Gravitational lensing offers unique insights into cosmology by bending light around massive objects. Strong gravitational lensing, in particular, produces magnified and often multiple images of distant sources, crucial for precise cosmological measurements and understanding the distribution of dark matter in the universe. Current studies are limited by the number of strong gravitational lenses. From upcoming cosmological surveys, we anticipate observing a several orders of magnitude increase in the number of lenses, for both static and transient phenomena. However, detecting and analyzing these events from vast surveys like Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) presents significant challenges. To prepare for these challenges, we introduce SLSim, a versatile simulation tool tailored for the Vera C. Rubin Observatory. SLSim integrates advanced astrophysical models with computational efficiency to generate synthetic strong lens populations under realistic observational conditions. SLSim simulates static and variable lensing scenarios, essential for cosmological studies, training and testing lens search and data analysis pipelines. This paper details SLSim,'s design and implementation, emphasizing its modularity and capabilities across various astrophysical regimes. Validation against observational data and existing simulations confirms SLSim's accuracy in reproducing observed lensing phenomena. SLSim is publicly available at https://github.com/LSST-strong-lensing/slsim, and we anticipate continued development and expansion of its capabilities. Users are encouraged to check the repository for updates and to contribute to ongoing community efforts in strong lensing simulations.

The Debreu Koopmans theorem restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable, additive or multiplicative, function is star quasiconvex, those with star shaped sublevel sets about minimizers, if and only if each component is star quasiconvex. This immediately yields star quasiconvexity of separable sums of quasiconvex functions, formally bridging diversification theory with the S shaped value functions of Prospect Theory. Furthermore, we develop a complete calculus, monotonic composition, pointwise minima, quasi arithmetic means, and we apply it to Cobb-Douglas functions, multifactor risk models, and constant function market makers in decentralized finance. Star quasiconvexity thus provides a unified framework for applications in optimization and economic modeling beyond the classical Debreu Koopmans constraint. The introduction discuss economic motivations.

Girko matrices have independent and identically distributed entries of mean zero and unit variance. In this note, we consider the random matrix model formed by the ratio of two independent Girko matrices, its entries are dependent and heavy-tailed. Our main message is that divided by the square root of the dimension, the spectral radius of the ratio converges in distribution, when the dimension tends to infinity, to a universal heavy-tailed distribution. We provide a mathematical proof of this high-dimensional phenomenon, under a fourth moment matching with a Gaussian case known as the complex Ginibre ensemble. In this Gaussian case, the model is known as the spherical ensemble, and its spectrum is a determinantal planar Coulomb gas. Its image by the inverse stereographic projection is a rotationally invariant gas on the two-sphere. A crucial observation is the invariance in law of the model under inversion, related to its spherical symmetry, and that makes, in a sense, edge and bulk equivalent. Our approach involves Girko Hermitization, local law estimates for Wigner matrices, lower bound estimates on the smallest singular value, and convergence of kernels of determinantal point processes. The universality of the high-dimensional fluctuation of the spectral radius of the ratio of Girko matrices turns out to be remarkably more accessible mathematically than for a single Girko matrix!

I show that a newly estimated fraction of normal type Ia supernovae (SNe Ia) that interact within about 100 days of explosion with circumstellar material (CSM), called SNe Ia-CSM, is compatible with a recently estimated fraction of normal SNe Ia that interact with an old planetary nebula, hence, supporting the core-degenerate (CD) scenario for normal SNe Ia. According to the CD scenario, a white dwarf (WD) merges with the core of an asymptotic giant branch star at the end of common envelope evolution (CEE) and forms a massive WD remnant close to the Chandrasekhar mass. The CEE ejects a planetary nebula that the WD remnant ionizes. Most explosions occur within a merger-to-explosion delay (MED) time of less than a million years, before the planetary nebula material disperses to the interstellar medium, leading to a SN Ia inside a planetary nebula (SNIP). I discuss two plausible MED time distributions and show that the newly determined SNe Ia-CSM fraction of all normal SNe Ia, ~0.04%, is compatible with the SNIP fraction of ~80%. Therefore, although the fraction of SNe Ia-CSM is very small, it does not require a rare evolutionary pathway. I argue that SNe Ia-CSM follow the same scenario that accounts for 70%-90% of all normal SNe Ia, namely, the CD scenario.

Robust Mixture Prior (RMP) is a popular Bayesian dynamic borrowing method, which combines an informative historical distribution with a less informative component (referred as robustification component) in a mixture prior to enhance the efficiency of hybrid-control randomized trials. Current practice typically focuses solely on the selection of the prior weight that governs the relative influence of these two components, often fixing the variance of the robustification component to that of a single observation. In this study we demonstrate that the performance of RMPs critically depends on the joint selection of both weight and variance of the robustification component. In particular, we show that a wide range of weight-variance pairs can yield practically identical posterior inferences (in particular regions of the parameter space) and that large variance robust components may be employed without incurring in the so called Lindley's paradox. We further show that the use of large variance robustification components leads to improved asymptotic Type I error control and enhanced robustness of the RMP to the specification of the location parameter of the robustification component. Finally, we leverage these theoretical results to propose a novel and practical hyper-parameter elicitation routine.

This study investigates, analytically and numerically, the role of an equatorially anti-symmetric lateral variation in heat flux at the outer boundary in polarity transitions in rapidly rotating dynamos. In an unstably stratified fluid, the frequencies of vertical and horizontal (lateral) buoyancy complement each other such that a polarity transition is induced by the boundary anti-symmetry through the suppression of the slow magnetic-Archimedean-Coriolis (MAC) waves at relatively small vertical buoyant forcing. A dipole-dominated dynamo in the low-inertia limit transitions to polarity reversing and multipolar states in succession as the relative intensity of horizontal buoyancy is progressively increased for a fixed vertical buoyancy. In the same parameter space, an equatorially symmetric heat flux variation does not induce a polarity transition. A composite boundary heterogeneity consisting of comparable magnitudes of symmetric and anti-symmetric variations induces the polarity transition at a horizontal buoyancy of the same order as that for the transition induced by a purely anti-symmetric variation. This makes the analysis relevant to Earth's core, which convects in response to a composite heat flux variation in the lowermost mantle. A heterogeneity with a dominant equatorially symmetric component does not favour polarity transitions, likely producing long periods in Earth's history without reversals. The fact that compositional buoyancy is much stronger than thermal buoyancy, together with the known order of magnitude of the peak field intensity in the inertia-free limit, indicates a large lower-mantle heat flux heterogeneity of O(10) times the mean superadiabatic heat flux at the core--mantle boundary.

The optimal regularization of infinite-dimensional gauge-field degrees of freedom is a central open problem in the simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the gauge group $G$ with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory $G_k$, with the level $k$ serving as the regularization parameter. We demonstrate how to couple these regularized gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the regularized Hamiltonian, in the Kogut-Susskind formulation, on fault-tolerant quantum computers. We provide explicit quantum circuit constructions for implementing the primitive gates in this model, the $F$ and $R$ symbols, for $U(1)_k$ and $SU(2)_k$ anyon theories.

Recent works on the decoherent histories formalism suggested that slow-evolving macroscopic quantities (extensive sums of local observables) in quantum many-body systems can be consistently monitored: The existence of past measurements does not alter future outcome distribution. Here, for Gaussian weak measurements, we show that fluctuations of macroscopic quantities cannot be consistently monitored in general, in contrast to their intensive mean value. Exceptions include fluctuations at infinite temperature, at critical points, and in semiclassical systems. We analytically quantify non-consistency in terms of susceptibility, and obtain related results on entropy growth under noisy unitary.

Contemporary large-scale surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Euclid present an unprecedented discovery potential for studying AGNs at the population level in the big data era. However, one major challenge is the accurate identification and classification of AGNs from optical/NIR photometry, or variability data alone. In order to optimize AGN selection, classification, and systematics, as well as to test different data analysis tools, we present AGILE (AGNs In the LSST Era), an LSST end-to-end simulation software. AGILE -- developed as part of the INAF LSST in-kind contribution -- is capable of simulating the anticipated AGN population in LSST and Euclid. We based AGILE on existing simulations of galaxies and stars, while we developed an AGN recipe based on empirical relations. AGILE populates complete galaxy samples with AGNs according to the observed AGN accretion rate distribution, and each AGN is assigned an optical/UV spectral energy distribution. Optical AGN variability is added using a damped random walk model connected to the AGN physical parameters. Finally, AGILE creates both LSST-like images and related data products. Using AGILE, we build a $24$ deg$^2$ complete mock truth catalog of AGNs, galaxies, and stars with $0.2 < z < 5.5$, $\log M/M_\odot > 8.5$ (AGNs and galaxies), and $r < 27.5$ mag (stars). We perform a pilot simulation (AGILE DR1) consisting of $1$ deg$^2$ of LSST operations in the COSMOS field observed up to three years according to the survey strategy. We use AGILE DR1 to quantify the accuracy of the LSST Science Pipelines in recovering true fluxes of AGNs, galaxies, and stars. We quantify the LSST completeness and purity in recovering Type 1 AGNs using typical color-color and variability selections. We share the AGILE DR1 dataset, an ideal test-bench for further scientific exploitation.

Ecologists have long debated whether biological communities are fundamentally continuous or composed of discrete units. Continuum views emphasize smooth compositional change and ambiguous boundaries, whereas classification-based approaches rely on discrete community types for analysis and management. We show how biological grouping, particularly species formation, can emerge from interactions among populations governed by number-theoretic structure. In our framework, a species is identified with a $p$-Sylow subgroup of a community occupying a single niche; this identification is suported by a topological analysis. We call the resulting framework the patch with zeta dominance (PzDom) model. We then examine the system's topological properties in detail and demonstrate that both hierarchical organization and temporal ordering are induced by a one-dimensional probability space endowed with an appropriate topology. To clarify the appearance of induced fractal structure and its relation to renormalization, we develop a theoretical account based on a new observation: the scaling parameters that play the role of magnetization analogs coincide exactly with the imaginary parts of the nontrivial zeros of the Riemann zeta function. In the PzDom model, all required computations reduce to the time-dependent density of individuals. The PzDom framework reconciles these perspectives by showing that continuous community variation, represented by small $s$, can give rise to discrete species-level structure when number-theoretic constraints stabilize specific configurations. Thus, continuity and discreteness emerge as different dynamical phases of the same system, offering a unified explanation for long-standing debates in community ecology and the **species problem**.

According to the classical Wagstaff heuristic, the probability that a Mersenne number $M_p=2^p-1$ is prime depends primarily on the size of the exponent $p$. We investigate whether the divisor structure of $p-1$ produces detectable secondary variations within this asymptotic framework. We introduce the normalized divisor parameter $S(p)=\log τ(p-1)/\log\log p$, which measures the divisor complexity of p-1, including prime multiplicities. Using the currently known Mersenne prime exponents (excluding small cases), we compare $S(p)$ against nearby prime controls of comparable size. Across several complementary distribution-free methods, including percentile analysis, conditional likelihood estimation, and permutation tests, Mersenne prime exponents consistently exhibit elevated values of $S(p)$. To interpret this effect, we develop a heuristic framework based on the cyclotomic decomposition $2^{p-1}-1=\prod_{d|(p-1)}Φ_d(2)$, in which divisors of $p-1$ generate effective modular constraint layers. This motivates a heuristic refinement of the Wagstaff model of the form $\Pr(M_p\ \text{prime}) \approx C(\log p)^{S(p)}/p$. The proposed refinement preserves the classical Wagstaff scale in the typical regime $S(p)\approx 1$, while suggesting that the finite-scale distribution of Mersenne prime exponents exhibits a weak arithmetic bias linked to the divisor structure of $p-1$.

Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these we obtain an explicit formula for fixed-point-free Cayley permutations and prove that their proportion tends to $1/e$, as for permutations and endofunctions. Our approach also yields counting formulas when the functional digraph is a tree, forest, or connected.

We present FlowSN, a statistical framework using simulation-based inference (SBI) with normalising flows to account for selection effects in observational astronomy. Failure to account for selection effects can lead to biased inference on global parameters. An example is Malmquist bias, where detection limits result in a sample skewed towards brighter objects. In Type Ia supernova (SN Ia) cosmology, these selection effects can systematically shift the inferred posterior distributions of cosmological parameters, necessitating the development of robust statistical frameworks to account for the biases. SBI enables us to implicitly learn probability distributions that are analytically intractable to calculate. In this work, we introduce a novel approach that employs a normalising flow to learn the non-analytic selected SN likelihood for a given survey from forward simulations, independent of the assumed cosmological model. The resulting likelihood approximation is incorporated into a hierarchical Bayesian framework and posterior sampling is performed using Hamiltonian Monte Carlo to obtain constraints on cosmological parameters conditioned on the observed data. The modular learnt likelihood approximation can be reused without retraining to evaluate different cosmological models, providing a key advantage over other SBI approaches. We demonstrate the performance of this methodology by training and testing the SBI technique using realistic LSST-like SNANA simulations for the first time. Our FlowSN approach yields accurate posterior estimates on cosmological parameters, including the dark energy equation of state $w_0$, that are an order of magnitude less biased than those obtained with conventional techniques and also exhibit improved frequentist calibration.

Warm inflation is commonly studied under the assumption that the stochastic force sourcing inflaton fluctuations is Markovian. Realistic thermal systems, however, possess finite relaxation times and can therefore generate colored noise with non-zero correlation time. In this work, we investigate warm inflation beyond the Markovian limit and determine how finite correlation time modifies the primordial scalar power spectrum. We show that memory effects suppress the scalar spectrum relative to the standard white-noise result and derive a simple expression for this correction in terms of the background thermal dynamics. In particular, we relate the size of the non-Markovian effect directly to the thermal ratio between the bath temperature and the Hubble scale, thereby establishing a transparent link between warm-inflation background quantities and the validity of the Markovian approximation. We also derive the corresponding modification of the tensor-to-scalar ratio and the induced shifts in the scalar spectral index and the running of the scalar spectral index. Our results provide a simple and practical diagnostic for identifying when finite correlation-time effects become relevant in warm-inflation model building.

Spin and polarization are central to precision tests of fundamental physics and for interpreting radiation from astrophysical sources and ultraintense laser-matter experiments. Here, focusing on the fundamental process of nonlinear Compton scattering, we demonstrate that a key assumption underlying current strong-field quantum electrodynamics (SFQED) models, i.e., that emission can be treated as an instantaneous random event sampled from a local differential rate, is inconsistent once emission angles, electron spin, and/or photon polarization are resolved. Namely, \emph{even in strictly constant and uniform fields}, the resulting fully differential distribution is sign-indefinite, yielding negative inferred probabilities. The physical reason is that the photon emission probability builds up over a finite length of the electron trajectory, the formation region, during which the electron direction changes by roughly the same small angle that defines the radiation cone. Therefore, we put forward a new method where we integrate over this formation region analytically to obtain a physically consistent electron spin and photon polarization model. Simulations of a GeV-class electron-laser collision accessible at current petawatt facilities and of emission in a pulsar-like magnetic field are shown to reveal spin and polarization patterns that differ even qualitatively from state-of-the-art local models. In particular, our new model predicts substantial angle-dependent circular photon polarization where the well-known collinear-emission approach yields none, and a pronounced helicity bias in the recoiling electrons absent from current predictions. These findings have direct implications for upcoming strong-field QED experiments and for interpreting polarized radiation from extreme astrophysical environments.

The Peanut cluster (SRGe J023820.8+200556, SRGe CL0238.3+2005, $z_{spec}$ = 0.42) has recently emerged as a candidate for a rare, massive merger, potentially analogous to the Bullet cluster. We present the results of optical identification and spectroscopic redshift measurements for 31 galaxies in the Peanut cluster, including 26 new redshifts obtained with the 6-m telescope BTA (Big Telescope Alt-azimuthal) at SAO RAS between October 2024 and January 2025. The derived distribution of line-of-sight velocities reveals the possible presence of two subclusters with a line-of-sight velocity difference of ~2000 km/s. However, statistical tests and the Dressler-Schectman test show that the hypothesis that the observed velocity distribution can be described by a normal distribution for a single cluster cannot be ruled out, and the evidence for the existence of two gravitationally bound substructures remains ambiguous. Assuming a single cluster with the normal velocity distribution, the estimated galaxy velocity dispersion is $σ_{los} = 1455 \pm 83$ km/s, corresponding to the total cluster mass of $M_{200} = 2 \times 10^{15} M_\odot$ based on the mass-velocity dispersion scaling relation. In either scenario -- a single extremely massive cluster or an ongoing merger -- the Peanut cluster appears to be a very rare and peculiar object, comparable to such extreme systems as the Bullet cluster (1E 0657-56) or El Gordo (ACT-CL J0102-4915).

Continuum field-theoretical descriptions of topological order are often constructed at long distances without direct reference to microscopic short-distance realizations, guided instead by general principles such as gauge invariance, locality, symmetry, response, and topological invariance. A classic example is provided by Chern--Simons-type topological field theories for two-dimensional anyon systems. Recently, this framework has been extended to three-dimensional topological orders, where particle and loop excitations exhibit highly nontrivial phenomena, including braiding, fusion, and shrinking. Field-theoretical approaches have further led to diagrammatic representations, pentagon and hexagon relations, and \textit{fusion--shrinking consistency} conditions governing these processes. Despite these advances, a long-standing question remains: do such long-distance field-theoretical structures admit faithful microscopic counterparts with tensor-product local Hilbert spaces and short-range interactions? In this work, we answer this question by establishing an explicit correspondence between continuum topological field theory and microscopic lattice constructions of three-dimensional non-Abelian topological order. While Wilson operators encode long-distance topological excitations, we construct microscopic lattice operators that create, fuse, shrink, and braid particles and loops. Using these operators, we compute fusion and shrinking rules, particle--loop and Borromean-Rings braiding phases, and show how non-Abelian shrinking channels can be selectively controlled by the internal degrees of freedom of loop operators. We further show that the lattice shrinking rules satisfy the \textit{fusion--shrinking consistency} relations previously obtained from field theory, establishing these relations as a microscopically verifiable organizing principle for 3D topological order. Remarkably, by...

We establish an operational connection between discrete rounds of generalized measurements and continuous-time decoherence, with an explicit correspondence between the number of measurement rounds and the evolution time. Operationally, we show that a single round of such a generalized measurement eliminates quasiprobability negativity in finite-dimensional systems. From the decoherence perspective, this loss of negativity occurs abruptly at a critical time. In particular, this critical time can be shorter than the conventional decoherence time, indicating that the latter does not always faithfully track the disappearance of nonclassicality. Our results provide new insight into the quantum-to-classical transition in finite-dimensional systems from the viewpoint of phase-space quasiprobability, and suggest feasible quantum-circuit tests as well as possible heralded resource extraction from noise.

As plans for the construction of third-generation gravitational wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalog derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering the earth rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three or five image systems with a detectable central image, a feature distinct from optical lensing. For the joint ET+CE network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ($μ> 3$), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

Dark matter direct detection experiments can observe solar neutrinos via coherent elastic neutrino-nucleus scattering, making it possible to test new physics in the neutrino sector. In this article, we study the sensitivity of RES-NOVA, a novel cryogenic calorimetric experiment employing PbWO$_4$ crystals grown from archaeological lead, to neutrino non-standard interactions (NSI). We perform a sensitivity study for a benchmark setup with a nominal energy threshold of 1 keV and an exposure of 1 ton$\cdot$y, both for a conservative (only heat readout) and ideal (heat and scintillation) background rejection scenario. We find that, in its nominal configuration, while not being sensitive to Standard Model solar $ν$ interactions, RES-NOVA can reach sensitivities to NSI at the level of current global fits. With moderate or significant improvements of the threshold down to $0.5$ keV and $0.2$ keV, RES-NOVA will be able to achieve sensitivities beyond NSI global fit results, testing new areas of the parameter space in the electron and tau sectors, $\varepsilon_{ee}$, $\varepsilon_{ττ}$, and $\varepsilon_{eτ}$. A similar improvement in sensitivities is expected when instead increasing the exposure to 10 ton$\cdot$y.

Single-shot fidelity is the standard benchmark for superconducting qubit readout, yet it does not directly minimize the wall-clock time needed to certify a quantum state. We treat the dispersive measurement record as a stochastic communication channel and compute the classical Chernoff information governing the multi-shot error exponent, using a trajectory model that incorporates T1 relaxation with full cavity memory. The integration time that maximizes single-shot fidelity and the time that minimizes total certification time do not coincide. For representative transmon parameters and hardware overheads, the throughput-optimal window is longer, cutting certification time by roughly 9-11%, with the gain saturating near 1.13x in the high-readout-power and high-overhead regime. Benchmarking the extracted classical information against the unit-efficiency Gaussian Chernoff limit defines an information-extraction efficiency: dispersive schemes capture ~45% at short integration times, dropping to eta_info(tau_rate) ~ 12% at tau_rate ~ 1.22 us as T1-induced trajectory smearing accumulates. These results connect readout calibration directly to the operational objective of minimizing certification time in high-throughput superconducting processors.

For a Galois number field $K$, the Galois group $\text{Gal}(K/\mathbb{Q})$ acts on the class group $\text{Cl}_K$ in a very natural way: $σ\cdot[I]=[σ(I)]$ for any $σ\in \text{Gal}(K/\mathbb{Q})$, $[I]\in \text{Cl}_K$. In this paper, we will explore how the unique properties of this group action work together to elucidate the relationship between these two groups -- developing and expanding upon some known results from a new perspective. To this end, we explore the class groups of localizations of the ring of integers $\mathcal{O}_K$. These turn out to be powerful tools for understanding $\text{Cl}_K$ and overrings of $\mathcal{O}_K$. The paper concludes with some interesting observations about normset arithmetic and complexity -- topics intimately related to this action.

Pauli-propagation simulation represents observables in the Pauli basis and evolves their coefficients in the Heisenberg picture. Its efficiency depends on whether the evolving operator can be accurately compressed by retaining only a limited number of Pauli terms. In this work, we bridge operator complexity and the resource cost of Pauli-propagation methods by proving that the truncation error is governed by the Operator Stabilizer Rényi entropy (OSE) $\mathcal{S}^α(O)$. Our a priori bounds quantify how OSE controls the compressibility of the evolving operator and give explicit prescriptions for the Top-$K$ budget required to achieve a target accuracy. As an analytic test case, we prove that for the 1D Heisenberg model at $J_z=0$, the number of non-zero Pauli coefficients generated from a local operator grows at most quadratically with the number of Trotter steps. We then benchmark the Top-$K$ Pauli propagation on XXZ Heisenberg chains. The numerical results show high accuracy with a small truncation number $K$ in the free regime ($J_z=0$) and competitive performance against tensor-network methods, such as TDVP, in the interacting case ($J_z=0.5$). These results position OSE as a resource measure for Pauli-propagation methods.

We study the gravitational dynamics of quasi-hierarchical triple systems, where the outer orbital period is significantly longer than the inner one, but the outer orbit is extremely eccentric, rendering the time at pericentre comparable to the inner period. Such systems are not amenable to the standard techniques of perturbation theory and orbit-averaging. Modelling the evolution of these triples as a sequence of impulses at the outer pericentre, we show, by comparing with direct three-body integrations, that such triples lend themselves to a description as an analytical map between subsequent outer pericentre passages. This map exhibits secular oscillations, going beyond the von Zeipel--Lidov--Kozai mechanism. We show that the time to coalescence due to gravitational waves in such systems is modified. We then study the long-term evolution under this map, which lead to a random-walk-like behaviour of the inner eccentricity. While this behaviour is probably absent from isolated triples, it could exist in triples where the outer orbit is weakly coupled to a system with which it can exchange angular momentum, and we describe some properties of this random walk.

We resolve two problems pertaining to indefinite integral ternary quadratic forms, one highlighted by Margulis and the other initiated by Serre, both from 1990. To do so we develop tools for dealing with high ramification in problems involving sums over classes of such forms weighted by their diophantine invariants.

High-resolution scattered-light imaging has revealed complex morphologies in protoplanetary and circumstellar disks. Measuring the vertical height of the scattering surface is key to understanding disk structure, evolution, and the properties of embedded dust. We develop a methodology for fitting elliptical shapes to scattered-light images of protoplanetary disks in order to extract vertical height profiles of the dust scattering surface across a large and morphologically diverse disk sample. The dataset consists of 92 near-infrared polarimetric images obtained with VLT/SPHERE. The aim is to identify trends in vertical structure across different disk morphologies and test for correlations with stellar mass, age, and disk dust mass, as well as to investigate the implications of the derived height profiles for the masses of potential embedded planets. We implement a structure extraction and ellipse fitting (SEEF) algorithm that uses edge detection and Gaussian fitting to locate disk structures. Ellipse fitting reveals spatial offsets between the ellipse centre and the stellar position, which are interpreted as vertical height assuming circular ring geometry. Disk inclination, position angle, and the aspect ratio h/r are also derived. The method yields vertical height measurements for 92 disks, showing profiles consistent with flared disk geometries. However, the full sample cannot be described by a single power-law relation. Subdivision by morphology shows no strong correlations for most disk classes, except for extended disks with outer radii larger than about 150 au, which exhibit a clear power-law flaring trend. The lack of strong correlations with other system properties suggests that either different morphologies exhibit distinct vertical structures or that additional physical factors influence disk flaring.

The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and parameterized complexity settings. Parameterized by treewidth $k$, OMM has long been known to be solvable on triangulations of $3$-manifolds in $2^{O(k^2)} n^{O(1)}$ time and in FPT time for triangulations of arbitrary manifolds, but the exact dependence on $k$ has remained an open question. We resolve this by giving a new $2^{O(k \log k)} n$-time algorithm for any finite regular CW complex, and show that no $2^{o(k \log k)} n^{O(1)}$-time algorithm exists unless the Exponential Time Hypothesis (ETH) fails.

We develop a generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data. The generative prior is built from a large ensemble of synthetic curves drawn from ten distinct functional classes rooted in different theoretical approaches to hadron structure. Applied to the proton gravitational form factors $A(t)$, $J(t)$, and $D(t)$, the framework yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range $0\le -t\le 2~\mathrm{GeV}^{2}$, remaining robust even when only one or two conditioning points are retained. The densely sampled output enables a direct extraction of the chiral low-energy constants $c_8=-4.6\pm 0.8~\mathrm{GeV}^{-1}$ and $c_9=-0.61\pm 0.19~\mathrm{GeV}^{-1}$. Using these values at the physical pion mass, we obtain $D(0)=-4.3\pm 0.8$ for the nucleon $D$-term.

Assessing the contribution of ionizing sources to cosmic reionization is a central goal of extragalactic astrophysics. Understanding and quantifying ionizing escape remains challenging near the epoch of reionization. We present the highest-redshift Lyman continuum (LyC) emitter detected to date, MXDFz4.4 at z=4.442 in the MUSE eXtremely Deep Field, observed only ~0.25Gyr after the end of reionization. A high confidence Ly-alpha line confirms the redshift. LyC flux is detected at 5.3sigma in the F435W filter with a flux of 4.2+/-0.8nJy, corresponding to a flux measurement at 5.2sigma. After correcting for the intrinsic production of LyC photons and the IGM opacity at z=4.44, we derive high escape fractions, ranging from 50 - 100%. We apply established low-redshift tracers of LyC escape and, for the first time at high redshift, promising Ly-alpha morphological tracers such as the halo fraction. SED fitting indicates the presence of a recent burst of star formation; we explore its impact on the production and escape of ionizing photons. Ly-alpha-based tracers of LyC escape reveal a complex scenario in which the recent burst strong influences LyC production and escape, combined with a more evolved stellar population. This interpretation is supported by UV diagnostics, including the star formation rate surface density and sSFR. Our results provide cautious support for the Ly-alpha halo fraction as a LyC escape tracer at high redshift. Considering the burst-driven enhancement in LyC production and escape, we conclude that stochastic star formation in the early Universe likely plays a significant role in the contribution of galaxies to cosmic reionization.

Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability. In particular, the absence or presence of barren plateaus (BPs) -- flat regions in parameter space that prevent the efficient training of variational quantum algorithms -- has recently been shown to be intimately related to quantities derived from the associated DLA. In this work, we investigate DLAs for the quantum approximate optimization algorithm (QAOA), one of the most studied variational quantum algorithms for solving graph MaxCut and other combinatorial optimization problems. While DLAs for QAOA circuits have been studied before, existing results have either been based on numerical evidence, or else correspond to DLA generators specifically chosen to be universal for quantum computation on a subspace of states. We initiate an analytical study of barren plateaus and other statistics of QAOA algorithms, and give bounds on the dimensions of the corresponding DLAs and their centers for general graphs. We then focus on the $n$-vertex cycle and complete graphs. For the cycle graph we give an explicit basis, identify its decomposition into the direct sum of a $2$-dimensional center and a semisimple component isomorphic to $n-1$ copies of $su(2)$. We give an explicit basis for this isomorphism, and a closed-form expression for the variance of the cost function, proving the absence of BPs. For the complete graph we prove that the dimension of the DLA is $O(n^3)$ and give an explicit basis for the DLA.