rayleigh-Plateau instability predicts that infinitesimal perturbations of a liquid jet grow only for kR < 1, with kR = 1 marking the classical stability boundary. Here, we show that femtosecond-laser-induced cavitation generates a localized, impulsive recoil perturbation on a flowing liquid jet, enabling a two-dimensional map of jet breakup across the (kR, epsilon/R) plane. The perturbation's spacing (wavelength) and strength (amplitude) are set independently by the laser repetition rate and pulse energy, respectively. At low amplitudes, tuning the repetition rate recovers the classical Rayleigh-Plateau dispersion relation and its kR = 1 cutoff, while increasing the wavelength enables controlled generation of monodisperse droplet trains, bidisperse droplet populations, and ultimately isolated single droplets. Along the amplitude axis, low pulse energies produce a seed that amplifies only the imposed wavenumber, whereas above a critical energy Ec, the seed broadens to excite many wavenumbers simultaneously. At still higher amplitudes, we demonstrate deterministic breakup for kR > 1, extending to kR = 1.9, with laser-synchronized droplet production rates up to 0.2 MHz. These results establish localized femtosecond-laser-induced cavitation as a route to controlled Rayleigh-Plateau breakup both within and beyond the classical linear-stability boundary.

A petal diagram of a knot is a projection with a single multi-crossing and no nested loops; it is encoded by a permutation of the heights of the strands through the multi-crossing. Colton, Glover, Hughes and Sandberg proved a Reidemeister-type theorem for petal diagrams: two petal permutations represent the same knot if and only if they are related by trivial petal additions and deletions and by crossing exchanges. We ask whether every petal diagram of the unknot can be reduced to the one-petal diagram without ever increasing the number of petals, in analogy with Dynnikov's monotonic simplification theorem for rectangular diagrams. By an exhaustive, certified computer search we show that this is true for diagrams with at most 7 petals and false for 9 petals. Of the 40320 petal diagrams with 9 petals, 24992 represent the unknot, and exactly 108 of them are hard: none of them admits a crossing exchange or a trivial petal deletion, even if two natural petal-number-preserving symmetries are allowed. Up to these symmetries and mirror image there are three hard diagrams. Two of them can be untangled by passing through 11 petals; the third cannot be untangled through diagrams with at most 11 petals, but can through 13. We explain why the phenomenon differs from the rectangular case: a petal diagram is an arc presentation whose cyclic order of pages is determined by the order of its vertices on the binding, and no elementary move of Cromwell and Dynnikov preserves this rigid structure.

Video Large Language Models (VideoLLMs) receive frames in sequential order and interpret how visual content evolves along the temporal axis, yet temporal reasoning remains a persistent weakness across architectures. Reversing the frame order of a video, a transformation that should invert temporal answers, often leaves the final prediction unchanged. We investigate where this failure originates by defining the temporal divergence vector $\tau_l$, the layer-wise representational difference induced by reversing temporal order. Tracking its magnitude across layers reveals a consistent temporal divergence profile where the divergence peaks at intermediate layers and progressively diminishes toward the output. We confirm this peak is specific to temporal reasoning and functionally critical for predictions, establishing that VideoLLMs acquire temporal information at intermediate layers but fail to maintain it to the output. This progressive fading motivates our method, Temporal Activation Injection (TAI), which extracts $\tau_l$ at the peak of the profile for each input and reinjects it into subsequent layers following the measured decay. TAI requires no training and consistently improves temporal reasoning across three VideoLLMs and four benchmarks with negligible impact on non-temporal tasks. Code is available at https://github.com/Youngwoo-git/Before-It-Fades.

In a polar material, a neutral exciton couples to phonons through the sum of the electron and hole deformation potentials. Because the total source vanishes by charge neutrality, the elastic exciton-phonon vertex is regularized by electron-hole interference. Here we determine the non-perturbative fate of this interference by exact diagonalization of a Holstein-exciton model. By parameterizing the mass asymmetry to decouple it from the small-polaron atomic limit, we map a regime map comprising an internal dressing crossover and a dissociation boundary. We prove analytically and verify numerically that for equal masses, the symmetric exciton ground state is protected from phonon dressing by an exact exchange selection rule, provided the phonon source is odd under electron-hole exchange (the neutral case). As mass asymmetry increases, this selection rule is broken and the exciton acquires a strong local polaronic cloud. We show that the dissociation boundary, conversely, is set by a global energy balance between Coulomb binding and polaronic stabilization, and is nearly independent of the internal dressing. Paradoxically, the very symmetry that protects the exciton from dressing denies it polaronic stabilization, driving it toward dissociation at strong coupling. We discuss these results in the context of lattice exciton-polaron models and their implications for sharp versus broad excitonic lines in mass-symmetric versus mass-asymmetric polar semiconductors.

This paper presents a cell-centred unstructured finite-volume method for time-harmonic two-phase acoustics. A volume-fraction representation supplies density and acoustic compressibility. Face fractions average available neighbouring planar interface cuts independently of velocity direction, retaining the established one-field face-density closure. Cartesian complex-coordinate stretching provides perfectly matched layers (PMLs). Real-imaginary splitting yields a real-valued block system, discretized with corrected non-orthogonal fluxes and consistent boundary contributions. Verification covers homogeneous waves, layered gas-liquid transmission with PML truncation, baffled-piston radiation with Kirchhoff far-field reconstruction, and resolved rigid-sphere radiation forces. Homogeneous-wave pressure converges at approximately second order on orthogonal meshes and on meshes with non-orthogonal interiors and orthogonal boundary cells. Reconstructed velocity converges at approximately second order on orthogonal meshes and with an observed order of about 1.7 on the latter mesh family. Under aligned refinement, the layered case's relative whole-domain complex-pressure $L_2$ error decreases to $2.657\times10^{-4}$. The resolved-sphere force differs from the Gorkov prediction by at most 1.5% over the tested Rayleigh size range. The results quantify the accuracy and current limitations of the heterogeneous Helmholtz-PML formulation.

Large Language Models (LLMs) are increasingly applied to process streaming data, with practitioners relying on benchmarks to select the best model even though these signals only approximate real performance. While oracle annotations can provide reliable feedback, they are often costly and difficult to obtain at scale. To address this challenge, we propose ONLINE LLM PICKER, the first framework for active model selection for LLMs in online settings. Given an arbitrary stream of queries and a limited annotation budget, ONLINE LLM PICKER selects the most informative prompts for annotation to identify the best LLM among candidate models. Across multiple tasks including 10 datasets, for over 130 language models, we show that ONLINE LLM PICKER saves annotation cost by up to 71.67% while reliably identifying the best or near-best model for the stream. We also show that using the returned model for sequential generation on unannotated prompts across the stream reduces regret by up to a factor of 2.51x, indicating that ONLINE LLM PICKER can identify the best or near-best model well before processing all streaming prompts.

We study the average-case matrix discrepancy problem: given independent normalized $d\times d$ Gaussian orthogonal ensemble matrices $A_1,\dots,A_N$ and a fixed margin $\kappa>0$, find signs $\sigma_1,\dots,\sigma_N\in\{-1,1\}$ such that the operator norm of $\sum_{i=1}^N \sigma_i A_i$ is at most $\kappa\sqrt{N}$. Focusing on the proportional regime $N/d^2\to \tau\in(0,\infty)$ as $d\to\infty$ followed by the small-margin limit $\kappa\downarrow 0$, we characterize the density required by stable offline algorithms and by online algorithms. In the offline setting, we construct a polynomial-time recenter-and-round algorithm that is noise-stable and succeeds whenever $\tau=\Omega(\frac{1}{\kappa^2\log(1/\kappa)})$, along with a matching lower bound for all stable algorithms. In the online setting where each sign must be chosen irrevocably upon observing the corresponding matrix, we determine the exact limiting performance of the Frobenius-greedy algorithm, establishing that it succeeds when $\tau>\tau_{\rm FG}(\kappa)\sim \frac{\pi}{4\kappa^2}$, as well as a matching lower bound for all online algorithms by conditioning on a revealed prefix. At the core of our algorithms lies rotational symmetry, which enables us to transfer Frobenius norm control into operator norm guarantees. Together, our results identify the algorithmic phase transition points for random matrix discrepancy: $\Theta(\frac{1}{\kappa^2\log(1/\kappa)})$ for stable offline algorithms and $\Theta(\frac{1}{\kappa^2})$ for online algorithms. Both thresholds lie far above the satisfiability scale $\Theta(\log(1/\kappa))$, as shown by Maillard~\cite{maillard2025}.

Continual learners that keep a task-specific adapter in every block of a pre-trained vision transformer accumulate storage linearly with the number of tasks; keeping task-specific adapters in only a few blocks curbs this growth but raises the question of where to place them. We investigate this question from two perspectives. Algorithmically, training all contiguous four-block placements yields an inverted U: final accuracy peaks at intermediate depth and varies by up to 3.5 percentage points (pp), while inexpensive criteria based on weight spectra or activation statistics favor the deepest blocks. From neuroscience, the hierarchical organization and intermediate-stage plasticity of the visual cortex motivate us to ask whether a measurement taken outside the learner can guide layer specialization without placement search. LS-B observes the first tasks through a frozen fMRI encoding model of twelve human visual areas and commits task-specific capacity once to the blocks whose readouts vary most across tasks relative to their stable structure. Across three ViT-B/16 backbones, LS-B yields stable, backbone-specific allocations. On the two backbones with placement search, AugReg and iBOT, the selected blocks overlap the intermediate-depth region identified by search. Under matched storage and observation budgets, the selected blocks outperform the shallowest and deepest four-block configurations. On Split ImageNet-R, LS-B uses 60% of full-BiLoRA adapter storage while remaining within 1.5 pp of its final accuracy. The allocation requires no labels or backpropagation, adds under 0.6% runtime, and exhibits backbone-specific cortical signatures.

Pretrained 3D encoders are typically developed on globally reconstructed scenes expressed in a consistent world coordinate frame, whereas embodied systems must reason from partial, viewpoint-dependent observations in camera coordinates. We show that this shift from globally learned 3D feature spaces to realistic partial observations exposes a severe representation mismatch, which we find consistently across representative state-of-the-art encoders, including Sonata and Concerto. A frozen Sonata encoder with a global linear probe achieves 72.47 mIoU on full ScanNet scenes, but 2.57 mIoU on single-frame camera-coordinate inputs. Training-free gravity alignment recovers performance to 41.64 mIoU, showing that coordinate-frame mismatch is a dominant source of degradation but cannot be fully resolved through canonicalization alone. We introduce PAGER, a label-free adaptation method that aligns partial-view features with a frozen global 3D semantic space using only paired partial/global geometry. It learns lightweight adaptation modules while keeping the pretrained encoder and global segmentation probe frozen. Matched-point feature alignment anchors partial features to their global counterparts, while relational supervision preserves their similarity structure with respect to the global representation. Global geometry provides supervision only during training. Inference operates directly on the partial observation. Without partial-view labels, PAGER outperforms label-supervised PEFT on both Sonata and Concerto, and in zero-shot ScanNet$\rightarrow$ScanNet++ transfer surpasses fully fine-tuned Sonata ($53.93$ vs.\ $48.09$ mIoU), suggesting that preserving the frozen global representation can improve cross-dataset transfer.

We study finite-time blow-up and global existence for semilinear heat equations with time-dependent reaction coefficients on metric measure spaces. For convex nonlinearities, we establish a blow-up criterion that retains the dependence on the initial datum through its linear evolution and does not require stochastic completeness. Under additional conservativity and heat kernel assumptions, we also prove blow-up at the critical Fujita exponent associated with polynomial volume growth. Our main global existence result is based on a heat-kernel-weighted functional space in which the mild solution map becomes a contraction. This yields a unified construction covering both polynomial and exponential heat kernel decay, general locally Lipschitz nonlinearities, and time-dependent reaction coefficients, without convexity or monotonicity assumptions. In particular, the global existence criterion only uses the behaviour of the nonlinearity on the range explored by the solution. Applications include Riemannian manifolds, metric graphs, and, within a separate discrete framework, weighted graphs. The arguments, especially the functional construction underlying global existence, are new and lead to new results even for the classical underlying spaces considered above.

Parallel applications are often designed for synchronous, lock-step execution, treating communication stalls as performance hazards. Yet, in a communication-light application without frequent synchronization points that alternates between compute-bound memory-bound execution, an MPI communication stall can act as an unintentional relief on memory-bandwidth contention. We demonstrate this using a Parallel Optical Flow Solver, which combines a compute-bound Ray Tracing kernel with a memory-bound Optical Flow Solver kernel and negligible inter-process communication. This program shows considerable speedup via desynchronization and automatic overlap between compute- and memory-bound phases, showing that natural desynchronization is an architecture-aware optimization. An optimal speedup is achieved when the number of processes concurrently executing the memory-bound phase on a ccNUMA domain is near the bandwidth saturation point. We also show a case where reducing communication overhead using MPI asynchronous progress significantly degrades performance because it allows too many ranks to contend for memory bandwidth simultaneously. In order to study the dynamics under more controlled conditions, we develop a tunable dual-kernel microbenchmark, with which we show that significant application or system noise (natural or injected) is required to achieve full desynchronization. Finally, we also validate these results using a bandwidth-aware, model-based simulator.

The total collision energy (TCE) approach originally developed for taking into account gas-phase chemistry in the direct simulation Monte Carlo method is applied to surface chemistry modeling. In the proposed surface TCE (sTCE) model probability of the impact process as a function of the translational energy of the molecule is found analytically from the finite-rate Arrhenius data. This probability function lacks some mathematical drawbacks typical of previous models. Effects of surface temperature, incident angle and internal energy can be taken into account in the sTCE model. Additionally the model is generalized to the specified reaction efficiency formulation.

We consider the distribution-constrained optimal stopping problem $\sup_{\tau\sim \mu} \mathbb E[B^*_\tau]$, where $\mu$ is a probability distribution on $\mathbb R_+$, and $(B^*_t)$ denotes the running maximum of a standard Brownian motion. This problem was introduced in Beiglbock et al. (PTRF, 2018), where a monotonicity principle is used to establish the optimal stopping time as the hitting time of a specific boundary. In this paper, we characterize this boundary by a variational inequality. In the spirit of Cox et al. (PTRF, 2019), we provide a novel probabilistic representation for the variational inequality as a time-reversed optimal stopping problem. A key ingredient for proving the viscosity solution property and comparison principle is a quantitative estimate near the singular corner of the time-space domain, where the initial and boundary conditions are incompatible. We then prove the optimality of the resulting hitting time through a discrete-time Snell envelope construction and a stability argument for the associated stopping times.

A dominating set $D$ of a graph $G$ is called $k$-limited if every vertex of $D$ has at most $k$ neighbors outside $D$. The minimum cardinality among all $k$-limited dominating sets of $G$ is the $k$-limited domination number, denoted by $\gamma_k^L(G)$. In this paper, we prove that the $1$-Limited Dominating Set problem is $\mathsf{NP}$-complete, answering an open question posed in the literature. We further show that, for every positive integer $k$, the $k$-Limited Dominating Set problem is $\mathsf{NP}$-complete even when restricted to planar graphs. In addition, we study the $k$-limited domination number of Sierpiński graphs. We determine the exact value of $\gamma_1^L(S(n,m))$ for all integers $n\ge 1$ and $m\ge 2$, and obtain the $k$-limited domination number for the planar family $S(n,3)$.

Despite many studies about causes and remedies of plasticity loss in Reinforcement Learning (RL) under continual task changes, no RL method has yet consistently achieved a good balance between adaptation and forgetting. Here we turn to an alternative optimization paradigm, neuroevolution (NE): algorithms that search directly in weight space through mutation and selection over a population of neural networks. Across a wide array of environments and environmental changes, with policies ranging from a few hundred parameters to million-parameter networks, we compare evolution strategies (ES) and genetic algorithms (GAs) against state-of-the-art continual RL variants and population-based RL. ES most consistently achieves a good stability-plasticity trade-off, while the GA is the most plastic method but forgets more than ES. To explain this, we study the return landscape around each method's solutions. ES finds the widest neighborhoods, i.e.\ regions of weight space in which perturbed policies still solve the task, and the size of the overlap between the neighborhoods of consecutive tasks correlates with a method's stability-plasticity trade-off. Rewarding behavioral diversity in a GA through novelty search makes the population even more plastic, at the cost of forgetting. Finally, symptoms of plasticity loss commonly reported in RL do not transfer to NE. Overall, these results establish NE as a competitive alternative to RL under continual task changes, and suggest that training under perturbations in weight space may be a useful mechanism for continual learning more broadly.

We establish viability conditions for a broad general class of stochastic differential equations formulated within the variational approach,% \[ dX_{t}=A\left( X_{t}\right) dt+B\left( X_{t}\right) dW_{t}. \] The underlying functional space setup is given by a general Gelfand triple $V\subset H\subset V^{\ast},$ where $H$ is a separable Hilbert space in which the stochastic evolution equation (SEE) is considered. Our approach to deriving viability conditions is inspired by the techniques developed by Aubin and Da Prato for finite-dimensional forward stochastic differential equations. We establish necessary and sufficient conditions for the viability of closed random constraint sets in terms of adapted variational tangent (and contingent) sets. Furthermore, we illustrate the applicability of the proposed framework by discussing several important classes of stochastic differential equations that fit naturally within our variational setting.

Generative AI models are increasingly used for scenario generation in autonomous driving. While they can generate realistic-looking scenarios, they often provide limited transparency into learned representations and consistency with real-world vehicle dynamics. This lack of formal assurance limits their use in safety-critical validation and certification workflows. To address this aspect, we introduce a layered evaluation protocol that complements existing methods by assessing models across five layers. The first four layers inspect internal representations and network layers through kinematic alignment, statistical baseline comparison, latent controllability, and activation analysis. The fifth layer evaluates model outputs against vehicle dynamics constraints such as lateral jerk thresholds. We demonstrate the protocol on a Variational Autoencoder (VAE)-based scenario generator. Although standard output-level metrics and visualizations suggest that the generated scenarios are realistic, our protocol provides deeper insight into the extent to which the model's latent space aligns with kinematic features and whether visually plausible trajectories satisfy vehicle-dynamics constraints. We further apply the protocol to additional generative models, demonstrating its applicability beyond the VAE architecture.

Credential-based Extensible Authentication Protocol (EAP) authentication cannot distinguish a legitimate credential holder from an adversary using compromised credentials. Physical Layer Deception (PLD) complements credential-based authentication by exposing a deceptive primary object over a primary transport while a separate recovery object travels with differentiated reliability over a secondary channel. Existing PLD studies remain, to our knowledge, at the physical/link-model level; using PLD's activation/deactivation mechanism as an authentication gate creates an authentication-specific design requirement, since an all-inactive attempt would exercise no recovery path. We present a batched PLD-based re-verification step for Enterprise Wi-Fi's TEAP/RADIUS/IEEE 802.11 authentication chain, implemented end to end across the server, access point, and device in the open-source hostap 2.12 codebase. Each attempt carries three rounds, at least one active, with no dedicated activation flag. Across four campaigns totaling 1593 attempts, the prototype evaluates batched recovery behavior, rejects the implemented naive credential-bearing attacker in all 30 attempts, measures successful-path latency, and evaluates the security-reliability trade-off for one, two, and three active rounds under two modeled recovery regimes. The evaluation exercises the protocol and software-MAC behavior directly and analyzes informed and retry-seeking attackers under the software recovery model.