The rapid expansion of Internet use has increased system exposure to cyber threats, with advanced persistent threats (APTs) being especially challenging due to their stealth, prolonged duration, and multi-stage attacks targeting high-value assets. In this study, we model APT evolution as a strategic interaction between an attacker and a defender on an attack graph. With limited information about the attacker's position and progress, the defender acts at random intervals by deploying intrusion detection sensors across the network. Once a compromise is detected, affected components are immediately secured through measures such as backdoor removal, patching, or system reconfiguration. Meanwhile, the attacker begins with reconnaissance and then proceeds through the network, exploiting vulnerabilities and installing backdoors to maintain persistent access and adaptive movement. Furthermore, the attacker may take several steps between consecutive defensive operations, resulting in an asymmetric temporal dynamic. The defender's goal is to reduce the likelihood that the attacker will gain access to a critical asset, whereas the attacker's purpose is to increase this likelihood. We investigate this interaction under three informational regimes, reflecting varying levels of attacker knowledge prior to action: (i) a Stackelberg scenario, in which the attacker has full knowledge of the defender's strategy and can optimize accordingly; (ii) a blind regime, where the attacker has no information and assumes uniform beliefs about defensive deployments; and (iii) a belief-based framework, where the attacker holds accurate probabilistic beliefs about the defender's actions. For each regime, we derive optimal defensive strategies by solving the corresponding optimization problems.

We review and elaborate on the issue of the dilaton transformation under the usual $r \rightarrow α'/r$ target space duality and its non-static generalization (or $σ$-model duality). It is found that the transformation law $r \rightarrow α'/r$, $ϕ\rightarrow ϕ- \ln(r/\sqrt{α'})$ which guarantees duality at the one-loop $σ$-model level should be modified at two (and higher) loop order. The non-static duality is illustrated on the example of cosmological solutions in $D \ge 2$ with time-dependent radii of space torus.

To extract bulk QGP properties, we perform a joint Bayesian calibration of bulk-medium parameters using low-$\pt$ bulk and high-$\pt$ tomography within a common medium evolution. Low-$\pt$ observables are computed with \textsc{TRENTo}+\textsc{VISHNU}; temperature profiles are passed to \textsc{DREENA-A} to predict light/heavy $R_{\mathrm{AA}}(\pt)$ and $v_2(\pt)$. Gaussian-process emulation enables Hamiltonian Monte Carlo sampling of the low-$\pt$-only and joint posteriors. The low-$\pt$-only case underpredicts high-$\pt$ anisotropy; the joint calibration matches both sectors and markedly tightens bulk-parameter constraints, demonstrating the added power of high-$\pt$ data.

Flow criteria are used to efficiently extract computations, either in the form of measurement patterns or quantum circuits, from ZX-diagrams. Existing criteria such as causal flow, generalised flow, and Pauli flow, were all originally formulated for graph states, so they require ZX-diagrams to be in a very particular graph-state-like form. This form is easily broken by applying basic ZX rules and makes establishing some desirable properties very complicated. Here, we introduce a new "ZX-native" flow criterion called ZX-flow, formulated using a new type of decoration of a ZX-diagram we call Pauli semiwebs. These are a generalisation of Pauli webs, which have recently been used extensively in reasoning about fault-tolerant computations in the ZX-calculus. We show that ZX-flow is straightforwardly preserved by all Clifford rewrites and furthermore that a ZX-diagram has ZX-flow if and only if it is Clifford-equivalent to a graph-like ZX-diagram with Pauli flow. Finally, we show that any diagram with ZX-flow can be readily interpreted either as a deterministic measurement-based computation or as a Clifford isometry followed by a sequence of Pauli exponentials. The latter can then be efficiently extracted to a quantum circuit.

Dynamic shortest-path routing, using real-time traffic data, enables path selection responsive to evolving conditions. Nevertheless, transportation planning tasks such as adaptive congestion pricing, fleet routing, and long-term operational decisions rely on offline traffic estimators. To address this problem, we develop a spatiotemporal predictor based on a low-rank decomposition of the traffic matrix and the temporal subspace coefficients. Using a recent large-scale measurement campaign over the Seoul road network, we show that our proposed predictor incurs an average excess travel time of less than 1.5 minutes. Moreover, our predictor's tail of the excess travel time distribution matches that of a near-real-time predictor. Results based on one year of traffic data are also demonstrated in simulations.

Magneto-optical effects like Kerr and Faraday rotations provide a direct probe of topological order in thin films of the magnetic topological insulator MnBi$_2$Te$_4$ (MBT). Motivated by recent experimental studies of spin-flip/flop transitions in MBT thin films, we investigate the interplay between interlayer spin configurations, topological order, and magneto-optical response in five septuple-layer (5-SL) MBT using first-principles calculations and a simplified coupled-Dirac-cone model. Our results reveal that, despite possessing a non-zero out-of-plane magnetization, 5-SL MBT thin films can be either ${\cal C}=+1$ topological insulators or ${\cal C}=0$ topologically trivial insulators depending on the relative spin orientations of the top and bottom SLs. We evaluate the Faraday and Kerr rotation angles using tight-binding models derived from \textit{ab-initio} calculations and by comparing our results with those of a simplified coupled Dirac-cone model clarify the macroscopic mechanisms underlying the magneto-optical response of spin-flip states. These theoretical findings highlight the tunability of topological and magneto-optical properties in MBT thin films and provide microscopic insight into the emergence of complex topological order in layered antiferromagnetic materials.

We establish the randomized distributed function computation (RDFC) framework, in which a sender transmits just enough information for a receiver to generate a randomized function of the input data. Describing RDFC as a form of semantic communication, which can be essentially seen as a generalized remote-source-coding problem, we show that security and privacy constraints naturally fit this model, as they generally require a randomization step. Using strong coordination metrics, we ensure (local differential) privacy for every input sequence and prove that such guarantees can be met even when no common randomness is shared between the transmitter and receiver. This work provides lower bounds on Wyner's common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness. Experiments illustrate that a sufficient amount of common randomness can reduce the semantic communication rate by up to two orders of magnitude compared to the WCI point, while RDFC without any shared randomness still outperforms lossless transmission by a large margin. A finite blocklength analysis further confirms that the privacy parameter gap between the asymptotic and non-asymptotic RDFC methods closes exponentially fast with input length. Our results position RDFC as an energy-efficient semantic communication strategy for privacy-aware distributed computation systems.

In this paper we modify a fundamental block construction of Kharaghani and Seberry and show how to use certain circulant $\{-1,1\}$-matrices of odd order $p$ to construct a complex Hadamard matrix of order $2p$. In particular, for $p=47$ we use computer-aided methods to discover the necessary circulant matrices, and consequently give a construction of a complex Hadamard matrix of order $94$ for the first time.

We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.

In this work, we argue that ignorance can be inherently understood as a hyperintensional notion. When faced with two logically or necessarily equivalent propositions, an agent may be ignorant of one while not of the other. To capture formally this intuition, we employ a topic-sensitive semantics, enabling the modeling of an agent's attitude toward the content of a proposition. Within this framework, we reevaluate three existing logical systems, usually characterized by standard Kripke semantics, to account for three forms of ignorance: ignorance whether, ignorance as unknown truth, and disbelieving ignorance. For each form, we present a sound and complete system. To highlight the advantage of this approach, we apply it to address the problem of logical omniscience rephrased in terms of ignorance. The resulting framework considers an agent's capacity to grasp the content of a proposition, bridging the gap between standard relational settings for ignorance representation and natural intuitions about the role of content in forming one's ignorance.

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large memory spaces, introducing redundancy and limiting scalability. Here, we introduce a \textit{variational quantum dimension reduction} framework that identifies and removes irrelevant memory degrees of freedom while preserving the recurrent dynamics of the target model. Our approach employs two parameterized quantum circuits: a decoupling unitary $V(θ_1)$ that isolates the essential memory subspace; and a compressed recurrent unitary $\tilde{U}(θ_2)$ that reconstructs the dynamics in the reduced space. The optimization is guided by a unified cost function combining decoupling fidelity and dynamical accuracy, evaluated using the \textit{Quantum Fidelity Divergence Rate} (QFDR), a metric that quantifies long-term fidelity per time step. Applied to a cyclic random walk model, our framework achieves up to three orders of magnitude smaller QFDR compared to variational matrix product state truncation, while requiring only trajectory samples rather than explicit state reconstructions. This establishes a scalable, data-driven paradigm for learning minimal recurrent quantum architectures, enabling variational circuit optimization and quantum process compression for near-term quantum devices.

With the advancement of synchrotron radiation and free-electron laser, X-ray quantum optics has emerged as a novel frontier for exploring light-matter interactions at high photon energies. A significant challenge in this field is achieving well-defined two-level systems through atomic inner-shell transitions, which are often hindered by broad natural linewidths and local electronic structure effects. This study aims to explore the potential of tungsten disilicide (WSi2) as a two-level system for X-ray quantum optics applications. Utilizing high-resolution resonant inelastic X-ray scattering (RIXS) near the W-L3 edge, in this work, the white line of bulk WSi2 is experimentally distinguished, overcoming the spectral broadening caused by short core-hole lifetime. The measurements are conducted by using a von Hamos spectrometer at the GALAXIES beamline of the SOLEIL synchrotron. The results reveal a single resonant emission feature with a fixed energy transfer, confirming the presence of a discrete 2p-5d transition characteristic of a two-level system. Additional high-resolution XAS spectra, obtained via high energy resolution fluorescence detection method and reconstructed from off-resonant emission (free from self-absorption effect for bulk WSi2 sample) method, further support the identification of a sharp white line. These findings demonstrate the feasibility of using WSi2 as a model system in X-ray cavity quantum optics and establish RIXS as a powerful technique to resolve fine inner-shell structures.

According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of wave function in three dimension. For a system of N identical particles, if the solution to the governing Schrodinger equation meets these criteria: a) the probability density remains invariant when any two particle positions are exchanged over time, b) the wave function is continuous and has a continuous gradient, and the system exhibits the following characteristics: c) the configuration space, which is 3N dimensional, is connected, and d) the potential term in the Hamiltonian is invariant under the exchange of any two particle positions, then the wave function must be either totally symmetric or totally antisymmetric over time.

Turbulence plays a critical role in the atmosphere, oceans, engineering, and astrophysics. The dissipation (heating) induced by turbulent flows is particularly important for the thermodynamics and chemistry of interstellar clouds, yet its structure and statistics remain poorly understood. Using high-resolution turbulence simulations with controlled explicit viscosity, we study the kinetic energy dissipation rate, $\varepsilon_{\mathrm{kin}}$, across subsonic and supersonic regimes. We find that dissipation lags large-scale kinetic energy injection events by $1.64\pm0.21$ and $0.48\pm0.07$ turbulent turnover times in subsonic and supersonic turbulence, respectively. Correlations show $\varepsilon_{\mathrm{kin}}\propto\vert\nabla\times\mathbf{v}\vert^2$ (vorticity squared) in the subsonic regime, where density fluctuations are negligible, while in the supersonic regime dissipation is primarily correlated with density, $\varepsilon_{\mathrm{kin}}\proptoρ^{3/2}$. A spectral analysis demonstrates that achieving numerical convergence of $\varepsilon_{\mathrm{kin}}$ across all scales is challenging, especially in the subsonic case, even at $2048^3$ resolution. Nonetheless, subsonic dissipation is clearly localised on small vorticity-dominated scales, while supersonic dissipation spans many scales, combining elongated, thin shocks with small-scale vorticity. Finally, we determine the fractal dimension of $\varepsilon_{\mathrm{kin}}$. In the subsonic regime, intense dissipation is predominantly organised in flattened vortex filaments embedded in thin shearing layers on small scales, becoming more volume-filling at larger scales. In the supersonic regime, $\varepsilon_{\mathrm{kin}}$ exhibits a fractal dimension between 1 and 2 across nearly all scales, likely reflecting shock surfaces and their intersections forming filaments.

This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd $\Rightarrow$ fc). We take a step toward a positive resolution of this conjecture by demonstrating that universal models generated by bdd rule sets cannot contain arbitrarily large tournaments (arbitrarily directed cliques) without entailing a loop query, $\exists{x} E(x, x)$. This simple yet elegant result narrows the space of potential counterexamples to the (bdd $\Rightarrow$ fc) conjecture.

The photoalignment technique for liquid crystal (LC) device fabrication, despite being a well-established method, remains of significant relevance because of its broad applicability. Among its applications, one of particular interest is the generation of structured light, specifically the manufacturing of Pancharatman-Berry (PB) devices, capable of generating optical vortices with angular momentum. In this work, we propose a thorough theoretical and experimental analysis of the optical response of dye-doped liquid crystal (DDLC) devices by examining their performance in terms of tunability and achromaticity across the whole visible spectrum, considering diattenuation effects and how they affect the efficiency of the devices. We experimentally demonstrate the fabrication of photoaligned devices in the visible range with 532 nm laser light and the robust generation of high-quality optical vortices, achieved by a straightforward and accessible technique using a commercial Variable Spiral Plate (VSP), avoiding the need for complex rotational systems or programmable spatial light modulators. Our results demonstrate that diattenuation effects do not prevent the functionality of the devices across the whole visible spectrum and with extended ranges of achromaticity.

Outsourcing encrypted data to the cloud creates a fundamental tension between data privacy and functional searchability. Current Searchable Symmetric Encryption (SSE) solutions frequently have significant limitations, such as excessive metadata leakage, or a lack of fine-grained access control. These issues restrict the scalability of secure searches in real-world applications where multiple clients require different levels of authorization. Our paper proposes MASSE, a dynamic multi-client SSE scheme incorporating attribute-based access control, which expands the OXT framework. With MASSE, clients are restricted sto searching for keywords authorized by their specific attribute sets, and the server remains unaware of the keywords and attributes. MASSE supports practical dynamic updates to documents, and client authorizations, including revocation, without requiring reencryption of the database or indices, or a large number of interactions. We formally prove the security of MASSE, that is, forward and backward privacy under a well-defined leakage profile, and token unforgeability. An experimental evaluation in a database containing 100 keywords, each associated with 150 documents, demonstrates the practical efficiency of MASSE. It takes less than two seconds to generate 10 to 100 keyword queries and 14 seconds to retrieve 50 matching documents. Theoretical results show that MASSE outperforms competing solutions, including OXT, and can be scaled to large encrypted databases. MASSE is also suitable for dynamic cloud deployments. Keywords: Searchable Encryption, SSE, Multi-Client, Attribute Based SSE, Access Control, Revocation, OXT

A hole is an induced cycle of length at least 4, and an odd hole is a hole of odd length. It is NP-hard to color the vertices of an odd hole-free graph. A graph $G$ is perfectly divisible if every induced subgraph $H$ of $G$ with at least one edge admits a partition of $V(H)$ into sets $A$ and $B$ such that $H[A]$ is perfect and $ω(H[B])<ω(H)$. $G$ is short-holed if every hole in $G$ has length 4. A hammer is the graph obtained by identifying one vertex of a $K_3$ and one end vertex of a $P_3$. In this paper, we prove that (i) (odd hole, hammer, $K_{2,3}$)-free graphs are perfectly divisible, (ii) $χ(G)\le 4ω(G)(ω(G)-1)$ if $G$ is short-holed and $(K_1+C_4)$-free, (iii) $χ(G)\le 2ω(G)-1$ if $G$ is short-holed and $(K_1\cup K_3)$-free, and (iv) $χ(G)\le 16ω(G)-24$ if $G$ is short-holed and $(K_1+(K_1\cup K_3))$-free.

Extreme mass-ratio inspirals (EMRIs) are long-duration gravitational-wave sources in which a compact object gradually spirals into a massive black hole. Their formation is governed by the interplay between stochastic angular-momentum diffusion driven by two-body relaxation and the dissipative evolution caused by gravitational-wave emission, with the loss-cone boundary deciding whether an object undergoes an inspiral or a direct plunge. Building on this physical picture, we construct a relativistically self-consistent analytic framework for estimating EMRI event rates. In Schwarzschild spacetime, we generalize the standard loss-cone angular momentum to an energy-dependent quantity and revise the plunge pericenter by using the minimum stable radius derived from general relativity. Relative to the Newtonian treatment, we show that incorporating these relativistic effects increases the predicted EMRI rates by roughly a factor of 8. This enhancement becomes more pronounced for shallower stellar density profiles and is insensitive to the mass of the central massive black hole, which emphasizes that relativistic effects are essential for EMRI rate estimations that are relevant for space-based gravitational-wave detectors, such as LISA and Taiji.

It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods depend heavily on the lower-level singleton (LLS) assumption, which greatly limits their practical applicabilities. To tackle this technical challenge, this paper focus on a particular type of nonsmooth convex sparse optimization problem and presents a new bilevel optimization framework. This framework effectively integrates the alternating direction method of multipliers (ADMM) with a bilevel descent aggregation (BDA) algorithm. Specifically, it employs ADMM to efficiently address the lower-level problem and uses BDA to explore the hyperparameter space, thereby integrating both the upper and lower-level problems. It is important to emphasize that a key contribution of this paper lies in the presentation of a novel convergence analysis. The analysis illustrates that the proposed ADMM-BDA algorithm achieves global convergence under significantly relaxed conditions, thereby departing from the LLS assumption that are often required in the literature. We conduct a series of numerical experiments utilizing synthetic and real-world data, and do performance comparisions against some state-of-the-art algorithms. The results indicates that ADMM-BDA exhibits superior effectiveness and robustness for solving bilevel programming problems, especially when the lower-level problem is an elastic-net penalized statistics problem.

We investigate the substructure of jets produced in photoproduction events with center-of-mass energies $\sqrt{s} = 30\text{--}140$ GeV at the proposed Electron-Ion Collider (EIC). Events are generated using PYTHIA and contributions from direct and resolved photoproduction subprocesses are analyzed at different center-of-mass energies. Jets are reconstructed using longitudinally invariant $k_T$ algorithm within the FastJet framework. Substructure of quark- and gluon-initiated jets in the selected di-jet photoproduction sample is studied in detail by using jet-shape variables. Predictions for subjet multiplicities and integrated jet shapes are presented in the gluon-initiated and quark-initiated jets. These results demonstrate the feasibility of distinguishing quark and gluon jets in the photo-production events at the EIC and provide a baseline for further QCD studies.

Software compartmentalization breaks down an application into compartments isolated from each other: an attacker taking over a compartment will be confined to it, limiting the damage they can cause to the rest of the application. Despite the security promises of this approach, recent studies have shown that most existing compartmentalized software is plagued by vulnerabilities at cross-compartment interfaces, allowing an attacker taking over a compartment to escape its confinement and negate the security guarantees expected from compartmentalization. In that context, securing cross-compartment interfaces is notoriously difficult and engineering-intensive. In light of recent advances in Automated Program Repair (APR), notably through the use of Large Language Models (LLMs), this paper presents a work in progress investigating the suitability of LLM-based APR at securing cross-compartment interfaces as automatically as possible. We observe that existing APR approaches and general purpose/code-centric LLMs used as is are unfit for this task, and present the design, implementation, and early results of a new APR framework dedicated to compartment interface safety. The framework integrates into a feedback loop 1) a specialized fuzzer uncovering cross-compartment interface vulnerabilities; 2) a patch generation component bridging the lack of compartmentalization awareness of existing LLMs with a series of analysis techniques; and 3) a patch validation component assessing the effectiveness of generated vulnerability fixes. We validate our framework over a sample interface vulnerability, comparing it to a naive use of general-purpose LLMs, and discuss future research avenues.

We introduce the sampling logit equilibrium (SLE), a stationary concept for population games in which agents evaluate actions using a finite sample of opponents' plays and respond according to a logit choice rule. This framework combines informational frictions from finite sampling with stochastic choice. When the sample size is large, SLE is well approximated by a logit equilibrium of a virtual game whose payoffs incorporate explicit distortion terms generated by sampling noise. Examples illustrate how finite sampling can systematically shift equilibrium behavior and generate equilibrium selection effects.

We give explicit formulas for the coproducts of modified Drinfeld-Cartan generating series for the Yangian in type $A$ and for the quantum affine algebras in the particular type $A_2$. As an auxiliary result of the latter, we give an explicit presentation of positive prefundamental representations of the quantum affine algebra in the particular type $A_2$

In virtual reality (VR) educational scenarios, Pedagogical agents (PAs) enhance immersive learning through realistic appearances and interactive behaviors. However, most existing PAs rely on static speech and simple gestures. This limitation reduces their ability to dynamically adapt to the semantic context of instructional content. As a result, interactions often lack naturalness and effectiveness in the teaching process. To address this challenge, this study proposes a large language model (LLM)-driven multimodal expression generation method that constructs semantically sensitive prompts to generate coordinated speech and gesture instructions, enabling dynamic alignment between instructional semantics and multimodal expressive behaviors. A VR-based PA prototype was developed and evaluated through user experience-oriented subjective experiments. Results indicate that dynamically generated multimodal expressions significantly enhance learners' perceived learning effectiveness, engagement, and intention to use, while effectively alleviating feelings of fatigue and boredom during the learning process. Furthermore, the combined dynamic expression of speech and gestures notably enhances learners' perceptions of human-likeness and social presence. The findings provide new insights and design guidelines for building more immersive and naturally expressive intelligent PAs.

The upgrade of the China Spallation Neutron Source (CSNS-II) will raise the proton beam power to 500 kW. Consequently, the existing Timepix3-based detector systems, limited to a count rate of 80 Mhits/s, will encounter severe saturation challenges. To address the demand of the Energy-Resolved Neutron Imaging instrument (ERNI) for next-generation higher count-rate electronics, this paper presents CTPX1, a high-performance data-driven camera system based on the Timepix4 ASIC. The system adopts a compact modular architecture, integrating readout electronics, a precision high-voltage bias unit, and a TEC temperature control subsystem. To fully exploit the readout potential of the Timepix4 ASIC's 16 high-speed serial links, this paper proposes a two-stage parallel processing architecture. This architecture achieves real-time data aggregation with a total bandwidth of up to 81.92 Gbps. Over a continuous 12-hour operation period, temperature fluctuations were kept within 0.1 °C while the high-voltage output noise remained below 1 mV. High-flux X-ray testing indicates that the system achieves a peak event readout rate of 1.17 Ghits/s, approaching the limit of the configured link speed. In-beam neutron verification at CSNS confirms that the camera successfully resolves fine spatial structures, achieving an imaging performance consistent with the 55 μm pixel pitch of the sensor. Furthermore, the clear observation of spectral features in the Time of flight (TOF) spectrum of a γ-Fe sample validates the system's good time resolution. This camera effectively addresses the data readout saturation challenges, validates the feasibility of Timepix4 technology for neutron imaging, and provides a viable solution for next-generation high-performance neutron imaging instruments.

We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two directions through one-dimensional eigendecompositions, while the third direction is solved directly. The resulting dense transforms are evaluated efficiently as GEMMs (General Matrix--Matrix Multiplications), allowing many independent one-dimensional operations to be combined into matrix-matrix products that map well to modern CPU and GPU hardware. For uniform grids, the method reduces to the classical eigenfunction-expansion approach, and it naturally supports hybrid combinations of FFT-based and GEMM-based transforms depending on grid uniformity. After coupling the solver to an incompressible Navier-Stokes code, we assess its accuracy and performance against geometric multigrid and block cyclic reduction with FFT diagonalization. The results show that the proposed method is robust and consistently achieves the best time-to-solution. In strong scaling, the more compute-intensive GEMM-based variants attain higher parallel efficiency by better amortizing communication costs, while weak scaling highlights the expected trade-off between FFT-based and dense-transform formulations. Overall, the method enables efficient high-resolution stretched-mesh simulations on modern heterogeneous systems.

Structural system identification in the presence of thermal loads is challenging, as unmeasured or poorly modeled thermal effects can mask or mimic damage, leading to unreliable conclusions. This work presents an optimization-driven, adjoint-based high-fidelity system identification framework for localizing structural weakness and recovering the temperature field in one-way thermo-mechanical coupled structures. The methodology builds upon a standard optimization formulation that minimizes weighted discrepancies between simulated responses and measured data from a sparse displacement and temperature sensor network. To account for thermal effects, two strategies are proposed: a monolithic approach, which simultaneously identifies Young's modulus and temperature distributions, and a partitioned approach, which iteratively couples two inexact sub-problems through a Gauss-Seidel type fixed-point scheme. The proposed approaches are evaluated using two numerical examples -- a Plate With a Hole and a Footbridge model -- under linearly varying and localized thermal fields, and for different sensor layouts. Both approaches successfully recover the Young's modulus and temperature distributions, even when sensor placement does not fully capture the underlying thermal trends. Compared with a constant-temperature assumption and interpolation of the temperature field from sensor data, the proposed approach achieves the most accurate damage localization and temperature reconstruction. The largest gains occur when localized thermal features are poorly sampled by sensors, where interpolation and constant-temperature assumptions underperform. Furthermore, results show that the location of the temperature sensors is as influential as the number of sensors: well-placed sensors substantially improve identification, while additional sensors that miss critical thermal features provide limited benefit.

We consider distributed nonconvex optimization over an undirected network, where each node privately possesses its local objective and communicates exclusively with its neighboring nodes, striving to collectively achieve a common optimal solution. To handle the nonconvexity of the objective, we linearize the augmented Lagrangian function and introduce a time-varying proximal term. This approach leads to a Unifying Primal-Dual Proximal (UPP) framework that unifies a variety of existing first-order and second-order methods. Building on this framework, we further derive two specialized realizations with different communication strategies, namely UPP-MC and UPP-SC. We prove that both UPP-MC and UPP-SC achieve stationary solutions for nonconvex smooth problems at a sublinear rate. Furthermore, under the additional Polyak-Łojasiewics (P-Ł) condition, UPP-MC is linearly convergent to the global optimum. These convergence results provide new or improved guarantees for many existing methods that can be viewed as specializations of UPP-MC or UPP-SC. To further optimize the mixing process, we incorporate Chebyshev acceleration into UPP-SC, resulting in UPP-SC-OPT, which attains an optimal communication complexity bound. Extensive experiments across diverse network topologies demonstrate that our proposed algorithms outperform state-of-the-art methods in both convergence speed and communication efficiency.

We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.