We investigate scalable two-level overlapping Schwarz domain decomposition methods with energy-minimizing coarse spaces of GDSW type (Generalized Dryja--Smith--Widlund type) as preconditioners for the sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph optimization back-end in Simultaneous Localization and Mapping (SLAM). After a brief introduction to SLAM and domain decomposition preconditioners, we describe the nonlinear least-squares formulation, its linearization, and the resulting matrix structure, to facilitate access for readers without prior knowledge of either field. Numerical experiments demonstrate the numerical scalability of the preconditioned conjugate gradient method (CG): Using the two-level overlapping Schwarz preconditioner, the number of CG iterations remains bounded independently of the problem size, overcoming the typical limitations of simple preconditioners, including one-level Schwarz approaches. We further show that a simplified SLAM problem can be interpreted as a finite element problem using linear elastic bars, reinforcing the analogy to continuum mechanics and motivating the use of scalable domain decomposition techniques.

The Euclid galaxy survey will provide unprecedented constraints on cosmology, but achieving unbiased results will require an optimal characterisation and mitigation of systematic effects. The intrinsic alignments (IAs) of galaxies are one of the dominant contaminants of the weak lensing (WL) and galaxy-galaxy lensing (GGL) probes. In this work, we assess IA modelling choices for Euclid DR1 3x2pt analyses by using synthetic data vectors and comparing the performance of the two most commonly used IA models, non-linear alignment (NLA) and tidal alignment tidal torquing (TATT), along with several variations. Our analyses combine three perspectives: (i) the constraining power on the IA and cosmological parameters for each IA model, (ii) the bias that results when the IA analysis model differs from the model used to generate the synthetic data vector, and (iii) the degeneracies between IAs and photometric redshift (photo-z) nuisance parameters. Amongst the IA models analysed, the redshift-dependent TATT model (zTATT) provides the most flexible description of IAs, with a constraining power similar to simpler IA models, making it a suitable choice for Euclid DR1 3x2pt analyses.

Fromager and Lasorne [Electron. Struct. 6 025002 (2024)] have recently derived an in-principle exact Kohn-Sham density functional theory (KS-DFT) of electrons and nuclei, where the nuclear density and the (so-called conditional) electronic density are mapped onto a fictitious electronically non-interacting KS molecule. In this work, we apply the exact factorization formalism to the molecular KS wavefunction, thus leading to disentangled (but coupled) marginal and conditional KS equations. We show that, while being equivalent to the original theory, these equations open new perspectives in the practical extension of regular (electronic) KS-DFT beyond the Born-Oppenheimer approximation. The importance and treatment of correlations induced in this context by second-order geometrical derivatives is also discussed.

In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non compact symmetric spaces $\mathrm{U/H}$ that are the mathematical model of hidden layers in the new paradigm of Cartan Neural Networks. We introduce a distinction between the generalized thermodynamics associated with Dynamical Systems and the challenging proposal of Gibbs probability distributions on $\mathrm{U/H}$ provided by generalized thermodynamics {à} la Souriau. Main result is the proof that $\mathrm{U/H}$.s supporting Gibbs distributions are only the Kähler ones. For the latter, we solve the problem of determining the space of temperatures, namely of Lie algebra elements for which the partition function converges. The space of generalized temperatures is the orbit under the adjoint action of $\mathrm{U}$ of a positivity domain in the Cartan subalgebra $C_c\subset\mathbb{H}$ of the maximal compact subalgebra $\mathbb{H}\subset\mathbb{U}$. We illustrate how our explicit constructions for the Poincaré and Siegel planes might be extended to the whole class of Calabi-Vesentini manifolds utilizing Paint Group symmetry. Furthermore we claim that Rao's, Chentsov's, Amari's Information Geometry and the thermodynamical geometry of Ruppeiner and Lychagin are the very same thing. The most important property of the Gibbs probability distributions provided by the here introduced setup is their covariance with respect to the action of the full group of symmetries $\mathrm{U}$. The partition function is invariant against $\mathrm{U}$ transformations and the set of its arguments, namely the generalized temperatures, can be always reduced to a minimal set whose cardinality is equal to the rank of the compact denominator group $\mathrm{H}\subset \mathrm{U}$.

We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with local Moment Tensor Potential and demonstrate that they reduce the training errors of the MTP models fitted on the same training sets including the CH$_3$COO$^-$+4-methylphenol and CH$_3$COO$^-$+4-methylimidazole organic dimers (non-periodic systems) and the NaCl crystal (periodic system). For the organic dimers, the proposed models also give qualitatively correct predictions of the binding curves. Furthermore, in this study we introduce a method for calculating phonon spectra of isotropic materials only via these long-range models fitted to energies, forces, and stresses. The developed long-range model with point charges dependent on atomic environments and conserving total charge is capable of predicting the correct value of the LO-TO splitting in the $Γ$-point in the isotropic NaCl. For this system, we also predict dielectric constant from dipole moment fluctuations calculated with molecular dynamics simulations conducted with the developed long-range model. The calculated dielectric constant is in good agreement with experiment. Finally, we demonstrate the broader applicability of the introduced approach by computing the phonon spectrum of uniaxial tetragonal PbTiO$_3$. Although the method is formally derived for isotropic materials, we show that it is also perspective for uniaxial materials (e.g., PbTiO$_3$) as the spectrum obtained with our long-range interatomic potential corresponds to the one calculated with density functional theory.

We investigate the magnetic moments of strange hidden-bottom pentaquark states within the constituent quark model, considering both molecular and compact configurations. The system with quark content $qqqb\bar{b}$ ($q=u,d,s$) is analyzed in three configurations: a baryon-meson molecular form $(\bar b q_1)(b q_2 q_3)$, a diquark-diquark-antiquark structure $(b q_1)(q_2 q_3)\bar b$, and a diquark-triquark configuration $(b q_1)(\bar b q_2 q_3)$. Negative-parity states with $J^P = 1/2^-$, $3/2^-$, and $5/2^-$ are studied for strangeness $\mathcal{S}=-1,-2,-3$. For the dominant spin couplings, the two compact configurations yield identical or numerically very close magnetic moments. This indicates that the magnetic properties are governed primarily by the global spin-flavor structure and heavy-quark suppression effects rather than by the specific clustering of quarks. A systematic suppression with increasing strangeness and a clear spin hierarchy are observed across all configurations. Due to the large bottom-quark mass, heavy-quark contributions are strongly suppressed, and the magnetic moments are dominated by light-strange spin correlations. These results provide useful theoretical benchmarks for future experimental and lattice studies of exotic multiquark states.

The state of the art in solving nonconvex nonsmooth games under uncertainty remains in its infancy. Existing studies primarily rely on stringent growth and sharpness conditions or local convexity-like properties, making the development of alternative algorithms desirable. In this work, we study the Clarke-Nash equilibria (CNE) computation of a class of stochastic $N$-player nonconvex nonsmooth games characterized by a potential function. We first consider the nonconvex smooth setting and develop a randomized stochastic gradient (RSG) scheme. The RSG scheme achieves the optimal sample complexity of $\mathcal{O}(N^{2}ε^{-4})$ for reaching a point whose expected residual has norm at most $ε$. Building on this result, we introduce a randomized smoothed RSG (RS-RSG) scheme for solving stochastic potential games afflicted by nonconvexity and nonsmoothness. We show that RS-RSG asymptotically converges to an equilibrium of the smoothed game with sample complexity $\mathcal{O}(L^{4}_{\max}n^{3/2}_{\max}N^{3}η^{-1}ε^{-4})$, where $η>0$ is the smoothing parameter. Under Lipschitz continuity of the Clarke subdifferentials, we show that the expected residual evaluated at the smoothed equilibrium is $\mathcal{O}(η^{2})$. In addition, we discuss the biased RSG and RS-RSG variants and demonstrate the effectiveness of the biased RS-RSG scheme on a class of stochastic potential hierarchical games where the exact lower-level solution is unavailable in finite time. Collectively, our results provide a new pathway that goes beyond classical conditions for solving stochastic nonconvex nonsmooth games. Some preliminary numerics are also provided.

The development and operation of large-scale particle physics facilities rely not only on accelerators and detectors, but also on sustained, high-precision simulation infrastructure. Originating in Lund in the late 1970s and continuously developed in Sweden for nearly five decades, PYTHIA has evolved into one of the most widely used Monte Carlo event generators in high-energy physics. Today it functions as a facility-scale software infrastructure underpinning the physics programmes of major international experiments, including those at the Large Hadron Collider, and plays a central role in validation, tuning, and uncertainty evaluation. In this article, we present PYTHIA as a Swedish contribution to big science facilities. We outline its historical development, analyze its contemporary user base through citation and text-based studies, and map its integration across experimental frameworks, generator ecosystems, validation infrastructures, and emerging machine-learning workflows. These analyses show that PYTHIA We discuss the operational model and sustainability challenges associated with maintaining long-lived research software at facility scale. As particle physics moves toward the High-Luminosity LHC era and future facilities such as the EIC and FCC, continued investment in robust, interoperable simulation infrastructure remains essential. We discuss the operational model and sustainability challenges associated with maintaining long-lived research software at facility scale. As particle physics moves toward the High-Luminosity LHC era and future facilities such as the EIC and FCC, continued investment in robust, interoperable simulation infrastructure remains essential.

Real-time analysis of epidemic trends and forecasts can help support public health planning and the response to seasonal respiratory disease. Here, we present two models that were used in a 2025 New Zealand winter situational assessment programme for three respiratory pathogens: SARS-CoV-2, influenza and respiratory syncytial virus (RSV). Data on SARS-CoV-2 were obtained from the national Covid-19 surveillance system; data on influenza and RSV were limited to a sentinel hospital surveillance programme. Models were run weekly from May to October 2025 on these real-time disease surveillance data and provided a quantitative representation of the current epidemic trend, along with estimates of the epidemic growth rate and 28-day ahead forecasts of case incidence. Model results and interpretation were provided in weekly reports to public health partners as part of a trans-Tasman winter programme run by the Australia--Aotearoa Consortium for Epidemic Forecasting and Analytics (ACEFA). We compare in-season results that were included in these reports to a retrospective analysis of the complete data for the season. We conclude that real-time analyses performed reasonably well, and identify some areas for improvement in future winter situational assessment programmes.

Ambient-pressure superconductivity in compressively strained bilayer nickelate films provides a unique platform to test pairing scenarios, yet the evolution of magnetism with carrier doping remains largely unexplored. Here, we utilize Ni $L_3$-edge resonant inelastic x-ray scattering to systematically track the evolution of spin and electronic excitations in coherently strained La$_{3-x}$Sr$_x$Ni$_2$O$_7$/SrLaAlO$_4$ thin films, spanning the superconducting ($x \le 0.21$) and overdoped non-superconducting ($x = 0.38$) regimes. We reveal that dispersive spin excitations, characterized by double-stripe correlations and nearly doping-independent exchange scales, persist robustly throughout the entire superconducting dome. In stark contrast, upon entering the overdoped non-superconducting state, this coherent magnetic framework undergoes an abrupt collapse, melting into a heavily damped, low-spectral-weight continuum. We show that this magnetic breakdown is fundamentally driven by a selective doping-induced orbital reconstruction. While the invariant $\sim\!1.0$~eV intra-atomic $dd$ peak confirms an intact local octahedral crystal field, the concurrent quenching of the $\sim\!0.4$~eV and $\sim\!1.6$~eV features signifies a severe degradation of the apical-oxygen-mediated $d_{z^2}$--$p_z$--$d_{z^2}$ singlet sector and bilayer charge-transfer coherence. The synchronized demise of coherent spin excitations and macroscopic pairing establishes a direct, doping-controlled link, underscoring that maintaining the localized $d_{z^2}$ magnetic framework and robust apical-oxygen coupling is the fundamental prerequisite for high-$T_c$ superconductivity in bilayer nickelates.

We consider the Cauchy problem for the hyperbolic-elliptic Ishimori system with general decoupling constant $κ\in \mathbb{R}$ and prove global well-posedness in the critical Sobolev space. The proof relies primarily on new bilinear estimates, which are established via a novel div-curl lemma first introduced by the second author in \cite{zhou_1+2dimensional_2022}. Our approach combines the caloric gauge technique with $U^p$-$V^p$ type Strichartz estimates to handle the hyperbolic structure of the equation. The results extend previous work on the integrable case $(κ= 1)$ to general $κ$ and provide a unified framework which also works for the hyperbolic and elliptic Schrödinger maps in dimensions $d \ge 2$.

We introduce and study a multiplicative analogue of additive indecomposability for linear order types that we call untranscendability, as well as a strengthening that we call $s$-untranscendability. We show that, with the unique exception of the two-point type, every untranscendable type is additively indecomposable, and every $σ$-scattered untranscendable type is strongly indecomposable. Under the Proper Forcing Axiom, every untranscendable Aronszajn type is strongly indecomposable. We also show that a theorem of Hagendorf and Jullien, that every strictly additively indecomposable type must be strictly indecomposable to either the left or right, has a natural analogue for $s$-untranscendable types.

The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on three generators. An order is a subring whose underlying additive group is a lattice. We give conditions for when such an order is realizable, and in particular show that in the simply-connected case any order is realizable if the generators of the exterior algebra are of odd degree.

The host galaxies of tidal disruption events (TDEs) show enhanced central stellar concentration and are preferentially found in poststarburst and green valley populations. This connection has led to the proposal that TDE host galaxies likely have gone through recent mergers. We conduct a new morphological study of 14 TDE host galaxies, using the r-band images from the Sloan Digital Sky Survey (SDSS), Dark Energy Camera Legacy Survey, and Ultraviolet Near-Infrared Optical Northern Survey, with the images from the latter two surveys having much higher depth and resolution than SDSS. We examine galaxy structures using conventional methods and also apply diagnostics of merger activity from a suite of machine learning models. Consistent with previous studies, our results show that TDE host galaxies are ~16% more centrally concentrated when compared to non-TDE-host controls. However, surprisingly, TDE hosts lack any indication of significant recent merger activity from both morphological analysis and the machine learning merger classifier. Instead, our results reveal that TDE host galaxies in the green valley are approximately 1.5-3 times more likely to have bar-like or ringlike structures compared to their controls. Based on these results, we propose that bar-driven secular evolution, instead of mergers, likely dominates the recent evolution of the TDE hosts found in the green valley, which can simultaneously explain their distinctive nuclear properties and enhanced TDE rates.

In this paper, we show that a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than $\left(\frac{1}{4}-\frac{c}{\log n}\right)$ for some universal constant $c>0$ , confirming the nearly optimal spectral gap conjecture in this model.

We present the first end-to-end calculation connecting the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf to observable kilonova signatures, combining 2D general-relativistic neutrino-magnetohydrodynamic simulations, followed by radiation hydrodynamics with in-situ nuclear network and 2D Monte Carlo radiative transfer with spatially resolved heating rates. Unlike all previous unmagnetized AIC models - which predicted proton-rich, $^{56}$Ni-dominated ejecta - strong magnetic fields eject ${\sim 0.2 M_\odot}$ of neutron-rich material $(\langle Y_e \rangle \sim 0.24)$ on dynamical timescales, before neutrino irradiation can raise the electron fraction, enabling strong $r$-process nucleosynthesis up to and beyond the third peak. The resulting kilonova is lanthanide-rich $(X_{\rm lan} \approx 8\%)$ and dominated by near-infrared emission. We compute synthetic light curves in the LSST and JWST bands and find striking agreement, without parameter tuning, between the observations of AT 2023vfi/GRB 230307A and our broadband light curves for polar viewing angles. These results establish magnetized AIC as a viable channel for heavy $r$-process element production and a compelling progenitor candidate for long-duration gamma-ray bursts with kilonova signatures.

Analytical treatments of tunneling in bilayer graphene have typically relied on minimal models including only the vertical interlayer hopping $γ_1$ and have been restricted to the weak interlayer bias regime $2\varepsilon \ll γ_1$. These simplifications limit the ability of analytical theories to describe lattice deformations and strong electric-field effects. In this work, we present an analytical theory of evanescent states in electrically gapped bilayer graphene that overcomes both limitations. Specifically, our approach explicitly incorporates the skew interlayer hoppings $γ_3$ and $γ_4$ and remains valid even when the interlayer bias $2\varepsilon$ is comparable to $γ_1$. Focusing on low-energy electronic states near the charge neutrality point, we analytically derive the complex longitudinal wave numbers, the gap width, and the sublattice pseudospin inside the electric-field-induced gap, and systematically analyze their dependence on the interlayer shear displacement $\vecδ=(δ_x,δ_y)$. The analytical expressions quantitatively reproduce exact numerical calculations, demonstrating that skew interlayer hoppings, in particular $γ_3$, play an essential role. Taking the zigzag direction as the longitudinal (transport) $x$ direction, the wave vector becomes complex along $x$ while remaining real along the transverse $y$ direction. For a monolayer--bilayer--monolayer junction with transport along this direction, we find that $δ_y$ has a significantly stronger impact on the conductance than $δ_x$. This anisotropic response is quantitatively explained by the analytical expressions. Furthermore, we identify a shear-induced phase proportional to $δ_y$ that appears universally in the analytical expressions for the gap width, the sublattice pseudospin, and the decay length.

The Central Molecular Zone (CMZ) of the Milky Way is the way station that primarily controls how much gas flows from the disk of the Galaxy towards the central nucleus. While this region is well documented to have extreme gas properties that clearly distinguish it from the rest of the Galaxy, the properties of the bulk molecular gas at high angular resolution are relatively unexplored. Band 3 data from the ALMA (Atacama Large Millimeter/Submillimeter Array) large program ACES (ALMA CMZ Exploration Survey) reveal the highly filamentary nature of CMZ molecular gas at high resolution (3" or 0.1pc) across the entire CMZ. Visual inspection of these data suggests that there are at least two general classes of elongated structures, which we identify as: i) large-scale (10 pc) filamentary structures (LFs) and ii) a ubiquitous population of small-scale (about 1 pc) filamentary structures (SFs). We present detailed morphological and kinematic properties towards three structures in each category, as well as their association with magnetic fields and the correlation of HNCO 4(0,4)-3(0,3) with other molecular species. Our investigation reveals that these structures are largely coherent in position-position-velocity space. The alignment with the magnetic field structure is mixed, with some parallel, some perpendicular, and some intermediate alignments. We find that LFs likely trace pieces of contiguous CMZ orbital structures and are a manifestation of global CMZ dynamics. The second class, SFs, are pervasive and may be the result of complicated turbulence and shearing dynamics in the CMZ gas flows, as seen in numerical simulations.

We study the discovery prospects for a doubly charged Higgs boson $H^{\pm\pm}$ in the 2-Higgs doublet model with type-II seesaw at future $e^+e^-$ colliders. Focusing on the three-body channels $e^+e^- \to H^{\pm\pm}H_1^{\mp}H_1^{\mp}$ and $e^+e^- \to H^{\pm\pm}H_1^{\mp}W^{\mp}$, we scan the model parameter space subject to theoretical consistency as well as current collider, flavor and electroWeak precision observables (EWPOs). We find that these $2\to3$ production modes can exceed the conventional pair-production rate $e^+e^- \to H^{++}H^{--}$, followed by $H^{\pm\pm}\to H_1^{\pm}H_1^{\pm}$ and $H^{\pm}_1W^{\pm}$ decays, over wide regions, particularly above the $H^{\pm\pm}\to H_1^{\pm}H_1^{\pm}$ and $H^{\pm\pm}\to H_1^{\pm}W^{\pm}$ thresholds, reaching cross sections up to ${\cal O}(10^2)$~fb for $\sqrt{s}=500$--$1500$~GeV. A detector-level analysis of the $4\ell + E_T^{\text{miss}}$ signature, including dominant multiboson and top quark backgrounds, shows that discovery sensitivity is achievable for $\sqrt{s}=1000$-$1500$~GeV with integrated luminosities in the few ab$^{-1}$ range, even in the presence of realistic systematic uncertainties.

The hydrostatic mass bias ($b_{\mathrm{HSE}}$) is a leading systematic uncertainty in cluster cosmology and a principal source of degeneracy with $σ_8$ and $Ω_m$. We investigate the capability of Stage-IV CMB and optical surveys to calibrate $b_{\mathrm{HSE}}$ using tomographic cross-correlations between the thermal Sunyaev--Zel'dovich (tSZ) effect, galaxy clustering, and weak lensing. We perform a Fisher forecast incorporating realistic survey noise, foreground modeling for clustered CIB and radio sources, and full marginalization over cosmological and astrophysical nuisance parameters, including per-bin galaxy bias perturbations, photometric redshift shifts, intrinsic alignments, and baryonic feedback modeled with HMCode2020. With optimized tomographic binning (10 lens and 5 source bins for LSST; 6 lens and 5 source bins for CSST), we forecast marginalized constraints of $0.98\%$ for SO+LSST, $1.60\%$ for CMB-S4+LSST, and $2.40\%$ for CMB-S4+CSST. Tomography improves $b_{\mathrm{HSE}}$ precision by factors of approximately three relative to non-tomographic analyses, reflecting the role of redshift information in breaking the $b_{\mathrm{HSE}}$--$σ_8$ degeneracy. Optical-only probes provide no direct constraint on $b_{\mathrm{HSE}}$, whereas inclusion of tSZ-containing spectra enables percent-level calibration under realistic systematic assumptions. The results demonstrate that multi-probe tomographic analyses with Stage-IV surveys can achieve robust control of hydrostatic mass bias, strengthening cluster-based constraints on structure growth.

We study a slow-fast parasite--host model featuring a singularity at the extinction state. Using techniques from Geometric Singular Perturbation Theory (GSPT), and in particular the so-called blow-up method, we desingularize that point and reconstruct the local and global dynamics. The system we consider is in non-standard GSPT form and is characterized by a rich dynamical behavior: families of slow-fast homoclinic orbits, canard-like transitions generated by trajectories that remain close to a repelling critical manifold, and topological changes produced by infinitesimal variations of the infection rate, including the creation and destruction of an endemic equilibrium. We also show that our model is able to reproduce dynamics observed in the spread of the Tasmanian devil facial tumor disease (DFTD), whose behavior resembles the one of a parasite. We conclude with a numerical exploration of the model, to illustrate our analytical results.

The ability to use tools is fundamental for large language model (LLM) agents. Given a task, existing systems use LLMs to plan and generate tool calls, which are executed by real-world tools to complete the task. However, tool calls are prone to errors because they are generated primarily from the intrinsic capabilities of LLMs. Moreover, while it is useful to let LLMs iteratively refine the tool-call sequence using execution results from real tools, this process can be expensive and may cause unsafe side effects. To improve LLM tool calls and address issues caused by using real tools for refinement, we introduce Gecko, a stateful simulation environment that provides informative feedback for refining LLM tool calls before real execution. Specifically, Gecko combines rules and LLMs to check the validity of tool names and arguments, synthesize schema-conforming and state-consistent responses, and judge task completion against the user objective. These three types of feedback allow LLMs to refine their tool calls in simulation, forming a simple yet effective test-time scaling method named GATS. On BFCLv3 and $τ^2$-bench, GATS consistently improves the performance of various LLMs.

Owing to the power-law anisotropy in the quasiparticle dispersion, yielding an enhanced density of states, the effects of long range Coulomb interaction get amplified in three-dimensional generalized Weyl semimetals, characterized by integer monopole charge $n>1$ of the underlying Weyl nodes. Using a Wilsonian renormalization group approach controlled by a large-$N$ expansion with $N$ as the number of Weyl fermion flavors and a gauge-consistent regularization fixed by the Ward-Takahashi identity, we uncover for $n\ge 2$ an extended interaction-dominated scaling regime with intrinsically anisotropic dynamic Coulomb screening, a finite fermionic anomalous dimension, and a power-law suppression of the quasiparticle residue, yielding an \emph{anisotropic} marginal non-Fermi liquid at intermediate energies. Ultimately, the effective fine structure constant flows to zero, albeit only logarithmically slowly, so the marginal Fermi liquid phenomenology emerges as a broad crossover, controlled by a slowly running coupling. By contrast, for $n=1$ the system retains an isotropic marginal Weyl-liquid character. These predictions can be tested via scaling in thermodynamics (specific heat and compressibility), direction-dependent optical conductivity, and by anisotropic broadening of the single-particle spectral function in angle-resolved photoemission spectroscopy.

Recent advancements in semantic communication have primarily focused on image transmission, where neural network-based joint source-channel coding modules play a central role. However, such systems often experience semantic communication errors due to mismatched knowledge bases between agents and performance degradation from outdated models, necessitating regular model updates. To address these challenges in vector quantization (VQ)-based image semantic communication systems, we propose FedSFR, a novel federated learning framework that incorporates semantic feature reconstruction (FR). FedSFR introduces an FR step at the parameter server and allows a subset of clients to transmit compact feature vectors in lieu of sending full local model updates, thereby improving training stability and communication efficiency. To enable effective FR learning, we design a loss function tailored for VQ-based image semantic communication and demonstrate its validity as a surrogate for image reconstruction error. We further establish a rigorous convergence analysis of FedSFR. Experimental results on two benchmark datasets validate the superiority of FedSFR over existing baselines, especially in capacity-constrained settings, confirming both its effectiveness and robustness.

Laser-assisted Atom Probe Tomography (LA-APT) has demonstrated a unique potential for the study of the 3D distribution of atomic species in semiconductor materials and devices, and in a growing list of inorganic non-metallic solids. A crucial and often underestimated issue with APT is its accuracy in compositional measurements of non-metallic systems. This work introduces the principles of APT as an experimental technique, recalling the aspects potentially leading to compositional biases and underlining in particular the role of the surface electric field in governing the different physical-chemical phenomena that enable the measurement. It reviews the possible mechanisms of specific losses, as well as the methods for assessing a compositional bias and proposing possible correction methods. Finally, it establishes a state of the art on compositional biases in APT of non-metallic materials, on the basis of which it will be possible to conclude on specific recommendations for best practices, and the perspective of application of APT to new materials.

There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We address the problem of how these should be treated. We propose a ''reduction of order'' approach which is applied not at the level of equations of motion but only to initial data. This specifies uniquely the data for the unphysical modes in terms of the data for the physical modes. We argue that the apparent breaking of Lorentz invariance associated with this approach is not a problem provided one restricts to Lorentz frames for which the assumptions of effective field theory are manifestly valid.

Let $k$ be a field, $f:X\rightarrow S$ a proper morphism between connected schemes proper over $k$, $x\in X(k)$ lying over $s\in S(k)$, $X_s$ the fibre of $f$ over $s$, $\mathcal{C}_X$, $\mathcal{C}_{S}$, $\mathcal{C}_{X_s}$ Tannakian categories over $X,S,X_s$ respectively, $π(\mathcal{C}_X,x)$, $π(\mathcal{C}_S,s)$, $π(\mathcal{C}_{X_s},x)$ the Tannaka group schemes respectively. We give a unified criterion for the exactness of the homotopy sequence of Tannakian fundamental group schemes $π(\mathcal{C}_{X_s},x)\rightarrow π(\mathcal{C}_X,x)\rightarrow π(\mathcal{C}_S,s)\rightarrow 1$. In particular, we obtain the equivalent conditions for the Künneth formula of fundamental group schemes for the product $X\times_k Y$ of two connected schemes $X$ and $Y$ proper over $k$. As an application, we obtain the Künneth formula of certain fundamental group schemes over any field, such as S, N, EN, F, EF, ét, Eét, Loc, ELoc and uni-fundamental group schemes.

We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e. exponentially convergent. In addition to that, we attach substitutions to this algorithm and study the $S$-adic languages generated by sequences of these substitutions. The negativity of the second Lyapunov exponent implies that almost all of these languages are balanced. By a thorough study of the combinatorics of the substitutions, we are even able to obtain a concrete generic family of balanced languages that is characterized in terms of a simple condition on the underlying sequence of substitutions.

Accurately simulating the non-Markovian dynamics of open quantum systems remains a significant challenge. While the recently proposed time-evolving matrix product operator (TEMPO) algorithm based on path integrals successfully circumvents the exponential scaling associated with memory length, its reliance on layer-by-layer tensor contractions and compressions leads to steep scaling with respect to the system Hilbert space dimension. In this work, we introduce the effective Hamiltonian-based TEMPO (EH-TEMPO) algorithm, which reformulates the calculation of the Feynman-Vernon influence functional as an imaginary time evolution governed by an effective Hamiltonian. We demonstrate that this effective Hamiltonian admits a highly compact matrix product operator representation, enabling substantial compression with negligible loss of accuracy. Combining a one-shot global evolution with a backward retrieval approach, EH-TEMPO significantly reduces algorithmic complexity and is naturally suited for GPU acceleration. We benchmark the method by simulating the energy transfer dynamics in the 7-site Fenna-Matthews-Olson complex model and 4-site perylene bisimide model. The results demonstrate that EH-TEMPO achieves numerically exact accuracy with superior efficiency, delivering speedups of up to 17.5$\times$ on GPU hardware compared to standard CPU implementations.

The quantum Cramér-Rao (QCR) bound sets the ultimate local precision limit for unbiased multiparameter estimation. Unlike in the single-parameter case, however, its saturability is not generally guaranteed and is often analyzed through a hierarchy of commutativity-based conditions. Here, we resolve the logical structure of these conditions for unitary parameter-encoding transformations. We identify strict separations among the conditions, reveal previously overlooked gaps in their implications, and construct explicit counterintuitive examples that expose the boundaries among distinct classes. In particular, we show that commutativity of the parameter-encoding generators alone does not guarantee saturation of the QCR bound when realistic noise leads to mixed probe states. Our results provide a systematic classification of saturation conditions in multiparameter quantum metrology and clarify fundamental precision limits of noisy distributed quantum sensing beyond idealized pure-state regimes.