Magnetized liner inertial fusion (MagLIF) operates in a regime where anisotropic transport phenomena fundamentally influence implosion dynamics. In strongly magnetized plasmas, the viscous stress tensor becomes highly anisotropic, yet no prior work has incorporated or examined magnetized viscosity effects in MagLIF configurations. We present the first implementation of the full Braginskii magnetized viscosity tensor for arbitrary magnetic field orientations in the Pacific Fusion branch of FLASH. The implementation is verified through analytical comparisons, direct verification against Braginskii's original formulation, Method of Manufactured Solutions, and against analytical shock solutions. Application to MagLIF-relevant configurations reveals that magnetized viscosity damps vortical structures, converts kinetic energy in those vortical structures into thermal energy, and mitigates the Rayleigh-Taylor instabilities. Simulations with seeded perturbations demonstrate yield preservation when magnetized viscosity is included. These results establish magnetized viscosity as a non-negligible physical mechanism in MagLIF plasmas and provide a validated capability for predictive modeling of magnetized high-energy-density plasmas.

This paper focuses on 3D localization of transmitting satellites in low Earth orbits (LEO). 3D localization of transmitters in low orbits is an important emerging problem for many applications such as spectrum management, orbit determination, and backup for GPS failures in orbit. We present StarLoc -- a system to geolocate transmitters in space using a combination of orbital modeling and a new interferometric 3D angle-of-arrival estimation technique. StarLoc's design relies on a unique insight -- the motion of satellites is governed by orbital dynamics and is therefore along a 2D manifold in a 3D space. This reduces the degrees of freedom in satellite motion and allows us to 3D-locate and track a satellite with just three antennas in a 2D plane. We evaluate the system using signal transmissions from 81 Starlink satellites. Our results show that StarLoc can estimate the 3D-angle of a satellite within 0.7 degrees and the orbital range within 5 km. Our dataset and implementation are available at: https://connectedsystemslab.github.io/starloc.

We consider the long-range random conductance model on $\mathbb{Z}^d$ at the critical exponent: the jump rate between sites $x$ and $y$ decays as $\mathbf{a}(x,y) |x-y|^{-(d+2)}$, where $\mathbf{a}(x,y)$ are i.i.d. uniformly elliptic conductances. Below the critical exponent $(d+2)$ the walk converges to a stable process; above it, to Brownian motion with diffusive $\sqrt{t}$ scaling. At criticality the second moment of the jump kernel diverges logarithmically. We establish quantitative homogenization of the associated elliptic equation to the Laplacian at the rate $1/\sqrt{|\ln\varepsilon|}$. As a consequence, we deduce quenched convergence of the random walk to Brownian motion under the anomalous $\sqrt{t \log t}$ scaling. Unlike in standard homogenization, the effective diffusivity is determined by the mean conductance alone, with no corrector contribution at leading order.

Internal DLA is a discrete random growth model describing growing clusters of particles. Its limiting shape and fluctuations are well understood when the underlying graph is the $d$-dimensional lattice or the cylinder $\mathbb{Z}_N \times \mathbb{Z}$. In the latter geometry, the average fluctuations of IDLA have been shown to converge to the GFF. In this note we generalise this result by showing that, for any vertex-transitive base graph $V_N$ satisfying an eigenvalue convergence condition, the average fluctuations of IDLA on the cylinder $V_N \times \mathbb{Z}$ are given by a GFF. On the way, we present an improved bound on the clusters' maximal fluctuations, which is of independent interest and which implies a shape theorem for IDLA on $V_N \times \mathbb{Z}$ for any vertex-transitive base graph $V_N$.

We continue the study on Kurzweil--Stieltjes integration on compact lines initiated in [doi:10.1007/s11117-025-01161-9]. Given a real valued function $G$ on a compact line, the presented integral is called the Kurzweil--Stieltjes integral with respect to $G$, or simply the $G$-integral. %Given a compact line $K$ and a right-continuous function $G:K\to\mathbb{R}$ of bounded variation, we consider the Radon measure $μ_G$ naturally induced by $G$. Our main results concern the relationship between $G$-integrability and measurability. We prove that, whenever $G$ is nondecreasing, every $G$-integrable function is $μ_G$-measurable, where $μ_G$ is the natural Radon measure induced by $G$. We also show that, for an arbitrary $G$ of bounded variation, every bounded $G$-integrable function is $μ_G$-measurable. %, where $|μ_G|$ denotes the total variation measure of $μ_G$. As an application, we provide a full characterization of Lebesgue integrablility with respect to Radon measures in terms of the $G$-integral, and demonstrate that the $G$-integral represents an extension of the Lebesgue integral with respect to $μ_G$ for suitable $G$. In addition, we establish a version of Hake's theorem for the $G$-integral in this setting.

This paper addresses the problem of identifying palindromic factors in texts that include wildcards -- special characters that match all others. These symbols challenge many classical algorithms, as numerous combinatorial properties are not satisfied in their presence. We apply existing wildcard-LCE techniques to obtain a continuous time-memory tradeoff, and present the first non-trivial linear-space algorithm for computing all maximal palindromes with wildcards, improving the best known time-memory product in certain parameter ranges. Our main results are algorithms to find and approximate all maximal palindromes in a given text. We also generalize both methods to the $k$-mismatches setting, with or without wildcards.

Various processes can induce long-lived overdense rings and arcs in protoplanetary and AGN accretion discs, such as the accumulation of gas at the outer edge of the dead zone, or the infall of material. Using the local approximation of dynamical friction, we investigate the orbital evolution of a low-mass highly-eccentric point-mass accretor (perturber) embedded in an isothermal disc hosting a density ring. We specifically consider the regime in which the eccentricity exceeds four times the disc aspect ratio. For prograde perturbers, orbits that cross the ring progressively circularize while their semi-major axes converge toward the ring radius. As a result, perturbers accumulate, forming a population ring superimposed on the gaseous ring. The ring therefore acts as a migration trap for these eccentric orbits. We also find that prograde orbits tangent to the ring, either at apocentre or pericentre, remain tangential throughout their evolution; perturbers confined to these trajectories experience the highest accretion rates. In contrast, retrograde perturbers always migrate inward. Once the semi-major axis becomes smaller than the ring radius, the eccentricity grows, but not enough for the orbit to intersect the ring again. We also discuss how feedback effects, such as jet launching and thermal torques, could modify the effective forces acting on the perturbers.

We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of additively graceful signed stars, while, for several sub-classes of additively graceful signed double stars, we establish existence, uniqueness and non-existence results.

Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic waves in a dielectric medium are described by Maxwell equations. The qubit lattice algorithm consists of a series of alternating unitary streaming and entanglement operators acting on qubit amplitudes constructed from the electric and magnetic fields. It is not a direct discretization of Maxwell equations, but recovers the desired equations to second order in lattice grid spacing. The resulting algorithm is implemented on a present-day supercomputer and is the basis of studying scattering of electromagnetic waves by an elliptical dielectric. As opposed to the steady state description of Mie scattering in frequency domain, the temporal evolution provides insights into transient scattering. The QLA simulations, reveal that a spatially localized wave packet propagating past an elliptic dielectric, embedded in vacuum, leads to several reflections generated by wave fields trapped within the dielectric. The physics insight brought forth by these simulations is not apparent from frequency domain studies of scattering. A complimentary simulation on transient scattering of a wave packet by an elliptical vacuum bubble inserted in a uniform dielectric demonstrates a stark contrast with respect to scattering off an elliptical dielectric in vacuum. Essentially, there is only a single internal reflection in which the field amplitudes are significantly smaller than those for side and forward scattering. A simple model based on the Kirchhoff tangent plane approximation helps explain the differences between these two scattering examples.

Complex criminal investigations are often hindered by large volumes of unstructured evidence and by the semantic gap between natural language investigative intent and technical search logic. To address this challenge, we present a design and feasibility study of a cloud-native microservice architecture tailored to private-cloud deployments, contributing to research in secure cloud computing and leveraging modern cloud paradigms under high security and scalability requirements. The proposed system integrates Large Language Models into a "Human-in-Control" workflow that translates natural-language queries into syntactically valid OpenSearch Domain-Specific Language expressions. We describe the implementation of a hybrid retrieval strategy within OpenSearch that combines BM25-based lexical search with nested semantic vector embeddings. The paper focuses on system design and preliminary functional validation, establishing an architectural baseline for future empirical evaluation. Technical feasibility is demonstrated through a functional prototype, and a rigorous evaluation methodology is outlined using the Enron Email Dataset as a structural proxy for restricted investigative corpora.

Adaptive Systems-on-Chips (SoCs) are increasingly being used in mixed criticality systems (MCSs), such as in autonomous driving, aviation and medical systems. In this context, AMD has proposed the Versal SoC, which has a heterogeneous architecture including, among other components, an Artificial Intelligence Engine (AIE), which is a 2D array of processors and memory tiles designed for AI and signal processing workloads. While this AIE offers significant potential for accelerating real-time data processing tasks, this has not yet been explored in the context of MCSs since individual tasks with different criticality levels cannot be dynamically assigned to tiles due to the static mapping of dataflow graphs and tasks. In this work, we propose a dynamic task dispatching infrastructure that enables task switching on the AIE at runtime. Based on this infrastructure, we present an MCS design that dynamically assigns tasks of different criticality to a pool of AIE tiles, depending on the criticality mode of the system. Our approach overcomes the limitations of static dataflow graph mappings and, for the first time, exploits the parallel processing capabilities of the AIE for MCSs. We also present a comprehensive timing analysis of the overhead introduced by the task dispatcher infrastructure, focusing on control logic, context switching and data copy operations. This shows that these operations have low variance and are negligible compared to the overall execution time, demonstrating that our infrastructure is suitable for MCSs. Finally, we evaluate the proposed infrastructure using an autonomous driving workload with tasks that have variable execution times and different criticality levels. In this case study, we maximized AIE utilization, reducing idle time by 65.5 %, while measuring an execution time overhead of less than 0.002 %, and doubling the throughput of low-criticality tasks.

We introduce a qubit- and gate-efficient higher-order unconstrained binary optimization (HUBO) encoding for graph partitioning problems requiring label-count minimization. This widely applicable class of problems includes minimum graph coloring, minimum $k$-cut, and community detection. To the best of our knowledge, this is the first work to address the optimization versions of these problems in a quantum setting, rather than only their decision counterparts. Our construction encodes each $k$-valued vertex variable using $\lceil \log_2 k \rceil$ bits and employs a novel lexicographic penalty system that implicitly minimizes partition count without requiring dedicated indicator variables. We derive provably sufficient conditions on all penalty coefficients, including those arising from Rosenberg quadratization, guaranteeing feasibility and optimality of the lowest-energy solution. Analogous conditions are derived for a one-hot encoding to enable controlled comparison. We also show that our encoding reduces two-qubit gate count per QAOA layer from $Θ(|V||k|^2 + |E||k|)$ for the one-hot encoding to $Θ(|E| \cdot |k| \lceil\log_2 |k|\rceil)$. Benchmarking on a quantum annealer demonstrates that our logarithmic encoding significantly improves solution quality and time-to-solution for minimum graph coloring relative to one-hot encoding, with greater advantage as problem size increases.

We study extremal problems for tuples of integers chosen from sets $A_i \subset [X_i,2X_i]$ for $1\le i\le k$, under large GCD and small LCM conditions. For the GCD problem, we extend the work of Green and Walker to higher dimensions. Specifically, for $k\ge 3$, if $\gcd(a_1,\dots,a_k)\ge D$ for at least a proportion $δ$ of the tuples in $\prod_{i=1}^k A_i$, then $$ \prod_{i=1}^k |A_i| \ll_{k,\varepsilon} δ^{-k/(k-1)-\varepsilon} \frac{\prod_{i=1}^k X_i}{D^k}. $$ The proof is based on a minimal counterexample argument and a new high-dimensional measure concentration lemma. We also establish a large sieve-type inequality to obtain a complementary estimate for the GCD problem. For the LCM problem, we use a quite different method to show that, for all $k\ge 2$, $$ \prod_{i=1}^k |A_i| \ll_{k,\varepsilon} δ^{-k/(k-1)} \frac{L^{k/(k-1)+\varepsilon}} {\bigl(\prod_{i=1}^k X_i\bigr)^{1/(k-1)}}, $$ whenever $\operatorname{lcm}(a_1,\dots,a_k)\le L$ for at least a proportion $δ$ of the $k$-tuples in $\prod_{i=1}^k A_i$. Finally, we show that these bounds are essentially best possible up to $\varepsilon$-losses in the exponent.

Understanding optical responses of topological matter is a central problem for enabling optoelectronic applications based on topological physics, which is of fundamental concern for photocurrents control and spectroscopy. Currently, schemes for sensing ultrafast photocurrents and separating their bulk/surface contributions are lacking. We introduce here double circular dichroism (DCD) harmonic spectroscopy as an all-optical probe of ultrafast dynamics in topological materials. In this scheme, pump and probe pulses are circular with helicities that are independently controlled, yielding the circular dichroism of the circular dichroism -- a time-resolved response evaluating how probe-induced dichroism depends on pump helicity. While DCD vanishes in symmetric systems, it survives in broken time-reversal symmetry materials including Chern insulators. We theoretically demonstrate this concept through simulations in a Haldane nanoflake, where a pump laser manipulates chiral current-carrying states, and intense probe pulses drive harmonic emission. We show that DCD originates from both bulk and edge-localized states, but these have opposite signs, similar magnitudes, and a different amplitude scaling. Hence, DCD could allow efficient separation of bulk/edge contributions to photocurrents. Variation of the electronic structure and laser parameters further reveals anomalies that might be useful for probing topological attributes of photocurrents in select harmonics. Overall, our work introduces DCD as a potentially powerful approach for disentangling bulk/boundary photo-responses in broken-symmetry quantum matter, and could also be implemented in other pump-probe spectroscopies based on photoelectrons and absorption, as well as other chiral systems.

The global topology of spacetime, though invisible to local curvature measurements, leaves signatures on the correlation functions of quantum fields. We study these signatures using an Unruh-DeWitt particle detector operating in four-dimensional Minkowski spacetime with two spatial directions periodically identified, yielding a spatial topology $\mathbb{R}\times T^2$. We compute detector transition rates for three trajectories: uniform inertial motion, uniform proper acceleration directed along one of the compact axes, and uniform proper acceleration along the non-compact axis. Our results show how a local quantum measurement can reveal features of the large-scale spatial topology.

This paper introduces a search algorithm for index structures based on a B+ tree, specifically optimized for execution on a field-programmable gate array (FPGA). Our implementation efficiently traverses and reuses tree nodes by processing a batch of search keys level by level. This approach reduces costly global memory accesses, improves reuse of loaded B+ tree nodes, and enables parallel search key comparisons directly on the FPGA. Using a high-level synthesis (HLS) approach, we developed a highly flexible and configurable search kernel design supporting variable batch sizes, customizable node sizes, and arbitrary tree depths. The final design was implemented on an AMD Alveo U250 Data Center Accelerator Card, and was evaluated against the B+ tree search algorithm from the TLX library running on an AMD EPYC 7542 processor (2.9 GHz). With a batch size of 1000 search keys, a B+ tree containing one million entries, and a tree order of 16, we measured a 4.9x speedup for the single-kernel FPGA design compared to a single-threaded CPU implementation. Running four kernel instances in parallel on the FPGA resulted in a 2.1$\times$ performance improvement over a CPU implementation using 16 threads.

Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced matrix AMP, complex AMP, and AMP for non-separable functions independently, a unified state evolution theory for complex AMP with non-separable denoisers has been lacking. This article fills that gap by establishing state evolution in the setting of complex, non-separable denoising functions. The proposed approach constructs an augmented real-valued system that lifts the problem to a higher-dimensional space, then recovers the complex domain through a many-to-one canonical transformation. Under this construction, the Onsager correction naturally involves Wirtinger derivatives, and the resulting state evolution reduces to scalar complex recursions despite the non-separable structure of the denoisers. The framework extends to the matrix-valued setting, accommodating multiple feature vectors simultaneously. This generalization enables AMP to exploit joint structural constraints, such as simultaneous group and element sparsity, in complex-valued recovery problems. The complex sparse group least absolute shrinkage and selection operator (LASSO) serves as a key instantiation, motivated by preamble detection in Orthogonal Time-Frequency Space (OTFS)-based unsourced random access. Numerical experiments confirm that state evolution accurately predicts performance and show that complex non-separable denoising can produce significant gains over separable and real-valued alternatives.

We construct new examples of special Lagrangian submanifolds $Y\subset \mathbf{C}^{n+1}$, $n\geq 3$ in a neighborhood of the origin, with an isolated singularity, but with cylindrical tangent cone $C\times\mathbf{R}$. Moreover, $Y\setminus\{0\}$ is connected while $(C\setminus\{0\})\times\mathbf{R}$ is not. Such examples exist, for example, when $C$ is a pair of transverse planes.

The internal structure of dark matter halos on sub-galactic scales remains a key open question, particularly in the context of the core-cusp problem. Ultra-faint dwarf galaxies (UFDs), owing to their extreme dark matter dominance, provide a promising laboratory to probe these density profiles through stellar tracers. In this work, we assess the capability of the Chinese Space Station Telescope (CSST) to detect and characterize wide binary stars in the nearby UFD Segue 1, using mock observations. We generate mock binary populations based on our existing $N$-body simulations and incorporate realistic CSST observational conditions, including the expected deep-field limiting magnitude ($g \sim 27.5$ mag) and a photometric completeness of approximately $90\%$. The two-point correlation function (2PCF) of stellar pairs is used as a statistical tool to recover the binary fraction under these assumptions. We find that CSST can robustly detect wide binaries at the $3σ$ level for binary fractions as low as $f_b \gtrsim 0.01$, provided a stellar sample size of $N_{\mathrm{star}} \gtrsim 2300$. However, distinguishing between cusped and cored dark matter profiles is significantly more demanding, requiring $N_{\mathrm{star}} \gtrsim 6000$ and $f_b \gtrsim 0.1$ within $\sim 40\mathrm{kpc}$.

Automated vulnerability detection tools are widely used to identify security vulnerabilities in software dependencies. However, the evaluation of such tools remains challenging due to the heterogeneous structure of vulnerability data sources, inconsistent identifier schemes, and ambiguities in version range specifications. In this paper, we present an empirical evaluation of vulnerability detection across multiple software ecosystems using a curated ground-truth dataset derived from the Open Source Vulnerabilities (OSV) database. The dataset explicitly maps vulnerabilities to concrete package versions and enables a systematic comparison of detection results across different tools and services. Since vulnerability databases such as OSV are continuously updated, the dataset used in this study represents a snapshot of the vulnerability landscape at the time of the evaluation. To support reproducibility and future studies, we provide an open-source tool that automatically reconstructs the dataset from the current OSV database using the methodology described in this paper. Our evaluation highlights systematic differences between vulnerability detection systems and demonstrates the importance of transparent dataset construction for reproducible empirical security research.

Logistic regression is widely used to model the propensity score in the analysis of nonignorable missing data. However, goodness-of-fit testing for this propensity score model has received limited attention in the literature. In this paper, we propose a new goodness-of-fit testing procedure for the logistic propensity score model under nonignorable missing data. The proposed test is based on an unweighted sum-of-squared residuals constructed from the marginal missingness mechanism and accommodates the partial observability of the outcome. We establish the asymptotic distribution of the test statistic under both the null hypothesis and general alternatives, and develop a bootstrap procedure with theoretical guarantees to approximate its null distribution. We show that the resulting bootstrap test attains asymptotically correct size and is consistent, with power converging to one under model misspecification. Simulation studies and a real data application demonstrate that the proposed method performs well in finite samples.

Structural glasses prepared by bulk quenching a liquid melt universally exhibit puzzling low-energy excitations commonly known as the ``two-level systems'' (TLSs). Recent studies indicate that ultrastable glassy films made by vapor deposition exhibit substantially fewer TLSs and, at the same time, are more stable enthalpically than conventional glasses made by quenching a melt. A similar phenomenon is observed in very stable glasses of model liquid mixtures prepared using swap Monte Carlo sampling. However, in a separate set of enthalpically stable solids, exemplified by amber matured over geological times, the two-level systems persist. In addressing this seeming conflict, we emphasize that a depletion of the TLSs, if any, means the configurational entropy of the material is lower than that of conventional glasses made by bulk-quenching a melt. Ageing does induce reduction in configurational entropy, but amber, we speculate, achieves enthalpic stabilization through increased bonding, not ageing. We separately comment on the discrepancy among existing predictions for the extent of cooperativity of the two-level systems. Several experiments are suggested to test the present picture.

Cohen, Lowrance, Madras, and Raanes computed the average (absolute value of) signature over all 2-bridge knots with crossing number $c$ by introducing the number $s(c,σ)$ of 2-bridge knots of crossing number $c$ and signature $σ$. Here we provide a closed formula for this number. We use these calculations to show that the distribution of the signatures of 2-bridge knots with crossing number $c$ approaches a normal distribution as $c$ tends to infinity.

Understanding the role of confinement while crystallizing nanocrystals is very relevant for predicting their structure and physical properties. With this aim we perform Langevin dynamics simulations of nanocrystals of the model system of few hundred vortices nucleated in micron-sized superconductors. We study the crystallization dynamics and the low-temperature structural properties of vortex nanocrystals nucleated in field-cooling conditions when changing vortex density or elasticity of the system and physical size of the samples. The low-temperature snapshots obtained in simulations present a healing effect at the edges that is in quantitative agreement with experimental data in Bi2Sr2CaCu2O8+δ micron-sized samples. We show that the low-temperature radial distribution of topological defects is a stationary profile frozen at a temperature below the melting line tuned by intrinsic properties of the vortex structure and on the confinement effect. These findings on the dynamics and spatial profile of topological defects can be applied to describe the physical properties of confined soft condensed matter nanocrystals in general.

Ultra high energy cosmic rays have been see coming from the direction of the local cosmic void. We use this fact to argue that at least some of these these cosmic rays are relatively light magnetic monopoles and that their relative fraction above 1020 eV can be found from full sky observations.

Motivation: Modern bioinformatics workflows, particularly in imaging and representation learning, can generate thousands to tens of thousands of quantitative phenotypes from a single cohort. In such settings, running genome-wide association analyses trait by trait rapidly becomes a computational bottleneck. While established GWAS tools are highly effective for individual traits, they are not optimized for phenotype-rich screening workflows in which the same genotype matrix is reused across a large phenotype panel. Results: We present TorchGWAS, a framework for high-throughput association testing of large phenotype panels through hardware acceleration. The current public release provides stable Python and command-line workflows for linear GWAS and multivariate phenotype screening, supports NumPy, PLINK, and BGEN genotype inputs, aligns phenotype and covariate tables by sample identifier, and performs covariate adjustment internally. In a benchmark with 8.9 million markers and 23,000 samples, fastGWA required approximately 100 second per phenotype on an AMD EPYC 7763 64-core CPU, whereas TorchGWAS completed 2,048 phenotypes in 10 minute and 20,480 phenotypes in 20 minutes on a single NVIDIA A100 GPU, corresponding to an approximately 300- to 1700-fold increase in phenotype throughput. TorchGWAS therefore makes large-scale GWAS screening practical in phenotype-rich settings where thousands of quantitative traits must be evaluated efficiently. Availability and implementation: TorchGWAS is implemented in Python and distributed as a documented source repository at https://github.com/ZhiGroup/TorchGWAS. The current release provides a command-line interface, packaged source code, tutorials, benchmark scripts, and example workflows.

Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries of the $2+1$-dimensional $O(2)$ and $O(3)$ Wilson-Fisher fixed points, realized microscopically by a bilayer Heisenberg model on the fuzzy sphere. Using the fuzzy-sphere state-operator correspondence, we obtain boundary operator spectra, identify low-lying boundary primary operators, extract operator-product-expansion (OPE) data, and estimate the boundary central charges for both boundary conditions. For the normal boundary condition, the universal amplitudes $a_σ$ and $b_t$ extracted from one- and two-point functions agree quantitatively with Monte Carlo benchmarks where available. For both $N=2$ and $N=3$, we find a positive extraordinary-log exponent $α$, providing independent microscopic evidence for extraordinary-log boundary criticality. Our results extend fuzzy-sphere BCFT spectroscopy beyond the Ising universality class to continuous $O(N)$ symmetry.

Estimating local observables in Gibbs states is a central problem in quantum simulation. While this task is BQP-complete at asymptotically low temperatures, the possibility of quantum advantage at constant temperature remains open. The Sachdev-Ye-Kitaev (SYK) model is a natural candidate: at any constant temperature, its Gibbs states have polynomial quantum circuit complexity and are not described by Gaussian states. Rigorous analyses of the SYK model are difficult due to the failure of known techniques using random matrix theory, cluster expansions, and rigorous formulations of the quantum path integral and replica trick. Despite this, we give a rigorous proof of a quasipolynomial-time classical algorithm that estimates SYK local thermal expectations at sufficiently high constant temperature. Our result introduces a new Wick-pair cluster expansion that we expect to be broadly useful for disordered quantum many-body systems.

We prove that the maximal graph-density of an independent set in a Penrose P3 tiling considered as a planar non-directed graph is equal to $(57 - 25 \sqrt{5})/2 \approx 0.54915$ despite the fact that the graph is bipartite. Accordingly, the extreme Gibbs measure of the nearest-neighbor hard core particle model on this graph is unique for sufficiently large values of the particle activity. This invalidates a natural expectation to observe the coexistence of even and odd phases.

Concurrent programming under weak memory concurrency faces substantial challenges to ensure correctness due to program behaviors that cannot be explained by thread interleaving, a.k.a. sequential consistency. While several program logics are proposed to reason about weak memory concurrency, their usage has been limited to intricate manual proofs. On the other hand, the VerCors verifier provides a rich toolset for automated deductive verification for sequential consistency. In this paper, we bridge this gap for automated deductive verification of weak memory concurrent programs with the VerCors deductive verification tool. We propose an approach to encode weak memory concurrency in VerCors. We develop VerCors-relaxed, where we extend the VerCors atomics support and bring concepts from several protocol automata to encode permission-based separation logics for weak memory concurrency models. To demonstrate the effectiveness of our approach, we encode the relaxed fragment of the SLR program logic, a recent state-of-the-art permission-based separation logic for weak memory concurrency in VerCors-relaxed, our extension of VerCors. We use the SLR encoding on VerCors-relaxed to automatically verify several examples from the literature within realistic performance.