The $n\times n$ doubly stochastic matrices constitute a polytope in $\mathbb{R}^{n^2}$, and by Birkhoff's theorem, its vertex set coincides with the set of order-$n$ permutation matrices.\\ A tristochastic array is an $n \times n\times n$ array of nonnegative reals, where each row, column, and shaft sums to one. These arrays constitute a polytope $Δ_n$ in $\mathbb{R}^{n^3}$. In analogy, it is easy to see that each of the $L_n$ order-$n$ Latin squares is a vertex of $Δ_n$, but in contrast to Birkhoff's theorem, Latin squares form a vanishingly small subset of $Δ_n$'s vertex set. We show here that $Δ_n$ has at least $L_n^{2-o(1)}$ vertices.

The dinuclear system model incorporates several essential input physical quantities, including nuclear mass, fission barrier, shell correction energy, level density parameter, and shell damping factor, etc., which are derived from diverse nuclear structure models. To achieve theoretical consistency, we try to generate these essential input physical quantities from the finite-temperature covariant density functional theory using PC-PK1 energy density functional, with pairing correlations treated via the BCS approach. With microscopically determined input parameters, the dinuclear system model can successfully reproduce experimental results for: (i) cold fusion reaction systems ($^{48}$Ca + $^{204,206-208}$Pb $\rightarrow$ $^{252,254-256}$No$^*$), and (ii) hot fusion reaction systems ($^{48}$Ca + $^{239,240,242,244}$Pu $\rightarrow$ $^{287,288,290,292}$Fl$^*$). Furthermore, we perform calculations for the fusion reactions $^{50}$Ti+$^{249}$Cf, $^{51}$V+$^{249}$Bk, $^{54}$Cr+$^{248}$Cm, and $^{55}$Mn+$^{243}$Am, targeting the synthesis of element 120. It is found that the maximum synthesis cross section for these four reactions are 48.20 fb, 12.33 fb, 5.25 fb, 0.47 fb corresponding to $^{50}$Ti($^{249}$Cf,4n)$^{295}$120 at $E^*_{\rm CN}$ = 41 MeV, $^{51}$V($^{249}$Bk,3n)$^{297}$120 at $E^*_{\rm CN}$ = 34 MeV, $^{54}$Cr($^{248}$Cm,3n)$^{299}$120 at $E^*_{\rm CN}$ = 32 MeV, $^{55}$Mn($^{243}$Am,5n)$^{293}$120 at $E^*_{\rm CN}$ = 53 MeV, respectively.

We propose an adaptive MCMC method that learns a linear preconditioner which is dense in its off-diagonal elements but sparse in its parametrisation. Due to this sparsity, we achieve a per-iteration computational complexity of $O(m^2d)$ for a user-determined parameter $m$, compared with the $O(d^2)$ complexity of existing adaptive strategies that can capture correlation information from the target. Diagonal preconditioning has an $O(d)$ per-iteration complexity, but is known to fail in the case that the target distribution is highly correlated, see \citet[Section 3.5]{hird2025a}. Our preconditioner is constructed using eigeninformation from the target covariance which we infer using online principal components analysis on the MCMC chain. It is composed of a diagonal matrix and a product of carefully chosen reflection matrices. On various numerical tests we show that it outperforms diagonal preconditioning in terms of absolute performance, and that it outperforms traditional dense preconditioning and multiple diagonal plus low-rank alternatives in terms of time-normalised performance.

We develop a systematic classification of asymmetric $\mathbb{Z}_2$ orbifold actions in Pati--Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifold vacua with an $SO(10)$ GUT, we allow the Pati--Salam breaking vector to act asymmetrically on the internal degrees of freedom. The asymmetric orbifold action freezes geometrical moduli whilst inducing doublet--triplet splitting in the untwisted sector. Notably, this doublet--triplet splitting operates for any asymmetric action, including pure asymmetric shifts that preserve all geometric moduli, and is therefore independent of moduli stabilisation. Classifying the breaking vector according to its twist action, we find six inequivalent classes of geometric moduli spaces characterised by 12, 8, 4 or 0 real untwisted moduli. Through combining these asymmetric twists with all compatible asymmetric shifts, 24 inequivalent cases are identified and characterised by their residual moduli content and internal Narain lattice. For each case we construct representative basis sets admitting three chiral generations, providing the starting point for further classification within each class. We perform explicit GGSO phase enumerations in representative model classes with 12, 8, 4 and 0 moduli, classify the resulting $\mathcal{N} = 1$ and $\mathcal{N} = 0$ vacua according to phenomenological criteria and identify exophobic, phenomenologically viable models. We compute the partition function and corresponding one-loop vacuum energy at the free fermionic point in moduli space for each phenomenologically viable model across the four classes. As the number of geometrical moduli decreases, the number of distinct partition functions for these vacua collapses to a small number, reflecting a pronounced degeneracy under GGSO phase variations.

We introduce a CUDA-Accelerated Timestepper for Alpha Particles Using Local Tricubics (CATAPULT) for use in Monte Carlo calculations of alpha particle confinement in stellarators. Our GPU implementation is significantly faster than existing parallelized CPU implementations, and handles both equilibrium magnetic fields and Shear Alfven Waves. We test our implementation on several example stellarators to exhibit both the speed and correctness of our code. The source code is included in the firm3d Python package.

Conservative dynamics are typically computed as floating-point approximations to continuum differential operators, which can obscure conservation through rounding and discretisation artefacts. Here we instead formulate conservative evolution directly as quantised interaction rules acting on countable states. The resulting Fast Quantised Numerical Method (FQNM) executes dynamics through antisymmetric integer transfer, with physical fields appearing only after reconstruction. In high-frequency transport, the method remains accurate deep into the Nyquist regime where a standard high-order floating-point baseline deteriorates. In nonlinear shock formation, it preserves grid-level structure and remains robust to cell drifting while maintaining exact discrete conservation. These results show that conservative dynamics can be executed directly through discrete interaction rules, with continuum behaviour emerging only as a reconstruction of underlying quantised states.

Military human robot interaction (MHRI) presents a novel opportunity to blend the capabilities of autonomous and Artificial Intelligence (AI)-enabled systems with the skills and expertise of humans. The concept promises military advantages and greater operational effectiveness and efficiencies. However, the associated human-AI dynamics create challenges when attempting to design, implement, and operationalise the increasingly symbiotic relationship between humans and machines. Meaningful human control (MHC) is a popularised conceptualisation of what is deemed a responsible interaction among human and artificial agents; however, this notion falls short in military contexts and hinders the realisation of military advantages that could be achieved by advancing the adoption of responsible AI. This paper presents meaningful human command (MHC1) as a more operationally effective concept for advanced military command and control systems that embed AI-enabled autonomous systems. We introduce, explore, and unpack meaningful human command in the context of military human-robot interaction, presenting a vignette that offers a technologically feasible concept of an AI-enabled system within military operations. The vignette is used to guide, contextualise, and add realism to the narrative describing the concept and highlights associated MHRI challenges.

In an oriented graph $\vec{G}$, the {\it inversion} of a subset $X$ of vertices consists in reversing the orientation of all arcs with both endvertices in $X$. The {\it $(\leq p)$-inversion graph} of a labelled graph $G$, denoted by ${\mathcal{I}}^{\leq p}(G)$, is the graph whose vertices are the labelled orientations of $G$ in which two labelled orientations $\vec{G}_1$ and $\vec{G}_2$ of $G$ are adjacent if and only if there is a set $X$ with $|X|\leq p$ whose inversion transforms $\vec{G}_1$ into $\vec{G}_2$. In this paper, we study the {\it $(\leq p)$-inversion diameter} of a graph, denoted by $\mathrm{id}^{\leq p}(G)$, which is the diameter of its $(\leq p)$-inversion graph. We show that there exists a smallest number $Ψ_p$ with $\frac{1}{4}p - \frac{3}{2} \leq Ψ_p \leq \frac{1}{2}p^2$ such that $\mathrm{id}^{\leq p}(G) \leq \left\lceil\frac{|E(G)|}{\lfloor p/2\rfloor}\right \rceil + Ψ_p$ for all graph $G$. We then establish better upper bounds for several families of graphs and in particular trees and planar graphs. Let us denote by $\mathrm{id}^{\leq p}_{\cal F}(n)$ (resp. $\mathrm{id}^{\leq p}_{\cal P}(n)$) the maximum $(\leq p)$-inversion diameter of a tree (resp. planar graph) of order $n$. For trees, we show $\mathrm{id}^{\leq 3}_{\cal F}(n) = \left\lceil \frac{n-1}{2}\right\rceil$, $\mathrm{id}^{\leq 4}_{\cal F}(n)=\frac{3}{8}n + Θ(1)$, $\mathrm{id}^{\leq 5}_{\cal F}(n)= \frac{2}{7}n + Θ(1)$, and $\mathrm{id}^{\leq p}_{\cal F}(n) \leq \frac{n-1}{p- c\sqrt{p}} + 2$ with $c = \sqrt{2 + \sqrt{2}}$ for all $p\geq 6$. For planar graphs, we prove $\mathrm{id}^{\leq 3}_{\cal P}(n) \leq \frac{11n}{6} - \frac{8}{3}$, $\mathrm{id}^{\leq 4}_{\cal P}(n) \leq \frac{4n}{3} + \frac{10}{3}$, and $\mathrm{id}^{\leq p}_{\cal P}(n) \leq \left\lceil\frac{3n-6}{\lfloor p/2\rfloor}\right \rceil + 8\lfloor p/2\rfloor - 8$ for all $p\geq 6$.

We construct an explicit canonical cycle in the top-dimensional homology of the Voronoi complex associated with an arithmetic group. This cycle relates to the cohomology of SL$_n(\mathbb{Z})$ with rational coefficients at the virtual cohomological dimension. This cycle has been previously identified in computational works and conjectured to provide an intrinsic generator. Our approach relies on a geometric rigidity property of Voronoi tessellations. Furthermore, an abstract framework for polyhedral tessellations of convex cones under group actions is established, elucidating the underlying mechanism of the construction of such cycles.

We examine whether model-based spot volatility estimators extracted from traded options data enhance the predictive power of the Heterogeneous Autoregressive (HAR) model for realized volatility. Specifically, we infer spot volatility under the rough stochastic volatility model via an iterative two-step approach following Andersen et al. (2015a) and adopt a deep learning surrogate to accelerate model estimation from large-scale options panels. Benchmarked against traditional stochastic volatility models (Heston, Bates, SVCJ) and the VIX index, our results demonstrate that the augmented HAR-RV-RHeston model improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month.

Understanding when inflationary perturbations become genuinely nonlinear near the horizon crossing requires methods that go beyond both linear perturbation theory and the gradient expansion. In this work, we introduce a nonlinear lattice framework for single-field inflation based on a shear-free, locally Friedmann-Lemaître-Robertson-Walker geometry. This approach captures inhomogeneous local expansion rates, curvature contributions to the local Friedmann equation, and proper-volume weighting at a fraction of the computational cost of full numerical relativity. We construct fully nonlinear $δN$ observables on uniform-density slices, together with other practical time-dependent estimators for the curvature perturbations. After validating the framework in a standard slow-roll regime, we apply it to Starobinsky's linear-potential model featuring an intermittent ultra-slow-roll (USR) phase and a sharp potential transition. During this non-attractor USR regime, the lattice captures the separation of curvature perturbation estimators, the growth and subsequent stabilisation of non-Gaussianity, and a transient weakening of the shear-free approximation when the inflaton velocity becomes very small. Our framework provides a practical intermediate approach between rigid background lattice simulations and full numerical relativity, offering a nonlinear bridge between lattice methods, the $δN$ formalism, and the stochastic inflation formalism.

Quantum networks (QNs) enable qubit transfer between distant nodes through quantum teleportation, which reconstructs a quantum state at a remote node by consuming a shared Bell pair. In multi-qubit quantum applications (QApps), the teleported qubits may need to remain stored in quantum memories until execution can start, while decoherence progressively reduces their fidelity with respect to the ideal target state. Such QApps can operate only if all teleported qubits simultaneously satisfy a minimum fidelity threshold. In this paper, we study how many qubits can be teleported under this fidelity-constrained operation in a two-node QN. To this end, we define a QApp-level reliability metric as the probability that all end-to-end Bell pairs satisfy the target fidelity when the multi-qubit teleportation stage is completed. We then develop a Monte Carlo simulator that captures stochastic Bell-pair generation, Quantum Repeater (QR)-assisted entanglement distribution, and fidelity degradation. The analysis considers fiber-based and terrestrial free-space optical (FSO) quantum links, as well as representative NV-center- and trapped-ion-based quantum memories. Results show that memory coherence is the main scalability bottleneck under stringent fidelity targets, while parallel entanglement generation is essential for multi-qubit teleportation.

This paper studies Radio Access Network (RAN) slicing strategies for 5G Industry~4.0 networks with ultra-reliable low-latency communication (uRLLC) requirements. We compare four RAN slicing deployment options that differ in slice sharing and in the degree of per-line or per-flow isolation. Unlike prior works that assume a fixed slicing structure, this work addresses how RAN slicing should be instantiated in the presence of multiple production lines and heterogeneous industrial flows. A Stochastic Network Calculus (SNC)-based analytical framework and a heuristic slice planner are used to evaluate per-flow delay guarantees and radio resource utilization. Within the considered RAN-level analytical model, the results show that, under resource scarcity, only per-flow slicing prevents delay violations, whereas slice-sharing and hybrid deployments improve aggregation efficiency at the cost of weaker protection for the most delay-critical flows. Execution-time results show that the proposed planner operates at non-real-time (Non-RT) time scales, supporting its implementation as an rApp within Open RAN (O-RAN) Non-RT RAN Intelligent Controller (RIC) control loops.

Millisecond pulsars (MSPs) are observed to emit multi-wavelength radiation, from radio to GeV. Spider MSPs, which interact with their low-mass companion in close orbit (orbital periods $< 1$ day), may lead to strong intrabinary shocks that can further accelerate electron and positron pairs produced in the magnetosphere, possibly emitting very-high-energy (0.1--100 TeV; VHE) photons through inverse Compton scattering. Using 2565 days of HAWC Pass 5 data, we search for VHE emission from spider MSPs and present upper limits on individual sources. We also perform a stacking analysis to examine whether the two sets of spider systems, classified as redbacks and black widows depending on the companion mass, exhibit different spectral properties. Our study places constraints on TeV emission from MSPs and suggests that they are unlikely to contribute significantly to the Galactic diffuse emission at TeV and higher energies.

Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard 2-point statistics such as the power spectrum. In this work we assess this potential for the $\textit{Euclid}$ mission using synthetic catalogues of H$α$ galaxies based on the 54 $\, h^{-3} \, {\rm Gpc}^3$ Flagship I simulation, designed to reproduce the $\textit{Euclid}$ spectroscopic sample. We comprehensively validate the one-loop galaxy power spectrum and tree-level bispectrum predictions from perturbation theory in both real and redshift space. Assuming scale cuts consistent with our previous power spectrum study on the same catalogues, this modelling yields unbiased cosmological constraints for the bispectrum up to $k_{\rm max} = 0.15\,\, h \, {\rm Mpc}^{-1}$ in real space and $0.08 \, (0.1)\,\, h \, {\rm Mpc}^{-1}$ at the lowest (highest) redshift, corresponding to $z=0.9$ ($z=1.8$), for the monopole and quadrupole in redshift space using statistical uncertainties corresponding to the full simulation volume. With these scale cuts, adding bispectrum information to the power spectrum improves constraints on the amplitude of scalar perturbations and the matter density by up to 30 %, increasing the overall figure of merit for key cosmological parameters by a factor of about 2.5. Similar conclusions hold when statistical uncertainties are rescaled to a $\textit{Euclid}$-like volume, highlighting the importance of the bispectrum for fully exploiting the forthcoming $\textit{Euclid}$ data. Our analysis also provides the first detailed characterisation of the nonlinear bias model of H$α$ emitters, showing that bias relations calibrated on low-resolution \textit{N}-body simulations do not adequately describe the clustering of H$α$ galaxies at low redshift, whereas excursion-set and co-evolution relations for tidal biases remain accurate.

We describe the explicit construction of configurations of several 10d string theories joining at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories, predicted by the Cobordism Conjecture. We provide the microscopic worldsheet description of the configuration in a generalization of the `going up and down the RG flow' interpolations recently used in the description of IIA/IIB domain wall. The interpolations involve additional degrees of freedom, which are gapped except at the branch point, at which the gap closes and triggers the branching transition. The extra degrees of freedom admit an interpretation in terms of additional dimensions in a supercritical string theory, which reduces to the 10d junction configuration upon closed tachyon condensation. Quantum corrections of the 2d worldsheet theory turn the junction into a strongly coupled lightlike core whose UV resolution lies beyond worldsheet techniques. We construct explicit examples of junctions of 10d heterotic string theories, type 0, and type II theories and orientifolds thereof. Our explicit examples include junctions of 10d chiral theories whose chiral fields flow between different branches. One particularly nice configuration is a 4-branch junction of the IIB theory, with type I, the non-supersymmetric $USp(32)$ theory and the $U(32)$ orientifold of 0B theory, thus assembling the four non-tachyonic descendants of type 0B theory.

Magnetic flux fills the heliosphere, expands outward from the solar corona, and is fundamentally related to the structure and dynamics of the solar corona and solar wind. Open magnetic flux and the fast wind are thought to originate from open magnetic field lines in coronal holes. Less understood processes in the streamer belt and the boundaries of coronal holes, associated with the more variable slow wind, may be formed by interchange reconnection between open and closed magnetic flux. Interchange reconnection is thought to give rise to field lines that are "folded," i.e. that turn back on themselves. The properties of strahl electrons measured in the solar wind give clues to the heliospheric magnetic connectivity. Unidirectionally outward strahl indicates open field lines, while bidirectional strahl is associated with closed magnetic flux and CMEs. Inward directed, unidirectional strahl is believed to indicate folded flux. We use two time-dependent, flux-evolutionary MHD models of the combined corona and heliosphere, one for a solar-minimum configuration, one for the 2024 total solar eclipse, to investigate the magnetic connectivity of the corona/heliosphere system. We examine how magnetic connectivity varies with distance from the Sun in the two configurations. We evaluate the evolutionary effects by contrasting time-dependent results with the corresponding steady-state calculations, and compare the model connectivities with statistical studies of strahl. The connectivities in the time-evolving simulations are roughly consistent with observed strahl occurrence rates, while those from the steady-state models are not. Our results suggest that complex magnetic connectivities are ubiquitous in the heliosphere.

We study the problem of implementing a fully-connected layer of a neural network using wireless over-the-air computing. We assume a multi hop system with a multi-antenna transmitter and receiver, along with a number of multi-hop amplify-and-forward relay devices in between. We formulate an optimization problem that optimizes the transmitter precoder, receiver combiner and amplify-and-forward gains, subject to relay device power constraint and transmitter power constraint. We propose an alternating optimization framework that optimizes the imitation accuracy. Simulation study results reveal that multi-hop relaying achieves an almost perfect classification accuracy when used in a neural network.

Recent gravitational wave (GW) detections showing signatures of eccentricity and spin precession underscore the need to model binary black holes (BBHs) possessing these features simultaneously. Most efforts over the past fifteen years to model spinning BBHs and their corresponding GWs have relied on heuristically twisting waveforms from non-precessing systems. This approach is based on empirical observations rather than first principles. This article aims to model the GWs from spinning and eccentric BBHs from a first-principles approach within general relativity and post-Newtonian (PN) approximation. Building on the already-existing 1.5 PN solution, we construct an analytical solution for the time evolution of the relative separation vector, the individual black hole spin vectors, and the orbital angular momentum vector at 2PN order for BBHs with arbitrary spins and eccentricity. Such a solution is not fully 2PN accurate in that the tiny orbital timescale fluctuations in the solutions for the spins are only leading 1.5PN order accurate, instead of 2PN. However, it is shown that our new 2PN solution is still an order of magnitude improvement over the earlier 1.5PN solution, underlining the sub-dominant nature of the neglected next-to-leading-order oscillations in the spin solutions.

For decades, it has been known that local hidden variable theories cannot be disproved by collider experiments involving decaying particles. However, if these theories satisfy a small set of mild assumptions, they become testable. In particular, they can be disproved using Bell-like inequalities for $μ^+ μ^-$ and $τ^+ τ^-$ pairs.

Statistical inference based on optimal transport offers a different perspective from that of maximum likelihood, and has increasingly gained attention in recent years. In this paper, we study univariate nonparametric shape-constrained density estimation via projection with respect to the $p$-Wasserstein distance, with a focus on the quadratic case $p = 2$. By considering shape constraints given by displacement convex subsets of the Wasserstein space, Wasserstein projection estimation is a convex optimization problem. We focus on two fundamental examples, namely non-increasing densities on $\mathbb{R}_+ := [0, \infty)$ and log-concave densities on $\mathbb{R}$. In each case, we prove structural properties of the Wasserstein projection estimator, propose a discretization which can be implemented by off-the-shelf solvers, and compare the projection estimator with the corresponding maximum likelihood estimator.

We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with $N_{\mathrm{f}}=2+1$ flavors of $\mathrm{O}(a)$-improved Wilson fermions, covering six lattice spacings between $0.039$ and $0.097\,$fm and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain as our final, continuum-extrapolated result $a_μ^{\mathrm{hvp,\,nlo}}=-101.57(26)_{\mathrm{stat}}(54)_{\mathrm{syst}}\times10^{-11}$. It lies below the estimate provided by the 2025 White Paper of the Muon $(g-2)$ Theory Initiative by $1.4σ$ but is two times more precise. It also exhibits a strong tension of $4.6σ$ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.

SPACE-Timers are a lightweight hierarchical profiling framework for C++ designed for modern high-performance computing (HPC) applications. It uses a stack-based timing model to capture deeply nested execution patterns with minimal overhead, representing runtime behaviour as a tree of timing nodes with precise attribution. The framework provides structured reports with recursive aggregation, detection of unaccounted time, and compact visual summaries of runtime distribution, supporting both quick inspection and detailed analysis. It also includes checkpointing and error detection mechanisms. SPACE-Timers supports multiple profiling backends, including NVTX, ITT, ROCtx, and Omnitrace, and integrates with the MERIC runtime system to enable energy-aware optimisation. Its successful use in OpenGadget3 demonstrates its effectiveness for large-scale scientific applications.

We provide a complete census of the baryons in early galaxies to investigate the phases in which gas and stars reside, their corresponding budgets, depletion times, and stellar return fraction as a function of redshift and stellar age. We use the ColdSIM hydrodynamical time-dependent non-equilibrium chemistry simulations and perform a detailed analysis of the cold, warm, hot, and stellar phases for both bound structures (galaxies/CGM) and the diffuse IGM. We investigate in depth the cold HI and H2 components, explicitly computed in our simulations, and their relations with host mass, SFR, metallicity and depletion times. We also provide observational insights and discuss the implications for stellar mass functions, PopIII star formation and changes in the IMF. We find that cosmic gas prior to reionisation is mostly cold, while at later epochs the warm phase becomes dominant due to enhanced star formation activity and increasing UV reionising radiation. Stellar return fractions at these times are ~0.15-0.20, a factor of two lower than the values usually adopted. Cold, warm, and hot gas masses as well as HI and H2 components show increasing trends with mass and SFR, while depletion times decrease down to 0.01-0.1 Gyr with a weak metallicity dependence. The resulting star formation efficiency remains at the level of a few per cent and gas-to-star fractions decline with mass, influenced by local feedback and environment. Our findings are consistent with ALMA, VLA and IRAM surveys at later epochs, including ALFALFA, xCOLDGASS, GASS, xGASS, EDGE-CALIFA, PHIBBS, and ASPECS. Gas phases are quantitatively related to the underlying stellar populations and can be used to infer unknown quantities. In the appendix we provide fit functions describing the trends of the stellar return fraction, the main sequence, phase mass relations, gas-to-star fractions and depletion times.

The US economy is transitioning away from fossil fuels toward sources of green energy. California policymakers have adopted the goal of carbon neutrality by 2045 or earlier. Within California, Kern County accounts for over 70 percent of oil produced within the state. To understand how the transition may affect opportunities in Kern, we propose a structural vector autoregressive model that jointly explains the global crude-oil market and the evolution of employment within Kern. We use monthly data from the Quarterly Census of Employment and Wages. While industries directly involved in the extraction of fossil fuels employ less than 2 percent of workers, the oil market is responsible for 11 percent of the variation in employment growth. Employment would be 6.4 percent lower currently absent the influence of the global oil market. We explain these large effects using a theoretical framework of production that relies on a network of input--output linkages. The findings may be useful to policymakers designing place-based policy aimed at helping vulnerable oil-dependent regions.

We study the possibility of a gradual improvement as time progresses of the regularity of solutions to evolution problems of parabolic type driven by Lévy-type operators, not necessarily translation invariant. In the course of our analysis we study the equivalence between general smoothing effects and a family of logarithmic Sobolev inequalities. This equivalence allows us to identify a new type of regularization, strong hypercontractivity, characterized by the existence of a time at which solutions belong to every $L^p$ space with $p$ finite. It can also be used to prove logarithmic Sobolev inequalities in a context not previously seen in the literature. We then show that any purely nonlocal Lévy-type operator whose kernel is comparable to that of $\log(I-Δ)$ is strongly hypercontractive, but fails to be supercontractive and, consequently, also fails to be ultracontractive. Furthermore, in the translation-invariant case, we also prove that solutions get bounded eventually and start improving in differentiability right after doing so. Finally, we show that this behaviour only appears if the kernel defining the operator behaves as $|x-y|^{-N}$ for small interactions ($0^+$-order operators): more singular kernels yield instantaneous smoothing, while less singular ones do not produce any regularization.

The response of amorphous solids to a mechanical perturbation consists in an elastic and a plastic deformation. The latter is mediated by localized irreversible rearrangements associated with Eshelby-like quadrupolar singularities in the displacement field. It has recently been argued that a density of such singularities leads to an anomalous elastic behavior taking the form of screening effects, which goes beyond classical elastic predictions. Here, we reexamine this scenario using general theoretical arguments and a description in terms of an elasto-plastic model, which we compare with atomistic simulations of the canonical Eshelby inclusion geometry. We discuss the conditions under which a finite, i.e., nonvanishing, density of quadrupolar events is created by an imposed perturbation. We argue that, except when the perturbation is macroscopic, there are many situations in which the density of quadrupolar defects is zero in the thermodynamic limit. In these cases, we find that plastically active quadrupoles emerge in a region whose size generically scales as the spatial extent $\ell$ of the mechanical perturbation. This mechanism leads to anomalous elasticity on a scale $\ell$ close to the perturbation and to conventional elasticity beyond. The simulations of the elasto-plastic model reproduce the emergence of plastic quadrupoles in a region set by $\ell$ and the associated renormalization of the effective shear modulus, but they do not exhibit the dipole-screening signatures reported in atomistic and experimental studies. Our analysis delineates the scale-dependent breakdown of long-wavelength elasticity in amorphous materials and suggests directions for incorporating anomalous screening into mesoscopic modeling frameworks.

Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are related by sign flip of the quartic coupling. Applications to dimensions $d<4$ recover previous results for the phase diagram, whereas $d=4$ is possibly new.

Characterizing compressible fluctuations in the solar wind is essential for understanding their role in solar wind acceleration and heating, yet their origin and evolution across different turbulence regimes remain poorly understood. In this study, we carry out a statistical analysis of the properties of compressible fluctuations in solar wind dominated by balanced and imbalanced turbulence. Using in-situ measurements from Wind, Solar Orbiter, and Parker Solar Probe, we investigate the scale dependence of density and magnetic field fluctuations and their correlations with plasma beta and radial distance. Our results indicate that solar wind compressibility is likely affected by both expansion effects and compressible dynamics governed by local plasma conditions. The non-Alfvenic wind is dominated by anti-correlated fluctuations, whereas the Alfvenic wind contains a mixture of correlated and anti-correlated fluctuations, though the latter remain prevalent. While the anti-correlated component is consistent with MHD slow magnetosonic modes, the correlated (fast mode-like) component is not reproduced by predictions from either linear MHD theory or nonlinear models of forced compressible fluctuations. Nevertheless, the dominant slow mode component explains the observed dependence on beta and the enhanced density fluctuations measured by Parker Solar Probe. This further suggests that slow mode waves contribute significantly to the compressible energy budget near the Sun and may play an important role in solar wind heating and acceleration close to the Sun.

Watermarking for large language models (LLMs) has emerged as an effective tool for distinguishing AI-generated text from human-written content. Statistically, watermark schemes induce dependence between generated tokens and a pseudo-random sequence, reducing watermark detection to a hypothesis testing problem on independence. We develop a unified framework for LLM watermark detection based on e-processes, providing anytime-valid guarantees for online testing. We propose various methods to construct empirically adaptive e-processes that can enhance the detection power. The proposed methods are applicable to any sequential testing problem where independent pivotal statistics are available. In addition, theoretical results are established to characterize the power properties of the proposed procedures. Some experiments demonstrate that the proposed framework achieves competitive performance compared to existing watermark detection methods.