We present a convergent and scalable multigrid solver for high-frequency Helmholtz equations. Standard multigrid methods do not converge for high-frequency Helmholtz problems, and a common cure is adding a complex shift and using the shifted operator as a preconditioner. Nevertheless, the complex shift prevents scalability. In this work we present a new method that achieves scalable convergence of a 3-level cycle without a complex shift. Our key idea is real-shifting the coarsest grid Galerkin operator, to correct the numerical dispersion between the grids. We show that this real-shifted coarse grid correction leads to a scalable 3-level method, for problems with 12 grid points per wavelength on the fine grid, and a convergent cycle with very few iterations for 11 grid points per wavelength, using standard point-smoothers. For problems with 10 grid points per wavelength, our method combined with a modest complex shift outperforms the standard complex shifted Laplacian method by an order of magnitude. We demonstrate wavenumber independent convergence for heterogeneous geophysical media in 2D and 3D.

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically plausible parameter distributions first be learned from observations. Bayesian inference offers a principled approach but can become ill-posed when observations weakly constrain parameters--a condition difficult to know prior to inference. Addressing this gap, we show that parameter sensitivity results from forward uncertainty quantification can guide a non-iterative strategy for identifying observations informative to Bayesian calibration. We explore both forward and inverse uncertainty quantification for parameterizations of atmospheric turbulence in the Weather Research and Forecasting (WRF) model. To overcome the computational bottleneck of $\mathcal{O}(10^5)$ model evaluations required for both analyses, we leverage Gaussian process emulators trained on several hundred WRF simulations. Using these emulators, we conduct a global sensitivity analysis across observation space, investigating how parameter contributions to output variance depend on quantity of interest, atmospheric stability, time-averaging length, and spatial location. We then introduce nondimensional diagnostic measures that systematically identify regions where a parameter's contribution to output variance exceeds observational noise and its independent effect exceeds interaction effects. We demonstrate that observations from these regions serve as a strong proxy for accurate Bayesian calibration and reduced posterior uncertainty. Through emulator-aided Bayesian inversion with synthetic observations, we show how parameter uncertainty can be systematically reduced by leveraging sensitivity information.

A single organic spin platform hosts both dimerized $S=\tfrac{1}{2}$ and effective Haldane $S=1$ sectors, linked by bond-texture inversion. At the junction, the fractional mode is controlled by termination parity: quenched by local fusion at one termination and released as an uncompensated spin-$\tfrac{1}{2}$-like degree of freedom at the parity-shifted one. Two such internal boundary modes of a finite embedded Haldane domain hybridize with an exponentially decaying splitting, establishing termination parity as a design principle for engineering and coupling fractional boundary modes.

POLAR-2, the successor of the POLAR experiment aboard China's Tiangong-2 space lab, is set to be deployed on the China Space Station. The POLAR-2 mission aims to conducting high-precision polarization measurements of high-energy transients with a primary focus on Gamma-Ray Bursts (GRBs), following POLAR's pioneering accurate polarization measurements of GRB prompt emission. One of the key advancements in POLAR-2 is the inclusion of a dedicated Broad-band Spectrometer Detector (BSD) instrument, designed to provide precise measurements of GRB location and spectral parameters, which are critical inputs for accurate polarization analysis of POLAR-2's dedicated High-energy Polarimetry Detector (HPD), which is made of plastic scintillator bars array. BSD employs a coded-aperture mask imaging technique and pixelated GAGG scintillation crystals, offering a wide half-coded field of view of ~132° x 125° and an operational energy range of 10-1000 keV. Simulation results indicate that the instrument can achieve a localization accuracy of approximately 1.5° for faint GRBs similar to GRB 170817A, satisfying the core requirements of GRB polarimetry with HPD. BSD also has moderate capability for GRB polarimetry, particularly at several hundred keV energy. This paper outlines the preliminary design of BSD and presents an overall evaluation of its expected scientific performance, based on extensive Monte Carlo simulations and preliminary ground-based calibration tests.

BusyBox is one of the most widely reused userland components in Linux-based Internet-of-Things (IoT) firmware, yet its security assessment remains difficult because firmware images are frequently stripped, vendor patch practices are inconsistent, and the same source component is compiled for heterogeneous architectures. We propose EvoPatch-IoT, an evolution-aware cross-architecture retrieval framework for stripped BusyBox firmware binaries. EvoPatch-IoT combines anonymous instruction/context features, graph-level statistics, per-binary geometric priors, and historical function prototypes to localize homologous and potentially vulnerable functions without relying on symbols, source paths, or version strings at test time. We further construct a large-scale BusyBox benchmark from 57 historical versions, 270 unstripped binaries, 285 stripped binaries, and 130 source releases, yielding 1,550,752 function-symbol rows, 1,290,369 analysis-function rows, and 155,845 high-confidence stripped-to-unstripped matches. On 57 fully covered versions and 1,020 directed architecture pairs, EvoPatch-IoT achieves a weighted Hit@1 of 34.56\% and Hit@10 of 56.24\%, outperforming the strongest baseline by 16.04\% and 26.85\%, respectively, and reducing the expected manual inspection space by 98.98\%. The method is best on 56 of 57 versions and maintains consistent advantages on difficult architecture pairs. In addition, a version-change transfer study reaches a mean ROC-AUC of 0.9887, and a CVE-2021-42386 patch-state proxy obtains 82.44\% mean accuracy and 88.47\% mean F1 across held-out architectures. These results show that evolution-aware binary retrieval is a practical foundation for scalable IoT firmware vulnerability auditing.

A search for quantum black holes in electron+jet or muon+jet final states with high invariant mass is performed. The analysis uses data from $\sqrt{s}=13.6~\textrm{TeV}$ $pp$ collisions recorded by the ATLAS detector between 2022 and 2024 during Run~3 of the Large Hadron Collider, corresponding to an integrated luminosity of $164~\mathrm{fb}^{-1}$. This search is strongly motivated by a dramatic increase of the production cross-section by up to an order of magnitude for the highest masses considered, thanks to the small increase of $0.6~\textrm{TeV}$ in centre-of-mass energy between Run~2 and Run~3. No significant excess above the Standard Model background is observed, and 95\% CL upper limits are set on the production cross-section times branching ratio in several benchmark models, reaching a mass scale of $9.4~\textrm{TeV}$. These represent the strongest exclusion limits to date on quantum black hole production.

Modern distributed file systems rely on uncoordinated, per node page caches that replicate hot data locally across the cluster. While ensuring fast local access, this architecture underutilizes aggregate cluster DRAM capacity through massive data redundancy and incurs prohibitive coherence overhead via heavyweight, lock-based protocols. In this paper, we focus on the design of a distributed page cache that treats the entire cluster's main memory as a single cache budget while preserving standard file-system interfaces and semantics. We present Distributed Page Cache (DPC), an OS-level, distributed page cache built on top of Compute Express Link (CXL) 3.0 memory semantics. DPC enforces a single-copy invariant at page granularity: each file page has exactly one owner node holding the sole resident DRAM copy, and other nodes access it via CXL-based remote mappings rather than creating replicas of the page. DPC is implemented end-to-end on a CXL-based emulation framework that models multi-host CXL 3.0 memory fabrics, enabling detailed evaluation in the absence of widespread hardware. Across real-world and representative data-sharing workloads, DPC delivers speedups of up to 12.4X, with a geometric-mean speedup of 5.6X.

The multivariate generalised Gaussian distribution (MGGD) is commonly used to model high-dimensional vectors with non-Gaussian radial behaviour, ranging from sharp-peaked to heavy-tailed profiles. However, because many classical multivariate tests are based on covariance inversion or high-dimensional density estimation, formal goodness-of-fit assessment for MGGD models remains challenging in modern regimes where the dimension is comparable to or exceeds the sample size. We introduce an affine-invariant, fully non-parametric goodness-of-fit procedure based on the nearest neighbour (NN) graph topology and the adapted zero principle. Following robust standardisation, we construct an independent reference sample from the adapted standardised MGGD and measure, on the combined NN graph, the cross-edge count to assess how well the observed and reference point clouds exhibit the mixture behaviour anticipated by the model. Calibration performed using a refitted parametric bootstrap accounts for nuisance-parameter uncertainty, thus ensuring reliable size under a composite specification. In this paper, we establish asymptotic validity under high-dimensional scaling and demonstrate consistency with respect to fixed elliptical departures, providing a geometric interpretation based on radial concentration and shell separation. Our simulation studies across a broad spectrum of dimensions and tail shapes reveal accurate Type I error control and robust power relative to heavy- and light-tailed alternatives, thus improving upon energy-distance benchmarks and normality-oriented graphical tests in contexts where MGGD modelling is most applicable.

In 2025 one million Anti-Social Behaviour (ASB) cases were recorded in England & Wales, impacting community cohesion. Statutory guidance presents punitive interventions that lack technological input and does not often root ethical frameworks within government system design. This work takes a novel approach in framing ASB intervention as a human-computer interaction problem by embedding an ethical framework into two digital designs, aiming to increase public responsibility and prevent ASB. The first design is extracted from UK public opinion research, the ethical themes include punitive proportionality, personalisation, and responsibility. The second are digital interventions that present a set of QR-based public reporting interfaces and a web-based ASB awareness course that precedes punitive escalation. Our methodology involves structured interviews and online surveys. Results positively evaluated the framework and QR interfaces. Such outcomes could inform the expansion of technological intervention utilisation that does not replace existing punitive approaches, but balances them.

In molecular liquids such as water, time-delayed influences between microscopic or mesoscopic variables are typically probed using time-correlation functions, which are symmetric under detailed balance and therefore blind to dynamical asymmetries. Here, we characterize waters dynamics using a causal inference metric that captures asymmetric couplings between collective variables. Analyzing equilibrium molecular dynamics simulations at ambient conditions and in the high-density liquid (HDL) regime of supercooled water, we uncover pronounced asymmetries in the couplings between orientational and translational degrees of freedom across multiple time and length scales. At room temperature, rotational modes remain largely decoupled from translations. In contrast, in the supercooled HDL regime, translational motions emerge as the primary drivers of the dynamics, suggesting facilitation-like relaxation mechanisms characteristic of glassy systems. These results reveal a qualitative reorganization of dynamical couplings across thermodynamic conditions, implying that molecular liquids at thermal equilibrium can exhibit an emergent directionality in their fluctuation couplings. As a consequence, our analysis reveals that external perturbations acting on specific degrees of freedom can induce a stronger arrow of time in the causal relations between translational and orientational modes.

We construct a one-to-one correspondence between the Verma basis vectors of a finite dimensional irreducible representation $L(λ)$ of the symplectic Lie algebra $\mathfrak{sp}_4$ and the Kashiwara-Nakashima tableaux of $\mathfrak{sp}_4$ with shape $λ$ naturally. We also give a proof of the linear independence of the Verma vector system directly.

We study the Falconer distance set problem in Euclidean space and obtain improved dimensional estimates under natural Fourier analytic assumptions cast in terms of the Fourier dimension and spectrum. Interestingly, under reasonably mild assumptions, we are able to beat the $d/2$ dimension threshold in dimensions $d \geq 5$. For example, we show that (in any ambient spatial dimension $d$) a Borel set with Fourier dimension at least $2$ has a distance set of full Hausdorff dimension. We also show that (in any ambient spatial dimension $d$) a Borel set with Fourier spectrum at least $d/4+1$ at $θ=1/2$ has a distance set of full Hausdorff dimension. In particular, this can hold for sets with Fourier dimension zero (provided $d \geq 4$). We also consider pinned variants of these problems and construct examples that demonstrate the sharpness (or near sharpness) of our results.

We prove that, for every fixed $θ_0>0$, selecting a subset of prescribed cardinality that maximizes the Solow--Polasky diversity indicator is NP-hard for finite point sets in $\mathbb{R}^2$ with the Euclidean metric, and therefore also for finite point sets in $\mathbb{R}^d$ for every fixed dimension $d \ge 2$. This strictly strengthens our earlier NP-hardness result for general metric spaces by showing that hardness persists under the severe geometric restriction to the Euclidean plane. At the same time, the Euclidean proof technique is different from the conceptually easier earlier argument for arbitrary metric spaces, and that general metric-space construction does not directly translate to the Euclidean setting. In the earlier proof one can use an exact construction tailored to arbitrary metrics, essentially exploiting a two-distance structure. In contrast, such an exact realization is unavailable in fixed-dimensional Euclidean space, so the present reduction requires a genuinely geometric argument. Our Euclidean proof is based on two distance thresholds, which allow us to separate yes-instances from no-instances by robust inequalities rather than by the exact construction used in the general metric setting. The main technical ingredient is a bounded-box comparison lemma for the nonlinear objective $\mathbf{1}^{\top}Z^{-1}\mathbf{1}$, where $Z_{ij}=e^{-θ_0 d(x_i,x_j)}$. This lemma controls the effect of perturbations in the pairwise distances well enough to transfer the gap created by the reduction. The reduction is from \emph{Geometric Unit-Disk Independent Set}. We present the main argument in geometric form for finite subsets of $\mathbb{R}^2$, with an appendix supplying the bit-complexity details needed for polynomial-time reducibility.

Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated by a straight line to the case where the switching manifold is a nonregular curve, showing that the loss of regularity significantly increases the algebraic complexity of the closing conditions defining crossing limit cycles. As a consequence, we derive explicit upper bounds for the number of crossing limit cycles in planar systems formed by a linear Hamiltonian saddle and quadratic isochronous centers, and construct explicit examples exhibiting four crossing limit cycles in each case, thereby providing sharp constructive lower bounds. While the upper bounds follow from classical algebraic arguments, the realization of multiple crossing limit cycles requires solving nonlinear systems of high degree and remains highly nontrivial. These results highlight how nonsmooth switching manifolds enhance dynamical complexity and promote multistability in discontinuous piecewise systems

We propose a fault-tolerant quantum computer architecture for trapped-ion devices, which we call the walking cat architecture. Our blueprint includes a compiler, a detailed description of all the quantum error-correction protocols, a micro-architecture, a sufficiently fast decoder, and thorough simulations. The backbone of the architecture is a cat factory, producing cat states distributed throughout the machine, which are consumed to perform logical operations. The walking cat architecture is based entirely on a modern quantum error-correction approach called low-density parity-check (LDPC) codes. We identify promising instances of the walking cat architecture, such as (1) a simple architecture based on a single LDPC code, (2) a fast architecture based on fast logical gates relying on a [[70, 6, 9]] code, equipped with Clifford-frame tracking for any 6-qubit Clifford gate, and (3) a dense architecture based on a [[102, 22, 9]]] code encoding 22 logical qubits per memory block. Our dense architecture provides a design with 110 logical qubits executing about one million T gates per day using only 2,514 physical qubits. We estimate that the quantum Hamiltonian simulation of a Heisenberg model on 100 sites can be executed within one month with 10,000 physical qubits, including all shots required to achieve chemical accuracy, suggesting that such a device could enter the regime of classically intractable physics simulations. Our design relies on hardware components that have been experimentally demonstrated on small devices. We emphasize simplicity over hypothetical performance to facilitate the practical realization of this machine. Based on this approach, we believe that a fault-tolerant quantum computer with hundreds of logical qubits capable of running millions of logical gates can be built in the near term, providing a platform to explore a broad range of applications.

We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voronoi cell whose geometry depends on the normal space at the point and the inner normal fan of the polyhedral ball. For codimension-one varieties, we decompose $X$ into sets of points whose Voronoi cones have the same dimension, which is the expected dimension of their Voronoi cell. We prove that this decomposition is a stratification of $X$ and that each strata is a semialgebraic set. We conclude by giving an algebraic description of the medial axis, which is the locus of points whose minimal distance to $X$ is achieved at more than one point on $X$.

In the rewriting logic framework, equational-based specifications are used to define deterministic functional behavior, abstract data types, and canonical representations of data. These specifications include a (possibly order-sorted) signature and equations interpreted modulo structural axioms, such as associativity, commutativity, and identity. While equational rewriting provides a powerful basis for execution and symbolic reasoning, it does not by itself offer native support for inductive or deductive reasoning. This paper presents maude2athena, a framework that systematically translates Maude's equational theories into Athena, a theorem proving language designed to support natural deduction proofs over many-sorted first-order logic specifications, including inductive reasoning, equational chaining, case-based reasoning, and proofs by contradiction. The translation supports induction-based reasoning modulo structural axioms with parametric induction rules; it faithfully encodes membership equational logic in a many-sorted setting without exponential blowup under reasonable conditions. This approach preserves the semantics of the original specification, while ensuring that the translation remains compact and amenable to deductive reasoning. This work helps bridge the gap between model checking and theorem proving, enabling formal verification efforts that can benefit from both of these approaches.

Reliable harmonization of heterogeneous magnetic resonance~(MR) image datasets, especially those acquired in pragmatic clinical trials, is critical to advance multi-center neuroimaging studies and translational machine learning in healthcare. We present an enhanced and rigorously validated version of the HACA3 harmonization algorithm, which we refer to as HACA3$^+$, incorporating key methodological enhancements: (1)~an improved artifact encoder to better isolate and mitigate image artifacts, (2)~background and foreground-sensitive attention mechanisms to increase harmonization specificity, and (3)~extensive training using data spanning 100+ scanners from 64 independent sites, providing a broader diversity of scanners than other harmonization methods. Our study focuses on four commonly acquired MR image contrasts (T1-weighted, T2-weighted, proton density, \& fluid-attenuated inversion recovery), reflecting realistic clinical protocols. We perform inter-site harmonization experiments using traveling subjects to assess the generalization and robustness of the harmonization model. We compare the results of the publicly available version of HACA3 and our implementation, HACA3$^+$. Downstream relevance is further established through whole brain segmentation and image imputation. Finally, we justify each enhancement through an ablation experiment. Pre-trained weights and code for HACA3$^+$ are made publicly available at https://github.com/shays15/haca3-plus.

Acetone (CH3COCH3) is a ubiquitous interstellar molecule, and serves as an important tracer of hot core chemistry. We conducted a line survey of acetone and its precursor acetaldehyde (CH3CHO) towards 60 hot cores by using the ALMA 3 mm lines observations. We calculated the rotational temperatures and column densities of acetone using the XCLASS software. Acetone was detected in 15 hot cores with rotational temperatures ranging from 89 to 176 K. Its column densities range from (0.9-24)x 10^16 cm^-2. The spatial distributions of acetone exhibit similarities with those of acetaldehyde. The emissions of acetone are concentrated toward the hot core regions and generally exhibit a compact spatial distribution, whereas the emission of acetaldehyde shows a more extended spatial profile. Combined with previous studies, we found a moderately positive correlation between the column densities and rotational temperatures of acetone for the high-mass hot cores (r = 0.59). We also found a strong positive correlation between the column densities of acetone and acetaldehyde (r = 0.82), indicating a chemical relationship between them. By comparing these observational results with the three-phase model results, we found that the models overpredict the ratio of acetone to methanol relative to the observational data. This discrepancy suggests that current chemical networks may inadequately account for acetone destruction pathways or potential missing physical conditions in the model. Therefore, our large sample observations can provide constraints on chemical models and reinforce the role of acetone as a tracer of complex organic chemistry in warm, dense regions.

This paper presents Map Reduce Graph (MRG), a novel unsupervised method for modeling and securing HTTP REST APIs. MRG learns API structure from real-world traffic without prior knowledge or labels, automatically generating OpenAPI-compliant documentation by reconstructing routes, methods, and parameter formats. MRG enables real-time updates, explainable visualization, and anomaly detection, helping identify undocumented or evolving behaviors. It detects malformed requests, structural deviations, and injection attacks using graph-based validation and a deep autoencoder for payload analysis. Compared to state-of-the-art methods like HRAL and FT-ANN, MRG achieves up to 11.4% higher recall, over 20 times faster inference, and perfect precision (100%) on multiple API-layer attacks. Designed for dynamic microservice environments, MRG operates in three phases - training, updating, and detection - and integrates smoothly with observability and security tools. This work contributes a fully automated, efficient pipeline for real-time API visibility, schema inference, and anomaly detection without manual tuning or labeled data.

Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with dynamically formulated wavefunction, and their coupled optimization leads to accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems and chemical processes with up to 144 qubits. These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated system.

We measure magneto-transport and critical currents in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ Hall bar devices. Above critical current in an applied magnetic field, we observe longitudinal differential voltage along one edge comparable in magnitude but opposite in sign to the other edge. This phenomenon is unaffected by reversal of the applied field, and seems unique to devices with invasive voltage contacts. We attribute the source of this behavior to particle-hole symmetry breaking in moving vortices and the formation of opposite Bernoulli potentials due to opposing vortex velocities at the edges where the invasive contacts create hotspots for rapid vortex nucleation and flux flow. These results are fundamental to the composition and flow of dissipative currents in layered superconductors.

A hypergraph is called uniform when every hyperedge contains the same number of vertices, otherwise, it is called non-uniform. In the real world, many systems give rise to non-uniform hypergraphs, such as email networks and co-authorship networks. A uniform hypergraph has a natural one-to-one correspondence with its adjacency tensor. In 2019, Benson proposed the eigenvector centrality of uniform hypergraphs via its adjacency tensor. In this paper, we define an adjacency tensor for hypergraphs and propose the eigenvector centrality for hypergraphs. When the hypergraph is uniform, our proposed eigenvector centrality reduces to Benson's. When each edge of the uniform hypergraph contains exactly two vertices, our proposed centrality reduces to the eigenvector centrality of graphs. We conducted experiments on several real-world hypergraph datasets. The results show that, compared to traditional centrality measures, the proposed centrality measure provides a unique perspective for identifying important vertices and can also effectively identify them.

The statistical analysis of cosmological data often assumes a Gaussian sampling distribution and relies on covariance matrices estimated from simulations. In this setting, the likelihood function of the data is not Gaussian but is instead a multivariate Student-t distribution, arising from marginalisation over an inverse-Wishart distribution for the true covariance matrix. This framework, introduced by Sellentin & Heavens(2016) and extended by Percival et al.(2022), provides a principled drop-in replacement to the Gaussian likelihood with Hartlap correction (Hartlap et al. 2007). The latter removes bias in the precision matrix; it is still widely used, despite failing to reproduce the heavy tails of the true distribution (thus yielding inaccurate probabilities, especially in the case of tensions between datasets). In practice, cosmological analyses frequently involve additional Gaussian error contributions, for example from instrumental noise, foregrounds, super-sample covariance, or emulator uncertainties. The resulting likelihood function is a convolution of the Sellentin-Heavens or Percival likelihoods with an extra Gaussian contribution, and does not have a simple expression. In this note, we derive an accurate approximation for the combined likelihood function, another multivariate Student-t distribution which inherits the heavy tails. The parameters of the Student-t distribution are determined by matching the covariance and multivariate kurtosis to those of the true distribution. We also include a slightly more expensive but fast sampling algorithm, based on the mixture representation of the Student-t distribution, which avoids the approximation altogether, but is not the drop-in replacement for the normal Gaussian or Hartlap likelihood function that the Student-t approximation in this paper provides. (Abridged)

When the objective has Lipschitz continuous $p$th-order derivatives, it is known that convex-concave minimax problems can be solved with $\mathcal{O}(ε^{-2/(p+1)})$ $p$th-order oracle calls. This complexity upper bound was speculated to be optimal as it is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/(3p+1)})$ by applying the Monteiro-Svaiter acceleration. We also establish a lower complexity bound of $Ω(ε^{-2/(3p-1)})$, suggesting a gap still exists for $p \ge 2$.

We present a physics-driven framework for accurate evaluation of discrete spectral bands using a low-cost multispectral setup built from off-the-shelf RGB cameras and narrow multi-band optical filters. The approach starts by explicitly formulating a linear measurement model. The camera responses are expressed as linear mixtures of unknown spectral components, with mixing coefficients determined by the overlap between the camera spectral sensitivities and the filter transmittances. For a multi-camera configuration, the per-camera models are stacked into a single global system whose structure is fully determined by the allocation of target wavelengths across the camera--filter units. We pose wavelength allocation as a deterministic design problem and select the configuration that minimizes the spectral condition number of the resulting system matrix. Guided by a frame-theoretic interpretation, this criterion promotes numerical stability, maximizes worst-case output signal-to-noise ratio, and improves the robustness of spectral reconstruction. The design space is finite, enabling the evaluation of all feasible configurations under practical constraints. We demonstrate the method on a representative example with 12 target wavelengths and four triband filters, and identify the wavelength allocation that yields the most stable and noise-robust recovery. The proposed framework includes redundant configurations, in which individual wavelengths are measured by multiple cameras, thereby providing additional degrees of freedom that further improve noise robustness.

This article establishes a first-principles statistical field theory of fully developed isotropic turbulence. Applying an exact Helmholtz decomposition to the local angular momentum field ($\Lvec = \rvec \times \uvec$) reveals a segregation into two orthogonally distinct topological phases: a longitudinal condensate of macroscopic coherent structures ($\PhiL$) and a volume-filling, transverse thermal bath ($\AL$). Constructing a Hamiltonian and evaluating the partition function of these decoupled fields demonstrates that their ergodic exploration of phase space is topologically quantized, mandating a strict $1:2$ equipartition of degrees of freedom. Inverting this topological projection back to the velocity domain isolates the radial velocity field ($\uvec_r$) (which strictly resides in the null space of the $\Lvec$ framework) revealing a recursive partitioning scheme across the cascade into a precise $1/3 : 2/9 : 4/9$ fractional hierarchy. This geometric constraint forces the turbulent steady state into a rigorous canonical equilibrium governed by the equalization of phase chemical potentials ($μ_Φ= μ_A$). The radial component acts as a non-equilibrium mechanical piston, continuously injecting energy into the tangential modes to sustain the canonical equilibrium -- a mechanism that mathematically formalizes the classical phenomenology of vortex stretching. Spectral evaluations from direct numerical simulation strongly corroborate this thermodynamic framework, establishing the universality of the partition ratios $1:2$ and $1/3 : 2/9 : 4/9$ as a fundamental signature of three-dimensional isotropic turbulence.

We propose a cavity-based scheme that uses photonic chirality to control braiding and read out non-Abelian anyons in a fractional quantum Hall platform. Counter-propagating cavity modes interfere with a classical reference tone to create a rotating pinning landscape whose direction is set by photon circulation, so that opposite photonic branches drive opposite anyon loops. This realizes a branch-conditioned braid operation and maps the resulting braid response onto cavity intermode coherence. We derive the rotating pinning term and the readout relation at the effective-theory level, identify an operating window set by subgap driving, adiabatic transport, localization, and cavity coherence, and provide phenomenological diagnostics of transport locking. In the minimal four-anyon Ising realization, the leading signal reduces to a calibrated phase; more generally, the same readout structure becomes state dependent when the relative braid operator is non-scalar. The scheme provides a cavity route to braid-sensitive readout of non-Abelian anyons without relying on fragile electronic interference fringes.

Rayleigh-Taylor Instability (RTI) typically arises when a dense fluid is superimposed on a lighter fluid, where the desta- bilizing gravitational force acting on miscible fluids drives chaotic mixing. We theoretically present an acoustofluidic method utilizing standing bulk acoustic waves (BAW) to counteract RTI and suppress the mixing of fluids. To success- fully achieve this suppression, we demonstrate that two concurrent conditions are to be satisfied: the acoustic energy density (Eac) of the standing waves must exceed its critical threshold (Ecr), and the orientation of the acoustic waves must be perpendicular to the fluid-fluid interface. This acoustofluidic mechanism reduces the mixing index (MI) by up to an order of magnitude compared to the mixing induced solely by gravity. By analyzing the interplay between acoustic and gravitational forces, this study provides a comprehensive understanding of acoustically modulated mixing dynamics in minichannels.

In this paper, we examine the use of self-stabilizing algorithms, operating in a hierarchical manner, to determine intellectual property risks at a macro level. We are both interested in finding a solution that will support all defined intellectual property dimensions as well as suboptimal solutions in order to minimize risk.