In Riemannian computing applications, it is crucial to map manifold data to a Euclidean domain, where vector space arithmetic is available, and back. Classical manifold theory guarantees the existence of such mappings, called charts and parameterizations, or, collectively, local coordinates. When computational efficiency is of the essence, practitioners usually resort to retraction maps to define local coordinates. Retractions yield first-order approximations of the Riemannian normal coordinates. This work introduces a new retraction on the symplectic Stiefel manifold that features a closed-form inverse. We expose essential features and compare the numerical performance to a selection of existing retractions. To the best of our knowledge, prior to this work, the so-called Cayley retraction was the only retraction on the symplectic Stiefel manifold with known closed-form inverse.

The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized algorithms, the exact parameterized complexity of the problem and the existence of efficient parameterized approximation schemes remained open. We advance this understanding on both the hardness and algorithmic fronts. We begin by showing that $k$-MSR is $W[2]$-hard parameterized by $k$, thereby pinpointing its location in the $W$-hierarchy. Moreover, via our reduction, we rule out efficient parameterized approximation schemes (EPAS)--that is, $(1+ε)$-approximations running in time $f(k,ε)\cdot \mathrm{poly}(n)$--unless $W[2] = FPT$. Assuming the Exponential Time Hypothesis, we further rule out such algorithms running in time $f(k,ε)\cdot n^{o(k)}$, strengthening recent lower bounds for the problem. On the algorithmic side, we study $k$-MSR under the framework of mergeable constraints, which captures a broad class of clustering constraints, including fairness, diversity, and lower bounds. We obtain an FPT $(\frac{8}{3}+ε)$-approximation, improving upon the previous best guarantee of $(4+ε)$. Moreover, given access to a suitable assignment subroutine, we achieve a $(2+ε)$-approximation, matching the best known bound for the unconstrained problem. This, in turn, yields $(2+ε)$ FPT-approximations for several important settings, including $(t,k)$-fair, $(α,β)$-fair, $\ell$-diversity, and private clustering.

The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation.

We analyze the dynamics towards partial thermalization and subsequent cooling in the defocusing two-dimensional nonlinear Schrödinger model, using direct simulations and insights from the wave-kinetic equations (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges--the quasi-thermal core and the ultraviolet tail--whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature--analogous to an ultraviolet catastrophe in a system of classical waves.

Self-hosted computer-use agents (SHCUAs), such as OpenClaw, combine natural-language interaction with direct access to host-side resources, including browsers, files, scripts, system commands, and external communication channels. While useful for automating real tasks, this capability also creates a host-level abuse surface: a legitimately deployed agent may be steered toward unsafe operations through malicious messages, indirect prompt injection, unsafe skills, or tampering along the host-side control path. We argue that such risks cannot be addressed by ad hoc blocking rules alone, because the security criticality of an operation depends jointly on its action type, target object, execution context, and potential effect. This paper presents an operation-centric model for risk-based confinement of SHCUA operations. The proposed design keeps ordinary functionality on the constrained REE path, while protecting security-critical classification, authorization, binding, evidence generation, and selected execution-control decisions inside a cloud-native TEE-backed trusted operation plane. We instantiate the architecture on OpenClaw using Intel TDX as the primary trusted backend, with remote terminal-side trusted components verifying TDX-audited commands before constrained local execution. The evaluation shows that the design can block unsafe or policy-disallowed operations before execution, preserve ordinary functionality for allowed workloads, and provide auditable evidence with deployment-dependent overhead.

Spatio-temporal Bayesian inference drives environmental and health sciences using latent Gaussian models. Integrated Nested Laplace Approximations (INLA) enable inference for these models at HPC scale but rely on derivative-based optimization over $d$ hyperparameters. State-of-the-art INLA implementations approximate derivatives via central finite differences (FD), requiring $2d{+}1$ evaluations. These evaluations are embarrassingly parallel, but total work and energy grow with $d$, limiting time-to-solution under fixed budgets. Reverse-mode automatic differentiation (AD) computes exact gradients independently of $d$, but its efficient application to INLA's structured-sparse kernels is an open challenge. We present ADELIA, the first AD-enabled INLA implementation with a structure-exploiting multi-GPU backward pass leveraging model sparsity. We evaluate ADELIA on ten benchmark models, including real-world air-pollution monitoring. We achieve $4.2$--$7.9\times$ per-gradient speedups and reliable convergence on production-scale models with up to 1.9M latent variables, where FD struggles. Even when scaled to 16--32 GPUs to match ADELIA's wall-clock time, FD consumes $5$--$8\times$ more energy.

This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for a class of constrained discrete-time linear systems. UOT compares measures with unequal total mass by balancing transport cost and fidelity to reference measures, while UDC incorporates system dynamics and constraints into this framework. Focusing on Gaussian references and discrete-time linear systems, we show that both problems admit globally optimal convex formulations, analogous to covariance steering. A numerical experiment is provided to illustrate our approach.

Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken, it becomes possible to remove the boundary modes without closing the bulk gap. In this work, we present construction schemes for HOTPs protected solely by the bulk gap, by fundamental symmetries, and by the global topology of the system shape (its genus, or number of holes), independent of any crystalline symmetries. As long as the fundamental local symmetries are preserved, the resulting boundary states cannot be removed by any purely-surface perturbation.

In this article we consider a restricted orbital counting problem for the action of certain discrete groups on suitable spaces. In particular, we present asymptotics for counting those points in an orbit restricted to a single conjugacy class. A classical example would be cocompact actions of a discrete group acting isometrically on a simply connected manifold with pinched negative curvature. More generally, we obtain results for convex cocompact actions on $CAT(-1)$ spaces.

The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework is introduced to systematically map the non-linear partial differential equations (PDEs) of Yang-Mills theory into tractable differential-algebraic systems. By promoting static pure-gauge backgrounds to dynamical variables, the reference state acts as a geometric template whose Maurer-Cartan forms generate the algebraic cross-terms necessary to stabilize non-linear self-interactions. To analytically resolve the resulting differential ideals, specific differential-algebraic quotient rings are employed as evaluation tools, and the solution space is organized by an algebraic bifurcation analysis. Applying this framework, three distinct classes of exact solutions are extracted: (i) relativistic $SU(2)$ color waves evaluated over an elliptic quotient ring, where the differential ideal bifurcates into a Decoupled Branch and two Coupled Branches, the latter exhibiting mass gap generation; (ii) dynamical dyonic flux tubes obtained from a time-dependent helical template, where the Gauss law ideal bifurcates the system into Coulomb, Dyonic, and symmetric Meissner branches. In the Meissner branch, an Artinian asymptotic truncation yields Bessel-type exponential screening, stabilized by a temporal dominance condition; and (iii) dynamical $SU(3)$ configurations where the Gauss law ideal bifurcates the solution space into four distinct phases. The non-trivial branches enforce a kinetic cancellation mechanism that maps the amplitude dynamics onto a generalized $x^2y^2$ chaotic oscillator. Across these settings, the framework provides a methodical approach to characterize the classical solution space of strongly coupled gauge theories.

In 2023, Gollin, Hendrey, Methuku, Tompkins and Zhang determined the maximum number of cliques in general 1-planar graphs with order $n$. Their extremal examples have connectivity at most three, except for a few small orders. At the high-connectivity end, we prove that every $n$-vertex 7-connected 1-planar graph has at most $4n-12$ edges, $4n-16$ triangles, and $n-6$ copies of $K_4$. Hence the total number of cliques is at most $10n-33$. All bounds are sharp for infinitely many values of $n$.

Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The $\cos(2φ)$ qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a $\cos(2φ)$ qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by $1/f$ flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.

Fix a prime power $q$ and parameters $1\leq t\leq k\leq n$, the corresponding Steiner system in the Grassmann scheme, or the $q$-Steiner system, is a collection $\mathfrak{B}$ of $k$-dimensional subspaces of $\mathbb{F}_{q}^n$ such that for each $t$-dimensional subspace $T$, there exists exactly one element of $\mathfrak{B}$ containing $T$. The dimension of Steiner systems in the Grassmann scheme is defined to be the dimension of the $\mathbb{Q}$-vector space spanned by the characteristic vectors of all these $q$-Steiner systems. In this paper, we prove that when a quadruple $(t,k,n,q)$ admits at least one $q$-Steiner system, the corresponding dimension is equal to ${n\brack k}_{q}-{n\brack t}_{q}+1$. This generalizes the 2019 work of Ghodrati \cite{ghodrati2019dimension} on ordinary Steiner systems.

We study bounds for correlation sums of automorphic coefficients on $\mathrm{GL}_{3,\mathbb{Q}}$ with trace functions of composite moduli. This is a sequel to our previous works with E. Kowalski and W. Sawin.

In this work, we perform a dedicated analysis of fermion mass fits in the minimal $SO(10)$ grand unified theory (GUT), going beyond the tree-level approximation by incorporating one-loop finite corrections to the neutrino mass matrix. We show that parameter regions that successfully reproduce all fermion masses and mixings at tree level can lead to significant deviations in neutrino masses and leptonic mixing parameters once the radiative corrections are included. These results expose a limitation of conventional tree-level fitting procedures and highlight the sensitivity of neutrino observables to loop effects. Since in the minimal $SO(10)$ GUT the same set of Yukawa parameters simultaneously governs quark masses, charged lepton masses, and neutrino properties, these radiative corrections propagate across all fermion sectors, reshaping the viable parameter space in a highly non-trivial and correlated manner. We find that the largest corrections to the masses and mixing angles are of order $\mathcal{O}(30\%)$-$\mathcal{O}(40\%)$, therefore, cannot be neglected. In light of the current precision of neutrino oscillation measurements, and the expected improvements from ongoing and future experiments, we demonstrate that the inclusion of one-loop effects is essential for a consistent and reliable exploration of the parameter space, with important implications for the predictivity of $SO(10)$ GUTs.

For any integer $n \geq 2$, let $(m_{1},\ldots,m_{n})$ be a strictly increasing $n$-tuple of positive integers. We show that any subset $A\subset [N]^n$ of density at least $(\log N)^{-c}$ contains a nontrivial configuration of the form \begin{equation*} \boldsymbol{x},\boldsymbol{x}+r^{m_{1}}\boldsymbol{e_{1}},\ldots,\boldsymbol{x}+r^{m_{n}}\boldsymbol{e_{n}}, \end{equation*} where $c=c(n,m_{1},\ldots,m_{n} )$ is a positive constant. This quantitative multidimensional Szemerédi theorem extends a recent two-dimensional result of Peluse, Prendiville, and Shao concerning the configuration of the form $(x,y),(x+r,y),\left(x,y+r^{2}\right)$. The theorem is obtained as a consequence of an effective ``popular'' version.

Real-time event detection in Internet of Things (IoT) mesh sensor networks presents significant challenges due to time-varying noise conditions, limited computational resources at edge nodes, and the need for autonomous operation without centralised coordination. This paper presents a comprehensive Monte Carlo simulation study comparing the Temporal Spectral Noise-Floor Adaptation (TSNFA) method against six alternative detection algorithms, evaluated across a 200-node mesh network over 24 hours with realistic noise models including 60 Hz electromagnetic interference (EMI), sinusoidally drifting noise power (+/- 6 dB), and intermittent digital switching bursts. TSNFA achieves 100% detection rate with zero false positives, uniquely combining three interlocking defences: spectral band selection, temporal persistence filtering, and adaptive noise-floor tracking. Every competing algorithm omits at least one of these three defences and fails correspondingly, with false-positive rates ranging from 0 (Send-on-Delta, which also detects nothing) to 13,387,930 (broadband energy ratio). These results identify the three-defence combination as necessary and sufficient for autonomous edge triggering in resource-constrained IoT deployments.

We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be recovered. If \(F\) is real analytic and \[ F(p)=F(q)\quad\Longrightarrow\quad R(p)=R(q), \] then \(R\) satisfies a Hölder stability estimate on every compact subset of \(U\). The proof uses a Hilbert--Schmidt scalarization of the operator equation \(F(p)=F(q)\) and the Łojasiewicz distance inequality. We also prove that, after fixing countable dense families of boundary inputs and tests, finitely many scalar matrix elements of the data give the same Hölder recovery on compact parameter sets. This finite-measurement conclusion is qualitative: the proof does not give an effective measurement list, exponent, or constant. The finite-measurement statement follows from finite determinacy of real analytic zero sets. We apply the result to local Neumann-to-Dirichlet data for piecewise constant anisotropic conductivities and to localized Dirichlet-to-Neumann data for piecewise homogeneous anisotropic elasticity.

Automatic sign language recognition (SLR) has become a key enabler of inclusive human-computer interaction, fostering seamless communication between deaf individuals and hearing communities. Despite significant advances in multimodal learning, existing SLR research remains dominated by vision-based datasets, which are limited by sensitivity to lighting and occlusion, privacy concerns, and a lack of cross-modal diversity. To address these challenges, we introduce SIGMA-ASL, a large-scale multimodal dataset for SLR. The dataset integrates an Azure Kinect RGB-D camera, a millimeter-wave (mmWave) radar, and two wrist-worn inertial measurement units (IMUs) to capture complementary visual, radio-reflection, and kinematic information. Collected in a controlled studio environment with 20 participants performing 160 common American sign language (ASL) signs, SIGMA-ASL provides 93,545 temporally synchronized word-level multimodal clips. A unified sensing framework achieves millisecond-level alignment across modalities, enabling reliable sensor fusion and cross-modal learning. We further design standardized preprocessing pipelines and benchmarking protocols under both user-dependent and user-independent settings, offering a comprehensive foundation for evaluating single and multimodal SLR. Extensive experiments validate the dataset's quality and demonstrate its potential as a valuable resource for developing robust, privacy-preserving, and ubiquitous sign language recognition systems.

We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation values as a learning problem in a reproducing kernel Hilbert space, in which the conditional expectation is represented as a linear operator acting on future payoffs. This perspective yields an offline-online decomposition: the operator is learned once from simulated data and subsequently reused across all exercise dates, eliminating the need to recompute regression models at each step of the backward recursion. We establish convergence guarantees and derive bounds quantifying the approximation errors across exercise dates. Numerical experiments demonstrate the speed and accuracy of the proposed approach relative to extant methods.

Strain has emerged as a promising approach for tuning electrocatalytic properties, yet its role in sputter-deposited thin films remains poorly understood. In this work, magnetron-sputtered platinum (Pt) thin films with different stress states were prepared by varying the sputter pressure. The resulting changes in microstructure, residual strain, and hydrogen evolution reaction (HER) activity were investigated using complementary characterization techniques and density functional theory (DFT) calculations. Structural analysis reveals a transition of (111)-textured Pt thin films from dense and smooth films at low pressures, to more porous microstructures with increased roughness at higher pressures. Electrochemical measurements show that films deposited at low sputter pressure exhibit the highest HER activity, while higher sputter pressures lead to reduced activity despite increased surface area. DFT calculations demonstrate that lattice strain alters hydrogen adsorption energetics and surface coverage on Pt(111), providing a mechanistic explanation for the observed activity trends. Overall, the results highlight that HER activity in sputtered Pt thin films is governed by the interplay of residual strain, microstructure, and hydrogen coverage.

The strong correlation between energy injection and mid-infrared (mid-IR) emission observed during solar flares can be used to probe energy deposition throughout the chromosphere, since the IR tracks prompt flare-induced changes in electron density. Despite its diagnostic value, solar mid-IR observations are relatively recent, with sporadic campaigns over the last decade resulting in only a few recorded flares. Earlier studies found time lags between mid-IR emissions from spatially resolved footpoints, offering clues about flare energy transport. Building on this, we analyse the time lags between emissions at two wavelengths (5.2 micrometers and 8.2 micrometers) for each footpoint. Using a local cross-correlation function, we show for the first time that the 8.2 micrometers emission channel peaks 0.3 s-0.45 s before the 5.2 micrometer channel. We investigate the origin of this lag, obtaining infrared emission estimates using results from the RADYN radiation hydrodynamics code. The theoretical lag values fall within the range of the observed ones. Variations in opacity-primarily due to flare-induced ionization-explain the wavelength-dependent temporal shift between emission maxima. In particular, longer wavelengths exhibit a smaller lag between the peak of energy injection and peak of intensity. These results contribute to a better understanding of how energy deposition during a flare affects the chromospheric layers of the atmosphere. Future observations with higher temporal resolution could exploit measurements of these time lags to more fully characterize the dynamics of energy deposition during solar flares, opening a new avenue for studying heating and energy transport processes in the solar atmosphere.

In this paper, we present a lightweight, embedded algorithm for autonomous edge event triggering in IoT sensor nodes suitable for operating in mesh networks. The device acquires local sensor data, performs deterministic FFT spectral feature extraction in firmware, and maintains a temporal spectral noise-floor baseline that absorbs non-stationary environmental excitations such as rain, wind, and mechanical vibration. While adaptive thresholds in IoT sensor nodes are often applied to manage communication load or stabilize long-term metrics, this work focuses on maintaining a time-evolving spectral noise floor to preserve event trigger reliability in dynamic environments. Our method targets trigger integrity under environmental non-stationary conditions, enabling calibration-free deployment of autonomous nodes; without shared noise models or cloud-side inference. Local decision authority preserves node responsiveness when connectivity is intermittent and mitigates security risks inherent in centralized remote-analysis systems. We validate the algorithm in a single node mesh sensor deployed in a dynamic outdoor environment using a radar-class proximity sensor as one example sensor modality. Results demonstrate substantial suppression of nuisance-induced triggers, reduced false-event traffic amplification in the mesh, bounded embedded execution, and reliable detection sensitivity to true spectral signatures.

Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint estimation of both the image and the forward model parameters. Standard approaches that assume a known linear forward operator fail to account for these uncertainties, resulting in significant reconstruction artifacts. We propose a nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. The method extends MM-GKS to nonlinear settings by combining majorization-minimization for nonsmooth regularization with Krylov subspace projection and subspace recycling, ensuring bounded memory usage. Two complementary formulations are developed: an alternating minimization approach that alternates between image updates and Gauss-Newton parameter estimation, and a variable projection approach that eliminates the image variable and optimizes directly over the parameters using inexact inner solves. We further introduce streaming variants that process data sequentially, enabling reconstruction from large or dynamically acquired datasets without storing the full operator. For dynamic problems, we incorporate two temporal regularization strategies -- optical flow and anisotropic total variation -- as plug-in choices within the framework. We carry out rigorous numerical experiments in fan-beam computed tomography and photoacoustic tomography to demonstrate that our proposed framework achieves high-quality reconstructions with bounded memory requirements, making it suitable for large-scale dynamic imaging problems.

Generative recommendation (GR) models generate items by autoregressively producing a sequence of discrete tokens that jointly index the target item. However, this autoregressive generation process also induces a structured decoding space whose impact on model expressiveness remains underexplored. Specifically, token-by-token generation can be viewed as traversing a decoding tree induced by semantic ID tokens, where leaf nodes correspond to candidate items. We observe that the item probabilities produced by GR models are strongly correlated with this tree structure: items that are close in the tree tend to receive similar probabilities for any given user, making it difficult to distinguish among them based on user-specific preferences. We further show theoretically that such structural correlations prevent GR models from representing even simple patterns that can be well captured by conventional collaborative filtering models. To mitigate this issue, we propose Latte, a simple modification that injects a latent token before each semantic ID, reshaping the decoding space from a single tree into multiple latent-token-conditioned trees. This design creates multiple paths with varying tree distances between items, relaxing tree-induced probability coupling and yielding an average of 3.45% relative improvement on NDCG@10. Our code is available at https://github.com/hyp1231/Latte.

We present a cut finite element method (CutFEM) for the Laplace--Beltrami equation on a smooth closed curve $Γ\subset\mathbb{R}^2$ coupled to a harmonic bulk problem in $Ω$ that requires \emph{no explicit stabilization}: no ghost penalty, normal-gradient penalty, or cell agglomeration. The classical ill-conditioning of trace finite element spaces on cut cells arises from basis functions with vanishingly small support on $Γ$; our observation is that coupling the surface discretization to a discrete bulk harmonic extension, realized through the lattice Green's function (LGF) on the background Cartesian grid, rigidly constrains the degrees of freedom responsible for this ill-conditioning. The reduced operator, obtained by a congruence transform of the full CutFEM stiffness, inherits symmetry and positive semi-definiteness from the variational form and has a condition number bounded uniformly in the smallest cut-cell ratio. The direct reconstruction has the standard $O(h^{-2})$ mesh conditioning; the single-layer density formulation acts as operator preconditioner and yields $O(1)$ conditioning, which is amenable to iterative solvers; the double-layer density formulation remains cut-independent with $O(h^{-2})$ scaling. We prove optimal $O(h)$/$O(h^2)$ error estimates in $H^1(Γ)$/$L^2(Γ)$ under standard regularity assumptions, establish the cut-independent conditioning rigorously, and demonstrate both the optimal convergence rate and robustness with respect to small cuts in numerical experiments.

Distributed optimization over time-varying directed graphs has shown promising performance in addressing challenges posed by complex communication constraints in real-world scenarios. In many practical settings, however, the direct application of distributed optimization algorithms encounters additional difficulties, most notably hyperparameter tuning, which our empirical observations suggest can be effectively mitigated by integrating bilevel optimization. Motivated by these findings, we study distributed bilevel optimization over time-varying directed networks, a problem that remains largely unexplored due to the compounded challenges arising from consensus bias in dynamic unbalanced communication and the nested optimization structure. In this work, we propose a fully first-order distributed gradient-based algorithm that integrates the Push-Pull (also known as AB) communication strategy with a value function-based penalty method and establish its non-asymptotic convergence properties. Notably, a simplified variant of our analysis framework for nonconvex single-level distributed optimization establishes a convergence rate for the Push-Pull algorithm, thereby resolving an open question concerning its convergence over time-varying directed graphs. Empirical evaluations across diverse tasks, including hyperparameter tuning, data hyper-cleaning, and reinforcement learning, validate the effectiveness and efficiency of the proposed algorithm.

In pursuit of higher energy efficiency in computer networks, one subfield of green traffic engineering aims at reducing the size of a network during times of low traffic, while still guaranteeing the ability to route all occurring demands. In this setting, we have to simultaneously solve a network design problem (choosing connections to deactivate) and a routing problem (routing paths in the active subnetwork, adhering to some routing protocol). Interestingly, there seems to be no available method to tackle the problem as a whole for the simplest (and still most commonly used) routing paradigm: shortest path routing. State-of-the-art methods either do not consider capacities, or assume that the routing paths should not change when deactivating network connections, or separate the problem into its two constituents, first solving the network design problem (using some estimators in lieu of the precise routing protocol) and only then the actual routing problem. In this paper, we present an algorithm to tackle the full combined problem exactly via a novel integer linear program, modeling dynamically changing shortest paths. To solve it, we need to devise a special-purpose column generation method. To speed up the solution process, we further propose additional provably strengthening constraints. Now having the means to yield true optimal solutions for (small) practical instances, we can for the first time give an in-depth experimental evaluation that includes the absolute quality intrinsic to the above simplifying algorithms. It turns out that the arguably simplest method--first computing a routing, fixing it, and turning off all superfluous connections--yields solutions surprisingly close to the true optimum in practice. When considering multiple different traffic demands, a recent traffic-oblivious approach (TOCA) performs best, while being comparatively straightforward to implement.

We present a photometric and spectroscopic analysis of the fast-declining Type II SN 2020aze, observed in optical bands from 2.2 to 137.4 days after explosion. The V-band light curve reaches a peak absolute magnitude of about minus 16.97$\pm$0.20 mag by 15 days, followed by a recombination phase with a decline rate of 2.04$\pm$0.13 mag per 100 days, lasting about 120 days. Early spectra (younger than 6 days) show a transient weak narrow emission line at 4687 Angstroms and a feature spanning 4400-4800 Angstroms, attributed to narrow and broad blue-shifted He II 4686, indicating interaction between the ejecta and dense circumstellar material. Comparison with spectral models suggests a red supergiant progenitor with a weak wind and a mass-loss rate of about 1e-3 solar masses per year. Semi-analytical light-curve modeling gives an initial radius of about 1100 solar radii, an ejecta mass of about 12 solar masses, an explosion energy of about 1.5e51 erg, and a progenitor mass of about 14 solar masses. These early interaction signatures, the steep decline, and the extended photospheric phase highlight the role of pre-supernova mass loss and circumstellar interaction in shaping the diversity of Type II supernovae.

We develop a general analytical framework for determining the probability distribution of random nonlinear wave fields governed by the focusing nonlinear Schrödinger equation (fNLSE) in regimes where typical realizations are dominated by solitons. We formulate the soliton gas resolution conjecture for the long-time evolution of slowly varying ("semiclassical") random initial states and implement a stochastic analogue of the inverse scattering transform by establishing a relationship between the spectral density of states of the underlying bound-state soliton gas and the probability density function (PDF) of the intensity of the resulting turbulent wave field. The derived explicit integral representation for the PDF is shown to be in excellent agreement with direct numerical simulations across several representative regimes of fNLSE integrable turbulence. The results have broad applicability to physical systems including water waves, nonlinear optics, and superfluids.