The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and fast irrelevant variables, but such a separation of scales is not always obvious or even available. In this work, we introduce an information-theoretic framework for dimensionality reduction in dynamical systems that bypasses this limitation by instead identifying relevant variables based on how predictive they are of the system's future. To do so, we mathematically formalize the intuition that model reduction is about keeping "relevant" information while throwing away "irrelevant" information. We characterize the solution of the resulting optimization problem and prove that it reduces to standard approaches when a separation of time scales is indeed present in the dynamics. Importantly, we find that within this framework, the problems of identifying relevant variables and identifying their effective dynamics decouple and may be solved separately. This makes the method tractable in practice and enables us to derive dimensionally-reduced variables from data with neural networks. Combined with existing equation learning methods, the procedure introduced in this work reveals the dynamical rules governing the system's evolution in a data-driven manner. We illustrate these tools in diverse settings including simulated chaotic systems, uncurated satellite recordings of atmospheric fluid flows, and experimental videos of cyanobacteria colonies in which we discover an emergent synchronization order parameter.

Many multi-agent scenarios require message sharing among agents to promote coordination, hastening the robustness of multi-agent communication when policies are deployed in a message perturbation environment. Major relevant works tackle this issue under specific assumptions, like a limited number of message channels would sustain perturbations, limiting the efficiency in complex scenarios. In this paper, we take a further step addressing this issue by learning a robust multi-agent communication policy via multi-view message certification, dubbed CroMAC. Agents trained under CroMAC can obtain guaranteed lower bounds on state-action values to identify and choose the optimal action under a worst-case deviation when the received messages are perturbed. Concretely, we first model multi-agent communication as a multi-view problem, where every message stands for a view of the state. Then we extract a certificated joint message representation by a multi-view variational autoencoder (MVAE) that uses a product-of-experts inference network. For the optimization phase, we do perturbations in the latent space of the state for a certificate guarantee. Then the learned joint message representation is used to approximate the certificated state representation during training. Extensive experiments in several cooperative multi-agent benchmarks validate the effectiveness of the proposed CroMAC.

Head motion is an omnipresent confounder of magnetic resonance image (MRI) analyses as it systematically affects morphometric measurements, even when visual quality control is performed. In order to estimate subtle head motion, that remains undetected by experts, we introduce a deep learning method to predict in-scanner head motion directly from T1-weighted (T1w), T2-weighted (T2w) and fluid-attenuated inversion recovery (FLAIR) images using motion estimates from an in-scanner depth camera as ground truth. Since we work with data from compliant healthy participants of the Rhineland Study, head motion and resulting imaging artifacts are less prevalent than in most clinical cohorts and more difficult to detect. Our method demonstrates improved performance compared to state-of-the-art motion estimation methods and can quantify drift and respiration movement independently. Finally, on unseen data, our predictions preserve the known, significant correlation with age.

JWST is transforming our ability to characterise small exoplanets, from sub-Neptunes to rocky worlds. A key open question is whether highly irradiated rocky planets can retain atmospheres or are stripped bare by stellar irradiation -- a boundary that remains to be mapped observationally. Here we present the first JWST secondary eclipse observations of the rocky exoplanet GJ 3473 b, obtained with MIRI F1500W photometry. Using four visits, we confidently detect the eclipse at an average depth of 186$\pm$45 ppm, somewhat lower than expected for a blackbody. We test a wide range of data reduction and analysis assumptions and provide new insights into MIRI detector settling behaviour that will benefit future observations. We model a suite of airless surfaces with varied compositions, textures, and degrees of space weathering, as well as idealised atmospheric scenarios including the possibility of atmospheric collapse. Both atmospheric and bare-rock interpretations remain consistent with the data, but we exclude thick CO$_2$ atmospheres, placing a 95 % credible upper limit of 1.2-6.5 bar on the surface pressure. We also find tentative evidence for visit-to-visit variability in eclipse depth (33-371 ppm), though additional data are required to confirm this. Our results highlight the challenges and intrinsic degeneracies in interpreting MIRI F1500W eclipse measurements of rocky exoplanets, indicating that such observations alone may not uniquely distinguish between bare-rock and atmospheric scenarios. Future spectroscopic or phase-curve observations will be required to determine whether or not GJ 3473 b hosts a substantial atmosphere

Barium titanate-based perovskites are important candidates for lead-free dielectric and electromechanical technologies. In Zr-substituted BaTiO$_3$ (BZT), functional behavior is usually discussed in terms of the average Zr concentration, while the influence of dopant spatial distribution beyond average concentration is less understood and difficult to explore systematically. Here we present an accelerated materials-design workflow that links controlled dopant distributions to full field-driven response curves. We generate a broad set of Zr distributions spanning a continuum of nanoscale arrangements, with layers, rods, dots, and lamellae serving as representative end-member motifs, and encode each configuration using a compact, parametrized descriptor model. Effective-Hamiltonian molecular dynamics is used to compute polarization-electric-field and strain-field hysteresis loops, and we train a conditional autoencoder surrogate to predict complete loops directly from the distribution parameters. This surrogate enables rapid screening and dense, property-selective design maps at scales that are not feasible with direct simulations alone, and it supports targeted follow-up simulations in regions of interest. Using the predicted loop database, we screen the distribution space for multiple functional targets, including energy-storage performance, electromechanical response, and switching behavior, and identify the corresponding dopant distribution motif families. The resulting design maps show that dopant distribution is an independent tuning parameter that can strongly affect hysteresis behavior and loop-derived figures of merit: layer-like motifs, vertical lamellae, and nanoplate-like inclusions emerge in different performance regimes. More generally, predicting full response curves enables screening of other loop-derived targets and multi-objective design in substituted ferroelectrics.

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.

We construct connected $2$-arc-transitive covers of complete graphs with non-abelian characteristically simple transformation groups. This solves the existence problem for non-solvable $2$-arc-transitive covers of complete graphs.

Single-photon sources with high single-photon purity and high brightness are key elements of many future quantum technologies. While photon blockade (PB) is widely exploited in the development of such sources, achieving the coexistence of high purity and high brightness remains a long-standing challenge. Here, we identify a novel mechanism for high-brightness PB and demonstrate that near-ideal purity and near-ideal brightness can be simultaneously achieved in an extended nondegenerate two-photon Jaynes-Cummings model with two-body and three-body interactions. This mechanism is underpinned by a distinctive energy-level structure arising from the combined action of the two interactions. The energy levels in the multi-excitation manifold essentially retain a harmonic ladder of degenerate doublets, whereas in the single-excitation subspace the doublet degeneracy is lifted, with a finite splitting between the two levels. Consequently, when one bosonic mode is driven by a coherent continuous-wave pump, the former degeneracy enables the other bosonic mode to exhibit near-perfect PB even in the strong driving regime, while the latter splitting allows the mean photon number of that mode to approach unity. Our proposed scheme overcomes the outstanding challenge and offers a promising pathway toward realizing ideal single-photon sources.

We study the Schrödinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by $β>0$, whose limiting regimes interpolate between the classical Schrödinger bridge, the Brenier-Strassen problem, and, after rescaling, the martingale Benamou-Brenier (Bass) problem. Our first main result is a static formulation. For each $β>0$, we prove that the dynamic Schrödinger-Bass problem is equivalent to a static weak optimal transport (WOT) problem with explicit cost $C_{\mathrm{SB}}^β$. This yields primal and dual attainment, as well as a structural characterization of the optimal semimartingales, through the general WOT framework. The cost $C_{\mathrm{SB}}^β$ is constructed via an infimal convolution and deconvolution of the Schrödinger cost with the Wasserstein distance. In a broader setting, we show that such infimal convolutions preserve the WOT structure and inherit continuity, coercivity, and stability of both values and optimizers with respect to the marginals. Building on this formulation, we propose a Sinkhorn-type algorithm for numerical computation. We establish monotone improvement of the dual objective and, under suitable integrability assumptions on the marginals, convergence of the iteration to the unique optimizer. We then study the asymptotic regimes $β\uparrow\infty$ and $β\downarrow0$. We prove that the costs $C_{\mathrm{SB}}^β$ converge pointwise to the Schrödinger cost and, after natural rescaling, to the Brenier-Strassen and Bass costs. The associated values and optimal solutions are shown to converge to those of the corresponding limiting problems.

Eclipsing pulsar binaries and binaries with a high mass companion are ideal systems for studying and understanding the properties of plasma in magneto-ionic environments. In this work, the first paper of a series, we present MeerKAT observations of three pulsar binaries: the high-mass binary PSR J1740$-$3052, the black widow PSR J2051$-$0827 and the redback PSR J1748$-$2446A (Terzan~5A). With the help of MeerKAT's high-sensitivity polarimetric observations, we characterise the properties of these sources, including the linear/circular polarization, dispersion measure (DM), rotation measure (RM) and scattering time. The two eclipsing millisecond pulsars exhibit strong orbital-phase-dependent propagation effects and we observe $\sim$2 eclipses in these systems during our observations. PSR J1740$-$3052 is a binary system with a 231 d orbital period. The relatively large separation results in a smooth RM variation, enabling us to resolve its variation timescale and constrain the small-scale magnetic structure. A gradual RM variation is observed over $\sim$1500 s, occurring near periastron. This behaviour implies a magnetic spatial scale of $\sim$0.003 AU in the companion wind, assuming a relative velocity of $\sim$250 km s$^{-1}$. The linear polarisation intensity profiles of PSR J2051$-$0827 show shape variations as a function of frequency, with a stronger leading component emerging at lower frequencies. We observe signatures of the propagation effect in the polarisation properties of PSR J1748$-$2446A during eclipse ingress and egress. This could arise from Faraday Conversion or multipath propagation of the pulsar signal and requires detailed analysis.

We combine Patankar-type methods with suitable relaxation procedures that are capable of ensuring correct dissipation or conservation of functionals such as entropy or energy while producing unconditionally positive and conservative approximations. To that end, we adapt the relaxation algorithm to enforce positivity by using either ideas from the dense output framework when a linear invariant must be preserved, or simply a geometric mean if the only constraint is positivity preservation. The latter merely requires the solution of a scalar nonlinear equation while former results in a coupled linear-nonlinear system of equations. We present sufficient conditions for the solvability of the respective equations. Several applications in the context of ordinary and partial differential equations are presented, and the theoretical findings are validated numerically.

Symmetry and entanglement are two fundamental concepts in quantum many-body physics. Their interplay is captured by symmetry-resolved entanglement, which decomposes the total entanglement into contributions from different symmetry sectors. Computing symmetry-resolved entanglement in strongly interacting higher-dimensional quantum systems remains challenging. Here, we introduce a quantum Monte Carlo (QMC) approach for computing symmetry-resolved Rényi entropies (SRRE) in large-scale interacting systems by measuring disorder (symmetry-twisted) operators on replica manifolds and reconstructing SRRE from the corresponding charged moments. We apply this method to the transverse-field Ising model (TFIM) in one and two dimensions. In one dimension, we recover the conformal-field-theory prediction for the logarithmic scaling of the disorder operator and observe the expected approach to entanglement equipartition. In two dimensions, our data provide numerical evidence consistent with entanglement equipartition at the (2+1)D Ising critical point. We further apply the framework to the 1D Heisenberg chain and obtain results consistent with the expected asymptotic scaling and finite-size corrections in the U(1)-resolved sectors. Our work establishes a practical numerical route to symmetry-resolved entanglement in interacting lattice models and provides a useful framework for future studies beyond one dimension.

In 1977 Montgomery and Vaughan gave tight bounds for exponential sums of the form $\sum_{n\leq x}f(n)e(nα)$ where $f$ is a $1$-bounded multiplicative function and $α\in\mathbb R$, close to the conjectured $\ll \frac{x}{\sqrt{q}}+ \frac{x}{\log x}$ where $α$ is best approximated by $|α-a/q|\leq 1/(qx)$, showing their results to be ``best-possible'' by observing that the first part of their bound is more-or-less attained when $f(n)=χ(n), α=\frac aq$ where $χ$ is a primitive character mod $q$, and the second part when $f(p)=e(-αp)$ for all large primes $p$. La Bretèche and Granville proved that when $α$ lies on a major arc the exponential sum is significantly smaller unless $f$ ``pretends to be'' $χ(n)n^{it}$ for some character $χ$ and real number $|t|<\log x$; and herein we prove that when $α$ lies on a minor arc, the exponential sum is significantly smaller unless $f(p)$ pretends to be $e(-hpα)$ for primes $p\leq x$ for some bounded integer $h$. We also study exponential sums $\sum_{n\leq x, P^+(n)\leq y} f(n) e(nα)$ restricted to $y$-smooth (or $y$-friable) integers $n$. We conjecture that this sum is $\ll \frac{Ψ(x, y)}{\sqrt{q}}+ \frac{\sqrt{xy}}{\log x} $ in a wide range of parameters, show that if true this is best possible, and prove an upper bound in a wide range that is only slightly weaker than the conjecture. Finally we study the logarithmically weighted exponential sums $\sum_{n\leq x} \frac{f(n)}{n} e(nα)$. We conjecture that this sum is $\ll \frac{\log x}{\sqrt{q}}+\log q$ in a wide range of parameters, show that if true this is best possible, and prove an upper bound in a wide range that is only slightly weaker than the conjecture. Along the way, we will prove various technical results about multiplicative functions which may be of use elsewhere.

On rank one Riemannian symmetric spaces of compact type (of dimension $\ge 2$), we first obtain a quantitative characterization of Hölder continuity in terms of Cesàro means. In addition to some approximation theoretic applications, we also apply it to study the celebrated physical phenomenon known as `Talbot effect' arising from diffraction theory. More precisely, for almost every fixed time instance, we study the Hölder continuity and the fractal profile of the Schrödinger propagation in terms of the decay of the Littlewood-Paley projections of the initial data. In the process, we also obtain oscillatory expansions of zonal spherical functions uniformly near the origin and near the cut locus respectively, which may be of independent interest.

We propose a structured prior for high-dimensional Bayesian inverse problems based on a disentangled deep generative model whose latent space is partitioned into auxiliary variables aligned with known and interpretable physical parameters and residual variables capturing remaining unknown variability. This yields a hierarchical prior in which interpretable coordinates carry domain-relevant uncertainty while the residual coordinates retain the flexibility of deep generative models. By linearizing the generator, we characterize the induced prior covariance and derive conditions under which the posterior exhibits approximate block-diagonal structure in the latent variables, clarifying when representation-level disentanglement translates into a separation of uncertainty in the inverse problem. We formulate the resulting latent-space inverse problem and solve it using MAP estimation and Markov chain Monte Carlo (MCMC) sampling. On elliptic PDE inverse problems, such as conductivity identification and source identification, the approach matches an oracle Gaussian process prior under correct specification and provides substantial improvement under prior misspecification, while recovering interpretable physical parameters and producing spatially calibrated uncertainty estimates.

A Boolean network (BN) is a transformation of the set of Boolean configurations of a given length. A trapspace of a BN is a subcube invariant by the BN; a principal trapspace is the smallest trapspace containing a given configuration; a minimal trapspace is one that does not contain any smaller trapspace. In an unrelated development, commutative BNs have been introduced as those networks where all local updates commute. In this paper, we relate those two aspects of BN theory via five main contributions. First, we introduce the trapping graph and the trapping closure of a BN. We also define trapping networks as the networks with transitive general asynchronous graphs and we prove that those are exactly the trapping closures. Second, we show that two BNs have the same collection of (principal) trapspaces if and only if they have the same trapping closure. We then characterise the collections of (principal) trapspaces of BNs. We finally give analogous results for the collections of minimal trapspaces. Third, we prove that commutative networks are trapping, and we classify the collections of principal trapspaces of commutative networks. Fourth, we focus on bijective commutative networks, which we call Marseille networks. We provide several alternative definitions for Marseille networks, and we classify them as special commutative or trapping networks. Fifth, we focus on idempotent commutative networks, which we call Lille networks. We provide several alternative definitions for Lille networks, we classify them as special commutative or trapping networks, and we relate them to globally idempotent networks. Our investigations of Marseille and Lille networks also highlight relations amongst the asynchronous, general asynchronous, and trapping graphs of Boolean networks, as well as the structure of trapping networks in general.

Retractions serve as an indicator of failures in research integrity, yet most analyses focus on absolute counts rather than risk per paper. We use one of the largest open bibliographic databases to develop incidence metrics normalized by population: retractions per publication and per active author annually. Applying an epidemiological framework that models counts with exposure, we find evidence of exponential growth in retraction incidence, with approximately a 5-year doubling time at both the paper and author levels. These patterns vary significantly across fields, publishers, and countries. While scientific output is becoming more democratized globally, retractions are concentrated in fewer countries, creating a "concentration" paradox that calls for targeted monitoring. Despite exponential growth, the absolute incidence remains low (0.12% in 2021), allowing for corrective intervention. Incidence-based monitoring provides a framework for evaluating policies that safeguard research integrity at scale.

In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter $η$ limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of $η^4$. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as $η^6$. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as $10^{-4}$ for $20$-ion chains.

Cosmological constraints on neutrino mass offer a promising avenue for advancing our understanding of both fundamental particle physics and the evolution of cosmic large-scale structure. To overcome challenges associated with traditional probes of neutrino mass, particularly degeneracies with other parameters, we consider topological summaries of the cosmic web based on the formalism of persistent homology. We introduce persistence strips, a novel representation that segments Betti curves by topological persistence, effectively condensing two-dimensional persistence diagrams into a set of one-dimensional curves. Applied to the FLAMINGO suite of cosmological simulations, these topological descriptors demonstrate pronounced sensitivity to neutrino mass. By constructing an emulator spanning a 10-dimensional $w_0 w_a\text{CDM} +ν$ cosmological parameter space that includes parameters degenerate with neutrino masses in conventional approaches, assuming a volume of only $(350 \, \mathrm{Mpc})^3$, we obtain neutrino mass constraints with an uncertainty of $0.05 \, \mathrm{eV}$ for the total matter field and $0.13 \, \mathrm{eV}$ for the dark matter-only field, with the strongest constraints coming from void topology. Persistence strips exhibit roughly twice the constraining power of unbinned Betti curves and, through their multi-scale, environment-dependent sensitivity, systematically break degeneracies between neutrino mass and other cosmological parameters. We pinpoint the precise physical origin of the signal, identifying two equally important contributions: sensitivity to the neutrino mass fraction, which is highest in underdense regions, and the impact of neutrinos on the distribution of dark matter. Our findings highlight the particular promise of applying topological statistics to weak lensing measurements, which directly probe the total matter distribution.

Modern adversarial campaigns unfold as sequences of behavioural phases - Reconnaissance, Lateral Movement, Intrusion, and Exfiltration - each often indistinguishable from legitimate traffic when viewed in isolation. Existing intrusion detection systems (IDS) fail to capture this structure: signature-based methods cannot detect zero-day attacks, deep-learning models provide opaque anomaly scores without stage attribution, and standard Kalman Filters cannot model non-stationary multi-modal dynamics. We present PARD-SSM, a probabilistic framework that models network telemetry as a Regime-Dependent Switching Linear Dynamical System with K = 4 hidden regimes. A structured variational approximation reduces inference complexity from exponential to O(TK^2), enabling real-time detection on standard CPU hardware. An online EM algorithm adapts model parameters, while KL-divergence gating suppresses false positives. Evaluated on CICIDS2017 and UNSW-NB15, PARD-SSM achieves F1 scores of 98.2% and 97.1%, with latency less than 1.2 ms per flow. The model also produces predictive alerts approximately 8 minutes before attack onset, a capability absent in prior systems.

We show that chiral superconductivity can be stabilized by hole doping a Chern ferromagnet. Performing exact diagonalization and density-matrix-renormalization-group calculations on the repulsive Kane-Mele-Hubbard model at hole doping relative to filling $ν=1$ electron per unit cell, we find that a Cooper pair formed by a magnon (spin-flip excitation) bound to two holes is stabilized at sufficiently strong interactions and sufficiently large Ising spin-orbit coupling (SOC). This Cooper pair exhibits both finite spin chirality -- signaling a noncoplanar skyrmionic spin texture -- and chiral $f$-wave symmetry. The pairing and spin chirality are set by the Chern number/polarization of the parent Chern ferromagnet. We further find that interactions between skyrmion Cooper pairs evolve from repulsive to attractive as the Ising SOC increases, revealing an intermediate-SOC region where chiral superconductivity can emerge from the condensation of hole-skyrmion Cooper pairs. Our findings provide a novel microscopic mechanism for chiral superconductivity and may be relevant for the recent observation of superconductivity in the MoTe$_2$ moiré superlattice.

We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of commutators of the one-body operators associated with these equilibria and the position and momentum operators. We also obtain upper bounds in the magnetic field case for the Fock-Darwin Hamiltonian. Our estimates, in particular, allow us to observe several regimes depending on the joint behavior of the Planck constant, the temperature, and the strength of the magnetic field.

Models of gravity in warped extra dimensions enjoy invariance under diffeomorphism. We derive the nonlinear transformation rules for the metric perturbations in the unitary gauge. As an off-shell symmetry, the main consequence of diffeomorphism is a set of recursive relations linking consecutive orders in the field expansion of the effective Lagrangian. The physical consequences are briefly explored for the Randall-Sundrum model with hard branes.

This paper proposes Covariate-Balanced Weighted Stacked Difference-in-Differences (CBWSDID), a design-based extension of weighted stacked DID for settings in which untreated trends may be conditionally rather than unconditionally parallel. The estimator separates within-subexperiment design adjustment from across-subexperiment aggregation: matching or weighting improves treated-control comparability within each stacked subexperiment, while the corrective stacked weights of Wing et al. recover the target aggregate ATT. I show that the same logic extends from absorbing treatment to repeated $0 \to 1$ and $1 \to 0$ episodes under a finite-memory assumption. The paper develops the identifying framework, discusses inference, presents simulation evidence, and illustrates the estimator in applications based on Trounstine (2020) and Acemoglu et al. (2019). Across these examples, CBWSDID serves as a bridge between weighted stacked DID and design-based panel matching. The accompanying R package cbwsdid is available on GitHub.

The upcoming integration of AI in the physical layer (PHY) of 6G radio access networks (RAN) will enable a higher quality of service in challenging transmission scenarios. However, deeply optimized AI-Native PHY models impose higher computational complexity compared to conventional baseband, challenging deployment under the sub-msec real-time constraints typical of modern PHYs. Additionally, following the extension to terahertz carriers, the upcoming densification of 6G cell-sites further limits the power consumption of base stations, constraining the budget available for compute ($\leq$ 100W). The desired flexibility to ensure long term sustainability and the imperative energy-efficiency gains on the high-throughput tensor computations dominating AI-Native PHYs can be achieved by domain-specialization of many-core programmable baseband processors. Following the domain-specialization strategy, we present TensorPool, a cluster of 256 RISCV32IMAF programmable cores, accelerated by 16 256 MACs/cycle (FP16) tensor engines with low-latency access to 4MiB of L1 scratchpad for maximal data-reuse. Implemented in TSMC's N7, TensorPool achieves 3643~MACs/cycle (89% tensor-unit utilization) on tensor operations for AI-RAN, 6$\times$ more than a core-only cluster without tensor acceleration, while simultaneously improving GOPS/W/mm$^2$ efficiency by 9.1$\times$. Further, we show that 3D-stacking the computing blocks of TensorPool to better unfold the tensor engines to L1-memory routing provides 2.32$\times$ footprint improvement with no frequency degradation, compared to a 2D implementation.

We prove asymptotics for the average error term in Bateman-Horn's conjecture in the exponential range.

Microbial interaction networks can rewire in response to host and environmental factors, yet most existing methods for network estimation treat the covariance structure as static across samples. We propose TRECOR, a Bayesian covariance regression framework for inferring covariate-dependent microbial covariation networks from zero-inflated compositional count data. The method models microbiome counts through a latent multivariate normal distribution defined on the internal nodes of a phylogenetic tree, where both the mean and covariance of the latent variables depend on covariates. The covariance is decomposed into a sparse baseline component, representing a stable microbial covariation network, and a low-rank covariate-dependent perturbation that captures network rewiring. By exploiting the binomial factorization of the multinomial distribution under the logistic-tree-normal representation, the model achieves full conjugacy and posterior inference proceeds via an efficient Gibbs sampler. In simulations, TRECOR substantially outperforms covariance regression applied to transformed counts, demonstrating the importance of explicitly modeling the compositional sampling layer. Applied to gut microbiome data from 531 individuals across three countries, we find that age has the largest effect on microbial covariation, which is a pattern not revealed by mean-based analysis alone. The age-associated differential network is enriched for Enterobacteriaceae and related families, consistent with known developmental shifts in the gut microbiota, while country-associated differential networks implicate diet-related taxa.

While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted towards second-order stationary points (SOSPs). In unconstrained settings, finding approximate SOSPs is PLS-complete (Kontogiannis et al.), matching the complexity of finding unconstrained FOSPs (Hollender and Zampetakis). However, the complexity of finding SOSPs in constrained settings remained notoriously unclear and was highlighted as an important open question by both aforementioned works. Under one strict definition, even verifying whether a point is an approximate SOSP is NP-hard (Murty and Kabadi). Under another widely adopted, relaxed definition where non-negative curvature is required only along the null space of the active constraints, the problem lies in TFNP, and algorithms with O(poly(1/epsilon)) running times have been proposed (Lu et al.). In this work, we settle the complexity of constrained SOSP by proving that computing an epsilon-approximate SOSP under the tractable definition is PLS-complete. We demonstrate that our result holds even in the 2D unit square [0,1]^2, and remarkably, even when stationary points are isolated at a distance of Omega(1) from the domain's boundary. Our result establishes a fundamental barrier: unless PLS is a subset of PPAD (implying PLS = CLS), no deterministic, iterative algorithm with an efficient, continuous update rule can exist for finding approximate SOSPs. This contrasts with the constrained first-order counterpart, for which Fearnley et al. showed that finding an approximate KKT point is CLS-complete. Finally, our result yields the first problem defined in a compact domain to be shown PLS-complete beyond the canonical Real-LocalOpt (Daskalakis and Papadimitriou)."

The Metaverse faces complex resource allocation challenges due to diverse Virtual Environments (VEs), Digital Twins (DTs), dynamic user demands, and strict immersion needs. This paper introduces CIVIC (Cooperative Immersion Via Intelligent Credit-sharing), a novel framework optimizing resource sharing among multiple Metaverse Service Providers (MSPs) to enhance user immersion. Unlike existing methods, CIVIC integrates VE rendering, DT synchronization, credit sharing, and immersion-aware provisioning within a cooperative multi-MSP model. The resource allocation problem is formulated as two NP-hard challenges: a non-cooperative setting where MSPs operate independently and a cooperative setting utilizing a General Credit Pool (GCP) for dynamic resource sharing. Using Deep Reinforcement Learning (DRL) for tuning resources and managing cooperating MSPs, CIVIC achieves 12-36% higher request completion, 23-70% higher fulfillment rates, 20-60% more served clients, and up to 51% more fairly distributed requests, all with competitive costs. Extensive experiments demonstrate CIVIC's resilience, adaptability, and robust performance under dynamic load conditions and unexpected demand surges, making it suitable for real-world distributed Metaverse infrastructures.

Solar Radiation Modification (SRM) may be the only way to limit global warming in the coming decades, leading to increased interest in the subject and to the expansion of related research & development (R&D) activity. Defining the safety and controllability requirements that any SRM system should meet is crucial for directing R&D activities and enabling governments to make informed decisions on the development and possible implementation of such systems. We present an initial proposal for this set of requirements, which also guides Stardust's R&D, as a basis for further discussion and consideration. While we focus on SRM systems based on Stratospheric Aerosol Injection (SAI), the proposed principles may be applicable more broadly.