Cross-linking mass spectrometry (XL-MS) has emerged as a powerful quantitative technique for probing intra-protein structural information as well as protein-protein interactions at an unprecedented scale. XL-MS data yield information on the pairwise spatial proximity of proteins through inter-molecular linkers. However, systematic methods for adapting such data for coarse-grained interacting particle models remain limited. Predominant focus is put on directly fitting radial distribution functions (RDFs), while numerous observables, e.g. coordination numbers, which are functionals of the RDF, cannot be uniquely inverted. In this work, we develop a framework for parameterizing interaction potentials from such observables in potentially phase-separated mixtures, as encountered in XL-MS results. We establish a connection between this problem and the inverse Henderson problem and adapt algorithms such as Iterative Boltzmann Inversion and Iterative Monte Carlo to its numerical solution. We derive exact and low-density limit gradient approximations and propose two new algorithms based on an adaptation of the predictor-corrector~framework. In total, we evaluate several optimization algorithms on biologically realistic ten-component test systems. We demonstrate that for homogeneous fluids, all methods achieve exceptional efficiency and accuracy. Critically, we further demonstrate successful parametrization in a challenging three-phase system. Here, three algorithms, namely Adam and gradient descent employing the low-density derivative as well as Newton's method with the exact gradient, reliably recover the correct parameters. These results establish a clear pathway from XL-MS experiments to coarse-grained protein models for systems where phase separation governs biological function, potentially enabling new investigations of biomolecular condensates and protein aggregation.

We explore a cosmological model in which dark energy is described by a bulk viscous fluid, providing a dissipative mechanism for late-time cosmic acceleration. Considering both minimally and non-minimally coupled scenarios, we constrain the model using SNe Ia, DESI DR2 BAO, and Planck 2018 CMB data. We find that viscous effects can successfully mimic dynamical dark energy and yield improved fits over $Λ$CDM, particularly in the interacting non-minimal case. Our results demonstrate that dissipative processes offer a viable and physically motivated alternative to the cosmological constant in explaining the current accelerated expansion of the universe.

In multi-behavior recommendation, auxiliary behaviors such as clicks, add-to-cart, and purchases can provide richer supervisory information for predicting target behaviors. Although existing graph and hypergraph methods are capable of modeling high-order relationships among users, items, and behaviors, they still have limitations in heterogeneous semantics, user-specific weighting, and sequence dependency modeling. While standard Transformers excel at sequence modeling, their shared feedforward mapping struggles to accommodate the differentiated requirements of heterogeneous latent patterns in multi-behavior scenarios. To address this, this paper proposes the Personalized Hypergraph-enhanced Kolmogorov-Arnold Network Transformer (PHKT). Specifically, we design a personalized dynamic hypergraph module that performs behavior-aware weighting of item similarities based on users' historical behavior sequences to capture user-specific heterogeneous high-order relationships. Meanwhile, a Transformer is used as the temporal backbone to model the evolution of short- and long-term preferences, and KAN is introduced to replace the traditional MLP in the feedforward network to enhance fine-grained modeling capability for nonlinear responses to different latent patterns. Experiments on three real datasets, Tmall, RetailRocket, and IJCAI, show that PHKT consistently outperforms nine strong baseline models across multiple evaluation metrics, demonstrating its effectiveness in multi-behavior preference modeling and target behavior prediction.

As grid-forming (GFM) battery energy storage systems (BESS) are increasingly deployed to enhance power system inertial response and frequency stability, incorporating their frequency support capabilities into day-ahead energy scheduling (DAES) is essential for achieving both frequency security and operational efficiency. However, accurately determining frequency metrics in grids with coexisting GFM inverters and synchronous generators requires electromagnetic transient (EMT) simulations, which are computationally prohibitive for direct embedding in grid operational optimization models. To bridge the gap between modeling accuracy and computational efficiency, a learning-assisted DAES (LA-DAES) framework is proposed in this work. By leveraging a surrogate model to represent the frequency support dynamics of GFM BESS, the proposed framework ensures frequency security with a reasonable solve time. Comparative results demonstrate that, relative to analytical frequency-constrained DAES, the proposed LA-DAES framework more accurately captures grid frequency metrics and improves the utilization of GFM BESS.

We extend the explicit study of $G_4$-fluxes and general Hodge cycles from the ordinary Fermat sextic fourfold to tame Fermat-type hypersurfaces in weighted projective space. The main new feature in the weighted setting is that the Galois action on the cyclotomic period data need not preserve the $(2,2)$-subspace. As a consequence, the rational reconstruction of an integral self-dual class can involve additional middle-cohomology components, increasing the norm of the corresponding flux. We work at maximally symmetric Fermat points, where the period matrices and symmetry-invariant Hodge loci can be computed explicitly. Using Movasati's description of periods, cyclotomic period matrices, and Hermite/Smith normal form reductions, we construct the relevant integral lattices of symmetric self-dual classes in middle cohomology. This gives a controlled test of whether symmetric general Hodge cycles can satisfy the M2-brane tadpole bound. Our main conclusion is empirical. In the degree 12 example in $\mathbb{P}_{1,1,1,1,4,4}$, and in the degree 8 weighted example used as a comparison, the shortest computed symmetric general Hodge cycles overshoot the tadpole bound. In the degree 36 example in $\mathbb{P}_{1,1,1,9,12,12}$, which has $h^{1,1}=11$, the most general example we have, the tadpole conjecture is indeed verified at the maximally symmetric locus, although the computations get difficult and computationally expensive. These computations suggest that, in weighted Fermat examples, the relevant notion of a ``symmetric flux'' must take into account not only automorphisms of the variety but also the Galois action on the period field. Non-uniform Galois orbits provide a natural arithmetic mechanism by which symmetric Hodge classes can acquire large tadpole charge.

For the near-contact binary AX Dra, we present the first time-series spectroscopy collected with the echelle spectrograph BOES. From spectral analysis, we measured the projected rotation of $v_1 \sin i$ = $120\pm21$ km s$^{-1}$ and effective temperature of $T_{\rm eff,1}$ = $7220\pm150$ K for the brighter primary component, together with radial velocities (RVs) for both stars. To obtain a consistent binary model, the RV curves were analyzed by combining the 2-min cadence photometric data observed in the TESS sectors 15, 21, 22, and 41. The modeling indicates that AX Dra is a semi-detached system exhibiting a total secondary eclipse, with the detached primary component having a large filling factor of 92 \%. The system has masses of $1.717\pm0.026$ $M_\odot$ and $0.804\pm0.014$ $M_\odot$, radii of $1.541\pm0.020$ $R_\odot$ and $1.237\pm0.014$ $R_\odot$, luminosities of $5.78\pm0.50$ $L_\odot$ and $0.83\pm0.05$ $L_\odot$, and a temperature difference of $Δ$($T_{\rm eff,1}$--$T_{\rm eff,2}$) = $2263\pm163$ K. Multi-frequency analyses of the TESS residual lights yielded 35 significant signals in the frequency range below 5 day$^{-1}$. Among them, four frequencies of $f_1$, $f_2$, $f_3$, and $f_5$ are independent $γ$ Dor pulsations of the primary star, for which two acceptable mode-identification solutions were obtained using the frequency ratio method. These results suggest that AX Dra is the shortest-period double-lined eclipsing binary containing a $γ$ Dor-type pulsator and that the pulsating primary is likely an accretor affected by mass transfer.

Classically testing for the presence of anti-commuting operators on a quantum device is a critical tool underpinning recent progress in classical verification of quantum computation. While such tests can be based on cryptographic assumptions, known constructions rely on highly structured assumptions, e.g. trapdoor claw-free functions. In this work, we seek to explain this state of affairs by constructing strong cryptography from (certain forms of) classical tests of anti-commutation. In particular, we formulate the notion of a test of non-commutation (ToNC), an interactive protocol between a quantum prover and classical verifier in which the prover's final-round response is obtained by measuring one of two binary observables $P_0,P_1$ depending on the verifier's challenge bit $c$. We prove that, for a broad range of parameters, ToNC implies classical-communication key agreement (KA), and ToNC combined with one-way functions implies oblivious transfer (OT). Along the way, we develop tools for and provide the first known results on hardness amplification for post-quantum KA and OT, where communication is classical but adversaries may be quantum. In particular, we prove the following results of independent interest. - Post-quantum hard-core measure theorem: For any efficiently sampleable high-min-entropy distribution $D$ over pairs $(x,b)$ such that quantum circuits have advantage at most $δ$ in predicting $b$ from $x$, there exists a sub-distribution $M\preceq D$ of density $(1-δ)$ on which $b$ is nearly optimally quantum-hard to predict. - Post-quantum interactive XOR lemma: Given any classically-interactive protocol, if quantum adversaries have advantage at most $δ$ in guessing a private challenger bit $b$, then two sequential repetitions reduce the advantage for predicting the XOR of the challenger bits $b_1\oplus b_2$ to at most $δ^2+\rm{negl}(λ)$.

In this paper, multi-target tracking and scanning are considered in a radar system operating in the track-while-scan mode. Specifically, time allocation for radar scanning and tracking of multiple maneuvering targets under a time budget constraint is addressed, aiming to jointly optimize the performance of both tracking and scanning in a cognitive radar. We first present the details of the model for tracking and scanning and formulate the time management task as a constrained optimization problem. Subsequently, we design a \gls{cdrl} framework to find the time allocation strategy for the problem. In the proposed \gls{cdrl} framework, the parameters of the neural networks and the dual variable are learned simultaneously. The deep deterministic policy gradient (DDPG) algorithm is introduced to tackle continuous action space and its performance is compared with deep Q-learning, heuristic approaches, and an optimization-based approach. Numerical results show that the radar with the proposed \gls{cdrl} framework can autonomously allocate more time to the tracking task that requires greater attention while providing time for scanning and also constraining the total time budget below the predefined threshold.

Classical spectral theory lacks a framework for understanding how spectra propagate through compositional systems like deep neural networks, feedback control loops, and quantum circuits. This paper develops a universal theory governed by three invariants: the operadic spectrum (local spectral data), spectral derivatives (perturbation sensitivity), and interaction residue (emergent interface-generated content). We prove three main theorems: the Spectral Propagation Theorem decomposes global output into propagated local spectra, residues, and derivative corrections; the Stability Theorem introduces the SOC stability radius and condition number; and the Universality Theorem shows any reasonable propagation rule is uniquely determined by the three invariants. These results provide a coordinate-free, representation-invariant language for spectral analysis of compositional operator systems.

We report the binary fraction of Wolf-Rayet (WR) stars within 0.5~pc of the Galactic center obtained through the longest time-baseline (1994-2024) kinematic study of this population of stars. The new radial velocity ($v_{z}$) data we present is primarily from the W. M. Keck Observatory, with additional $v_{z}$ measurements from Gemini North Observatory. When combining our new $v_{z}$ measurements with literature measurements, we find $v_{z}$ variations suggesting the presence of a companion for five out of 27 WR stars, of which two are newly identified here (IRS~13E4, S8-181), along with three previously detected binaries (IRS~16SW, IRS~16NE, S4-258). Based on our experimental sensitivity and expected properties of the underlying population, we infer the binary fraction of the WR stars in the Galactic center to be 0.56$\pm$0.18. This is consistent with previous photometric studies of the young stars in the Galactic center, and with the binary fraction of field WR stars. When our results are combined with the results of previous photometric work, we find a binary fraction of 0.69$\pm$0.17 for the WR stars in the Galactic center.

We provide a complete classification of extensions of a trivial linear cycle set H by an abelian group I, under the assumption that both H and I are finite cyclic p-groups with p odd, or p = 2 and H has at most four elements. This yields an explicit parametrization of all possible extensions, offering a classification that is both comprehensive and computable. We also compute the socle and the center of all the linear cycle sets obtained.

Tackling complex coding tasks often requires autonomous agents and iterative repair pipelines. These increasingly rely on large amounts of test-time computation, often spending many decoding and repair steps before discovering whether a program compiles, runs, or validates. Executable parallel-code translation is an effective setting for earlier guidance because success is behavioral rather than textual. However, most guidance methods act only after complete programs or textual traces are decoded. This motivates the question: can latent reasoning provide an earlier intervention point, before the model commits to code? We study a test-time latent guidance method for this setting that trains a smaller Process Reward Model (PRM) over continuous latent prefixes and uses it to select among alternate hidden-state trajectories before final code decoding, separately from but compatible with post-decoding optimization. On a 76-task ParaTrans benchmark evaluation, latent PRM guidance improves mean validation rate from 32.89% with unguided latent reasoning to 42.1%, outperforming fine-tuned and vanilla baselines in the same setting. These gains persist under the same three-iteration repair loop. These results provide bounded evidence that useful alternative latent continuations exist and that PRM-scored latent branch selection can improve executable outcomes in this setting without retraining the main generative model.

We present a universal framework to harness fermionic ultracold atom platforms for quantum simulation, showing how variational algorithms on existing hardware can simulate many-body systems well beyond the hardware's native Hamiltonian. Our analysis provides evidence that one can quantum simulate the ground-state properties of a broad class of gapless target Hamiltonians of local observables in a quantum evolution time that grows polynomially with the inverse relative error, $T\sim O(\mathrm{poly}(1/ε))$ up to logarithmic corrections, offering an exponential speedup over na{ï}ve classical algorithms such as exact diagonalization. We provide numerical evidence and theoretical argument that this holds for energy density, density-density, and spin-spin correlations in three qualitatively distinct models -- the repulsive Hubbard model; a Hubbard model augmented with nearest-neighbor attractive interactions, which introduces the phenomenon of pairing; and the Hofstadter-Hubbard model, which introduces a gauge field and fractional quantum Hall physics. This work demonstrates quantum simulation using current fermionic platforms far beyond the models natively implemented in the hardware.

Ultra-high energy cosmic rays (UHECR) can produce relativistic cascades that emit radio-frequency (RF) pulses in the 0.05-1 GHz bandwidth via two distinct effects: the geomagnetic effect, and the Askaryan effect. The geomagnetic effect occurs when the magnetic field of the Earth causes cascade charges to form a transverse current that radiates linearly polarized radiation aligned with the Lorentz force direction. The Askaryan effect is caused by the net negative charge excess in the cascade that radiates linearly polarized radiation along the Cherenkov cone. When UHECR cascades enter solid, RF transparent matter at altitudes where the cascade develops, Askaryan radiation can propagate through the solid matter to RF detectors. The Askaryan Radio Array (ARA) at the South Pole has observed 13 UHECR candidates in precisely this fashion. We present an analytical model that confirms the events are UHECRs. The model includes Askaryan radiation and the ARA RF channel response. The coherently summed waveforms (CSWs) from the UHECR candidates match our model with correlation coefficients between 0.69 and 0.86, and with minimal fractional power differences. Finally, we demonstrate how to use the analytic formalism to obtain the Askaryan $\vec{E}$-field, and that it matches the results from ARA.

A Boolean function in CNF format is of type Positive$\wedge$Negative} if each clause C is either positive (i.e. all literals of C are positive) or negative (i.e. all literals of C are negative). As is well known, deciding the satisfiability of such CNFs is NP-complete. We say that a CNF is of type DisjointPositive if its clauses are positive and mutually disjoint. Dually define DisjointNegative. It is shown that the satisfiability of CNFs of type DisjointPositive$\wedge$DisjointNegative can be decided in quadratic time. Moreover, the modelset can be output in polynomial total time. This is relevant since it affects not only the modelsets of CNFs of type Positive$\wedge$Negative, but more generally of type Horn$\wedge$AntiHorn. As to the latter CNFs, they e.g. occur in connection with the fixpoints of a Monotone Boolean Network.

Large language model inference on processing-in-memory (PIM) architectures promises to break the memory wall by performing multiply-accumulate (MAC) operations directly within HBM3 DRAM banks. Prior work identifies the power constraint timing parameter nCCDAB as the primary performance bottleneck and optimizes scheduling accordingly. We demonstrate that for GEMV operations that dominate autoregressive decoding, the DRAM row cycle time (nRC) is 10 to 11 times larger than nCCDAB. Consequently, nCCDAB is entirely masked, rendering prior nCCDAB-focused optimizations ineffective for these workloads. The root cause is inherited host-centric address interleaving, which forces every all-bank MAC command into a different DRAM row. We propose RH+ scheduling, a simple stride change that keeps 32 consecutive MAC operations within the same row. Cycle-accurate simulation across four LLM workloads shows that RH+ delivers 8-12x speedup, over 74% energy reduction, and up to 52x EDP improvement.

We construct a new class of black-bounce solutions sourced by a self-interacting 3-form field minimally coupled to general relativity and a scalar field. The 3-form field, which naturally arises in string theory, supergravity, and cosmological models, provides the anisotropic effective stresses required to sustain regular geometries that interpolate smoothly between black holes and traversable wormholes. By exploiting the Hodge duality between a 3-form and a 1-form in four dimensions, we reduce the field equations and obtain exact solutions through the direct integration of the coupled equations of motion. In particular, the solutions are derived from algebraic combinations and manipulations of the Einstein, scalar, and 3-form field equations, starting from a complete action principle, without employing the usual reconstruction procedure in which the metric ansatz is imposed a priori and the matter sector is reconstructed afterwards. This approach reveals two distinct classes of solutions. The first one yields a globally phantom scalar field and a metric function with a characteristic arctangent dependence, reducing to the Schwarzschild-(anti) de Sitter spacetime in the limit of vanishing 3-form coupling. The second class produces a constant 3-form Lagrangian and, remarkably, a partially canonical scalar field, namely phantom only near the bounce and canonical outside the event horizon, a feature previously attainable mainly in modified theories of gravity, but which emerges here within pure general relativity. Both families are globally regular, as confirmed by the finiteness of the Kretschmann scalar, and exhibit an asymmetric horizon structure inherited from the 3-form energy-density distribution. These results demonstrate that the 3-form black-bounce framework is both mathematically consistent and observationally viable.

We consider the renormalization group improvement of unimodular black hole metrics with an identification of the renormalization scale as a function of the radial coordinate that is self-consistent in that it depends on parameters of the improved metric. Considering identifications that are motivated by minimality and dimensional analysis, we arrive at a number of non-singular unimodular black hole metrics. We determine the black hole mass gaps and note the qualitative similarities to other non-singular black hole metrics that have been discussed in the literature.

We study evolution in Einstein-Hilbert gravity with Dirichlet boundary conditions imposed on a finite surface. We argue that there are open sets of initial data where such evolutions terminate at finite times due to singularities that reach the boundary. In any dimension, the simplest such examples occur in cosmologies. However, in 2+1 dimensions we also show that Dirichlet walls initially outside a BTZ black hole can fall through the horizon, and that this also leads to generic singularities. A similar construction in higher dimensions leads to trapped surfaces that reach the wall, though the end result of such evolutions is more difficult to study.

We determine the sharp Sadov constant for Shapiro--Diananda cyclic sums. Sadov proved the lower bound C >= log 2; we prove the matching upper bound by an explicit asymptotic construction, obtaining C = log 2. We also develop a local spectral stability theory for the equal point of the Shapiro--Diananda cyclic sums. The Hessian is diagonalized by Fourier modes, giving an exact local minimum/saddle/quadratic-degeneracy criterion for all n and k, periodic equality families, and explicit classifications for k = 2 and k = 3. The result determines the global infimum over all n and k, but does not solve the separate fixed-k asymptotic minimization problems.

Bitcoin's block reward is scheduled to decline to zero, raising concerns about whether the network can remain secure once miners rely solely on transaction fees. This paper seeks to identify the conditions under which large-scale and persistent deviation from honest mining can arise. We analyze and compare the payoffs of honest and deviating miners in a sequential decision model, and identify a deviation threshold $G_t$ at which honest mining ceases to be privately optimal. Around the 2024 Bitcoin halving, we show that current mining behavior does not exhibit large-scale or structural deviation. However, when the block reward is removed, the $G_t$ criterion implies that deviation can arise even with a very small fraction of transaction fees. Finally, we evaluate three protocol-level mechanisms: Base Fee, Fee Floor, and an adaptive maximum block size rule, and show that their combination raises the deviation threshold and mitigates incentive breakdown in a fee-only regime. These results provide a practical benchmark for assessing Bitcoin's security as block rewards disappear.

The Fermi sea is a simple and common concept in physics. However, a related and equally simple concept -- the Dyson orbital -- is far less discussed in physics, especially in textbooks. Yet, Dyson orbitals offer a valuable tool for characterizing the complexity of a fermionic wave functions, particularly in distinguishing between Fermi-sea-like and non-Fermi-sea-like states. As a preliminary application, we examine the Laughlin wave function and find the fortunate fact that the Dyson orbitals can be determined analytically. Further numerical data provides \emph{quantitative} evidence that the Laughlin wave function describes a strongly correlated, non-Fermi liquid state.

Mutation testing is widely used to evaluate test-suite effectiveness, yet IEC 61131-3 Structured Text (ST) programs still lack a publicly available benchmark that supports reproducible mutation-based research. This gap is especially important because ST is extensively used in Programmable Logic Controllers (PLCs) that operate in real-time, safety-critical industrial environments, where software faults may cause equipment damage, production loss, or unsafe system behavior. To address this need, we present STMutants, a curated mutation testing dataset for industrial automation software. STMutants contains 110 generated first-order mutants derived from 11 ST programs collected from the OSCAT basic library and industrially relevant sources, of which 108 are retained after observability and equivalence screening. The dataset covers seven mutation operator categories adapted from classical taxonomies for the PLC domain, including value, relational, arithmetic, logical, negation, operation insertion/omission, and initialization faults. Each mutant is constructed through a four-phase methodology: fault-type profiling and operator selection, syntactic transformation, compilability verification, and manual equivalence screening with strong inter-rater agreement (kappa = 0.87). To demonstrate the usefulness of the dataset, we evaluate three large language models (LLMs) in a two-phase setting: test-suite generation followed by mutation kill/survive prediction. Across 108 retained mutants, the models achieve mutation detection accuracies of 86.1%, 94.4%, and 86.1%, respectively, with statistical analysis confirming significant performance differences. By providing the first publicly available mutation benchmark for ST programs, STMutants enables reproducible research on automated test generation, mutation analysis, fault localization, and AI-assisted quality assurance for PLC software.

Quantum geometry plays a fundamental role in many aspects of condensed matter physics. Among its central objects are the Berry curvature and the quantum metric -- quantities that, while distinct, are intertwined through geometric constraints. In this article, we survey recent progress in understanding when and how this bound is saturated, with particular emphasis on the emergence of momentum-space holomorphicity of Bloch states. These developments highlight a profound connection between certain ideal Bloch bands and the Hilbert space structure of the lowest Landau level. We elucidate this relationship through a review of quantum Hall physics in both homogeneous and spatially varying magnetic fields, and conclude by exploring its implications for the search for fractionalized phases in emerging platforms, including moiré materials.

Achieving peak GPU performance remains a significant challenge as the system throughput is constrained by host-device synchronization delays and kernel scheduling overheads, even with aggressive kernel optimizations and batch processing. Furthermore, existing approaches often underutilize hardware resources such as compute cores and copy engines due to scheduling overheads. To address these problems, we propose a CUDA runtime framework for task-parallel pipelines to minimize the synchronization overheads and the gap between kernel executions. The proposed solution combines two innovations: (1) a multi-stream task-parallel pipeline programming model that leverages event-chaining and work-stealing mechanisms to fully utilize available hardware resources; (2) a graph-based execution flow with per-stream buffers to ensure memory safety for multiple in-flight jobs running concurrently. Extensive evaluations on representative real-world workloads show 1.15--1.44X speedup and reduce scheduling overheads by 18--54% compared to state-of-the-art CUDA graph baselines.

Reverse engineering (RE) is a critical activity in software engineering and cybersecurity, supporting tasks such as malware analysis, vulnerability discovery, legacy system maintenance, and firmware inspection. Despite its importance, there is limited empirical understanding of the challenges, topics, and knowledge gaps faced by RE practitioners in real-world settings, and no publicly available dataset has systematically captured RE discussions from developer Q&A forums. In this paper, we present REStack, a large-scale dataset of RE discussions collected from Stack Overflow and the dedicated Reverse Engineering Stack Exchange site. The dataset comprises over 12,000 RE-related posts spanning more than 15 years. Using Latent Dirichlet Allocation (LDA) with Genetic Algorithm (GA)-based hyperparameter optimization, followed by manual topic labeling, we identify 23 semantically coherent RE topics grouped into six high-level thematic categories. The dataset is further enriched with metadata and difficulty indicators derived from community interaction signals, such as unanswered rates and response times. Our analysis reveals that RE discussions are predominantly practical and task-oriented, with strong emphasis on debugging, decompilation, and system-level analysis, while topics related to memory, firmware, and file format analysis exhibit high difficulty and unresolved rates. Beyond empirical characterization, REStack provides a reusable resource for empirical studies, educational research, and the development and evaluation of AI- and LLM-based developer assistance tools for RE. By releasing the dataset and accompanying scripts, this work aims to facilitate reproducible research and advance data-driven support for RE practice.

Let $X$ be a finite-area translation surface whose vertical flow is uniquely ergodic. Given a slit joining two nonsingular points of $X$, one can form a branched cyclic cover by gluing $\mathrm{N}$ copies of $X$ crosswise along the slit. We study when the vertical flow on the resulting cover is uniquely ergodic. We first prove a geometric criterion for unique ergodicity of the branched cover. We show that if, for a sequence of times along the Teichmüller geodesic, one endpoint of the slit is contained in embedded Euclidean disks of uniformly positive radius that avoid the other endpoint, then the branched cover is uniquely ergodic. The proof uses the special symmetry of the cover together with an analysis of forward and backward generic points for the vertical flow. We then show that this criterion applies for Lebesgue-almost every choice of slit endpoint under a natural geometric hypothesis on the Teichmüller orbit of $X$, namely a uniform lower bound for the embedded radius along a subsequence. Finally, we give sufficient conditions for such a lower bound in terms of the cylinder geometry of $g_tX$, introducing the notion of pipe cylinders and proving that embedded disks of definite size must exist. As a consequence, for the class of uniquely ergodic translation surfaces, almost every slit produces a uniquely ergodic branched $\mathrm{N}$-cover.

This work focuses on optimal experimental design (OED) methods for passive imaging. We adopt a Bayesian inverse problem framework for passive imaging source problems, primarily focusing on spatially uncorrelated sources and systems governed by the Helmholtz equation. A major challenge in passive imaging is that the use of correlation data causes the observation dimension to grow quadratically with the number of sensor locations, compounding the computational difficulty of finding optimal designs. To overcome the computational bottleneck of repeated PDE solves in optimal design algorithms, we develop a two-level, low-rank approximation of the A-optimal design objective. This effectively decouples the problem into an offline and an online phase, enabling efficient evaluation of the design objective and its gradient without additional PDE solves. Our numerical results demonstrate that the proposed algorithm efficiently scales to large problems and that the resulting optimal designs significantly outperform random sensor placements in minimizing posterior uncertainty.

Computed Tomography Angiography (CTA) is widely used to reconstruct vascular geometry from projection measurements, with conventional approaches such as Filtered Back-Projection (FBP) and Iterative Reconstruction (IR) forming the clinical standard. Blood flow is subsequently estimated through Computational Fluid Dynamics (CFD) simulations, which require vascular geometry and boundary conditions to be specified a priori. Since the geometry is fixed prior to flow estimation, the recovery of unknown anatomical features (e.g., missing branches or stenoses) is precluded. In this work, we present a fluid-physics-constrained reconstruction framework that leverages topology optimization (TO) to jointly recover vascular geometry and blood velocity directly from time-resolved CTA sinograms. The formulation couples a steady incompressible flow model with a transient advection-diffusion contrast transport model, mapped to sinogram space through a differentiable projection operator. The recovered velocity fields provide hemodynamic information and can support downstream estimation of wall shear stress and flow distribution, without requiring a separate CFD pipeline. The proposed method is demonstrated on synthetic phantoms under varying sparsity and noise levels, and on representative projection data.

This paper presents a comprehensive 2D analytical model of a toroidal magnetic ring with a square cross-section, subjected to sinusoidal excitation. By applying Maxwell's equations in local Cartesian coordinates and utilizing a complex permeability framework, the exact analytical expressions for the internal magnetic field, flux, complex impedance, and losses are derived. The model rigorously separates eddy current losses, hysteresis losses, and winding losses, explicitly accounting for the skin effect and complex permeability within the conductive core using separation of variables and hyperbolic functions. Furthermore, parameter for apparent permeability is expressed to map the core behavior onto simplified linear material models. The derivations establish a mathematical foundation highly suitable for standardized material characterizations, such as Brockhaus and Iwatsu ring measurements, by avoiding the heavy computational cost of 2D and 3D Finite Element Analysis.