The weighted difference of squared norms (WDSN) penalty $\ell_1^2-η\ell_2^2$ with $0\leq η\leq 1$ has attracted considerable attention due to its strong sparsity-promoting ability and favorable reconstruction performance in compressed sensing and inverse problems. However, exact recovery guarantees and restricted isometry property (RIP) analysis for WDSN minimization have not yet been established. In this paper, we address this gap. First, we establish sufficient conditions for the exact recovery of $k$-sparse signals based on the null space property (NSP). Then, under the $δ_{2k}$-RIP condition, we derive stable recovery guarantees for both $k$-sparse signals and general signals, and characterize upper bounds on the reconstruction error. Furthermore, we propose a WDSN-based regularized model to handle both noiseless and noisy observations in a unified framework. To design an efficient algorithm, we derive an explicit formula for the proximal operator of the WDSN functional. Based on this proximal solver, we develop a suitable variable-splitting scheme within the alternating direction method of multipliers (ADMM) and establish its global convergence under some mild conditions. Finally, numerical experiments show that the proposed method outperforms the iterative half variation method in both noiseless and noisy sparse recovery tasks.

The thermo-refractive effect is a cornerstone of frequency and phase tuning in photonic integrated circuits. In particular, it enables control of phase-matching for integrated nonlinear processes. Chromatic dispersion of the group and effective refractive indices and modal confinement are standard considerations in design, but material thermo-refractive coefficients (TRCs) are typically taken to be fixed for the guiding and cladding materials. Here, we demonstrate that the assumption of non-dispersive TRCs across an octave of bandwidth between the telecom and visible results in a significant discrepancy between measured and simulated resonance frequencies of an integrated Si3N4/SiO2 microring resonator. We uncover a 7 % variation in Si3N4 and SiO2 material TRCs across this range, finding that the variation of dneff /dT from material TRCs is 1.3 times that from modal confinement. This accurately matches a temperature-dependent Lorentz oscillator model describing their chromatic dispersion. By integrating these dispersive TRCs into a multi-physics finite-element model, we achieve precise correspondence with experimentally measured temperature-dependent resonance frequency shifts across the octave, including in the context of second harmonic generation devices. Our results provide a physical framework and a universal predictive workflow for the design of high-efficiency, multi-wavelength nonlinear optical processes, fundamentally improving the thermal control of integrated photonic devices.

We report the results of a high-sensitivity survey for Herbig-Haro (HH) outflows in the Serpens-Aquila Rift using the DECam instrument on the 4-meter telescope. We have detected 88 new HH objects, more than tripling the total known in this region. We have also identified likely progenitors for most of these outflows. By combining HH object and progenitor locations with literature dust maps and Gaia astrometry, we find that HH objects mark five spatially distinct clouds hosting active star formation: the Serpens Molecular Cloud and LDN 673 at 400-500 pc, the more distant West and East components of the Aquila Rift at ~600 and 700 pc, respectively, and a near cloud in Serpens at ~250 pc. In both the Serpens Molecular Cloud and the Western Aquila Rift, HH objects broadly trace gas structures on the edges of low-density cavities surrounding known stellar populations, consistent with active star formation in feedback-driven shells. The near cloud in Serpens is not associated with any established stellar population, but its position and velocity suggest that it is part of the Local Bubble. And the HH objects there may mark the start of a new stellar generation connected to the Scutum North Association. Our Herbig-Haro objects therefore serve as a powerful indicator of star formation sites even in the absence of astrometrically characterized young stars, making them a useful tool for guiding future YSO surveys.

The 2023 Uruguayan Census recorded a population of 3,444,451 with an estimated undercoverage of 10.3%. Post-enumeration evidence shows that omission was non-random, concentrated in vulnerable areas, rural territories, and among young adults. Integrating administrative records (AR) recovered aggregate counts but did not resolve selection bias in outcome variables, as AR lack core census variables, exhibit urbanicity and institutional-visibility biases, and do not reconstruct households. Estimates derived from enumerated microdata remain biased. We treat effectively enumerated households as a non-probability sample with an unknown selection mechanism and construct weights using a doubly robust (DR) estimator. This framework combines a segment-level response-propensity model, using the web linkage rate as a contact proxy, with calibration to combined-census demographic totals (sex, age, department). Because the DR estimator is consistent when either model is correctly specified, it provides robustness against undercoverage misspecification. We describe the application at a scale of three million records, document its effect on social indicators, and present a variance approximation based on an equivalent stratified cluster design. Finally, we establish a methodological framework to guide national statistical offices on optimizing non-response adjustments based on their available registers and paradata.

In recent years, the spacetime code has arisen as a candidate for a unifying view of fault tolerance in space and time. On the other hand, the recent study of dynamical phases has increasingly turned its attention to fault tolerance as a notion of a dynamically stable process. In this work, I explore one pathway between the two, achieved by gauging the spacetime code. This gives rise to a lattice gauge theory that inherits the elements of fault tolerance associated with a circuit, with Gauss laws corresponding to equivalence relations between configurations of spacetime errors and Wilson loops corresponding to detectors. The obtained gauge theory finds a surprisingly wide array of applications, from quantum error correction to condensed matter physics, and even learning theory: (1) It contains in its description foliated computation, and hence gives rise to one version of a gauge theory for measurement-based quantum computation. (2) For a class of topologically ordered mixed states, it gives us a gauge-theoretic language to describe the classical memory associated with the state. (3) The gauge-invariant observables of the theory which describe detectors also coincide with the learnable degrees of freedom of circuit Pauli noise.

Production analytics products often depend on reusable methodologies: multi-step definitions such as headcount growth, top-skill growth, or differentially-private impression distributions. Although these methodologies define business-critical numbers, they are commonly implemented as imperative glue around OLAP queries, service calls, joins, transformations, and conditional logic. As a result, teams duplicate orchestration code, definitions drift across products, and methodologies are difficult to test or analyze. We present QDAG, a production system at LinkedIn that represents an analytics methodology as a declarative directed acyclic graph of typed steps. Nodes may execute Apache Pinot queries, downstream service calls, in-memory SQLite joins, jq transformations, conditionals, differentially-private aggregations, or calls to other QDAGs. The engine evaluates graphs demand-driven, memoized, pruned, and parallelized in the per-request analytics mid-tier. QDAG is deployed across more than 500 hosts and over 100 production use cases, adding roughly 10 ms median orchestration overhead and under 50 ms at the 99th percentile. Our experience shows that making methodologies declarative improves reuse, testability, and cross-product consistency while preserving interactive latency.

Large main-belt asteroids with visible geometric albedos below 0.1 are predominantly classified within the C- and X-complex spectroscopic classes. C-type and dark X-type asteroids typically exhibit flat to slightly negative and positive spectral slopes, respectively. They are further distinguished by the presence (for C-types) or absence (for dark X-types) of a shallow absorption feature near 1.0-1.3 micron. We serendipitously discovered that the asteroids 1093 Freda and 1390 Abastumani display spectral characteristics intermediate between these two classes, combining a positive visible-to-near-infrared spectral slope with a shallow absorption band. A search in the literature reveals additional asteroids with similar properties. The existence of such objects, spanning a continuum of spectral shapes between C- and dark X-types, may point to a common genetic origin. Their spectral behavior could be explained by the presence of cronstedtite, an Fe-rich serpentine, on their surfaces.

Sparse recovery aims to reconstruct sparse signals from underdetermined and possibly noisy linear measurements. Existing $\ell_{1-2}$ iterative thresholding schemes are first-order methods. We propose an iterative thresholding pursuit method with continuation (ITP-C) for $\ell_{1-2}$-regularized sparse recovery. The method goes beyond first-order thresholding by combining the active-set identification capability of the $\ell_{1-2}$ proximal step with a restricted least-squares pursuit step that provides a second-order update on the identified support. The support is generated adaptively by the thresholding update, and no prior knowledge of the true sparsity level is required. To control the possible instability of the pursuit step while preserving the descent structure of the continuation scheme, we impose a strict descent check with respect to the dynamic objective. We establish convergence of the generated sequence under the Kurdyka-Lojasiewicz framework and prove a local oracle-type property after correct support identification. Numerical experiments on synthetic sparse recovery and image reconstruction illustrate the descent preservation of the proposed safeguard and demonstrate the improved recovery performance of ITP-C over the state-of-the-art baselines.

We investigate the quantum aspects of gauging continuous 1-form global symmetries. In this paper, we study the BV-BRST quantization of a $U(1)$ 2-form gauge field, described geometrically by a $U(1)$ gerbe. Starting from the local Čech data of the gerbe, we construct the corresponding infinitesimal symmetry structure in terms of a Lie 2-algebroid, and show that, together with the associated exact Courant algebroid, it provides a natural geometric framework for the BV-BRST complex of this higher-form gauge theory. In this formulation, the field-ghost tower is encoded directly in the local gerbe data, and the higher Russian formula arises naturally from the relations among the connective structure, the curving, and the 3-form curvature. We further show that the resulting Čech-de Rham bicomplex provides a natural setting for anomaly descent for $U(1)$ 1-form symmetries, and illustrate the construction with explicit examples in Maxwell theory.

The ratio of voting power between a permanent member and a non-permanent member of the United Nations Security Council varies substantially across indices: approximately 100 to 1 according to the Shapley-Shubik index, 10 to 1 according to the Banzhaf index, and 2.5 to 1 according to the Deegan-Packel index. Such comparisons depend on the choice of power index and are meaningful only in settings where players are divided into two types. To address these limitations, this paper proposes and characterizes a function that measures the level of power concentration in monotonic approval voting games. The proposed measure assigns a single value to each voting game, reflecting the extent to which voting power is unevenly distributed among players. The proposed measure is proportional to the sum of squared Deegan-Packel power indices and can also be interpreted as the degree of overlap among minimal winning coalitions. An application to the United Nations Security Council is also provided.

Fermi arcs observed in underdoped cuprates have sparked debate over whether they represent segments of a large Fermi surface or small Fermi pockets. This ambiguity has long hindered their classification as either the conventional Bardeen-Cooper-Schrieffer (BCS) regime or the strongly coupled Bose-Einstein condensation (BEC) crossover limit. Here, using angle-resolved photoemission spectroscopy and quantum oscillations, we demonstrate the coexistence of a small Fermi pocket and a large superconducting gap in the clean inner CuO2 layers of the four-layer cuprate Ba2Ca3Cu4O8(F,O)2. This coexistence constitutes a hallmark of the BCS-BEC crossover and has remained elusive for decades. Despite the presence of antiferromagnetic (AF) order, the superconducting gap in the small pocket is remarkably large, yielding a gap-to-Fermi-energy ratio (Delta_pocket/e_F ~ 0.6) and a critical-to-Fermi-temperature ratio (Tc/TF ~ 1.3) that reach the theoretical upper bound for two-dimensional superconductivity. Unexpectedly, this BCS-BEC crossover emerges not as the carrier density decreases but as it increases, abruptly within a narrow doping range of less than 1%. These results provide a long-sought microscopic foundation for the d-wave pairing mechanism in doped AF-Mott insulators.

This paper addresses the question: How can mission effectiveness be systematically defined or approximated in the absence of customer requirements? Legacy requirements engineering frameworks presuppose customer input to define specifications but leave a gap in the process when stakeholder input is ill-defined or missing. Rapid build and development programs (such as military acquisition, space assets, infrastructure projects, etc.) often see requirement and objective evolutions throughout the proposal process, so a more adaptive method is needed. To address this gap, a structured approach is proposed that decomposes mission intent into mission context, functions, constraints, critical dimensions, effectiveness attributes, and architecture alternatives. This method conducts a mission feasibility assessment, prioritizes mission-critical dimensions using Best-Worst Scaling, and introduces a mission complexity factor to quantitatively understand the impacts of external mission difficulties, technology maturity, evidence and confidence standards, and mission utility. The resulting method provides a traceable basis for deriving Tier 1 and 2 requirements. The approach is structured to support future Unified Architecture Framework (UAF) and Systems Modeling Language (SysML) artifact integration. The proposed framework is demonstrated using a notional close air support mission example.

The k-nearest neighbor query (kNNQ) is a core component of modern location-based services (LBS) and has been widely adopted in popular features such as ``people nearby''. However, its potential privacy risks have long been overlooked. In this work, we present the first two attacks against kNNQ, namely the geometric intersection location inference attack (GI-LIA) and the zero-order optimization location inference attack (ZO-LIA), revealing the inherent location privacy risks posed by kNNQ. To mitigate these privacy risks, we further propose DPRS, a differential privacy framework for kNNQ protection. The core idea of DPRS is to incorporate a rejection sampling mechanism within a constrained perturbation interval, thereby mitigating the distance distortion caused by excessive noise injection. In addition, we design a private interval construction algorithm to construct the perturbation interval, enabling the rejection sampling mechanism to achieve a more favorable trade-off between privacy protection and query utility in kNNQ. Extensive experiments on real-world spatial datasets demonstrate that DPRS outperforms existing methods in both privacy protection and query utility. Our code is available at https://github.com/reanatom/DPRS.

In this work, we discuss the $γW$-exchange contributions in neutron $β$ decay with an elastic intermediate state, beyond the forward-angle limit (FAL). By decomposing the one-$W$-exchange and $γW$-exchange amplitudes in terms of $16$ independent Pauli-spinor structures, we calculate the $γW$-exchange corrections to the relevant coefficients. Our numerical results show that the relative corrections to the Fermi Born term $C_{\text{Born}}^{\text{F}}$ and the Gamow-Teller Born term $C_{\text{Born}}^{\text{GT}}$ are enhanced by about 8\% and 18\%, respectively. In particular, we find a non-zero contribution to $C_{\text{Born}}^{\text{GT}}$ from the axial-vector current, which is identically zero in the FAL. The corresponding effect on the extracted $V_{ud}$ from the neutron lifetime is also analyzed, and we find the correction to be at the $10^{-4}$ level.

This paper considers large-scale T-Sylvester equations of the form $AX - X^\top E^\top + B_1B_2^\top = 0$, which admit a low-rank solution. It is shown that when the unique solution of the T-Sylvester equation is low-rank, the problem naturally reduces to a tangential interpolation problem via oblique projection. The specific interpolation points and tangential directions needed to obtain the low-rank solution are not known a priori, thus requiring an iterative approach. An iterative interpolatory projection algorithm is proposed based on these interpolation conditions, which iteratively refines the interpolation data as the projection matrices expand in the number of columns. Numerical examples demonstrate that the proposed algorithm converges with projection matrices having significantly fewer columns compared to existing Krylov-subspace-based projection methods, confirming the superiority of the proposed algorithm over existing approaches.

In this work, we study a compact hexaquark configuration motivated by the same quark content as $D^{+} D^{-} K^+$ using QCD sum rules, where the $D D K$ system has been extensively studied within theoretical frameworks of few-body hadronic dynamics and coupled-channel interactions. The state is constructed from three color-octet quark--antiquark clusters coupled to an overall color singlet. We construct six independent local interpolating currents with the quantum numbers $J^{P}=0^{-}$ and analyze the corresponding two-point correlation functions. Both perturbative contributions and nonperturbative condensates up to dimension ten are included in the operator product expansion. Our analysis indicates that, within Borel windows satisfying standard sum rule criteria and with a reasonable choice of continuum threshold, the mass of the $J^{P}=0^{-}$ hidden-charm hexaquark state is estimated to be in the range $3.94$--$4.41~\mathrm{GeV}$. This prediction can provide a valuable theoretical reference for identifying such exotic hidden-charm hexaquark state in future experiments.

In a multi-domain edge intelligence cloud (MDEIC) managed by multiple network operators, AI services are delivered by chains of virtual network functions (VNFs) executed in sequence, called AI service chains (AISCs). Therefore, achieving an efficient and economical AISC provisioning approach is essential. However, the interaction between the environmental characteristics (heterogeneity, resource constraints and limited information visibility) of MDEIC and the time-dependence of AISCs, introduces various challenges to AISC provisioning in MDEIC. In this paper, we first formulate the AISC provisioning problem as a partially observable stochastic game (POSG). Then, we propose a graph-and-time-based multi-agent AISC provisioning (GT-MAAISCP) approach to achieve the collaborative optimization of AISC provisioning cost, delay and availability. Specifically, each agent uses the graph-time dueling network (GTDN) architecture to extract network topology information and temporal relationships. Finally, the experimental results demonstrate that the proposed approach outperforms benchmark approaches in MDEIC and also illustrate its performance under varying network topologies and different numbers of local EICs (LEICs).

Market stress rarely harms investors through one channel alone. Losses, volatility spikes, and deteriorating tradability often arrive together. We examine whether ESG is associated with lower exposure to clustered fragility in equity markets. Using monthly data on S&P 500 constituents from 2014 to 2025, we study downside returns, volatility, illiquidity, and a cofragility state that captures their joint occurrence within the same firm month. The evidence supports a stress-amplified resilience interpretation rather than an unconditional ESG return premium. In the return channel, the ESG association is concentrated in the extreme downside tail during stress months. In the volatility channel, higher ESG is associated with smaller risk spikes when aggregate conditions are weak. In the illiquidity channel, the association is more persistent, suggesting a liquidity-quality component whose relevance increases when market-wide trading conditions deteriorate. The central evidence comes from the joint analysis: a one-standard-deviation increase in ESG lowers the stress-period probability of severe cofragility by 0.92 percentage points, about 9% relative to the baseline. Double Machine Learning shows a similar negative ESG association after flexible adjustment for observable firm characteristics. Pillar evidence suggests stronger baseline resilience for Environmental scores and clearer stress amplification for Social scores. Overall, the findings characterize ESG as a multi-channel fragility signal for tail-risk monitoring, stress analysis, and pillar-level ESG assessment.

All existing convergence rate estimates of Halpern iterations are established only for the case where the anchor coincides with the initial guess. This paper aims to investigate the convergence rate of general Halpern iterations, where the anchor and the initial guess may not necessarily be the same. We present tight convergence rate estimates for both predetermined and adaptive anchoring parameters. These results generalize existing related work.

We present a short proof that the book Ramsey number $R(B_8,B_{10})$ equals 37. The lower bound $R(B_8,B_{10}) \ge 37$ is already available in the literature, so it is enough to rule out a 37-vertex graph containing neither a copy of $B_8$ nor a copy of $B_{10}$ in its complement. The problem as well as the proof were found with AutoMath, an AI-assisted mathematical discovery workflow developed by the first author. A Lean formalization of the upper-bound argument is available in the accompanying repository.

Focused ultrasound (FUS) offers a promising, non-invasive method for modulating neural activity and delivering therapies deep within the brain with immense clinical potential. However, progress in developing transcranial ultrasound (TUS) for clinical applications has been hindered by several factors. The complexity of the human skull causes focal aberrations and attenuation, thereby presenting a major obstacle to the precise targeting of ultrasound waves. Although phased arrays can correct for these aberrations, their high cost and continuous reliance on magnetic resonance imaging (MRI) pose significant obstacles for widespread academic research and clinical translation. To address these challenges, this thesis proposes an innovative framework for the design, registration, and clinical application of acoustic holograms. First, we introduce a novel frequency-domain topology optimization method that overcomes the breakdown of traditional phase-only designs in the megahertz regime by accounting for volumetric wave-propagation effects, thereby achieving high-fidelity focusing. Second, we present a non-invasive registration strategy that utilizes the nonlinear parametric array (PA) effect to enable precise lens alignment without requiring any imaging modalities, such as MRI. Finally, we demonstrate the utility of this nonlinear parametric array (PA) effect as a tool for monitoring ventricular dilation as a non-invasive proxy for intracranial pressure changes in hydrocephalus. Collectively, these developments provide a path toward accessible, high-precision transcranial ultrasound systems for research and clinical use. In addition, we demonstrate a novel platform for in vitro focused ultrasound neuromodulation that leverages acoustics to advance therapeutic discovery.

In this paper, we propose a full-space quantization-driven architecture (FQA) for the hardware-efficient piecewise polynomial approximations (PPAs) of nonlinear activation functions. FQA comprehensively considers both fractional-bit truncation error and quantization error that cause the deviation of the optimal approximation coefficients. Crucially, FQA can precisely determine and search the complete range of optimal coefficients. Based on the proposed FQA, we develop two distinct hardware implementation schemes to cater to different resource-performance trade-offs. Furthermore, we decouple all the fractional word lengths (FWLs) involved in the calculation process to enable the exploration of superior hardware architectures. To mitigate the increased software computation time caused by the expanded quantization space, we design an acceleration method named TBW (target-guided bisection window) to expedite the piecewise calculation and searching process. Experimental results demonstrate that, compared to existing architectures, FQA can significantly reduce the number of required segments while achieving the optimal Maximum Absolute Error (MAE). For the hardware design of the Sigmoid function, our approach achieves over 50% reduction in area and power consumption compared to the state-of-the-art PPA architecture. Finally, we present a complete design workflow for deploying PPA on configurable hardware, maximizing the utilization of existing hardware resources and minimizing MAE.

Bankruptcy is a low-frequency but high-impact corporate event, making early risk identification important for creditors, investors, regulators, and risk managers. Traditional bankruptcy-prediction models rely primarily on accounting ratios, but these measures may reflect financial deterioration only after it appears in reported financial statements. Narrative disclosures in annual 10-K filings may therefore provide incremental warning signals about emerging distress. This study examines whether 10-K narratives improve bankruptcy prediction beyond conventional accounting variables. Using firm-year observations matched to 10-K text, SEC financial statement data, and bankruptcy events from the Florida-UCLA-LoPucki Bankruptcy Research Database, the analysis evaluates bankruptcy risk over the year following the 10-K filing date. The paper develops a transparent Pre-Bankruptcy Stress (PB Stress) Score, a dictionary-based measure designed to capture distress-specific language related to liquidity and funding stress, debt covenant and refinancing stress, operating deterioration, restructuring and legal distress, and business fragility. The score is evaluated against a five-variable accounting baseline and a Loughran-McDonald dictionary benchmark. In the primary one-year holdout test, adding the PB Stress Score increases AUC from 0.8323 to 0.9019 and raises top-decile bankruptcy capture from 44.12% to 64.71%. The positive incremental pattern remains visible across bootstrap inference, alternative accounting benchmarks, alternative outcome definitions, and out-of-time validation. The findings indicate that distress-specific 10-K narratives provide interpretable incremental information for bankruptcy-risk monitoring beyond conventional accounting ratios.

Distilling accurate user preferences from noisy implicit feedback remains a fundamental bottleneck in recommendation systems, highlighting the need for recommendation denoising. However, real-world data lack explicit noise annotations, forcing existing methods to rely on unsupervised side information or handcrafted heuristics. These approaches often incur high external costs, generalize poorly, or depend on unreliable priors, causing noise misidentification and corrupting true user preference representations. To address these limitations, we propose a paradigm-level reformulation of recommendation denoising. Instead of indirectly inferring noisy interactions through heuristics, our Creation-Recognition paradigm proactively creates labeled noisy interactions and trains a dedicated recognizer to identify them, transforming denoising from heuristic filtering into supervised learning. Based on this paradigm, we present ANCHOR, an agent-based framework inspired by recent LLM-as-User research. ANCHOR simulates user behaviors to generate realistic noise labels and enables supervised denoising through two stages: noise creation and noise recognition. In the noise creation stage, ANCHOR adopts a recommender-in-the-loop agentic architecture to synthesize both diverse out-of-preference noise and informative boundary-adjacent noise. For out-of-preference noise, it implements five extensible simulation mechanisms to approximate major sources of noisy implicit feedback. For boundary-adjacent noise, an adversarial boundary refinement mechanism generates ambiguous interactions that challenge the recognizer and target the decision boundary. In the noise recognition stage, ANCHOR leverages the generated labels to train a reusable parametric recognizer that integrates collaborative signals and semantic representations to detect noise patterns in real interaction data.

Suppose that for a mixing $Z^n$-action, $n>1$, there exists a Kirillov-Kushnirenko entropy that is zero for this action and completely positive for its inverse. We prove that this property is generic for the mixing $Z^n$-actions.

We develop parallel and batch-cutting variants of the norm-minimization-based outer approximation algorithm for convex vector optimization. The standard algorithm solves $N_k$ independent subproblems at each iteration~$k$ to evaluate all vertices of the current polyhedral approximation, but processes only the single best cut. We propose two improvements. First, we parallelize the \revise{subproblem evaluations} across $\nw$ workers, reducing per-iteration wall-clock time. Second, we introduce a batch-cutting strategy that adds up to $K$ supporting halfspaces per iteration, using information from all solved subproblems rather than discarding it. We prove that the batch-cutting variant inherits the convergence rate $O(k^{2/(1-q)})$ of the standard algorithm, where $k$ is the number of outer iterations and $q$ is the number of objectives. Computational experiments on eight test problems with $q \in \{2,3,4,5\}$ show that parallelism on 8 cores \revise{increases the speed by a factor of 1.1 to 4.2}, and batch cutting consistently reduces the iteration count by 62--80\%. However, the wall-clock benefit of batch cutting is problem-dependent: the additional cuts per iteration accelerate vertex count growth, so batch cutting is most effective when per-vertex subproblem cost dominates.

We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces, with arbitrary fixed Sobolev order k >= 1, on fitted interface meshes. The cells are coordinate-compatible cuboids, the local spaces are Q_{p_K}(K) with arbitrary elementwise degrees satisfying p_K >= 2k-1, and the coefficient may have arbitrarily large jumps across material interfaces. Under local coefficient oscillation bounds and a local high-side connectivity condition, both the conforming H^k space and the nonconforming spaces V_h^{(s)}, 0 <= s <= k, admit stable decompositions with constants which may depend on the fixed parameters d and k, but are independent of the mesh size, all polynomial degrees, neighboring degree ratios, and the global coefficient contrast. The argument combines a Hermite endpoint transform for endpoint jets of order 0,...,k-1, its tensor-product extension, weighted broken patch Poincare inequalities, and a successive correction of normal derivative jumps. Numerical experiments for a three-dimensional DG problem with large coefficient jumps and strongly varying local polynomial degrees support the predicted robustness. For k = 1 the same conclusions hold on uniformly regular mapped cubical meshes whose neighboring element maps agree on each common face.

We report on a new class of mode-locked fiber laser that allows direct creation of ultrafast vector vortex beams at arbitrary positions on the higher-order Poincaré sphere. The on-demand generation of space-variant polarization patterns was realized by controlling geometric phases inside the laser resonator to map polarization to orbital angular momentum. Thanks to the ingenious cavity design, the required intracavity manipulation of the geometric phase imposed no disturbance on the passively mode-locked operation, thus demonstrating robust and flexible switching of vectorial modes with a 8.5-ps pulse duration. Analytical expressions were deduced to model the generated cylindrically-symmetric polarization profiles, and agreed exceedingly well with experimental observations. The presented fiber laser would constitute a compact light source for producing ultrafast pulses in high-purity structured modes, which may find broad applications in classical and quantum optics.

Si-doped $β$-Ga$_2$O$_3$ films were heteroepitaxially grown on sapphire substrates using HVPE. The influence of sapphire offcut on growth kinetics, surface morphology, crystalline quality, and electrical transport properties was systematically investigated. Growth kinetics studies revealed a strong dependence of deposition rate on HCl flow, growth pressure, and source-to-substrate distance, with growth rates reaching up to 30 $μ$m/hr. Increasing sapphire offcut angle from 0$^\circ$ to 8$^\circ$ promoted a transition from multidirectional growth to highly aligned terrace-dominated surfaces, reducing the surface roughness from 14.69 to 2.74 nm. The improved surface morphology was accompanied by enhanced crystalline quality, with phase-pure (-201)-oriented $β$-Ga$_2$O$_3$ growth and a reduction in the rocking-curve full width at half maximum from 994 to 414 arcsec as the sapphire offcut increased. Electrical characterization of films grown on 6$^\circ$ offcut substrates yielded carrier concentrations ranging from $1.0\times10^{17}$ to $3.4\times10^{18}$ cm$^{-3}$. A maximum room-temperature electron mobility of 100cm$^2$/V$\cdot$s was achieved at a carrier concentration of $1.0\times10^{17}$cm$^{-3}$, representing the highest reported room-temperature mobility for HVPE-grown $β$-Ga$_2$O$_3$ on a foreign substrate. Analysis of the temperature-dependent transport characteristics yielded donor activation energies of 35 and 90 meV together with a low acceptor concentration of $3\times10^{15}$ cm$^{-3}$, consistent with the improved crystalline quality achieved on the offcut sapphire substrates. These results demonstrate that HVPE is capable of producing high-quality $β$-Ga$_2$O$_3$ heteroepitaxial layers with good crystalline quality and carrier transport characteristics, providing a promising pathway for scalable $β$-Ga$_2$O$_3$ epitaxy on low-cost foreign substrates.

In compression-based quantum relaxations like QRAO, classical variables are encoded into qubits and decoded after optimization. We formalize that the choice of the quantum Hamiltonian is fundamentally determined by this decoder. By representing the decoder as a POVM, we define a unique decoder-consistent Hamiltonian via the pullback of the post-decoding expected objective value. Using this framework, we reveal that standard QRAO Hamiltonians are inconsistent for certain mixed-degree quadratic functions, and we provide new approximation guarantees for the MaxCut problem based directly on POVM decoder design.