We introduce a method for detecting regularity loss in solutions to the three-dimensional Navier-Stokes equations using the approximation error of Sinusoidal Representation Networks (SIRENs). SIRENs use sin() activations, producing C-infinity outputs that cannot represent non-smooth features. By classical spectral approximation theory, the SIREN error is bounded by O(N^{-s}) where s is the local Sobolev regularity. At a singularity (s to 0), the error is O(1) and localizes via the Gibbs phenomenon. We decompose the velocity field into a cheap analytical baseline (advection-diffusion) and a learned residual (pressure correction), training a compact SIREN (4,867 parameters). We validate on the 3D Taylor-Green vortex, where error concentration increases from 4.9x to 13.6x as viscosity decreases from 0.01 to 0.0001, localizing to the stagnation point -- the geometry matching the singularity proven by Chen and Hou (2025) for 3D Euler. On axisymmetric equations, we reproduce blowup signatures (T* converging across resolutions) and identify a critical viscosity nu_c = 0.00582 for the regularization transition.

Longitudinal coupling offers a compelling pathway for quantum nondemolition (QND) readout, but pulse design is constrained by hardware limitations such as the coupling strength and the photon number required to stay within the linear regime. We develop a reinforcement learning framework to optimize the longitudinal coupling waveform under such constraints. Building upon the theoretical foundation of shortcuts to adiabaticity (STA), we parameterize an auxiliary trajectory with cubic B-splines and reconstruct the physical control. At a fixed short readout time, the optimized pulse converges to a constraint saturating flat-top protocol and yields a approximately $50\%$ improvement in $\mathrm{SNR}$ over an STA baseline, while exhibiting enhanced robustness to parameter drifts. Simulation results demonstrate the efficacy of reinforcement learning in optimizing longitudinal readout pulses. The optimized protocol attains substantial performance gains and yields smooth, hardware-compatible waveforms governed by an interpretable ``saturate-and-hold'' mechanism.

Tool-using automation systems, from scripts and CI bots to agentic assistants, fail in recurring patterns. Common failures include unsafe side effects, invalid arguments, uncontrolled retries, and leakage of sensitive outputs. Many mitigations are model-centric and prompt-dependent, so they are brittle and do not generalize to non-LLM callers. We present Policy-First Tooling, a model-agnostic permission layer that mediates tool invocation through explicit constraints, risk-aware gating, recovery controls, and auditable explanations. The paper contributes a compact policy DSL, a runtime enforcement architecture with actionable rationale and fix hints, and a reproducible benchmark based on trace replay with controlled fault and misuse injection. In 225 controlled runs across five policy packs and three fault profiles, stricter packs improve violation prevention from 0.000 in P0 to 0.681 in P4, while task success drops from 0.356 to 0.067. Retry amplification decreases from 3.774 in P0 to 1.378 in P4, and leakage recall reaches 0.875 under injected secret outputs. These results make safety to utility trade-offs explicit and measurable.

Ferroelectric materials with switchable spontaneous polarization underpin non-volatile memories, transistors, sensors, and emerging neuromorphic chips. Their performance and stability are governed by polarization dynamics and domain kinetics, making a microscopic understanding of these processes and precise atomic level control of polarization domains key challenges for next-generation ferroelectric electronics. Due to the limitations of the characterization technology with atomic level in experiment, high precision atomic simulations become important. First principles calculations are inherently limited in accessible length and time scales, making it difficult to capture the complex features of dynamic processes. Machine learning molecular dynamics (MLMD) offers a compelling solution by encoding quantum-mechanical accuracy into force fields, thereby enabling large scale dynamic simulations with near first-principles fidelity. This Perspective highlights the advantages of MLMD for simulating polarization switching, domain nucleation and migration, topological polar textures and curvature-driven ferroelectric phenomena, while providing a systematic overview of recent progress in these areas. We further discuss methodological challenges that limit predictive capability, including long range electrostatics, coupled lattice-spin degrees of freedom in multiferroics, and data efficient pre-training of large atomistic models. Corresponding advances in long range aware force fields, spin dependent machine learning models, and large scale pretraining are expected to move MLMD toward a genuinely predictive framework for the design of ferroelectric and multiferroic materials.

A recent paper, Phys. Rev. Research 8, 013261 (2026), claims that the polaromechanical normal-mode splitting (NMS) measured in Nat. Commun. 16, 5652 (2025) is not true based on their two results: $i$) there is no true splitting in the linear-scale spectrum; $ii$) the total or intrinsic decay rate of the cavity-magnon polariton, set by the imaginary part of the pole of the total output spectrum, remains unchanged under the coherent-perfect-absorption (CPA) condition. In this comment, we indicate that $i$) there is NMS in both the linear and logarithmic scales of our spectra in {\it a narrow frequency range} around the CPA frequency; $ii$) the total decay rate defined via the {\it pole} of the spectrum cannot characterize the vanishing {\it effective} decay rate at the CPA frequency (known as the monochromaticity of the CPA), and thus this parameter is irrelevant to the NMS measured in our experiment in {\it a narrow frequency range} around the CPA frequency. Consequently, their results above are either false or irrelevant, and thus cannot support their claim on the polaromechanical strong coupling measured in our experiment.

Rydberg-state hopping is demonstrated in a wavemeter-locked two-photon rubidium system (Rb D2 probe at 780 nm and 480 nm coupler), enabling rapid and repeatable switching between the 65S1/2 and 63D5/2 states without cavity or frequency-comb stabilization. A Fizeau-interferometer wavemeter provides the error signal for a digital feedback loop that simultaneously stabilizes the coupler and commands discrete Rydberg-state changes. The lock achieves sub MHz frequency stability and acquisition rates up to 6.5 GHz/s (0.4283 GHz engaged in 66 ms), extrapolating to ~0.93 s for a ~6 GHz 65S to 63D transition. Time resolved spectra reveal reemergent dissipative time-crystal oscillations after each hop, with distinct state dependent fundamentals and harmonics. This approach addresses the need for dynamically reconfigurable Rydberg state control for on resonant multi band field detection, while the DTC frequency reconfigurability enables adaptive, low frequency E field sensing in compact, cavity free architectures.

Simulation of open quantum systems via the Lindblad master equation is a computational bottleneck in near-term quantum control workflows, including optimal pulse engineering (GRAPE), trajectory-based robustness analysis, and feedback controller design. For the system sizes relevant to near-term quantum control ($d = 3$ for a single transmon with leakage, $d = 9$ for two-qubit, and $d = 27$ for three-qubit), the dominant cost per timestep is a $(d^2 \times d^2)$ complex matrix-vector multiplication: a $9\times9$, $81\times81$, or $729\times729$ dense matvec, respectively. The working set sizes (1.5 KB, 105 KB, and 8.1 MB) straddle the L1, L2, and L3 cache boundaries of modern CPUs, making this an ideal system for cache-hierarchy performance analysis. We characterize the arithmetic intensity ($\approx 1/2$ FLOP/byte in the large-$d$ limit), construct a Roofline model for the propagation kernel, and systematically vary compiler flags and data layout to isolate the contributions of auto-vectorization, fused multiply-add, and structure-of-arrays (SoA) memory layout. We show that SoA layout combined with -O3 -march=native -ffast-math yields $2$--$4\times$ speedup over scalar array-of-structures baselines, and that -ffast-math is essential for enabling GCC auto-vectorization of complex arithmetic. These results motivate a set of concrete recommendations for authors of quantum simulation libraries targeting near-term system sizes.

We investigate whether low-frequency pulsar observations can provide LoS magnetic field estimates and whether these are consistent with synthetic LoS signatures extracted from a three-dimensional CME reconstruction constrained by Solar Orbiter data. We analyze a CME occultation of the LoS to PSR J1022+1001 on 20 August 2021, observed simultaneously with LOFAR and NenuFAR. From LOFAR, we derive time-resolved dispersion measure (DM) and rotation measure (RM) and isolate the CME contributions using background estimates for interstellar, solar wind and ionospheric components. We then infer the density-weighted LoS-averaged magnetic field component <B||>_PSR from the ratio delta-RM/delta-DM. In parallel, we reconstruct the CME using a semi-empirical 3DCORE model fitted to Solar Orbiter in-situ magnetic field observations at 0.65 au. We sample the modeled magnetic field along the pulsar LoS using fixed spatial sampling points and compute synthetic LoS-averaged signatures <B||>_3D for different flux rope configurations. The derived <B||>_PSR increases from approximately -9 nT to a peak near 63 nT during the observed interval. Comparison with synthetic signatures shows that the polarity and temporal evolution of the LoS signal are strongly dependent on the flux rope configuration and only a South-West-North (SWN) configuration (confirmed by Solar Orbiter in-situ data) reproduces the observed sign and overall evolution, whereas alternative configurations are incompatible. The modeled amplitudes, however, are systematically larger than the pulsar-derived values by roughly a factor of five. We show that simultaneous low-frequency pulsar DM and RM measurements can provide LoS magnetic field estimates for a CME and can be used to test CME magnetic structure against data-constrained three-dimensional reconstructions.

Quality assessment of brain structural MR images is critical for large-scale neuroimaging studies, where motion artifacts can significantly bias clinical estimates. While visual rating remains the gold standard, it is time-consuming and subjective. This study evaluates the relative performance and generalization capabilities of two prominent Automated Quality Assessment (AQA) methods: MRIQC, which uses hand-crafted image-quality metrics with traditional machine learning, and CNNQC, which utilizes a deep learning (DL) architecture. Using a heterogeneous dataset of 1,098 T1-weighted volumes from 17 different sites, we assessed performance on both seen sites and entirely new sites using a leave-one-site-out (LOSO) approach. Our results indicate that both DL and traditional ML methods struggle to generalize to new scanners or sites. While MRIQC generally achieved higher accuracy across most unseen sites, CNNQC demonstrated higher sensitivity for detecting poor-quality scans. Given that DL-based methods like CNNQC offer higher computational efficiency and do not require expensive pre-processing, they may be preferred for widespread deployment, provided that future work focuses on improving cross-site generalizability.

As the ECMAScript specification evolves, industrial-scale JavaScript compilers face the challenge of supporting modern language syntax while maintaining compatibility for diverse execution environments. Traditionally, compilers solve this by running transpilation passes in a monolithic pipeline, where the transpilation passes are chosen to execute strictly based on a target language level. This results in significant computational waste, as compilers perform expensive Abstract Syntax Tree (AST) traversals to lower features that may not exist in the actual input source code. We present a compiler improvement that conditionally executes transpiler passes based on accurately tracking and dynamically maintaining the exact set of language features present in the compilation unit throughout the transpilation process. It is implemented in the production Google Closure Compiler. By populating and maintaining a FeatureSet at every JavaScript script-level, it dynamically skips running unnecessary lowering passes. We detail the architectural safeguards -- including strategic pass ordering and dynamic validation of the transpiled code for feature-correctness. Evaluation of this improvement on large-scale production monorepos produced a considerable reduction in compilation time and saved compute and memory usage.

The central theme of my thesis is to explore various simple prototype models that are exactly solvable in the framework of time dependent noncommutative spaces. By adopting the methodology provided by the Lewis Riesenfeld theory, we developed a procedure for obtaining a class of exact solutions for such model systems. We analyzed these solutions by deriving the energy expectation values analytically and representing those energy dynamics graphically. We also examined the explicit existence of a non-zero Berry geometric phase in the noncommutative framework and analyzed the role of noncommutativity in generating a non-trivial Berry phase when the model Hamiltonian and the noncommutative parameters are periodic in time. Overall, my thesis contributes to a deeper understanding of quantum theory in time dependent noncommutative backgrounds and indicates a strong possibility for developing a consistent quantum theory within such frameworks.

In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal evolution. Existing techniques can effectively quantify the overall clustering tendency of events using global statistical measures. However, these macroscopic approaches leave a critical gap, as they do not attempt to investigate the dynamics of individual clusters. Analyzing individual clusters is essential, as it helps comprehend the local interactions that actively drive the system dynamics, which may be obscured by global averaging, while simultaneously revealing the time scales involved. To address these limitations, we propose a complex network-based framework for analyzing clustering of events occurring at irregular intervals. The framework establishes connections using arrival times, transforming the time series into a network. Network properties are then used to quantify the clustering. Further, a community detection algorithm is used to identify individual clusters in time series. We illustrate the method by applying it to standard arrival processes, such as the Poisson process and the Markov-modulated Poisson process. To further demonstrate its scope, we apply the method to two diverse systems: the time series of droplet arrivals in turbulent flows and the R-R intervals in electrocardiogram (ECG) signals.

The ductile-to-brittle transition (DBT) in body-centred cubic systems is a central design constraint for cryogenic structures. Performing parametric studies to enhance the understanding on DBT using fully coupled thermomechanical continuum DBT models is computationally expensive. Therefore, in this work, a lightweight phase-field surrogate is proposed. This surrogate approach captures key \emph{DBT-like} trends within a standard isothermal two-field (displacement--damage) setting by prescribing temperature dependence through three phenomenological mechanisms: (i) a temperature-dependent degradation exponent $n(T)$ that sharpens stiffness loss from gradual (ductile-like, $n=2.0$ at 293\,K) to abrupt (brittle-like, $n=3.5$ at 77\,K), (ii) temperature-dependent yield stress and elastic modulus to modulate the balance between plastic dissipation and elastic energy storage, and (iii) an effective fracture toughness and driving-force scaling to represent reduced crack-tip shielding at cryogenic temperatures. The model is implemented in FEniCSx using small-strain $J_2$ return mapping and a staggered solution scheme. Simulations of a single-edge-notched specimen over 77--293\,K demonstrate a systematic progression from brittle-like to ductile-like response, characterised by reduced displacement to unstable fracture, a transition from abrupt post-peak load drop to extended softening, and a shift from narrow, localised damage bands with confined plasticity to broader process zones. A sensitivity study comparing four interpolation schemes (linear, smoothstep, exponential, hybrid) shows that the qualitative transition trends are robust, with interpolation primarily affecting intermediate-temperature responses while endpoint behaviours remain unchanged.

This paper addresses the Bi-Objective Traveling Thief Problem (BI-TTP), a challenging multi-objective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the $\varepsilon$-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable $\varepsilon$-levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting $\varepsilon$ parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.

This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete asymptotic characterization of Quantum Neural Network Operators in the approximation of arbitrary quantum channels. The result extends the classical Voronovskaya theorem from scalar approximation to the non-commutative operator framework of quantum information theory. We introduce rigorous quantum analogues of Sobolev and Hölder spaces defined through Fréchet differentiability in the Liouville representation and measured using the completely bounded (diamond) norm. Within this framework, we derive an explicit asymptotic expansion of the approximation error and identify the fundamental mechanisms governing convergence. The expansion separates integer-order differential contributions, fractional corrections associated with limited regularity, and intrinsically non-commutative effects arising from operator algebra structure. We also establish a sharp remainder estimate with explicit dependence on the regularity of the channel and the dimension of the underlying Hilbert space. Several applications demonstrate the scope of the theory. These include a quantum central limit theorem describing the fluctuation regime of quantum neural network operators, an optimal interpolation method based on operator geometric means, and a convergence acceleration procedure inspired by Richardson extrapolation. The results provide a rigorous mathematical foundation for the asymptotic analysis of quantum neural network models and establish a direct connection between classical approximation theory, operator algebras, and quantum information science, with implications for quantum algorithms and quantum machine learning.

The ADAMOS (Axion Daily Modulation Searches) project aims to explore the nature of dark matter (DM) through a novel axion haloscope experiment. We propose to construct a fixed-frequency cavity resonator operating at 20 GHz at the University of Hamburg, using an innovative "thin-shell" design that preserves a large detection volume at high frequencies. The experiment will be installed in an existing 14 T superconducting magnet and connected to a highly sensitive RF chain with continuous in situ calibration to eliminate temperature-dependent gain drifts, constituting an essential improvement based on lessons learned from previous attempts. ADAMOS will conduct simultaneous searches for three classes of axion signals: (1) conventional cold DM axions, (2) relativistic axions from axion quark nugget annihilations exhibiting daily modulations, and (3) transient enhancements from streaming DM. By targeting this unexplored frequency regime with a robust, calibrated, and versatile setup, ADAMOS will open new discovery channels in a previously unexplored region of the dark sector.

Information Retrieval (IR) is fundamental to many modern NLP applications. The rise of dense retrieval (DR), using neural networks to learn semantic vector representations, has significantly advanced IR performance. Central to training effective dense retrievers through contrastive learning is the selection of informative negative samples. Synthesizing 35 seminal papers, this survey provides a comprehensive and up-to-date overview of negative sampling techniques in dense IR. Our unique contribution is the focus on modern NLP applications and the inclusion of recent Large Language Model (LLM)-driven methods, an area absent in prior reviews. We propose a taxonomy that categorizes techniques including random, static/dynamically mined, and synthetic datasets. We then analyze these approaches with respect to trade-offs between effectiveness, computational cost, and implementation difficulty. The survey concludes by outlining current challenges and promising future directions for the use of LLM-generated synthetic data.

We have developed a non-isothermal analytical model for the impedance of the cathode catalyst layer (CCL) in a PEM fuel cell. In-phase harmonic perturbations to the current density and temperature reduce the impedance and the static polarisation resistivity of the CCL due to lowering proton transport losses. A special selection of the current and temperature perturbation amplitudes allows for complete elimination of these losses.

A graph is $\mathrm{ISK}_4$-free if it contains no induced subdivision of $K_4$. Lévêque et al. [\emph{J. Combin. Theory Ser. B} \textbf{102} (2012) 924--947] conjectured that all $\mathrm{ISK}_4$-free graphs are 4-colorable. Chen et al. [\emph{J. Graph Theory} \textbf{96} (2021) 554--577] proved that $\{\mathrm{ISK}_4, \mathrm{diamond}, \mathrm{bowtie}\}$-free graphs are 4-colorable and asked whether such graphs are 3-colorable, where a diamond is $K_4$ minus one edge and a bowtie consists of two triangles sharing a vertex. In this paper, we characterize the structures of $\{\mathrm{ISK}_4, \mathrm{diamond}, \mathrm{bowtie}\}$-free graphs and prove that such graphs are 3-colorable, which answers a question of Chen et al. [\emph{J. Graph Theory} \textbf{96} (2021) 554--577] affirmatively and extends a result of Chudnovsky et al. [\emph{J. Graph Theory} \textbf{92} (2019) 67--95]. Furthermore, our structural theorem yields a polynomial-time algorithm for decomposing $\{\mathrm{ISK}_4, \mathrm{diamond}, \mathrm{bowtie}\}$-free graphs, and consequently a polynomial-time algorithm for coloring this class of graphs.

Postselection of quantum trajectories is known effectively introduce nonlinearity into dynamics of open quantum systems. We study the effect of such non-linearity in continuous-time quantum walks (CTQWs) on networks with homogeneous and heterogeneous degree distributions. Using the recently proposed nonlinear Lindblad master equation (NLME), we investigate the dynamics under two decoherence mechanisms: Haken-Strobl and quantum stochastic walk (QSW). Our analysis reveals a striking dichotomy: under Haken-Strobl decoherence the nonlinear contributions precisely cancel, yielding a uniform steady state independent of postselection details. In stark contrast, QSW decoherence permits postselection to break dynamical balance on heterogeneous networks, inducing robust localization preferentially at low-degree (peripheral) nodes. Remarkably, this localized state maintains finite quantum coherence. Extending our results to many-body spin systems, we demonstrate that degree heterogeneity similarly stabilizes localization of spin-up excitations in spin-down backgrounds, enhancing entanglement preservation. These findings establish degree heterogeneity and postselection as joint control parameters for engineering quantum transport and localization in dissipative dynamics.

Cyber deception assists in increasing the attacker's budget in reconnaissance or any early phases of threat intrusions. In the past, numerous methods of cyber deception have been adopted, such as IP address randomization, the creation of honeypots and honeynets mimicking an actual set of services, and networks deployed within an enterprise or operational technology(OT) network. These types of strategies follow naive approaches of recreating services that are expensive and that need a lot of human intervention. The advent of cloud services and other automations of containerized applications, such as Kubernetes, makes cyber defense easier. Yet, there remains a lot of potential to improve the accuracy of these deception strategies and to make them cost-effective using artificial intelligence (AI)-based solutions by making the deception more dynamic. Hence, in this work, we review various AI-based solutions in building network- and device-level cyber deception methods in contested environments. Specifically, we focus on leveraging the fusion of large language models (LLMs) and reinforcement learning(RL) in optimally learning these cyber deception strategies and validating the efficacy of such strategies in some stealthy attacks against OT systems in the literature.

In a web-based review platform, papers from various research fields must be assigned to a group of reviewers. Each paper has an inherent cost, which represents the effort required for reading and evaluating it (e.g., the paper's length). Reviewers can bid on papers they are interested in, and if they are assigned a paper they have bid on, no cost is incurred. Otherwise, the inherent cost $c(e)$ for paper $e$ applies. We capture this with a model of restricted additive costs: every item $e$ has a cost $c(e)$, and each agent either incurs $0$ or $c(e)$ for $e$. In this work, we study how to allocate such chores fairly and efficiently. We propose an algorithm for computing allocations that are both EFX and MMS. Furthermore, we show that our algorithm achieves a $2$-approximation of the optimal social cost, and the approximation ratio is optimal. We also show that slightly weaker fairness guarantees can be obtained if one requires the algorithm to run in polynomial time.

Background: Cheating in university education is commonly described as context dependent and influenced by assessment design, institutional norms, and student interpretation. In software engineering education, programming oriented coursework has historically involved ambiguity around collaboration, reuse, and external assistance. Recently, large language models (LLMs) have introduced additional mediation in the production of code and related artifacts. Aims: This study investigates how software engineering students describe experiences of using LLMs in ways they perceived as inappropriate, disallowed, or misaligned with course expectations. Method: A cross sectional survey was conducted with 116 undergraduate software engineering students from multiple countries, combining quantitative summaries with qualitative data. Results: Reported LLM cheating practices occurred primarily in programming assignments, routine coursework, and documentation tasks, often in contexts of time pressure and unclear guidance. Use during quizzes and exams was less frequent and more consistently identified as a violation. Students reported awareness of academic and professional consequences regarding LLM cheating, while formal sanctions were perceived as limited. Conclusions: Our study indicates that reported LLM misuse in software engineering is associated with assessment and instructional conditions, suggesting a need for clearer alignment between assessment design, learning objectives, and expectations for LLM use.

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned proximal subproblem admits a closed-form solution through its dual formulation. However, such a structure-driven preconditioner may be poorly aligned with the local curvature of the smooth component, which can lead to slow practical convergence. To address this issue, we develop a subspace proximal Newton framework that incorporates curvature information within a low-dimensional subspace. At each iteration, the search direction is obtained by minimizing a proximal Newton model restricted to a two-dimensional subspace spanned by the current preconditioned proximal gradient direction and a momentum direction derived from the previous iterate. By orthogonalizing the subspace basis with respect to the local Hessian-induced metric, the resulting two-dimensional nonsmooth subproblem can be efficiently approximated by solving two one-dimensional optimization problems. This orthogonalization plays a crucial role: it allows a single pass of alternating one-dimensional updates to provide a good approximation to the original coupled two-dimensional subproblem while keeping the per-iteration computational cost low. We establish global convergence of the proposed method and prove a $Q$-linear convergence rate under strong convexity. Comparative numerical experiments demonstrate the effectiveness of the proposed algorithm, particularly on high-dimensional and ill-conditioned problems.

In this short paper, we show a characterization of Birkhoff Billiards inside discs which is related to the expansion of the formal Lazutkin conjugacy at the boundary.

In the previous paper we derived Gauss-Givental integral representation for the wave functions of quantum BC Toda chain and also introduced Baxter operators for this model. In the present paper we prove commutativity of Baxter operators, as well as show that the constructed wave functions are symmetric with respect to signed permutations of spectral parameters and diagonalize Baxter operators. Furthermore, we derive Mellin-Barnes integral representation for the wave functions. With its help we show that wave functions satisfy dual system of difference equations with respect to spectral parameters and coincide with hyperoctahedral Whittaker functions. Finally, we give heuristic proofs of orthogonality and completeness of the wave functions.

We obtain Gauss-Givental integral representation for the eigenfunctions of quantum Toda chain with boundary interaction of BC type. For this we introduce reflection operator satisfying reflection equation with DST chain Lax matrices. Besides, we define Baxter operators for BC Toda chain, prove their commutativity with Hamiltonians and derive the corresponding Baxter equation.

Phononic Crystals provide a versatile platform for controlling phonons in applications such as waveguiding, filtering, and sensing. To minimize dissipation, cavity resonators are often embedded within the bandgap of phononic crystals and integrated with suitable transduction techniques. Here, we demonstrate one-dimensional (1D) phononic transmission using electrostatic transduction, enabling the realization of high-quality mechanical oscillators. Using a double-ended tuning fork resonator embedded in a 1D phononic crystal, we observe degenerate flexural modes (in-phase and out-phase) exhibiting enhanced and comparable quality factors within the same device due to mode degeneracy. The in-phase mode, whose frequency lies inside the phononic bandgap, shows an approximately two-fold increase in quality factor compared to an anchored resonator, while this enhancement diminishes for the out-phase mode (frequency outside the bandgap) at temperatures where thermoelastic dissipation is negligible. This approach offers a promising route toward low-loss, encapsulated phononic devices for sensing and signal processing applications.

Large-scale AI training workloads in modern data centers exhibit rapid and periodic power fluctuations, which may induce significant voltage deviations in power distribution systems. Existing voltage regulation methods, such as droop control, are primarily designed for slowly varying loads and may therefore be ineffective in mitigating these fast fluctuations. In addition, repeated control actions can incur substantial cost. To address this challenge, this paper proposes a decentralized switching-reference voltage control framework that exploits the structured behavior of AI training workloads. We establish conditions for voltage convergence and characterize an effective reference design that aligns with the two dominant operating levels of the AI training workload. The switching rule for voltage references is implemented solely using local voltage measurements, enabling simple local implementation while significantly reducing control effort. Simulation studies demonstrate that the proposed method substantially reduces both voltage deviations and reactive control effort, while remaining compatible with internal data center control strategies without requiring extensive coordination.

Elastic similarity measures are fundamental to time series similarity search because of their ability to handle temporal misalignments. These measures are inherently computationally expensive, therefore necessitating the use of lower bounds to prune unnecessary comparisons. This paper proposes a new \emph{Bipartite Graph Edge-Cover Paradigm} for deriving lower bounds, which applies to a broad class of elastic similarity measures. This paradigm formulates lower bounding as a vertex-weighting problem on a weighted bipartite graph induced from the input time series. Under this paradigm, most of the existing lower bounds of elastic similarity measures can be viewed as simple instantiations. We further propose \textit{BGLB}, an instantiation of the proposed paradigm that incorporates an additional augmentation term, yielding lower bounds that are provably tighter. Theoretical analysis and extensive experiments on 128 real-world datasets demonstrate that \textit{BGLB} achieves the tightest known lower bounds for six elastic measures (ERP, MSM, TWED, LCSS, EDR, and SWALE). Moreover, \textit{BGLB} remains highly competitive for \textit{DTW} with a favorable trade-off between tightness and computational efficiency. In nearest neighbor search, integrating \textit{BGLB} into filter pipelines consistently outperforms state-of-the-art methods, achieving speedups ranging from $24.6\%$ to $84.9\%$ across various elastic similarity measures. Besides, \textit{BGLB} also delivers a significant acceleration in density-based clustering applications, validating the practical potential of \textit{BGLB} in time series similarity search tasks based on elastic similarity measures.