We study the first nontrivial Steklov eigenvalue of perimeter-normalized regular \(N\)-gons and show that it is strictly increasing in \(N\). The proof mainly relies on an analytic framework that establishes a refined asymptotic expansion in three steps: first, identifying the Steklov eigenvalue as the maximal eigenvalue of a Toeplitz-type operator; second, deriving the eigenvalue and its associated eigenfunctions simultaneously via Schur reduction; and finally, obtaining the exact coefficients in the Schur moment expansion by evaluating Euler-type sums. The monotonicity is proved to be eventual, holding for \(N\ge 20\). For the remaining cases \(3\le N\le 20\), we provide complementary computer-assisted verification, confirming monotonicity across the full range of \(N\).

Controllability scores provide principled information on where intervention should be applied in large-scale network systems when explicit control design is difficult. Two representative controllability scores are the volumetric controllability score (VCS) and the average energy controllability score (AECS). While both are important, the standard AECS treats all state-transition directions uniformly. In this paper, we propose the weighted average energy controllability score (W-AECS), a task-dependent extension of AECS that incorporates a prescribed transition of interest through a weighting matrix. We show that the proposed formulation admits a control-theoretic interpretation via expected minimum-energy steering, and establish strict convexity and generic uniqueness. These results support the interpretation of W-AECS as a well-defined node-wise task-dependent intervention score. We also illustrate the proposed method on a structural brain-network dataset, where transition-dependent weighting reshapes the scoring pattern, yielding a VCS-like preference among the highest-ranked regions while preserving an overall structure distinct from both standard AECS and VCS.

For a non-decreasing sequence $S=(s_1,s_2,\dots,s_k)$, an $S$-packing coloring of a graph $G$ is a vertex coloring using the colors $s_1,s_2,\dots,s_k$ such that any two vertices assigned the same color $s_i$ are at distance greater than $s_i$. A subcubic graph is said to be $k$-saturated, for $0\le k\le3$, if every vertex of degree 3 is adjacent to at most $k$ vertices of degree~3. The \emph{local girth} of a vertex is the length of the smallest cycle containing it. Brešar, Kuenzel, and Rall [\textit{Discrete Math.} 348(8) (2025),~114477] proved that every claw-free cubic graph is $(1,1,2,2)$-packing colorable, confirming the conjecture for this family. Equivalently, a claw-free cubic graph is one in which each $3$-vertex has local girth~3. Motivated by this observation and by recent progress on $S$-packing colorings of $k$-saturated subcubic graphs, we study the influence of local girth on their $S$-packing colorability. We establish a series of results describing how the parameters of saturation and local girth jointly determine the admissible $S$-packing sequences. Sharpness is verified through explicit constructions, and several open problems are posed to delineate the remaining cases.

Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but lacks a simple analytical framework. We demonstrate such a framework using a shell model of turbulence, in which external forcing breaks the phase symmetry of the governing equations. This symmetry breaking suppresses the linear instability of the laminar state, while the energy cascade and spectrum of the developed turbulent state are preserved. A complementary single-triad model admits an exact elliptic neutral stability curve, revealing that the stabilization depends only on the breaking strength and not on the nonlinear coupling coefficients. Since the phase symmetry of the shell model corresponds to Galilean invariance in the Navier--Stokes equations, this mechanism may offer a new perspective on subcritical transition in fluid systems.

While there are a number of proposed formation channels for subsolar mass compact objects, including black holes formed primordially, or neutron stars that form in collapsar disks, there have yet to be any conclusive observations of such objects. Motivated by the possibility that, if such objects exist, gravitational waves from binary mergers may reveal them, we study binary neutron star mergers where one star has a subsolar-mass in order to determine how well such systems are described by current models, and when they could be distinguished from a system with a subsolar-mass black hole. We perform fully general-relativistic simulations of a $1.7\ M_{\odot}$ star merging with a $0.8\ M_{\odot}$ star, leading to tidal deformabilities of up to $\mathcal{O}(10^4)$ for the latter, and quantify how this affects the merger dynamics and associated gravitation and electromagnetic signals. In this regime, we find mass transfer between the stars, as well as significantly lower disruption frequencies. Though this is not captured by current gravitational waveform models, we conclude that this does not significantly impact the sensitivity of current gravitational wave detectors to these sources. Assuming design sensitivity of the LIGO and Virgo detectors, we find no biases in the recovered intrinsic parameters for signal-to-noise ratios $\lesssim 100$. We also find that the large deformabilities lead to a significant increase in the amount of dynamically ejected matter compared to equal mass systems, exceeding the predictions of current phenomenological models.

We study a symmetrized (half-space) version of geometric last passage percolation with a boundary parameter $c$ that interpolates between subcritical, critical, and supercritical behavior. This model gives rise to a family of interlacing random curves, or a line ensemble, which encode both the usual last passage time and its higher-rank analogues. Although these ensembles are understood in most space-time regions, their behavior near the diagonal -- where the boundary effects are strongest -- has remained unclear outside the critical regime. We determine the universal scaling limits of the line ensemble in this near-diagonal region for both subcritical ($c < 1$) and supercritical ($c > 1$) phases. In the subcritical case, after appropriate centering and scaling, the entire line ensemble converges to the pinned half-space Airy line ensemble, a universal Brownian Gibbsian object recently constructed as a canonical limit for half-space models in the KPZ universality class in arXiv:2601.04546. In the supercritical case, we prove an analogous convergence together with a curve-separation phenomenon: the lower curves converge to the same pinned half-space Airy limit, while the top curve decouples and converges to Brownian motion. These results essentially complete the asymptotic description of half-space geometric last passage percolation and provide a new rigorous instance of the pinned half-space Airy line ensemble as a universal scaling limit.

We obtain the phase diagrams of field theories of intertwined orders in the presence of periodic driving by an external field which preserves all symmetries. We consider both a conventional Landau theory of competing orders, and a fractionalized theory in which the order parameters are distinct composites of an underlying multi-component Higgs field. We work in the large $N$ limit and couple to a Markovian bath. The long time limits are characterized by non-zero average values, oscillations with the drive period and/or half the drive period, quasi-periodic oscillations, or chaotic behavior.

HAT-P-11 is a well-studied, active K dwarf hosting an eccentric, misaligned transiting sub-Neptune. As part of the HST Stellar Treasure Trove program (HST-AR-17551), we analyze absolutely calibrated out-of-transit \HST{} spectra from \texttt{STIS} and \texttt{WFC3} across the \textsc{G430L}, \textsc{G750L}, \textsc{G102}, and \textsc{G141} bandpasses to constrain the surface heterogeneity of HAT-P-11 and its impact on transmission spectroscopy. Grid-based spectral retrievals using NewEra \texttt{PHOENIX} models robustly favor two-component photospheres in the \texttt{WFC3} G102 and G141 data, with a ${\sim}4950$\,K photospheric component and a cooler ($\sim$3400\,K) component covering 26{--}33\% of the stellar disk. By contrast, retrievals on the \texttt{STIS} optical spectra do not yield a satisfactory fit, reflecting current limitations of stellar atmosphere models in the optical regime compared to the \HST{} observational precision. We contextualize these results using long-term photometric monitoring and chromospheric activity indices. The inferred high spot covering fractions are broadly consistent with the elevated photometric variability observed during the \textit{Kepler} era ($f_{\rm spot}$$\sim$10--20\%) but are in tension with the much lower rotational amplitudes observed from TESS in the mid 2020s ($f_{\rm spot}$$\sim$1--10\%). This secular decline in variability is mirrored by a $\sim$20\% decrease in the Ca\,\textsc{ii} H\&K index. These results imply that HAT-P-11 undergoes comparatively quiescent phases that offer more favorable windows for atmospheric characterization, which serendipitously coincided with some of the recent JWST observations. More generally, our study demonstrates that multi-epoch, space-based stellar spectra provides a physically grounded pathway for mitigating stellar contamination in high-precision transmission spectra in the JWST era.

Dopamine levels are linked to neurological illnesses like Parkinson's and Alzheimer's. Thus, reliable and sensitive detection of dopamine is crucial for early diagnosis and surveillance of neurodegenerative diseases. Non-noble-metal-based nanomaterials are ideal for light-mediated sensing of organic molecules. Among these, 2D quasicrystal structures consisting of five elements, namely Al70Co10Fe5Ni10Cu5, provide active sites due to their high surface-to-volume ratio, making them excellent for organic chemical sensing. Here, we propose a simple, label-free, spatial self-phase-modulation (SSPM)-based sensing method in liquid form. SSPM-based time evolution of the diffraction pattern for varied mixing levels of a 1100 ppb dopamine solution shows a shift in the active 2D Al QC solution. The 1100 ppb solution shows a distinct value, indicating a change in the nonlinear refractive index. Time-evolution analysis is used to calculate sensitivities to changes in the nonlinear refractive index and time constant. The SPR-activated 2D Al QC nanostructure is used to demonstrate dopamine sensing and to perform qualitative and quantitative evaluations. The SSPM-based sensing has been further compared with other optical-based sensing methods such as Raman spectroscopy, UV-Vis spectroscopy, and FTIR spectroscopy. The experimental observations are also explained using DFT-based simulations. The current SSPM method can be used for rapid, large-scale medical diagnostics.

The redshifted 21 cm absorption trough from cosmic atomic hydrogen is one of the most promising probes of the early Universe, but its detection is challenged by bright foregrounds and instrumental systematics. In this work we quantify the impact of antenna mismodelling on signal recovery within a fully Bayesian, forward-modelled data analysis pipeline. We show that discrepancies between simulated and modelled antenna beams lead to frequency dependent errors in antenna temperature that can bias parameter inference. In particular, we demonstrate that orientation mismatches at the level of 0.25 degrees can significantly bias recovered signal parameters in typical observing scenarios. However, we also show that Bayesian evidence can be used to infer antenna orientation within this precision by scanning over model realisations. For structural mismodelling, we find that broadband recovery of all signal parameters requires accurate beam knowledge, but that partial recovery remains possible. Signal frequency and width can be robustly recovered under restricted frequency bands even when the antenna structure is imperfectly modelled, but signal depth is highly sensitive to beam errors. These results quantify the level of beam knowledge required for forward-modelled global 21 cm experiments and highlight the importance of observing strategy and antenna design in mitigating beam-sky coupling systematics.

Microarchitectural vulnerabilities increasingly undermine the assumption that hardware can be treated as a reliable root of trust. Prevention mechanisms often lag behind evolving attack techniques, leaving deployed systems unable to assume continued trustworthiness. We propose a shift from prevention to detection through microarchitectural-aware remote attestation. As a first instantiation of this idea, we present HammerWatch, a Rowhammer-aware remote attestation protocol that enables an external verifier to assess whether a system exhibits hardware-induced disturbance behavior. HammerWatch leverages memory-level evidence available on commodity platforms, specifically Machine-Check Exceptions (MCEs) from ECC DRAM and counter-based indicators from Per-Row Activation Counting (PRAC), and protects these measurements against kernel-level adversaries using TPM-anchored hash chains. We implement HammerWatch on commodity hardware and evaluate it on 20000 simulated benign and malicious access patterns. Our results show that the verifier reliably distinguishes Rowhammer-like behavior from benign operation under conservative heuristics, demonstrating that detection-oriented attestation is feasible and can complement incomplete prevention mechanisms

Background: Electronic health records (EHRs) enable machine learning for diagnosis, prognosis, and clinical decision support. However, EHR standards vary by country and hospital, making records often incompatible. This limits large-scale and cross-clinical machine learning. To address such complexity, a metadata repository cataloguing available data elements, their value domains, and their compatibility is an essential tool. This allows researchers to leverage relevant data for tasks such as identifying undiagnosed rare disease patients. Results: Within the Screen4Care project, we developed S4CMDR, an open-source metadata repository built on ISO 11179-3, based on a middle-out metadata standardisation approach. It automates cataloguing to reduce errors and enable the discovery of compatible feature sets across data registries. S4CMDR supports on-premise Linux deployment and cloud hosting, with state-of-the-art user authentication and an accessible interface. Conclusions: S4CMDR is a clinical metadata repository registering and discovering compatible EHR records. Novel contributions include a microservice architecture, a middle-out standardisation approach, and a user-friendly interface for error-free data registration and visualisation of metadata compatibility. We validate S4CMDR's case studies involving rare disease patients. We invite clinical data holders to populate S4CMDR using their metadata to validate the generalisability and support further development.

We study the two-dimensional (geometric) knapsack problem with rotations (2DKR), in which we are given a square knapsack and a set of rectangles with associated profits. The objective is to find a maximum profit subset of rectangles that can be packed without overlap in an axis-aligned manner, possibly by rotating some rectangles by $90^{\circ}$. The best-known polynomial time algorithm for the problem has an approximation ratio of $3/2+ε$ for any constant $ε>0$, with an improvement to $4/3+ε$ in the cardinality case, due to G{á}lvez et al. (FOCS 2017, TALG 2021). Obtaining a PTAS for the problem, even in the cardinality case, has remained a major open question in the setting of multidimensional packing problems, as mentioned in the survey by Christensen et al. (Computer Science Review, 2017). In this paper, we present a PTAS for the cardinality case of 2DKR. In contrast to the setting without rotations, we show that there are $(1+ε)$-approximate solutions in which all items are packed greedily inside a constant number of rectangular {\em containers}. Our result is based on a new resource contraction lemma, which might be of independent interest. In contrast, for the general weighted case, we prove that this simple type of packing is not sufficient to obtain a better approximation ratio than $1.5$. However, we break this structural barrier and design a $(1.497+ε)$-approximation algorithm for 2DKR in the weighted case. Our arguments also improve the best-known approximation ratio for the (weighted) case {\em without rotations} to $13/7+ε\approx 1.857+ε$. Finally, we establish a lower bound of $n^{Ω(1/ε)}$ on the running time of any $(1+ε)$-approximation algorithm for our problem with or without rotations -- even in the cardinality setting, assuming the $k$-\textsc{Sum} Conjecture.

We investigate the electronic structure at the surface of the correlated oxide Ca$_3$Ru$_2$O$_7$, a low-symmetry ruthenate oxide which hosts an unconventional polar-metal phase. From a combination of angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy measurements, we demonstrate that the surface hosts an insulating phase, a distinct departure from metallicity within the bulk. Utilizing quantitative low-energy electron diffraction in conjunction with electronic structure calculations, we show how this results from a combined surface structure relaxation and the impact of marked electronic correlations in this system. Our findings highlight the proximity of Ca$_3$Ru$_2$O$_7$ to an insulating metallic state, and illustrate how subtle structural distortions can control its emergent electronic phases.

I present a reanalysis of temperature data from a publicly available certified laboratory report that documented the self-discharging behavior of an energy-storage device during 10 days. Graphs of temperature variations of both the tested device itself and the test chamber (fume hood) were given mainly for monitoring without further analysis, and variations in the ambient temperature signal were attributed to "other cells being cycled simultaneously in the same fume hood". I show that the ambient temperature signal alone -- together with some quite mild and reasonable assumptions -- allow to extract previously unpublished information on the simultaneously run test on the other cells: 1) the number of charge/discharge cycles 2) the cycle period, 3) the charge/discharge half-cycle asymmetry, and -- most significantly -- evidence that 4) the mentioned "other device" completed 338 full charge/discharge cycles at 3C rate at room temperature without any detectable thermal degradation signature.

Certain radiation detectors are 'paralyzed' with high input count rates. When applied to count rates close to the event discriminator working rate the one-parameter dead time model fails. Here we present a corrected paralyzable detector model accounting for the event discriminator's finite response time. This two-parameter analytical model, when compared to the experimental data from a commercial x-ray detector, gives an improved description of the input and output count rate relations. Furthermore, it can independently determine the discriminator response time and the pulse shaper dead time, critical parameters for understanding a detector's performance. Finally, this model also provides a post-acquisition pile-up correction that greatly reduces artifacts in high-throughput spectra. In some situations, applying this model to optimize the acquisition and post-acquisition correction allows a user to acquire data an order of magnitude faster without compromising accuracy.

India generates substantial volumes of public agricultural data, yet artificial intelligence (AI) adoption in farming remains limited and largely confined to pilot initiatives. This paper examines this gap by assessing India's agricultural data infrastructure against the requirements of AI systems deployed at scale. Drawing on a systematic review of major national datasets and digital initiatives including Soil Health Cards, crop insurance, AgriStack, and selected state platforms we identify persistent structural constraints, including temporal misalignment between data collection and agricultural decision cycles, spatial fragmentation arising from the absence of common geocodes linking soil, weather, and yield information, limited machine readability due to reliance on static data formats, and unclear governance frameworks that restrict data access and reuse. These deficiencies impede cross-dataset integration and automated decision support, with disproportionate consequences for smallholders, who constitute 86~\% of India's farmers and lack the capacity to compensate for weak data infrastructure. Drawing on implementation evidence from India and comparative international experiences, the paper identifies recurring features associated with scalable digital agriculture systems, including incentives linked to data provision, service bundling through local institutions, and sensor-enabled risk management.

We present the NCS-models, a family of seismic foundation models pretrained on a large share of full-stack seismic cubes from the Norwegian Continental Shelf (NCS) available through the public DISKOS database. The model weights are open-sourced for the wider geoscience community. Foundation models trained with large-scale self-supervision are emerging as a promising basis for automatic seismic interpretation. However, most existing seismic models rely on limited or proprietary datasets, and it remains unclear how well natural-image foundation models transfer to seismic data. Our goals are to develop basin-scale seismic foundation models, provide practical recipes for scalable 3D training, and quantify the effects of basin-targeted pretraining and token dimensionality on downstream interpretation performance. Using masked autoencoders with Vision Transformer backbones, we pretrain models on a DISKOS-derived corpus of 3D time- and depth-migrated seismic volumes. The NCS-model variants use 2D, 2.5D multi-view, and 3D tokenization within a matched training setup. Transfer is evaluated on interpretation benchmarks using frozen backbones and a simple k-nearest neighbor classifier. Baselines include an ImageNet-pretrained MAE, a frontier vision foundation model, and a globally pretrained seismic model. Natural-image pretrained models do not reliably transfer, reflecting the large domain gap between natural images and seismic data. Seismic pretraining is necessary for robust transfer, and large-scale basin-targeted pretraining yields further gains over a smaller globally pretrained seismic baseline. The NCS-models achieve the best overall performance without fine-tuning, while 2.5D tokenization offers the strongest accuracy-efficiency tradeoff and the embeddings support similarity search for interactive interpretation.

Qualitatively, a no-dimensional Helly-type theorem says that if every small subfamily of convex sets has a common point in a bounded region, then suitable neighborhoods of all the sets in the whole family have a common point. Quantitative bounds, when available, depend on the ambient metric. We say that a Banach space has the Helly approximation property if the radii of these neighborhoods tend to zero as the size of the subfamilies tends to infinity. In this paper, we show that the Helly approximation property holds if and only if the dual space has non-trivial Rademacher type. The argument combines Maurey's empirical method with a duality argument at a minimizer of the maximal distance function. We also prove a colorful version of this theorem, with control over the average of the radii.

We examine how neurodivergent individuals experience creating, interacting with, and reflecting on personal data about masking. Although self-tracking is often framed as enabling self-insight, this is rarely our experience as neurodivergent individuals and researchers. To better understand this disconnect, we conducted a two-phase qualitative study. First, a workshop where six participants with autism and/or ADHD crafted visual representations of masking experiences. Then, three participants continued by designing and using personalized self-tracking focused on unmasking over two weeks. Using reflexive thematic analysis of activities and interviews, we find that self-tracking imposes substantial interpretive and emotional demands, shaped by context-dependencies that challenge assumptions in self-tracking. We also find that facilitated sharing of experiences might validate emotional responses and support reflection. We identify three emotional dimensions that shape engagement with personal data in a working model of emotion in self-tracking, and discuss implications for designing self-tracking and reflective practices that incorporate peer support and better account for context and emotional labor.

This paper studies the problem of finite-time convergence to a prescribed safe set for nonlinear systems whose initial states violate the safety constraints. Existing Control Lyapunov-Barrier Functions (CLBFs) can enforce recovery to the safe set but may suffer from the issue of chattering and they do not explicitly consider control bounds. To address these limitations, we propose a new Control Barrier Function (CBF) formulation that guarantees finite-time convergence to the safe set while ensuring feasibility under control constraints. Specifically, we strengthen the initially violated safety constraint by introducing a parameter which enables the exploitation of the asymptotic property of a CBF to converge to the safe set in finite time. Furthermore, the conditions for the existence of such a CBF under control bounds to achieve finite-time convergence are derived via reachability analysis and constraint comparison, providing a systematic approach for parameter design. A case study on 2D obstacle avoidance is presented to demonstrate the effectiveness and advantages of the proposed method.

We present a standalone frequency-offset locking system for controlling narrow-linewidth lasers using off-the-shelf electronic components. We lock two frequency-doubled 1560 nm lasers to a stable primary laser operating at 780 nm via their optical beat note. This radio-frequency beat note is fed through a broadband variable divider, a frequency-to-voltage converter, and a proportional-integrator controller to lock each follower laser to a tunable offset frequency relative to the primary. This architecture provides a large capture range ($> 1$ GHz), fast response times ($< 1$ ms), and high linearity. We achieve a frequency resolution of 1.9 kHz and a short-term fractional frequency instability $10^{-11}/\sqrt{τ\rm (s)}$ at 780 nm without the need for a dedicated, precise clock reference. We perform high-resolution spectroscopy of cold $^{87}$Rb atoms to demonstrate the tunability and precision of our locking system. We designed the system to be modular and extensible, making it applicable to a wide variety of atomic physics experiments, including laser cooling, spectroscopy, and quantum sensing with atoms, ions, and molecules.

We present GateANN, an I/O-efficient SSD-based graph ANNS system that supports filtered vector search on an unmodified graph index. Existing SSD-based systems either waste I/O by post-filtering, or require expensive filter-aware index rebuilds. GateANN avoids both by decoupling graph traversal from vector retrieval. Our key insight is that traversing a node requires only its neighbor list and an approximate distance, neither of which needs the full-precision vector on SSD. Based on this, GateANN introduces graph tunneling. It checks each node's filter predicate in memory before issuing I/O and routes through non-matching nodes entirely in memory, preserving graph connectivity without any SSD read for non-matching nodes. Our experimental results show that it reduces SSD reads by up to 10x and improves throughput by up to 7.6x.

Data literacy has become a key learning objective in K-12 education, but it remains an ambiguous concept as teachers interpret it differently. When creating assessments, teachers turn broad ideas about "working with data" into concrete decisions about what materials to include. Since working with data visualizations is a core component of data literacy, teachers' decisions about how to include them on assessments offer insight into how they interpret data literacy more broadly. Drawing on interviews with 13 teachers, we identify four challenges in enacting data literacy in assessments: (1) conceptual ambiguity between data visualization and data literacy, (2) tradeoffs between using real-world or synthetic data, (3) difficulty finding and adapting domain-appropriate visual representations and data visualizations, and (4) balancing assessing data literacy and domain-specific learning goals. Drawing on lessons from data visualization, human-computer interaction, and the learning sciences, we discuss opportunities to better support teachers in assessing data literacy.

We examine parameter degeneracies in Culetu, Bardeen and Hayward regular black holes across lensing, shadow and quasinormal mode regimes. Our analysis reveals that while Einstein ring data yield extremely loose constraints, with the regularization parameter $q$ exceeding $\mathcal{O}(10^3)$, they fail to improve the parameter estimation when combined with strong lensing observables. In contrast, the Event Horizon Telescope observations provide remarkably tight limits: $0 \leq q < 0.0466 <0.0847$ for Culetu, $0 \leq q < 0.5115 <0.6682$ for Bardeen and $0 \leq q < 1.0258 <1.1881$ for Hayward, which shows that the strong field regime alone dominates the available parameter space. Despite these bounds, leading order geometric observables remain highly degenerate, which masks the microscopic details of non-singular cores. To break this ``macroscopic universality,'' we identify high order signatures, such as the Lyapunov exponent and subleading time delays, as sensitive probes of near horizon curvature. Crucially, we discover that the brightness hierarchy of accretion induced intensity profiles undergoes a fundamental inversion when transitioning from lensing dominated static flows to dynamics dominated infalling flows. These results demonstrate that high resolution temporal and intensity profiles are essential for distinguishing between regular black hole geometries.

Localized cavitation in liquids and soft tissues, typically initiated by the rarefaction phase of high-amplitude ultrasound waves, is leveraged in several biomedical applications such as ablation techniques and drug delivery with vaporizing agents. However, safety considerations aimed at avoiding unwanted bubble activity outside the targeted region pose a limit to the maximum allowed peak rarefaction pressure, which on the other hand can hinder the therapeutic efficacy of these techniques. This study shows that a purely compressive shock wave can generate localized, negative pressure and initiate cavitation inside a sub-millimetric perfluorohexane droplet, without requiring any externally applied rarefaction wave. The Gouy phase shift is identified as the physical mechanism responsible for the conversion of positive pressure into tension during shock focusing, and its occurrence is demonstrated through numerical simulations and direct experimental measurements. Comparison of the regions affected by cavitation, visualized \emph{in-situ} by means of high-speed x-ray phase-contrast imaging, with prediction from Classical Nucleation Theory suggests homogeneous nucleation as the underlying mechanism behind bubble formation. The presented findings offer valuable insights into the physics of shock wave propagation which can inspire the development of novel acoustic driving strategies for cavitation generation, facilitating the reduction of negative pressures outside the target region and improving the safety and precision of biomedical treatments.

Quantitative high-resolution transmission electron microscopy (HRTEM) provides an indispensable means to understand the structure-property relationships of a material in atomic dimensions. Successful quantification requires reliable retrieval of essential atomic structural information despite artifacts arising from unwanted but practically unavoidable imaging imperfections. Experimental observation carried out in tandem with model-based iterative image simulation shows vast applications in quantitative structural and chemical determination of objects spanning zero to three dimensions [Prog. Mater. Sci. 133, 101037, 2023]. However, the large number of parameters involved in the simulations make the current multi-step, user-guided iterative approach highly time consuming, thereby restricting its application primarily to small sample areas and to experienced users. In this work, we implement and apply a physics-informed Bayesian optimization (BO) framework to advance HRTEM quantification towards full automation and large-field-of-view analysis. Unlike conventional optimization approaches, our method adopts a stepwise strategy that fully leverages the strength of BO in handling high-dimensional parameters, while its probabilistic engine rigorously and efficiently refines the parameter space to enable rapid quantification. Using a BaTiO3 single crystal that contains heavy, medium and light elements as a model system, we demonstrate that the three-dimensional crystal structure can be determined from a single HRTEM image with a three to four order-of-magnitude improvement in time efficiency. This approach thus opens new avenues for fast and automated image quantification over larger sample volumes and, potentially, in the time domain.

In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux equation in R^n with subcritical power type nonlinearity. By introducing an improved test function, we obtain an enhanced lower bound for the functional including the spacetime integral of the nonlinear term with an additional logarithmic growth, which finally yields the blow up result and upper bound of lifespan estimate for the corresponding Cauchy problem with "critical" nonlinear power. And this gives some partial answer to the open problem 1 posed by D'Abbicco (J. Differential Equations 286 (2021), 531-556).

Using preservations of piecewise linear (PL) homeomorphism types under edge contractions (the link condition) as a topological proxy for flagness, we give a quantitative description of the effect flagness on on gamma positivity of simplicial spheres. In particular, we show that the link condition has a trivial effect on the $g$-vectors (and thus gamma vectors) of high-dimensional simplicial spheres with nonnegative gamma vectors in many cases. Note that this reflects a dichotomy between quantitative behavior arising from $g_1$ components (e.g. measuring ``net number of edge subdivisions'' from the boundary of a cross polytope) that are linear in the dimension and those that are superlinear in the dimension. When the link condition is nontrivial, we show that it gives a lower bound for growth rates of $g$-vector components. This lower bound increases as the number of edges and the distance of the $M$-vector condition on $g$-vectors of simplicial spheres from equality decrease. These lower bounds translate to ones on top gamma vector components and give lower bounds on gamma vector growth rates when the gamma vector components are dominant terms in the $g$-vector components with the same index (e.g. $g$-vectors with components increasing quickly compared to the dimension). Finally, we show that the same results apply to positivity properties generalizing gamma positivity arising from connections between orthogonal polynomials and lattice paths. In the course of doing this, we describe gamma vector components in terms of monomer/dimer covers and point out connections between repeated (stellar) edge subdivisions (Tchebyshev subdivisions) and dimer covers.

We review the recent quantum advantage experiments by IBM, D-Wave, and Google, focusing on cases where efficient classical simulations of the experiment were demonstrated or attempted using tensor network methods. We assess the strengths and limitations of these tensor network-based approaches and examine how the interplay between classical simulation and quantum hardware has advanced both fields. Our goal is to clarify what these results imply for the next generation of quantum advantage experiments. We identify regimes and system features that remain challenging for current tensor network approaches, and we outline directions where improved classical methods could further raise the standard for claiming quantum advantage. By analyzing this evolving competition, we aim to provide a clear view of where genuine, scalable quantum advantage is most likely to emerge.