Current learning-based Automated Vulnerability Repair (AVR) approaches, while promising, often fail to generalize effectively in real-world scenarios. Our diagnostic analysis reveals three fundamental weaknesses in state-of-the-art AVR approaches: (1) limited cross-repository generalization, with performance drops on unseen codebases; (2) inability to capture long-range dependencies, causing a performance degradation on complex, multi-hunk repairs; and (3) over-reliance on superficial lexical patterns, leading to significant performance drops on vulnerabilities with minor syntactic variations like variable renaming. To address these limitations, we propose SeCuRepair, a semantics-aligned, curriculum-driven, and reasoning-enhanced framework for vulnerability repair. At its core, SeCuRepair adopts a reason-then-edit paradigm, requiring the model to articulate why and how a vulnerability should be fixed before generating the patch. This explicit reasoning enforces a genuine understanding of repair logic rather than superficial memorization of lexical patterns. SeCuRepair also moves beyond traditional supervised fine-tuning and employs semantics-aware reinforcement learning, rewarding patches for their syntactic and semantic alignment with the oracle patch rather than mere token overlap. Complementing this, a difficulty-aware curriculum progressively trains the model, starting with simple fixes and advancing to complex, multi-hunk coordinated edits. We evaluate SeCuRepair on strict, repository-level splits of BigVul and newly crafted PrimeVul_AVR datasets. SeCuRepair significantly outperforms all baselines, surpassing the best-performing baselines by 34.52% on BigVul and 31.52% on PrimeVul\textsubscript{AVR} in terms of CodeBLEU, respectively. Comprehensive ablation studies further confirm that each component of our framework contributes to its final performance.

We study the production of hypothetical vector portal mediators, dark photons $γ^\prime$, with masses in the range 0.4-3.5 GeV in the negatively charged pion-proton collisions $π^-p\rightarrow γ^\prime X$ via inelastic pion bremsstrahlung and QCD Drell-Yan-like process. In both cases we estimate the value of total dark photon production cross section and obtain the energy distribution for dark photons that could be produced in the NA64h experiment. We also present the mean energies of dark photons produced in the same way by the secondary pions with momenta typical for T2K, DUNE and SHiP experiments.

We study a joint communication and sensing setting comprising a transmitter, a receiver, and a sensor, all equipped with multiple antennas. The transmitter sends an encoded signal over the channel with the dual purpose of communicating an information message to the receiver, and enabling the sensor to estimate a target parameter vector by generating back-scattered signals. We assume that the transmitter and sensor are co-located, or fully connected, giving the latter access to the transmitted signal. The target parameter vector is randomly drawn from a continuous distribution, yet remains fixed throughout the transmission block. We establish the fundamental performance trade-off between the communication and sensing tasks, captured in terms of a capacity-MSE function. In doing so, we identify optimal coding schemes for this multi-antenna joint communication and sensing setting. Moreover, we particularize our result to two practically-inspired scenarios where we showcase optimal schemes and trade-offs.

We develop a block-activated decomposition algorithm for multi-stage stochastic variational inequalities with nonanticipativity constraints, which features two computational novelties: (i) At each iteration, our method activates only a user-chosen subset of scenarios. (ii) For each activated scenario, it employs the resolvent of the cost operator and the projector onto the constraint set separately. These reduce computational load and enhance tractability, in contrast with existing approaches, which often rely on evaluating the resolvent of the sum of the cost operator and normal cone operator of the constraint set. As an application, we demonstrate that in risk-averse stochastic programming with conditional value-at-risk objective functions, our method requires only projecting onto constraint sets, together with solving univariate equations involving the proximity operators of the cost functions, thereby avoiding solving high-dimensional constrained subproblems as required by existing methods.

We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the ground-state energy within inverse-polynomial precision. This setting captures real-world scenarios in quantum chemistry and many-body physics, where trial states derived from classical heuristics can be used to guide quantum algorithms. We identify families of physically-motivated guiding states for which the computational hardness of ground-state energy estimation persists in the guided setting. Extending prior results for semi-classical subset states, we prove BQP-hardness for classes including fixed-weight states, matrix product states, Gaussian states, and Fendley states. Our hardness results are obtained via refined Feynman-Kitaev circuit-to-Hamiltonian constructions that explicitly expose the structural role of the guiding state in the reduction. Complementing these results, we give a constructive proof of BQP containment when the guiding state admits a polynomial-size classical description, establishing BQP-completeness for the canonical formulation of the problem. Our results show that quantum advantage persists for the newly introduced state classes, and classical methods also remain viable when said guiding states admit appropriate descriptions. Together, our results identify a Goldilocks zone of guiding states that are efficiently preparable, succinctly described, and sample-query accessible, within which quantum advantage for ground-state estimation can be meaningfully assessed. We additionally formalise the Guided Fermi-Hubbard Hamiltonian problem and prove BQP-completeness on 2D square and triangular lattices, both with and without magnetic fields, when provided with an appropriate fermionic guiding state.

Given a finite simple connected graph $Γ$, the graphical configuration space $\mathrm{Conf}_Γ(X)$ is the space of collections of points in $X$ indexed by the vertices of $Γ$, where points corresponding to adjacent vertices must be distinct. When $X=\mathbb{R}^d$ and the points are replaced by small disks, the resulting spaces for all possible graphs fit together into an algebraic structure that extends the little disks operad, called the little disks contractad $\mathcal{D}_d$. In this paper, we investigate the homotopical and algebraic properties of the little disks contractad $\mathcal{D}_d$. We construct and study Fulton-MacPherson compactifications of graphical configuration spaces, which provide a convenient model for $\mathcal{D}_d$ within the class of compact manifolds with boundary. Using these and wonderful compactifications, we prove that $\mathcal{D}_d$ is formal in the category of (Hopf) contractads for $d=1$, $d=2$, and for chordal graphs for any $d$. We also identify the first obstructions to coformality in the case of cyclic graphs. In addition, we give a combinatorial description of the cell structure of $\mathcal{D}_2$ and present applications to the study of graphical configuration spaces $\mathrm{Conf}_Γ(X)$ using the language of twisted algebras.

Topology optimization is a promising approach for mitigating congestion and managing changing grid conditions, but it is computationally challenging and requires approximations. Conventional distribution factors like PTDFs and LODFs, based on DC power flow, fail to capture voltage variations, reactive power, and losses, thereby limiting their use in detailed optimization tasks such as busbar splitting. This paper introduces generalized distribution factors derived from a voltage-sensitive linearization of the full AC power flow equations. The proposed formulation accurately reflects reactive power flows, Ohmic losses, and voltage deviations while remaining computationally efficient. We derive and evaluate generalized PTDFs, LODFs, and topology modification factors using matrix identities. We discuss potential applications including voltage-aware N-1 security analysis and topology optimization with a focus on busbar splitting. Numerical experiments demonstrate close agreement with full AC solutions, significantly outperforming the traditional DC approximation.

A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate a system's intrinsic functional logic with statistical artifacts of limited data. As a result, distinct systems can yield identical observations, rendering information decomposition fundamentally underdetermined and obscuring true higher-order interactions. We introduce Functional Information Decomposition (FID), both a computational and theoretical framework, which defines informational components with respect to a system's complete input-output mapping, thereby addressing a core cross-scale inference problem: determining how information carried by individual components combines to shape system-level behavior. When the mapping is fully specified, FID provides a unique decomposition into independent and synergistic contributions. Crucially, given only partial observations, FID characterizes the entire space of consistent decompositions by sampling compatible functions, making inferential limits explicit. A complementary geometric perspective clarifies the structural origin of informational components. We demonstrate FID's interdisciplinary utility on canonical logical functions, Conway's Game of Life, and gene-expression-based prediction of cancer drug response, and provide an open-source implementation. By separating functional architecture from observational distribution, FID offers a principled foundation for analyzing multivariate dependence in both fully and partially observed complex systems.

Traditionally, gravity is generally considered to exert an extremely weak effect in chemistry because the Newtonian gravitation is typically negligible compared to the dominant Coulomb potentials in a molecular system. In this work, we porpose a primitive framework of chemical dynamics in curved spacetime through fiducial-observer $[3+1]$ formulation by revising the nuclear Hamiltonian operator through the metric tensor of configuration space rather than by adding Newtonian gravitation in the potential energy term, where the absolute-sapce and universal-time viewpoint of Galileo is adopted. Using frames fixed on normal observers in the $[3+1]$ formalism ensures possibility of this treatment. Taking spherically symmetric curved spacetime ({\it i.e.} Schwarzschild spacetime) as numerical demonstration, we explore (1) the H + H$_2$ reaction dynamics, (2) the H$_2$ + H$_2$ scattering dynamics, (3) dynamics of dissociative chemsorption of H$_2$O on Cu(111), (4) the spectrum band of anthracene cation, and (5) the Berry phase in the nuclear wave function of a 98D surface scattering model. These calculations predict that (i) reaction or scattering probability and (ii) spectrum band decrease abruptly to zero as the spacetime curvature increases; meanwhile, the geometric phase is unaffected by the spacetime curvature. Finally, discussions on these numerical results, together with perspectives on the applications of quantum field theory to chemical dynamics in curved spacetime are given.

A field $F$ is a $\mathfrak{B}_s$-field if, for every finite extension $E'/E$ of $F$, the norm map $K_s^M(E')\to K_s^M(E)$ of the Milnor $K$-groups is surjective. In particular, finite fields ($s=1$), local fields, and certain global fields (with $s=2$) satisfy this condition. For such a field $F$ and a $d$-dimensional variety $X$ over $F$, we prove that $CH^{d+n}(X,n)$ is divisible for $n \geq s+1$, and $CH^{d+s}(X,s)$ is isomorphic to the direct sum of the Milnor $K$-group $K_{s}^M(F)$ and a divisible group. As an application, we study the Kato homology groups $KH_0^{(n)}(X,\mathbb{Z}/l^r\mathbb{Z})$ for any prime $l$ different from the characteristic of $F$.

The discovery and understanding of new quantum phases has time and again transformed both fundamental physics and technology, yet progress often relies on slow, intuition-based theoretical considerations or experimental serendipity. Here, we introduce a general gradient-based framework for targeted phase discovery. We define a differentiable function, dubbed "target-phase loss function", which encodes fingerprints of a quantum state, thereby recasting phase search as a tractable optimization problem in Hamiltonian space. The method is broadly applicable to a wide range of symmetry-broken and topological orders and can be interfaced with most many-body numerical solvers. As a demonstration, we apply it to spinless fermions on the kagome lattice using exact diagonalization and discover two distinctive fractional Chern insulators (FCIs): (i) at filling $ν= 1/3$, a "non-ideal" Abelian FCI whose band geometry lies far beyond the Landau-level mimicry paradigm and all recent generalizations; and (ii) at $ν= 1/2$, a non-Abelian FCI stabilized purely by finite-range two-body interactions. These results provide the first explicit realization of such types of FCIs and establish a versatile paradigm for systematic quantum-phase discovery.

We demonstrate a continuous spectroscopy technique with frequency sensitivity well below the natural transition linewidth, while maintaining a locking range hundreds of times larger. The method exploits the position dependence of a continuous, broadband magneto-optical trap operating on the 7.5 kHz-wide intercombination line of strontium. We show that the frequency sensitivity is fundamentally insensitive to the effective MOT laser linewidth. By applying active feedback on the MOT position to a dispersion-optimized frequency comb, which serves as the reference for stabilizing the MOT laser [1], we achieve a frequency instability below $4.4\times10^{-13}$ after 400 s of averaging in both the optical and radio-frequency domains, surpassing the performance of conventional hot-vapor modulation transfer spectroscopy. Our method is a broadly applicable alternative route to frequency references in the high $10^{-14}$ range around 100 s.

We propose a method for calculating exciton spectra and wavefunctions for model lattice Hamiltonians, based on real-space electron-hole propagators. We verify that our results agree with those of the continuum approximation in the limit of large Wannier excitons, and propose a simple criterion to estimate the exciton size above which the continuum approximation is quantitatively accurate. We then investigate simple one- and two-dimensional multi-orbital lattice models and show that small, Frenkel-like excitons, whose size approaches the lattice constant, can display physics that disagrees with the simplest continuum descriptions (a single-valley quadratic expansion around the minimum gap) not just quantitatively, but qualitatively. Specifically, we identify sharp transitions in the character and momentum of the lowest-energy exciton, enabled by the multi-orbital nature of the lattice models.

Understanding the source of the universe's asymmetry between matter and antimatter is one of the major open questions in particle physics. In this work, the sensitivity of novel machine-learning-based inference techniques to CP-odd and CP-even $HWW$ anomalous couplings is studied in the $\\WH \rightarrow \ell νb\bar{b}$ channel ($\ell = e, μ$), within the Standard Model Effective Field Theory (SMEFT) framework. Two machine-learning simulation-based inference (SBI) methods are explored: a per-event likelihood-ratio estimator, which directly approximates the ratio of probability densities between competing hypotheses, is benchmarked against a per-event optimal-observable estimator optimized for sensitivity to the parameters of interest. Both approaches are also compared to traditional summary statistics, in this case histograms of kinematic and angular observables, as commonly used in experimental analyses. SBI methods provide tighter constraints than one-dimensional summary statistics, though their performance is comparable to two-dimensional histogram analysis. The optimal-observable approach remains promising for its ability to probe multiple couplings simultaneously. Restricting the analysis to a region of high $S/B$ also enhances sensitivity to CP-odd operators while preserving sensitivity to CP-even operators, which histogram analyses often lose. Although the likelihood-ratio estimator sometimes struggles with likelihood minima and shapes, optimisations that target its robustness could make it more sensitive than both the optimal-observable estimator and the histogram method. These results underscore the potential of advanced simulation-based inference techniques, encouraging further exploration with LHC Run 3 data to surpass current ATLAS and CMS sensitivities.

Intensity Mapping (IM) of the 21-cm line of the neutral hydrogen (\textsc{Hi}) has become a compelling new technique to map the large-scale structure of the Universe. One of the main challenges is the presence of strong foreground emissions of several orders of magnitude larger than the \textsc{Hi}~signal. Here, we implement a version of the Principal Component Analysis, a blind component-separation technique, based on a kind of spherical wavelets called needlets. These functions exploit double localization both in real and in harmonic space. We test Need-PCA performances on a set of maps that simulates the SKA MID radio telescope in the AA4 configuration. We compare our results with other component separation methods such as Generalised Morphological Component Analysis (GMCA) and Generalized Needlet Internal Linear Combination (GNILC). All the methods have comparable results, recovering the \textsc{Hi}~signal within 10\% accuracy across the frequency channels, in the multipole range 30 $\lesssim \ell \lesssim$ 136. We also test our pipeline in the presence of systematics such as polarization leakage. We find that the cleaning methods are insensitive to the presence of such systematic, yielding the same results as in the leakage-free case. Finally, under the assumption of a realistic telescope beam with sidelobes, we find that standard PCA and GMCA fails to recover the \textsc{Hi}~signal at larger scales, while the Need-PCA and Need-GMCA are less affected. GNILC tends to over-clean, yielding to a loss of the signal.

Causal analysis on relational databases is challenging, as analysis datasets must be repeatedly queried from complex schemas. Recent LLM systems can automate individual steps, but they hardly manage dependencies across analysis stages, making it difficult to preserve consistency between causal hypothesis. We propose ORCA (ORchestrating Causal Agent), an interactive multi-agent framework to enable coherent causal analysis on relational databases by maintaining shared state and introducing human checkpoints. In a controlled user study, participants using ORCA successfully completed end-to-end analysis more often than with a baseline LLM (GPT-4o-mini) assistant by 42 percentage points, achieved substantially lower ATE error, and reduced time spent on repetitive data exploration and query refinement by 76\% on average. These results show that ORCA improves both how users interact with the causal analysis pipeline and the reliability of the resulting causal conclusions.

Stochastic optimization via Stochastic Gradient Descent (SGD) is a fundamental problem in statistics and optimization. This paper revisits Stochastic Gradient Descent (SGD) for strongly convex objectives, establishing tight, uniform-in-time convergence bounds. We prove that, with probability at least $1 - β$, a convergence rate of order $\frac{\log \log k + \log (1/β)}{k}$ simultaneously holds for all $ k \in \mathbb{N}_+ $, and demonstrate this bound is tight up to constant factors. We also provide an improved last-iterate convergence rate for such objectives. While focused on strongly convex objectives, our results generalize to the Polyak-Łojasiewicz functions and indicate an $\mathcal{O}(k^{-1} \log \log k)$ convergence rate for contractive stochastic approximation with additive noise.

A central open question in extremal design theory is Nash-Williams' Conjecture from 1970 that every $K_3$-divisible graph on $n$ vertices (for $n$ large enough) with minimum degree at least $3n/4$ has a $K_3$-decomposition. A folklore generalization of Nash-Williams' Conjecture extends this to all $q\ge 4$ by positing that every $K_q$-divisible graph on $n$ vertices (for $n$ large enough) with minimum degree at least $\left(1-\frac{1}{q+1}\right)n$ has a $K_q$-decomposition. We disprove this conjecture for all $q\ge 4$; namely, we show that for each $q\ge 4$, there exists $c > 1$ such that there exist infinitely many $K_q$-divisible graphs $G$ with minimum degree at least $\left(1-\frac{1}{c\cdot(q+1)}\right)v(G)$ and no $K_q$-decomposition; indeed we construct them admitting no fractional $K_q$-decomposition thus disproving the fractional relaxation of this conjecture. Our result also disproves the more general partite version. Indeed, we even show the folklore conjecture is off by a multiplicative factor by showing that for every $\varepsilon > 0$ and every large enough integer $q$, there exist infinitely many $K_q$-divisible graphs $G$ with minimum degree at least $\bigg(1-\frac{1}{\left(\frac{1+\sqrt{2}}{2}-\varepsilon\right)\cdot (q+1)}\bigg)v(G)$ with no (fractional) $K_q$-decomposition.

The cross sections of 103Rh(n,gamma) and 103Rh(gamma,n) play a crucial role in the stellar nucleosynthesis, rhodium-based self-powered neutron detectors, and nuclear medicine. The cross sections of 103Rh(n,gamma) was measured by the time-of-flight(TOF) method from 1 eV to 1000 keV at the Back-n facility of the Chinese Spallation Neutron Source. In the resolved resonance region, the data reported multiple new resonance structures for the first time. And some discrepancies were observed, offering valuable insights into the differences between the evaluated libraries. Maxwellian-averaged cross sections (MACSs) were calculated within the temperature range of the s process nucleosynthesis model, based on the averaged cross sections in the unresolved resonance region. Meanwhile the cross sections of 103Rh(gamma,n) within the range of p process nucleosynthesis were measured using laser Compton scattering (LCS) gamma rays and a new neutron flat efficiency detector (FED) array at the Shanghai Laser Electron Gamma Source (SLEGS), Shanghai Synchrotron Radiation Facility (SSRF). Using an unfolding iteration method, 103Rh(gamma,n) data were obtained with uncertainty less than 5%, and the inconsistencies between the available experimental data and the evaluated libraries were discussed. This study provides a reliable benchmark for nuclear data evaluation and model optimization, and lays a solid foundation for Rh medical isotope applications and astrophysical research.

We study the thermodynamics of $D$-dimensional Gauss-Bonnet black holes with Barrow entropy. It is found that the Gauss-Bonnet coupling and the Barrow factor revise the thermodynamic variables such as event horizon, Hawking temperature, entropy and heat capacity. It is interesting that the larger five-dimensional black holes exist stably and the smaller ones evaporate to disappear owing to the nature of heat capacities amended by the coupling and factor. The discussions exhibit that the $D$-dimensional black holes with $D=6, 7$ set free all of their energy to vanish because of the minus heat capacities as functions of Hawking temperature although the extra term and the fractal power bring about their revisions on the functions, but they cannot change the heat capacity signs, so they also cannot change the fate of six- or seven-dimensional black holes.

This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection--diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [Afr22, Rab23, Rab25, RAN25, RN24], we aim to recover the shape of an unknown inclusion via shape optimization driven by a cost functional constructed from the imaginary part of the complex-valued state variable over the entire domain. We rigorously derive the associated shape derivative in variational form and provide explicit expressions for the gradient and second-order information. Optimization is carried out using a Sobolev gradient method within a finite element framework. To address difficulties in reconstructing obstacles with concave boundaries, particularly under measurement noise and the combined effects of advection and diffusion, we introduce a state-of-the-art numerical scheme inspired by the Alternating Direction Method of Multipliers (ADMM). In addition to implementing this non-conventional approach, we demonstrate how the adjoint method can be efficiently applied and utilize partial gradients todevelop a more efficient CCBM-ADMM scheme. The accuracy and robustness of the proposed computational approach are validated through various numerical experiments.

Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of $SU(3)$ fermions on a kagome lattice which may realize a DSL phase, described at low energies by $(2 + 1)d$ quantum electrodynamics (QED$_3$) with $N_f=6$ Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED$_3$ theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the $SU(3)$ Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.

Fluorite structure ferroelectrics, especially hafnium oxide, are widely investigated for their application in non-volatile memories, sensors, actuators, RF devices and energy harvesters. Due to the metastable nature of the ferroelectric phase in these materials, dopants and process parameters need to be optimized for its stabilization. Here, we present clear evidence of how dopants affect the properties in this material system and solutions to achieve improved reliability, desired crystallization behavior and polarization hysteresis shape/position through co-doping. Finally, the benefits of co-doping in a variety of application fields are demonstrated.

We construct a family of invariant measures from the perspective of a shock in the KPZ fixed point. These measures are parameterized by a positive number $θ> 0$, and are supported on functions $f$ satisfying $\lim_{|x| \to \infty} \frac{f(x)}{|x|} = 2θ$. Each can be described as the sum of a Brownian motion and an independent Bessel-$3$ process with drift. We show that these measures appear as the $L \to \infty$ limit of the measures constructed by Barraquand, Corwin, and Yang for the conjectural open KPZ fixed point on $[0,L]$, after recentering by an appropriately defined shock location. Furthermore, we show that, with respect to the standard, deterministic recentering at $x = 0$, all extremal invariant measures for the KPZ fixed point are Brownian motions with drift. To do this, we first show that any extremal invariant measures must be supported on functions having fixed asymptotic slopes at $\pm \infty$. Using a one-force-one-solution principle from the work of Busani, Seppäläinen, and the second author, this rules out all other invariant measures except those having left slope $-2θ$ and right slope $+2θ$ for some $θ> 0$. To handle this case, we derive the limiting fluctuations of the shock for a special choice of initial condition. Additionally, we derive the limiting fluctuations of the shock for the case of the invariant measure from the perspective of a shock, and for the case of initial data $f(x) = 2θ|x|$.

We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the fill-in method to transfer this to classes of conditional frames without extra structure. The fill-in method closes the gap between descriptive conditional frames, which do not have a canonical underlying frame, and conditional frames.

We study an effective spectral deformation flow for mode amplitudes $C_n(τ)$, governed by a second-order self-adjoint operator $\hat{C}$ on a compact interval. The flow is encoded in the multi-function $C(v,τ,n)$ and exhibits global stabilization toward a symmetric spectral attractor. To connect this dynamics with geometry, we introduce a deformation-spectrum encoding of compact Riemannian manifolds through a shifted Laplace--Beltrami spectrum. Within this framework, we analyze energy decay, entropy decay, and the bulk asymptotic spectral density of the encoded manifold spectrum, obtaining an information-theoretic and spectral route to dimension recovery. We further formulate a rigidity criterion showing that, when the deformation spectral invariants coincide with those of the round sphere, the spherical profile is the unique manifold-compatible asymptotic realization within the present framework. In dimension four, this yields a topological conclusion together with a spectral obstruction against exotic smooth structures that produce distinct invariants. The results position the spectral flow as an effective geometric model, rather than as a direct replacement for tensorial geometric flows on arbitrary manifolds.

Wildfires pose a major threat to Portugal, with over 115,000 hectares burned annually on average during 1980-2024, and the country has faced devastating mega-fires such as those in 2017. Accurate forecasts of wildfire occurrence and burned area are therefore essential for firefighting resource allocation and emergency preparedness. In this study, we propose a novel two-stage ensemble that extends the widely used latent Gaussian modelling framework with integrated nested Laplace approximation (INLA) for spatio-temporal wildfire forecasting. Stage 1 applies a gradient boosting model (XGBoost) to environmental covariates and historical fire records to produce one-month-ahead point forecasts of fire counts and burned area. Stage 2 uses these predictions as external covariates in a latent Gaussian model with additional spatiotemporal random effects to generate probabilistic forecasts of monthly total fire counts and burned area at the council level. To capture both moderate and extreme events, we implement the extended generalised Pareto (eGP) likelihood (a sub-asymptotic distribution) within INLA, develop Penalised Complexity (PC) priors for its parameters, and compare the eGP likelihood with common alternatives (e.g., Gamma and Weibull). Our framework tackles the unavailability of future environmental covariates at prediction time and performs strongly for one-month-ahead forecasts.

Quantum gases of atoms and molecules in optical cavities offer a formidable laboratory for studying the out-of-equilibrium dynamics of open quantum systems with long-range interactions. Long-range interactions are here mediated by multiple scattering of cavity photons and can induce the formation of quantum structures in space and time. Control of these dynamics requires a detailed understanding of all relevant mechanisms at play. Due to the strong correlations induced by light, however, perturbative theoretical models, which reduce the number of degrees of freedom, do not correctly capture the regime where the interplay of photon-mediated long-range forces and quantum fluctuations of light and matter become significant, such as across the transition to self-organization. In this work, we present the derivation of an effective Lindblad master equation for the dynamics of the sole motional variables of polarizable particles, such as atoms or molecules, that dispersively couple to cavity fields. The master equation is valid even for relatively large intracavity photon numbers, and is apt to study both the steady-state regime and the out-of-equilibrium dynamics where quantum fluctuations of the field seed the onset of macroscopic coherences. We validate the theoretical description by showing that it captures the dynamics across a wide temperature interval, from Doppler cooling down to the ultra-cold regime, and from weak to strong cavity-mediated interactions. Our theory provides a powerful framework for the description of cavity-induced dynamics of quantum matter. In doing so, it permits to connect models of statistical mechanics with cavity-QED experimental platforms, thus enabling quantum simulation of long-range interacting matter.

In this paper, we investigate the inflationary phenomenology of parity-violating (PV) extensions of symmetric teleparallel gravity by applying this PV gravity theory to axion inflation. The presence of PV terms induces velocity birefringence in the tensor perturbations. During inflation, when the inflaton rapidly traverses the cliff-like region in its potential, the tensor modes at specific scales for one of the two circular polarization states undergo significant amplification due to tachyonic instability. Consequently, the resulting primordial gravitational waves (GWs), characterized by a one-handed polarization and a multi-peak structure in their energy spectrum, exhibit a significant amplitude potentially detectable by LISA and Taiji, and their chirality could be determined by the LISA-Taiji network. The detection of such a chiral GW signal provides an opportunity to probe inflation and PV gravity theory. Moreover, we perform the Fisher matrix analysis to forecast the constraints on the model parameters with the LISA-Taiji network.

We present a term rewriting system that models the dynamic aspects of the free cornering with protocol choice of a monoidal category, which has been proposed as a categorical model of process interaction. This term rewriting system is confluent and terminating in an appropriate sense. We use this machinery to prove a coherence theorem for the free cornering with protocol choice.