Photometric missions such as Kepler and TESS have generated millions of light curves covering almost the entire sky, offering unprecedented opportunities to study stellar variability and advance our understanding of the Universe. In this data-rich environment, machine learning has emerged as a powerful tool to efficiently and accurately process and classify light curves according to their type of stellar variability. In this work, we introduce ASTRAFier: a novel Transformer-based model for variability classification that integrates Bidirectional Long Short-Term Memory (BiLSTM) and Convolutional Neural Networks (CNNs). The model operates directly on time series without requiring feature engineering, creating an easy-to-maintain and efficient end-to-end classification framework. We train and validate our model using both Kepler and TESS light curves and, respectively, achieve a classification accuracy of $94.26\%$ on Kepler and $88.22\%$ on TESS. We demonstrate scalability by deploying our model on $\sim 2.8$ million TESS light curves from sectors 14, 15, and 26 (Kepler Field-of-View) delivered by MIT's Quick-look Pipeline (QLP) and release the resulting stellar variability catalog.

Magnetic dipole (MD) transitions are intrinsically weak and highly sensitive to emitter orientation and position, making their controlled enhancement at optical frequencies particularly challenging. Here we show that structural symmetry provides a powerful route to robust magnetic light-matter interactions. We systematically investigate plasmonic core-satellite resonators composed of N metallic nanoparticles arranged on a dielectric core. We evaluate their performance using a unified figure of merit that accounts for magnetic Purcell enhancement, electric dipole suppression, quantum efficiency, and robustness to emitter orientation and fabrication tolerances. We find that the optimal structures correspond to the highest-symmetry geometries, which naturally produce spatially homogeneous and orientation-independent magnetic Purcell enhancement. In particular, the dodecapod configuration yields strong magnetic emission with Purcell factors approaching 250, high radiative efficiency, and suppressed electric dipole contributions. Quasinormal-mode and complex mode-volume analysis reveal that symmetry enforces uniform magnetic modal confinement within the core, explaining both the enhancement and its robustness. These results establish symmetry as a guiding principle for designing nanophotonic resonators with controlled multipolar light-matter interactions and provide a practical route toward bright and selective magnetic dipole emitters.

In stochastic optimal control (SOC), uncertainty may arise from incomplete knowledge of the true probability distribution of the underlying environment, which is known as Knightian or epistemic uncertainty. Distributionally robust optimal control (DROC) models are subsequently proposed to tackle this source of uncertainty. While such models are effective in some practical applications, most existing DROC models are offline and can be overly conservative when data are scarce. Moreover, they cannot be applied to the case when samples are generated episodically. Motivated by the Bayesian SOC framework recently proposed by Shapiro et al.~\cite{shapiro2025episodic}, we propose an adaptive DROC model in which the ambiguity set is updated via Bayesian learning from new data. Under some moderate conditions, we derive a tractable risk-averse reformulation, establish consistency of the optimal value function and optimal policy for an infinite-horizon SOC and establish a finite-sample posterior credibility guarantee for the policy value induced by the proposed episodic Bayesian DROC model. We also study the stability and statistical robustness of the proposed model with respect to sample perturbations that often arise in data-driven environments. To solve the episodic Bayesian DROC model, we propose a Bellman-operator cutting-plane (BOCP) algorithm that is computationally efficient and provably convergent. Numerical results on an inventory control problem demonstrate the effectiveness, adaptivity, and robust performance of the proposed model and algorithm.

Target Speaker Extraction (TSE) aims to isolate a specific speaker's voice from a mixture, guided by a pre-recorded enrollment. While TSE bypasses the global permutation ambiguity of blind source separation, it remains vulnerable to speaker confusion, where models mistakenly extract the interfering speaker. Furthermore, conventional TSE relies on static inference pipeline, where performance is limited by the quality of the fixed enrollment. To overcome these limitations, we propose EvoTSE, an evolving TSE framework in which the enrollment is continuously updated through reliability-filtered retrieval over high-confidence historical estimates. This mechanism reduces speaker confusion and relaxes the quality requirements for pre-recorded enrollment without relying on additional annotated data. Experiments across multiple benchmarks demonstrate that EvoTSE achieves consistent improvements, especially when evaluated on out-of-domain (OOD) scenarios. Our code and checkpoints are available.

While recent approaches leverage large language models (LLMs) and multi-agent pipelines to automatically generate proof-of-concept (PoC) exploits from vulnerability reports, existing systems often suffer from two fundamental limitations: unreliable validation based on surface-level execution signals and high operational cost caused by extensive trial-and-error during exploit generation. In this paper, we present PoC-Adapt, an end-to-end framework for automated PoC generation and verification, architected upon a foundation semantic runtime validation and adaptive policy learning. At the core of PoC-Adapt is a Semantic Oracle that validates exploits by comparing structured pre- and post-execution system states, enabling reliable distinction between true vulnerability exploitation and incidental behavioral changes. To reduce exploration cost, we further introduce an Adaptive Policy Learning mechanism that learns an exploitation policy over semantic states and actions, guiding the exploit agent toward effective strategies with fewer failed attempts. PoC-Adapt is implemented as a multi-agent system comprising specialized agents for root cause analysis, environment building, exploit generation, and semantic validation, coordinated through structured feedback loops. Experimenting on the CWE-Bench-Java and PrimeVul benchmarks shows that PoC-Adapt significantly improves verification reliability by 25% and reduces exploit generation cost compared to prior LLM-based systems, highlighting the importance of semantic validation and learned action policies in automated vulnerability reproduction. Applied to the latest CVE corpus, PoC-Adapt confirmed 12 verified PoC out of 80 reproduce attempts at a cost of $0.42 per generated exploit

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the main sources of gravitational waves expected in the low-frequency band, where space-based detectors like Laser Interferometer Space Antenna (LISA) will operate. The large number of gravitational-wave cycles accumulated in the EMRI signal in the strong-field regime makes them precise probes of the local spacetime geometry, highly sensitive to deviations from the Kerr black hole paradigm. In this work, we investigate EMRIs around generic, non-Kerr compact objects characterized by a rich multipolar structure. At leading post-Newtonian and linear mass-ratio orders, we incorporate in the waveform model both axisymmetric and non-axisymmetric components of the mass quadrupole and octupole moments, parameterizing the breaking of two fundamental symmetries of the Kerr metric. We study the impact of these modifications on the waveform following the philosophy of EMRI \emph{Analytic Kludge} models. Then, using Fisher-matrix analysis, we assess LISA's capability to constrain deviations of the multipole moments from their Kerr values and the detection of symmetry-breaking effects. We analyze how effectively LISA will probe models beyond General Relativity that predict horizon-scale modifications, such as the fuzzball model proposed in string theory. Our results demonstrate that future LISA observations of EMRIs will provide powerful tests of black hole structure and the underlying theory of gravity. In particular, with one year of LISA data from the inspiral of a $10 M_{\odot}$ compact object into a rotating supermassive black hole of $10^{6} M_{\odot}$ and signal-to-noise ratio of 30, it will be possible to place tight bounds on deviations from the two fundamental symmetries of the Kerr metric, constraining equatorial symmetry breaking to the $10^{-2}$ level and axial symmetry breaking to the $10^{-3}$ level.

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test the fuzzball proposal, a quantum gravity-inspired alternative to Kerr black holes. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA's ability to constrain deviations from the Kerr geometry in the near-horizon region. We show that EMRI signals with realistic signal-to-noise ratios can constrain multiple higher-order multipoles at levels orders of magnitude beyond current electromagnetic and ground-based gravitational-wave bounds, opening a new observational window onto horizon-scale structure. In particular, we find that LISA can constrain generic non-axisymmetric mass quadrupole deformations at the $10^{-3}$ level and axisymmetric mass octupole deformations at the $10^{-2}$ level, providing concrete observational targets for identifying fuzzball geometries. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer the first direct empirical constraints on quantum-gravity-motivated models of compact objects.

A combined view of the Jefferson Lab data on nuclear transparency in $A(e,e'π^+)$ and $A(e,e'K^+)$ reveals two simple but nontrivial features of the onset of color transparency. First, normalization to deuterium does not play the same role in the two reactions. In pion electroproduction, the missing-mass selection suppresses the neutron-induced $Δ$ channel so strongly that the deuteron normalization becomes effectively proton dominated. In kaon electroproduction, the nearby hyperon channels cannot be removed in the same way, and the deuteron retains a genuine proton--neutron average. Second, the $Q^2$ dependence indicates different in-medium formation dynamics. The pion transparency is well reproduced by the standard quantum diffusion model with $ΔM_π^2 \simeq 0.7~\mathrm{GeV}^2$, whereas the kaon data favor a faster geometric expansion characterized by the scale $R_K \sim \sqrt{σ_{KN}/π}$ and are strongly underestimated by the same pion-like diffusion scale. These results suggest that the pion and kaon data already contain evidence that the onset of color transparency is reaction dependent both in normalization and in propagation through nuclear matter.

Driven by advances in hardware and software technologies, nonlinear model predictive control (NMPC) has gained increasing adoption in both industry and academia over the past decades. However, its practical deployment is often limited by the computational cost of simulating the embedded process model, especially for high-dimensional, multi-time-scale, or nonlinear systems commonly found in real-world applications. Thus, this paper introduces Surrogate Dynamics Optimization (SDO), a warm-start framework for full-scale NMPC to address the limitation of standard initialization strategies. The approach relies on a machine learning surrogate model to solve a lightweight auxiliary problem that approximates the original one. The methodology is reproducible and compatible with inhouse simulation and optimization tools, a key consideration in industrial contexts. Data efficiency of SDO, as well as the impact of surrogate design on the overall performance, are evaluated through a non-trivial simulation case study: 24-hour optimal load-following control of a pressurized water reactor. The results show consistent improvements in NMPC convergence speed within a fixed computational budget, while reducing training data generation costs by two orders of magnitude compared to behavior cloning.

We study how intrinsic hard constraints on the decision dynamics of social agents shape collective decisions on multiple alternatives in a heterogeneous group. Such constraints may arise due to structural and behavioral limitations, such as adherence to belief systems in social networks or hardware limitations in autonomous networks. In this work, agent constraints are encoded as projections in a multi-alternative nonlinear opinion dynamics framework. We prove that projections induce an invariant subspace on which the constraints are always satisfied and study the dynamics of networked opinions on this subspace. We then show that heterogeneous pairwise alignments between individuals' constraint vectors generate an effective weighted social graph on the invariant subspace, even when agents exchange opinions over an unweighted communication graph in practice. With analysis and simulation studies, we illustrate how the effective constraint-induced weighted graph reshapes the centrality of agents in the decision process and the group's sensitivity to distributed inputs.

Advances in hybrid bonding and packaging have driven growing interest in 3D DRAM-stacked accelerators with higher memory bandwidth and capacity. As LLMs scale to hundreds of billions or trillions of parameters, distributed inference across multiple 3D chips becomes essential. With cross-stack co-design increasingly critical, we propose DeepStack, an accurate and efficient performance model and tool to enable early-stage system-hardware co-design space exploration (DSE) for distributed 3D-stacked AI systems. At the hardware level, DeepStack captures fine-grained 3D memory semantics such as transaction-aware bandwidth, bank activation constraints, buffering limitations, and thermal-power modeling. At the system level, DeepStack incorporates comprehensive parallelization strategies and execution scheduling for distributed LLM inference. With novel modeling techniques such as dual-stage network abstraction and tile-level compute-communication overlap, we achieve up to 100,000x faster runtime over state-of-the-art simulators at comparable accuracy, cross-validated against our in-house 3D designs, NS-3 backend (2.12%), and vLLM serving on 8xB200 GPUs (12.18%). With hierarchical design space search, DeepStack enables efficient exploration over 2.5x10^14 design points spanning 3D-stacked DRAM layers, DRAM vertical connectivity, interconnect, compute-memory allocation, and distributed scheduling. Compared with baseline designs, DeepStack achieves up to 9.5x higher throughput through co-optimized parallelism and 3D architecture search. Our DSE further reveals that batch size drives a more fundamental architectural divide than the prefill/decode distinction, and that parallelism strategy and hardware architecture are tightly coupled -- incomplete schedule search leads to permanently suboptimal silicon irrecoverable by software tuning. We intend to open source DeepStack to support future research.

We report the empirical detection of a multi-planet quasi-commensurability in the Solar System and identify an anomalous exclusion that may bear on the dynamical history of Uranus. An exhaustive search identifies T* = 420,403 days (approx. 1,151 years) as the global minimum of a series-comparison similarity metric applied to daily heliocentric ecliptic longitudes of seven planets -- Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Neptune -- computed from the DE441 ephemeris over +/-1,300 years. At this interval, the mean simultaneous angular displacement of all seven planets is 13.4 degrees, with a standard deviation of 0.65 degrees sustained over a century-long window and stable across 1,200 years of reference epochs. T* ranks first among all 2,600 candidates, with a gap of 1.09 degrees to the second best. No sub-multiple produces a comparable result. Seven of the eight planets participate in the synchronism. The sole exception is Uranus, whose sidereal residue at T* is -108.3 degrees -- nearly one-third of a full orbit -- while Neptune's residue is only -5.2 degrees, one of the smallest among all seven planets after Earth's. This sharp asymmetry between the two ice giants constitutes an independent empirical signature consistent with the hypothesis that Uranus's orbital period was substantially modified by a catastrophic early impact. The interval 1,151 years was identified by Babylonian astronomers as the Venus return period (de Jong 2019); the present work shows it is simultaneously optimal for six additional planets. Source code and data are publicly available.

We propose a new non-minimally coupled quintessence model to account for the late-time dark energy dynamics indicated by recent DESI measurements. Within this framework, the quintessence density begins to decrease only when it starts to dominate the universe, which naturally accounts for the late-time onset of dark energy weakening. The coupling also induces a sign change in the effective energy transfer between dark matter and dark energy during cosmic evolution. While the scalar field itself remains canonical and never crosses the phantom divide, the modified evolution of the dark matter density gives rise to an effective crossing behavior in the observationally inferred dark energy sector. Compared with both $Λ$CDM and $w_0w_a$CDM models, our model is favored more strongly by current cosmological data. This work may provide a promising avenue for understanding the observational late-time weakening of dark energy and the origin of its dynamics.

We prove that the Fischer-Servi logic $\mathsf{IK}$ does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as $\mathsf{IT}$, $\mathsf{IK4}$, $\mathsf{IS4}$, and $\mathsf{IGL}$.

The Exact Matching problem asks whether a bipartite graph with edges colored red and blue admits a perfect matching with exactly $t$ red edges. Introduced by Papadimitriou and Yannakakis in 1982, the problem has resisted deterministic polynomial-time algorithms for over four decades, despite admitting a randomized solution via the Schwartz-Zippel lemma since 1987. We establish the Affine-Slice Nonvanishing Theorem (ASNC) for all bipartite braces: a Vandermonde-weighted determinant polynomial is nonzero whenever the exact-$t$ fiber is nonempty. This yields a deterministic $O(n^6)$ algorithm for Exact Matching on all bipartite graphs via the tight-cut decomposition into brace blocks. The proof proceeds by structural induction on McCuaig's brace decomposition. We handle the McCuaig exceptional families via a parity-resolved cylindric-network positivity argument, the replacement determinant algebra, and the narrow-extension cases (KA, $J3 \to D1$). For the superfluous-edge step, we introduce two closure tools: a matching-induced Two-extra Hall theorem that resolves the rank-$(m-2)$ branch via projective-collapse contradiction, and a distinguished-state $q$-circuit lemma that eliminates the rank-$(m-1)$ branch entirely by showing that any minimal dependent set containing the superfluous state forces rank $m-2$. A Lean 4 formalization accompanies the paper. The formalization reduces the main theorem to eight explicit hypotheses corresponding to results proved here and in McCuaig (2001), with all algebraic tools, the induction skeleton, and the combinatorial infrastructure fully machine-checked.

In this paper we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator $\mathcal{H}_V:=-\operatorname{div}(A\nabla)+V$, where $V$ is convex and Kato decomposable, using the trace class property of the generated semigroup. As a consequence, using the ultracontractivity of the semigroup we obtain the log-concavity of the ground state which is also strong log-concave under additional assumptions on $Ω$ and $V$.

Assistive technologies increasingly support independence, accessibility, and safety for older adults, people with disabilities, and individuals requiring continuous care. Two major categories are virtual assistive systems and robotic assistive systems operating in physical environments. Although both offer significant benefits, they introduce important security and privacy risks due to their reliance on artificial intelligence, network connectivity, and sensor-based perception. Virtual systems are primarily exposed to threats involving data privacy, unauthorized access, and adversarial voice manipulation. In contrast, robotic systems introduce additional cyber-physical risks such as sensor spoofing, perception manipulation, command injection, and physical safety hazards. In this paper, we present a comparative analysis of security and privacy challenges across these systems. We develop a unified comparative threat-modeling framework that enables structured analysis of attack surfaces, risk profiles, and safety implications across both systems. Moreover, we provide design recommendations for developing secure, privacy-preserving, and trustworthy assistive technologies.

We analytically solve the finite-time control problem of driving an overdamped particle via an optical trap under costly measurement. By formulating this mesoscopic information engine within the Partially Observable Markov Decision Process (POMDP) framework, we demonstrate that the underlying Linear-Quadratic-Gaussian (LQG) dynamics decouple the optimal measurement and driving protocols. We derive the optimal feedback control law for the trap placement, which recovers the discontinuous Schmiedl-Seifert driving protocol in the open-loop limit and extends it to any measurement scheduling. For a costly, binary (on/off) sensor, we evaluate the optimal measurement protocol and derive physical bounds on the maximum net gain that can be extracted from thermal fluctuations. We show the emergence of deadline-induced blindness, a phenomenon where all measurements cease as the deadline approaches regardless of their cost. Taking the infinite-horizon limit, we find the exact periodic measurement schedules for the steady state as a function of the measurement cost $C$ and derive the macroscopic velocity envelopes beyond which viscous drag forces the engine into a net-dissipative regime. Finally, we generalize the results to a variable-precision sensor.

We introduce a weighted version of the module of logarithmic derivations of a divisor in weighted projective space, and provide a generalization of Saito's criterion for freeness in terms of weighted multiple eigenschemes (wME-schemes). Freeness of the nonstandard Z-graded module allows one to consider big families of free divisors in affine and standard projective space, i.e. when the module of logarithmic derivations of the divisor is free over the respective coordinate rings. We present a method to identify and construct these new families of free divisors in affine and projective space in any dimension, and give numerous explicit examples.

Context. A statistically significant sampling of H2 rotational excitation in the diffuse interstellar medium (ISM) is essential to identifying its excitation mechanisms and assessing the importance of H2 in the cooling of the gas and the regulation of thermal pressure. Aims. To complement the statistics provided by ancillary telescopes, we conducted a search for pure rotational H2 emission lines in all publicly available background observations obtained with the Medium Resolution Spectrometer (MRS) aboard the JWST. Methods. The sample consists of 276 background observations acquired over the past three years. Departing from the standard pipeline, each uncalibrated MRS background file was reprocessed, enabling the analysis of H2 pure rotational emission. Lines of sight likely associated with star-forming complexes were excluded to focus on emission from the diffuse ISM. The results were compared with FUSE absorption data and were analyzed in relation to the column densities of H and H2 and to dust emission derived from HI4PI, Planck, and WISE data. Results. This analysis reveals widespread H2 emission throughout the Galaxy. We report the first detections of the pure rotational S(4), S(5), and S(7) lines in the diffuse ISM. The S(1) line is detected along 84 lines of sight, corresponding to a detection rate of 41%. Its integrated intensity decreases steeply with Galactic latitude, spanning nearly two orders of magnitude, in remarkable agreement with absorption measurements. The T\_34 and T\_35 excitation temperatures vary between 200 and $\sim$1000 K, are correlated with each other, and are anticorrelated with the column density of H2 , as expected from ancillary data. All lines of sight in the sample have undergone the H-H2 transition, at N\_H ___ 10 +20 cm -2 , and are partly molecular, with f\_H2 ___ 0.1. Under these conditions, the cooling rate associated with the S(1) line, expressed per hydrogen atom, is found to be remarkably constant, with a characteristic value of $\sim$4x10 -27 erg s-1 H-1. Conclusions. This study demonstrates that the high sensitivity of the JWST enables measurements that both strengthen and complement those from absorption studies. Observations collected over just a fraction of JWST's lifetime have already yielded detections along dozens of lines of sight, significantly expanding the statistical sample of H2 rotational excitation in the diffuse ISM.

Current single molecule methods either rely on fluorescence or lack chemical information. Here we report stimulated Raman photothermal encoded scattering (SRPSCAT) microscopy for quantitative bond-selective imaging of single-biomolecule structures and interactions in native environments. In this approach, scattering of the target molecule is modulated by the deposited energy from stimulated Raman gain and loss processes, thereby encoding vibrational spectroscopic information. Leveraging single-molecule sensitivity of interferometric scattering, SRPSCAT can map single proteins with chemical specificity, determine their mass, and distinguish protein secondary structures based on their Raman fingerprints. Furthermore, single protein binding kinetics are quantified and the conformational dynamics of single de novo designed allosteric proteins are observed. Together, these results highlight the potential of SRPSCAT for label-free structural, functional and dynamic analysis at the single-molecule level.

In this article we construct evolutionary soliton hierarchies from pencils of Novikov algebras of Stäckel type. We start by defining a special class of associative Novikov algebras, which we call Novikov algebras of Stäckel type, as they are associated with classical Stäckel metrics in Viète coordinates. We obtain sufficient conditions for pencils of these algebras so that the corresponding Dubrovin-Novikov Hamiltonian operators can be centrally extended, producing sets of pairwise compatible Poisson operators. These operators lead to coupled Korteweg-de~Vries (cKdV) and coupled Harry Dym (cHD) hierarchies, as well as to a triangular cKdV hierarchy and a triangular cHD hierarchy.

Henri Poincare Saint Louis lecture, delivered on 24 September 1904 at the International Congress of Arts and Science, occupies a distinctive place in the pre history of twentieth century theoretical physics. In this text, Poincare formulated the principle of relativity in explicit and general terms, not as a narrow empirical rule limited to electrodynamics, but as one of the major guiding principles of mathematical physics. The lecture also offered a principle based conception of theory centered on invariance, least action, and general theoretical coherence. Although the conceptual importance of the Saint Louis lecture has long been recognized in the historiography of relativity, far less attention has been devoted to the material conditions under which it entered international circulation. This article examines the editorial, commercial, and institutional pathways through which the lecture was disseminated between late 1904 and early 1905. It reconstructs the three principal early publication channels of the text: its first printed appearance in La Revue des idees in November 1904, which inserted it into a commercially organized and interdisciplinary intellectual review; its republication in the Bulletin des sciences mathematiques in December 1904, which brought it into a widely distributed specialized mathematical network and later provided the standard reference most often used by historians; and its English translation in The Monist in January 1905, which extended its reach into a transatlantic forum devoted to philosophy, science, and the foundations of knowledge.

The $p(n,γ)$ and $d(p,γ)$ reactions are key nuclear inputs for Big Bang nucleosynthesis. In this work, both reactions are analyzed within a consistent two-body potential framework based on the Malfliet-Tjon interaction, including contributions from both $E1$ and $M1$ transitions. A single scaling factor $λ$ controlling the low-energy scattering dynamics is constrained by the $p(n,γ)$ and propagated consistently to the $d(p,γ)$. The obtained abundance, $\mathrm{D/H} = 2.479^{+0.350}_{-0.177}\times 10^{-5}$, is in good agreement with values inferred from metal-poor damped Lyman-$α$ systems. The modest variations of $λ$ lead to a significant change in the predicted $\mathrm{D/H}$ ratio and light-element abundances.

The AKM model introduced by Abowd, Kramarz and Margolis (1999) has become a workhorse to study worker and firm heterogeneity, and to understand the sources of wage dispersion in the labor market using linked employer-employee data. In this article, we introduce the model and estimator, discuss some best practices for estimation, and review some empirical findings on the role of worker and firm heterogeneity in wage dispersion. While the AKM methodology has proven useful to analyze a host of questions in a variety of settings within labor economics and beyond, we also point to the need for methodological developments.

We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary Dirichlet-to-Neumann map uniquely determines the nonlinear coefficients $β$ in the Westervelt-type model, and the pair $(β,κ)$ in the Kuznetsov-type model, provided that the observation time is greater than the maximal boundary-to-boundary geodesic travel time. The results are obtained in both the Euclidean setting and on compact Riemannian manifolds with proper geometric assumptions. The proof is based on the idea of second order linearization combined with the construction of geometric optics and Gaussian beam solutions, reducing the inverse problem of uniqueness to the injectivity of associated geodesic ray transforms.

To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the trace of the kinetic operator in the residual space, generalizing the spillage minimizing scheme [M. Chen et al., J. Phys. Condens. Matter 22, 445501 (2010); P. Lin et al., Phys. Rev. B 103, 235131 (2021)]. In addition to the systematic improvability inherited from previous schemes, the use of TSW instead of plane waves as the expansion basis bridges reference states and NAOs more effectively, and eliminates spurious interactions between periodic images, thereby enabling better transferability through the inclusion of extensive reference states. Benchmarks demonstrate that the constructed NAO achieves satisfactory precision for various properties of both molecules and bulk systems, including total energy, bond length, atomization energy, lattice constant, cohesive energy, band gap, and energy-level alignment. By incorporating unoccupied states, the improved transferability in describing the conduction band is demonstrated to be effective and substantial.

We consider the Frank-Wolfe algorithm for solving variational inequalities over compact, convex sets under a monotone $C^1$ operator and vanishing, nonsummable step sizes. We introduce a continuous-time interpolation of the discrete iteration and use tools from dynamical systems theory to analyze its asymptotic behavior. This allows us to derive convergence results for the original discrete algorithm. Consequently, every cluster point of the iterates is a solution of the underlying variational inequality, the distance from the iterates to the solution set converges to zero, and the Frank-Wolfe gap vanishes asymptotically. In the strongly monotone case, the solution is unique and the iterates converge to it. In particular, this proves Hammond's conjecture on the convergence of generalized fictitious play. We also discuss rates of convergence and under what assumptions rates can be shown.

Understanding fluid flow in wedge-shaped geometries is essential for predicting hydrodynamic interactions in confined systems, such as microfluidic devices and near-corner transport phenomena. This article reviews analytical methods and techniques for addressing wedge problems in low-Reynolds-number hydrodynamics, focusing on solutions of the Stokes equations for a point force (Stokeslet) and a point torque (rotlet). The formulation is based on the Papkovich-Neuber representation, which uses four harmonic functions to characterize the fluid flow. A concise overview of the Fourier-Kontorovich-Lebedev (FKL) transform method is provided, highlighting key properties and steps employed in deriving these solutions. This offers a versatile framework for predicting particle dynamics in wedge confinements and for designing microfluidic systems with corner geometries.

Characterizing noise in superconducting qubits is essential for improving coherence and gate performance. Conventional noise-sensing methods typically use the qubit itself as the sensor, which limits both accessible bandwidth and applicability during driven operation. Here, we demonstrate a method for measuring qubit frequency noise by converting it into photon loss in a coupled high-Q superconducting cavity. We use repeated mid-circuit qubit measurements with post-selection to separate this induced loss from intrinsic cavity decay. We validate the protocol using injected noise and show that the extracted loss scales as expected with the applied noise strength. Without added noise, we place an upper bound of $5\times10^3\,\mathrm{Hz}^2/\,\mathrm{Hz}$ on the qubit frequency-noise power spectral density at 508 MHz. The protocol opens access to a higher-frequency spectral window than standard qubit-based spectroscopy and may enable noise characterization during strong driving.