Ly$α$ blobs (LABs) are large, spatially extended Ly$α$-emitting objects whose nature remains unclear. Their statistical properties such as number densities and luminosity functions are still uncertain because of small sample sizes and large cosmic variance. The One-hundred-deg$^2$ DECam Imaging in Narrowbands (ODIN) survey, with its large volume, offers an opportunity to overcome these limitations. We describe our LAB selection method and present 112 new LABs in the 9 deg$^2$ E-COSMOS field. We begin with the conventional LAB selection approach, cross-matching LAEs with extended Ly$α$ sources, yielding 89 LAB candidates. To obtain a more complete LAB sample, we introduce a new selection pipeline that models all galaxies detected in deep broadband imaging, subtracts them from the narrowband image, and then directly detects extended Ly$α$ emission. This method successfully identifies 23 additional low-surface-brightness LABs which could otherwise be missed by the conventional method. The number density of ODIN LABs near an ODIN protocluster ($n=7.5\times10^{-5}$ cMpc$^{-3}$) is comparable to that found in the SSA22 proto-cluster and is four times higher than the average across the field. The cumulative Ly$α$ luminosity function within the protocluster regions is similar to that measured for the LABs in the SSA22 proto-cluster, suggesting a large excess of luminous LABs relative to the average field. These findings suggest the Ly$α$ luminosities and number densities of LABs are environment-dependent. ODIN will provide an expansive LAB and protocluster samples across six additional fields and two more redshifts, allowing us to investigate the nature of LABs in relation to their environments.

Scanning transmission X-ray microscopy (STXM) is a nanoscale imaging technique that can utilize several powerful contrast mechanisms for the quantitative mapping of chemical and physical materials properties. Spatial resolutions down to 7~nm at the soft X-ray energy range have been demonstrated. A limiting factor for high-resolution STXM imaging is given by the positioning precision of the sample with respect to the focusing optic, with the current state-of-the-art leading to significant overheads, especially at low pixel dwell times, and being vulnerable to unavoidable external vibrations sources. In this work, we present a method, called supersampled scanning microscopy, that allows for a significant reduction of overhead times while simultaneously removing the effects of vibrational noise by sampling the position of the sample at a rate significantly higher than the vibration spectrum and reconstructing the sample transmission image from the recorded list of positions and detector counts. We demonstrate the performance of the technique with a set of proof-of-concept high-resolution imaging experiments.

This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported potentials on the real line. That class includes the Regge-Wheeler potentials obtained from separation of variables for SdS. The novelty lies in allowing non-compact supports -- all exact Poisson formulae of Lax-Phillips, Melrose, and other authors required compactness of the support of the perturbation. A key feature of the analysis is the presence of an exceptional class of potentials for which outgoing solutions may vanish at certain non-resonant frequencies. We identify and describe this class, which we call the resonant condition.

In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the dynamic saddle-node bifurcation. This allows us to then obtain a scaling law for the slow flow dynamics and to improve the accuracy of the theoretical prediction of the mitigation limit of the NES previously obtained as part of a zeroth-order approximation. For that purpose, the governing equations of the coupled system are first simplified using a reduced-order model for the primary structure by keeping only its unstable modal coordinates. The slow flow is then derived by means of the complexification-averaging method and, by the presence of a small perturbation parameter related to the mass ratio between the NES and the primary structure, it appears as a fast-slow system. The center manifold theorem is finally used to obtain the reduced form of the slow flow which is solved analytically leading to the scaling law. The latter reveals a nontrivial dependence with respect to the small perturbation parameter of the slow flow dynamics near the fold point, involving the fractional exponents 1/3 and 2/3. Finally, a new theoretical prediction of the mitigation limit is deduced from the scaling law. In the end, the proposed methodology is exemplified and validated numerically using an aeroelastic aircraft wing model coupled to one NES.

We study the birational geometry (i.e., Kähler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes of these geometries are not exhausted by toric hypersurfaces arising from fine, regular, star triangulations (FRSTs). We begin by introducing a classification problem: enumeration of birational classes of toric varieties, which is equivalent to enumeration of certain triangulations/fans. We consider this problem from the complementary perspectives of triangulation theory and toric geometry, reviewing both theories in detail; this culminates in an explanation of how to generate all fine regular triangulations of a vector configuration (i.e., fine regular simplicial fans) which we implement in a Python package regfans [1]. We then apply this theory to the Kreuzer--Skarke (KS) database, where we encounter both FRSTs and vex triangulations. We study the non-weak-Fano toric varieties arising from vex triangulations, along with their CY hypersurfaces. In particular, we show that all fine regular triangulations of a fixed 4D reflexive polytope give rise to smooth birational CY hypersurfaces, extending Batyrev's result from FRSTs to vex triangulations. We exhaustively enumerate all $24,023,940$ fine regular triangulations in the KS database with $h^{1,1}\leq 7$, of which over $70\%$ are vex triangulations, and provide an upper bound of $10^{979}$ for fine regular triangulations in the entire KS database. We conclude that vex triangulations of four-dimensional reflexive polytopes give rise to a large number of smooth Calabi--Yau threefolds and importantly provide toric descriptions for novel regions in the Kähler moduli space.

Starting from the most general effective $|ΔB| = 1$ Hamiltonian describing non-leptonic $b$-quark decays $b\to q_1 \bar q_2 q_3$, we compute analytic expressions for all matching coefficients of the two-quark operator contributions in the heavy quark expansion~(HQE) of a $B$ meson, up to mass-dimension-six. In addition, we calculate the weak-annihilation contributions, which enter the matching of four-quark operators in the HQE at dimension-six and were previously missing. Our results complete the calculation of beyond Standard Model (BSM) effects in non-leptonic, tree-level, $b$-quark decays relevant for $B$ meson lifetimes and lifetime ratios such as $τ(B^0_s)/τ(B^0_d)$. Such BSM contributions naturally arise in generic extensions of the Standard Model (SM) that aim to address the observed tensions between experimental measurements and theoretical predictions based on QCD factorisation in several colour-allowed non-leptonic $B$-meson decays. As a by-product of our calculation, we also determine the matching coefficients in the HQE induced by the QCD-penguin operators within the SM, including both the interference between current-current and penguin operators and the contributions quadratic in the penguin operators. Owing to the suppression of the QCD-penguin Wilson coefficients within the SM, these effects are typically regarded as corrections of order $α_s$ and $α_s^2$ in the strong coupling, respectively. Our results reproduce the known expressions at dimension-three and provide new results for the coefficients of the chromomagnetic operator at dimension-five and of the Darwin operator at dimension-six.

We investigate quantum inverse problems in one-dimensional (1D) electronic disordered systems strongly coupled to optical cavities. More specifically, we consider the Anderson and the Aubry-Andre-Harper models connected to electronic reservoirs and embedded in a single-mode optical cavity. The light-matter interaction enables photon-assisted hopping processes that significantly modify the transmittance spectrum. Within the nonequilibrium Green's function formalism, we implement an inversion-based approach capable of accurately extracting the electron-photon coupling strength directly from transmittance spectra. While cavity coupling acts as a minor perturbation within the Anderson model, yielding broad yet precise parameter estimates, its influence is markedly different in the Aubry-André-Harper model. The latter exhibits a sharp metal-insulator transition in 1D, thus resulting in more pronounced cavity-induced spectral changes. This renders even more accurate inverse solutions, offering unparalleled precision in the characterization of low-dimensional disordered systems. Altogether, our results demonstrate that the quantum inverse problem provides a robust diagnostic tool for quantum materials, particularly effective for systems exhibiting metal-insulator transitions.

We discuss the ultraviolet fixed point of asymptotically safe dilaton quantum gravity. It differs from the Reuter fixed point by the dependence of the Planck mass on a scalar field. The gauge invariant functional flow equation in the most general approximation with up to two derivatives strengthens the argument for the existence of this fixed point. The quantum effective action obtained from the scaling solution for dilaton quantum gravity can describe inflation for early cosmology and dynamical dark energy for late cosmology.

We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo-pressure. This parabolic-typed equation can be degenerate and/or singular in the spatial variables, the unknown and its gradient. We establish the $L^α$-estimate for the solutions, for any positive number $α$, in terms of the initial and boundary data and the angular speed of rotation. It requires new elliptic and parabolic Sobolev inequalities and trace theorem with multiple weights that are suitable to the nonlinear structure of the equation. The $L^\infty$-estimate is then obtained without imposing any conditions on the $L^\infty$-norms of the weights and the initial and boundary data.

High-performance computing (HPC) systems consume enormous amounts of energy, with idle nodes as a major source of energy waste. Powering down idle nodes can mitigate this problem, but long boot/shutdown delays can introduce significant queueing penalties if transitions are poorly timed. To address this trade-off, we present SPARS, a reinforcement learning-enabled simulator for power management in HPC job scheduling. SPARS integrates job scheduling and node power-state management within a discrete-event simulation framework. It supports traditional scheduling policies such as First Come First Serve and EASY Backfilling, along with enhanced variants that employ reinforcement learning agents to dynamically decide when nodes should be powered on or off. Users can configure workloads and platforms in JSON format, specifying job arrivals, execution times, node power models, and transition delays. The simulator records comprehensive metrics-including energy usage, wasted power, job waiting times, and node utilization-and provides Gantt chart visualizations to analyze scheduling dynamics and power transitions. Unlike widely used Batsim-based frameworks that rely on heavy inter-process communication, SPARS provides lightweight event handling and consistent simulation results, making experiments easier to reproduce and extend. Its modular design allows new scheduling heuristics or learning algorithms to be integrated with minimal effort. By providing a flexible, reproducible, and extensible platform, SPARS enables researchers and practitioners to systematically evaluate power-aware scheduling strategies, explore the trade-offs between energy efficiency and performance, and accelerate the development of sustainable HPC operations.

Non-Hermitian (NH) systems have attracted great attention due to their exotic phenomena beyond Hermitian domains. Here we study the wave-packet dynamics in general one-dimensional NH lattices and uncover several unexpected phenomena. The group velocity of a wave packet during the time evolution in such NH lattices is not only governed by the real part of the band structure but also by its imaginary part. The momentum also evolves due to the imaginary part of the band structure, which can lead to a self-induced Bloch oscillation in the absence of external fields. Furthermore, we discover the wave-packet dynamics can exhibit disorder-free NH jumps even when the energy spectra are entirely real. Finally, we show that the NH jumps can lead to both positive and negative temporal Goos--Hänchen shifts at the edge.

Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce solvable tuple patterns (STPs) and conjunctive STPs (CSTPs), novel formalisms for expressing and inferring invariants between list-like recursive data structures. A distinguishing feature of STPs is that they can be efficiently inferred from only a small number of positive samples; no negative samples are required. After presenting properties and inference algorithms of STPs and CSTPs, we show how to incorporate the CSTP inference into a CHC (Constrained Horn Clauses) solver supporting list-like data structures, which serves as a uniform backend for automated program verification tools. A CHC solver incorporating the (C)STP inference has won the ADT-LIN category of CHC-COMP 2025 by a significant margin.

Coherent elastic neutrino-nucleus scattering (CE$ν$NS) has been experimentally confirmed using neutrinos from pion decay at rest, solar neutrinos and reactor antineutrinos. Future CE$ν$NS experiments will foreseeable lead to precision measurements which will be a powerful tool to search for new physics beyond the Standard Model. In this work, we investigate possible deviations from unitarity in the $3\times3$ leptonic mixing matrix that controls the propagation of active neutrinos. Such deviations may originate from the mixing with additional gauge singlet fermions and depending on their mass scale and mixing, the resulting phenomenology can differ substantially. We explore two well-motivated regimes: the \textit{seesaw limit}, where the new fermions are heavy and kinematically inaccessible, leading to effective deviations from unitarity in the active sector; and the \textit{light sterile limit}, where they are light enough to be produced and participate in neutrino propagation and scattering processes. We show how these scenarios modify both CE$ν$NS and elastic neutrino--electron scattering (E$νe$S), and we present the corresponding sensitivity projections for a future CE$ν$NS reactor experiment obtained by upscaling the CONUS+ experiment, which reported the first observation of reactor CE$ν$NS. We identify the leading experimental systematics relevant for such an upscaling and demonstrate the resulting capability to probe TeV-scale new physics. Our results highlight the strong potential of CE$ν$NS to test the structure of the lepton sector and to search for physics beyond the Standard Model.

We consider the critical dissipative surface quasi-geostrophic (SQG) equation on $\mathbb{R}^2$ or $\mathbb{T}^2$. Despite global regularity of the equation, we show that the data-to-solution map at the critical level $H^1$ is not uniformly bounded. We construct solutions that experience $H^1$ norm inflation from smooth, compactly supported initial data with large $H^1$ norm. We also demonstrate small-data norm inflation in supercritical Sobolev spaces $W^{β,p}$ for $1<p<2$ and $1\leβ<\tfrac{2}{p}$.

In an emerging pandemic, policymakers need to make important decisions with limited information, for example choosing between a mitigation, suppression or elimination strategy. These strategies may require trade-offs to be made between the health impact of the pandemic and the economic costs of the interventions introduced in response. Mathematical models are a useful tool that can help understand the consequences of alternative policy options on the future dynamics and impact of the epidemic. Most models have focused on direct health impacts, neglecting the economic costs of control measures. Here, we introduce a model framework that captures both health and economic costs. We use this framework to compare the expected aggregate costs of mitigation, suppression and elimination strategies, across a range of different epidemiological and economic parameters. We find that for diseases with low severity, mitigation tends to be the most cost-effective option. For more severe diseases, suppression tends to be most cost effective if the basic reproduction number $R_0$ is relatively low, while elimination tends to be more cost-effective if $R_0$ is high. We use the example of New Zealand's elimination response to the Covid-19 pandemic in 2020 to anchor our framework to a real-world case study. We find that parameter estimates for Covid-19 in New Zealand put it close to or above the threshold at which elimination becomes more cost-effective than mitigation. We conclude that our proposed framework holds promise as a decision-support tool for future pandemic threats, although further work is needed to account for population heterogeneity and other factors relevant to decision-making.

We investigate binary mergers of galaxy clusters, the formation of shocks, and the resulting radio relics using three-dimensional simulations. The initial setup consists of two idealized spherical subclusters with a mass ratio below three, each permeated by turbulent magnetic fields, and we follow their merger with a high-order accurate magnetohydrodynamic (MHD) code. In parallel, we track the acceleration of cosmic-ray electrons (CRe) via diffusive shock acceleration (DSA) at merger-driven shocks, together with radiative cooling and Fermi-II (turbulent) acceleration in the postshock region, employing a newly developed Eulerian Fokker-Planck solver. Synchrotron emission is computed from the simulated CRe distribution and magnetic fields. In this paper, we detail these numerical approaches and present the first results obtained with them. Two prominent axial shocks emerge along the merger axis; the shock ahead of the heavier subcluster systematically attains a higher Mach number, although it is more compact, than that ahead of the lighter subcluster. Turbulent magnetic fields, which are both inherited from the initial conditions and amplified during the merger, produce patchy, fine-scale structures in the radio surface brightness. Because of the combined effects of turbulent acceleration, spatially nonuniform magnetic fields, and the curved geometry of merger shocks, the volume-integrated radio spectra show deviations from the canonical power-law steepening expected for a planar shock with a uniform field. Reacceleration of preexisting fossil CRe enhances the surface brightness. Our results highlight the coupled roles of merger dynamics, MHD turbulence, and CRe physics in shaping the observed properties of radio relics in cluster outskirts.

We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball system. In the former case it is illustrated by means of two-dimensional plots of the scattering angle and of the number of bounces. We draw similar patterns for the quantum differential cross-section for various geometries of the disks. We find that the eigenvalues of the S-matrix are distributed according to the Circular Orthogonal Ensemble (COE) in random matrix theory (RMT), provided the setup be asymmetric and the wave-number be large enough. We then consider the electric potential associated with charges randomly located on a plane as a toy model that generalizes the scattering from a leaky torus. We propose several methods to analyze the distribution of spacings between the extrema of such functions. We show that these follow a repulsive Gaussian β-ensemble distribution even for Poisson-distributed positions of the charges. A generalization of the spectral form factor is introduced and determined. We apply these methods to the cases of a chaotic S-matrix and of the quantum pinball scattering. The spacings between nearest neighbor extrema points and ratios between adjacent spacings follow a logistic and Beta distributions correspondingly. We conjecture about a potential relation with random tensor theory.

The aggregate flexibility region of distributed energy resources (DERs) quantifies the aggregate power shaping capabilities of DERs. It characterizes the distribution network's potential for wholesale market participation and grid service provision at the transmission level. To enhance flexibility and fully exploit the potential of DERs, this paper proposes a method to optimize the aggregate flexibility region through distribution network reconfiguration. First, we formulate the ellipsoidal aggregate flexibility region characterization problem as a two-stage adaptive robust optimization problem and derive an exact convex reformulation with a large number of second-order cone constraints. By exploiting the problem structure, we propose a scalable Benders decomposition algorithm with provable finite convergence to the optimal solution. Finally, we propose an optimal reconfiguration problem for aggregate flexibility region optimization and solve it using the custom Benders decomposition. Numerical simulations on the IEEE 123-bus test feeder demonstrate that, compared to existing approaches, substantial improvements in the aggregate flexibility region can be achieved over multiple scenarios with the optimized topology.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

This work investigates a cosmological model featuring an interaction between dark energy and dark matter, where the dark energy component is described by the Generalized Chaplygin-Jacobi gas (GCJG). In this study, we establish a system in which the GCJG and a pressureless dark matter fluid exchange energy via a linear interaction term, $Q \propto ρ_x$, being $ρ_{x}$ the dark energy density. By solving the conservation equations, we derive analytical expressions for the evolution of the dark energy and dark matter densities. The thermodynamic properties of this interacting system are then thoroughly analyzed. The thermodynamic analysis reveals that both dark components maintain positive temperatures, ensuring stability. Notably, the dark energy component transitions to a phantom regime in the past, a feature of interest for recent cosmological observations, without violating thermodynamic principles. The total entropy production is shown to be in agreement with the second law of thermodynamics. Furthermore, an analysis of the specific heats suggests that while the dark matter sector remains thermodynamically stable, the dark energy sector undergoes a late-time phase transition, consistent with its entering into the phantom domain at effective level.

We introduce a novel class of bosonic dark matter candidates that we dub wallions, featuring boundaries in field space. The wallion mass is exponentially suppressed when the separation between boundaries far exceeds their intrinsic width and remains radiatively stable under self-interactions. We study the early-universe evolution of wallions and the associated cosmological signatures. Finally, we show that instanton effects can dynamically generate field-space boundaries and discuss possible experimental probes once the wallion couples to Standard Model fields.

We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure $γ$ with a unit diffusion operator and a drift of the form $-x+v(p,x)$, where $v$ is a bounded mapping with values in the Cameron-Martin space $H$ of $γ$ and $v$ is defined on the space $E\times X$, where is $E$ is the subset of $L^2(γ)$ consisting of probability densities. The equation has the form $L_{b(p,\bullet)} ^*(p\cdot γ)=0$ with $L_{b(p,\bullet)}φ=Δ_H φ+ (b(p,\bullet) , D_{_H}φ)_{_H}$, so that the drift coefficient depends on the unknown solution, which makes the equation nonlinear. This dependence is assumed to satisfy a suitable continuity condition. This result is applied to drifts of Vlasov type defined by means of the convolution of a vector field with the solution. In addition, we consider a more general situation where only the components of $v$ are uniformly bounded and prove the existence of a probability solution under some stronger continuity condition on the drift.

For many compound $A_n$ ($cA_n$) singularities $R_f=\mathbb{C}[u,v,x,y]/(uv-f(x,y))$ with crepant resolutions $Y_f$, their mirrors are affine $A_n$ plumbings $W^\circ_f$ of $3$-dimensional lens spaces along circles. We prove two versions of homological mirror symmetry for these Stein $3$-folds. (i) The uncompleted version: there is an equivalence $D^\mathit{perf}\mathcal{W}(W_f^\circ)\simeq D^b\mathit{Coh}(Y^\circ_f)$ between the derived wrapped Fukaya category and the bounded derived category of coherent sheaves on some divisor complement $Y^\circ_f=Y_f\setminus D$. (ii) The completed version: there is an equivalence $D^\mathit{perf}\widehat{\mathcal{W}}(W^\circ_f)\simeq D^b\mathit{Coh}(\widehat{Y}_f)$, where $\widehat{\mathcal{W}}(W^\circ_f)$ is the completion of $\mathcal{W}(W^\circ_f)$ with respect to the word-length filtration of Hamiltonian chords, and $\widehat{Y}_f$ is the complete local version of $Y_f$. As an application of (i), we show that certain infinitely generated subgroup of the pure braid group $\mathit{PBr}_{n+2}$ split injects into the compactly supported symplectic mapping class group of $W^\circ_f$ as long as $R_f$ is isolated, generalizing the work of Keating-Smith in the case of a conifold smoothing. Applying categorical localization to (ii), we obtain an equivalence between the (uncompleted) derived wrapped Fukaya category of the corresponding (non-affine) $A_n$ plumbing $W_f$ of lens spaces along circles and the relative singularity category of $Y_f$. This generalizes the result of Smith-Wemyss in the case of double bubble plumbings and partially answers their realization question.

We demonstrate the emergence of a robust tetrahedral magnetic ground state in monolayer graphene doped to the van Hove singularity (vHS). This noncoplanar, gapped spin configuration - featuring four equally inclined moments - has been previously identified as a candidate instability. Here, not only do we confirm its stability across all finite interactions using fully self-consistent, real-space-resolved calculations, but we also go beyond earlier work by charting the full surrounding phase diagram. In doing so, we unravel a cascade of symmetry-broken magnetic states - pseudo-tetrahedral, planar, collinear, and modulated textures - which we classify using spin structure factors and vector order parameters. These results stem from unrestricted Hartree-Fock simulations on large supercells with dense k-point sampling, enabling us to resolve interaction-driven magnetic and charge inhomogeneities. Our findings connect directly with recent ARPES and doping experiments near the vHS in graphene, and establish the tetrahedral state as the central correlated instability in this regime, offering predictive insight into emergent magnetism in correlated Dirac materials.

We consider a random walk on a homogeneous space $G/Λ$ where $G$ is a non-compact simple Lie group and $Λ$ is a lattice. The walk is driven by a probability measure $μ$ on $G$ whose support generates a Zariski-dense subgroup. We show that the random walk equidistributes towards the Haar measure unless it is trapped in a finite $μ$-invariant set. Moreover, under arithmetic assumptions on the pair $(Λ, μ)$, we show the convergence occurs at an exponential rate, tempered by the obstructions that the starting point may be high in a cusp or close to a finite orbit. The main challenge is to show that the dimensional properties of a given probability distribution on $G/Λ$ improve under convolution by $μ$. For this, we develop a new method, which combines a dimensional interpolation result and a dimensional increase alternative. This approach allows us to bypass inherent geometric obstructions. To show dimensional interpolation, we establish a general subcritical projection theorem under optimal non-concentration assumptions on the projector, and a corresponding submodular inequality for irreducible representations which allows its application to random walks. Both are of independent interest. The dimensional increase alternative aligns with the spirit of Bourgain's projection theorem. It is fine-tuned for random walks and has the advantage of being valid in situations lacking transversality.

Pulsar Timing Arrays (PTAs) are approaching the sensitivity required for a $5σ$ detection of the nanohertz stochastic gravitational-wave background (GWB). This makes it crucial to deeply understand the behaviour of our analysis pipelines. A counterintuitive feature of the European Pulsar Timing Array (EPTA) second data release is that restricting the dataset to the last 10.3 years (DR2new) increases the inferred GWB significance from $\leq2σ$ for the full 25-year dataset (DR2full) to $\geq3.5σ$. We investigate whether this behaviour indicates an anomaly or is a possible outcome of the pipeline. Using realistic, DR2-like simulations with varying timespans, we find that the first 10 years contribute little to the GWB evidence due to their limited frequency coverage. This produces substantial overlap between the HD S/N distributions of DR2full and DR2new. Random noise fluctuations therefore yield a higher GWB evidence in DR2new than in DR2full in $15\%$ of cases. Furthermore, $5\%$ of simulations match the HD S/N of the real data, indicating that the observed behaviour is consistent with being a $\sim2σ$ outcome due to noise fluctuations. Regardless of significance, DR2new simulations introduce biases in the GWB parameter estimation due to spectral leakage effects that are ignored in standard analyses and which flatten the inferred spectrum. Including leakage removes these biases, demonstrating the reliability of DR2new when the signal is properly modelled. Furthermore, we demonstrate that combining EPTA DR2full with long-baseline data from NANOGrav and PPTA, as well as low-frequency data from LOFAR and NenuFAR, significantly enhances GWB evidence and parameter accuracy. Finally, we examine the impact of the observation timespan and find that short-baseline datasets introduce strong amplitude biases and are ineffective at constraining the GWB.

In asymptotically AdS spacetimes, the mathematical structure of the set of entanglement wedges reflects the algebraic structure of the underlying holographic description. For more general spacetimes, Bousso and Penington (BP) have recently proposed a generalization of entanglement wedges sharing many of the same properties as usual entanglement wedges. In this paper, we explore the hypothesis that each generalized entanglement wedge can be associated with an algebra in the (generally unknown) fundamental description (in a semiclassical limit). We postulate features of the map from entanglement wedges to algebras that provide a natural algebraic interpretation for some of the basic mathematical properties of the set of entanglement wedges. Quantitatively, we suggest a possible generalization of the Ryu-Takayanagi formula that associates the gravitational entropy of a generalized entanglement wedge with an entropic quantity for the associated algebra. Through this assignment, inclusion monotonicity and strong-subadditivity properties shown by BP for generalized entanglement wedges would follow from various inequalities satisfied by algebraic entropies. We include a detailed appendix reviewing relevant algebraic background, including a discussion of algebraic entropies and their inequalities.

We present an open-source software package IRSSG for investigating magnetic systems with spin space groups (SSGs). The package works within the density functional theory (DFT) framework and requires wavefunctions from DFT codes, such as VASP, Quantum ESPRESSO, as well as any other code that has an interface to Wannier90. We introduce a set of compact SSG international symbols by combining non-crystallographic point groups with the 230 crystallographic space groups. The program first identifies all SSG operations and determines the SSG international symbol for a given magnetic system. It then generates the SSG character tables of little groups at any $k$ point. Finally, it computes the traces of matrix representations of SSG operations and assigns irreducible corepresentation labels to magnetic energy bands. The program is not only timely but also essential for advancing research on the study of magnons, altermagnetism, magnetic topology, and novel high-degeneracy excitations in SSG systems.

The goal of this paper is to study the $L^p$-solvability of the strongly-coupled nonlocal system \[ \mathbb{L} \mathbf{u} (\mathbf{x}) + λ\mathbf{u}(\mathbf{x})= \mathbf{f}(\mathbf{x}) \quad \text{in $\mathbb{R}^{d}$ } \] where $\mathbb{L}$ is a linear nonlocal coupled vector-valued operator associated with a kernel $K$ comparable to $|\mathbf{y}|^{-(d+2s)}$ for $s \in (0,1)$, satisfying certain ellipticity and cancellation conditions. For any $\mathbf{f} \in [L^p(\mathbb{R}^d)]^d$, $1< p < \infty$, the existence of a unique strong solution $\mathbf{u} \in [H^{2s,p}(\mathbb{R}^d)]^d$ is proved via the method of continuity. To apply this method, we establish the continuity of the operator $\mathbb{L}$ and the necessary \textit{a priori} estimates. These are obtained through the study of the corresponding parabolic system. The proof strategy follows and extends recent ideas developed for the scalar setting, combining commutator estimates, Sobolev embeddings, a level set estimates and a bootstrap argument.

We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.