We present a Mock Data Challenge (MDC) to characterize the sensitivity limits of the gravi-signal-ml pipeline (Cirfeta 2026) for unsupervised gravitational-wave glitch detection. Strain-domain synthetic injections of eight morphological families into public LIGO O4a L1 data reveal two threshold-dependent sensitivity regimes. With a session-adaptive dynamic threshold (tau_dyn = mu_bg - 2.5 * sigma_bg), the pipeline recovers visually anisotropic morphologies (Butterfly, ZSweep) at matched-filter SNR >= 70, reaching Recall = 1.0, though the False Positive Rate (FPR) remains uncontrolled across sessions. Characterization of the full O4a embedding distribution (N = 188,142 segments) reveals extreme non-Gaussianity (skewness = -4.12, excess kurtosis = 15.38, Shapiro-Wilk p-value near 0), with the left tail best modeled by a Generalized Extreme Value (GEV) distribution. Under a statistically rigorous operational threshold (tau_op = 0.874) calibrated at the empirical 5x10^-5 quantile (FPR < 0.01%), the MDC yields Recall = 0 for all eight morphologies at all tested SNR levels, including narrowband structures (HarmonicComb, NarrowChirp) and impulsive transients (AsymBlip) at SNR up to 430. We trace this insensitivity to the global average pooling of the DINOv2 [CLS] token, which dilutes signals occupying a small fraction (<5%) of the spectrogram's 37x37 patch grid. The null result of Cirfeta (2026) is conditionally reinterpreted: it confirms the absence of novel macro-structures but cannot exclude localized micro-structures. These findings provide a quantitative roadmap for next-generation ViT-based pipelines using patch-level scoring and multi-scale windowing.

Many areas of astrophysics, including exoplanetary studies, rely on precise and accurate stellar parameters. This demands that uncertainties on these parameters truly reflect all biases and systematics. Within this second work of the \texttt{gr8stars} collaboration, we take a set of 585 bright FGK dwarfs with high resolution, high signal-to-noise ratio spectra from the SOPHIE spectrograph. We determine stellar effective temperature, surface gravity, and metallicity using five different spectroscopic methods for each star, with an additional method used for comparisons. We find a typical scatter of 76 K in \teff, 0.14 dex in \logg, and 0.07 dex in \feh. These deviations are significantly larger than the average precision error on these parameters. We furthermore use isochrone fitting to determine mass, radius, and age for all 585 stars, using input from all results. We use the radii determined by SED fitting in the first \texttt{gr8stars} paper as a comparison to our isochronal radii from this work, in addition to comparing the isochronal \logg to spectroscopic \logg. The scatter in mass and radius from the use of different spectroscopic methods is investigated and propagated to exoplanetary parameters. The induced fractional uncertainties in planetary radius ($\lesssim$ 3 \%) and mass ($\lesssim$ 5\%) are found to be below those typically found in the literature. We estimate a lower limit on planetary equilibrium temperature fractional uncertainty of $\approx$ 4\%, a noise floor that is currently not sufficiently represented in the literature.

Laser plasma accelerators can deliver high-energy, quasi-monoenergetic electron beams over centimeter-scale distances. In this work, we report on the generation of narrow, quasi-monoenergetic electron bunch trains with periodic energy spacing issued from downramp injection in a laser driven wakefield accelerator. The periodicity in energy is shaped via relativistic lengthening of the wakefield during the acceleration phase, while the spatial periodicity is obtained via injection into multiple plasma periods. At the end of the accelerator, a rotation in phase-space is performed to compress each bunch in energy, producing narrow periodic spikes in the spectrum. The experimental observations are supported by particle-in-cell simulations, which reproduce the formation and evolution of the periodic bunch trains, providing an insight into the underlying plasma dynamics.

We develop a method for bounding the sensitivity of solutions to stochastic differential equations (SDEs) to changes in the drift, $F$, and diffusion, $σ$, by using a combination of information-theoretic uncertainty quantification bounds, functional inequalities, and judiciously chosen coupled auxiliary SDEs. The method is capable of producing non-asymptotic bounds which are well behaved in the $T\to \infty$ limit and does not require the perturbations to $F$ and $σ$ to be small. Our approach applies to expectations of both time-averaged and exponentially discounted observables and also produces sensitivity bounds for linear parabolic PDEs. When applied to stationary solutions and Lipschitz observables, our results produce bounds on the $1$-Wasserstein distance between invariant measures which have optimal scaling in each error term. The present method significantly expands on prior information-theoretic SDE sensitivity bounds, which are only applicable to perturbations of the drift.

Peas-in-a-Pod (PIAP) systems have been shown to be common across exoplanet systems, with regular planet spacings and similar planet sizes. In contrast, ultra-short-period planets have displayed distinct differences from PIAP systems, including higher mutual inclinations, ages, and planet sizes. Using Laplace-Lagrange secular theory, we investigate the ability of stellar spindown to decouple PIAP systems. We find that strictly PIAP systems with regular spacings cannot undergo secular resonance crossings for the expected stellar $J_2$ evolution, and that we instead require the inner planet to migrate inward to undergo this resonance crossing. As a result, there is no inner edge to PIAP systems where systems will always cross a secular resonance and decouple the inner planet. Using expected $J_2$ evolution tracks from stellar evolution models, we find a diversity of expected resonance crossing times, highlighting the ability to test migration pathways and initial stellar obliquities using this framework.

We prove the existence of a bounded Sobolev extension operator $E:W^{p,1}\left( B,P \right) \rightarrow W^{p,1}\left( \ell^{2} ,P \right)$ using a completely new method, where $B\subset \ell^{2}$ is the unit ball and $P$ is any non-trivial centered Gaussian measure on $\ell^{2}$. This solves an open problem posed in the literatures.

We report the fastest quasar outflow first detected in the ultraviolet, via variable C IV and Si IV absorption at outflow velocities $-77,000$ km s$^{-1}$ to at least $-90,000$ km s$^{-1}$, in the radio-quiet quasar SDSS J231854.31+243954.2 (J2318). J2318 is a weak-lined quasar in the rest-frame ultraviolet, but Gemini GNIRS spectroscopy reveals an H$α$ redshift of $z=2.6781\pm0.0004$. A twenty-year photometric time series shows peak-to-peak variability of 0.5 mag in the $g$ band. The C IV outflow strengthened monotonically over three epochs spanning $\sim$2.2 rest-frame years. The existence of such a high-velocity outflow implies that models of quasar outflows must be able to either accelerate gas to $0.3c$ while still preserving C IV and Si IV ions, or enable the formation of C IV and Si IV ions in gas which has been accelerated to $0.3c$. Virial estimates reveal a black-hole mass of $1.65\times10^9~M_\odot$, which leads to an Eddington luminosity and Eddington ratio of $2.4\times10^{47}$ erg s$^{-1}$ and $0.45$, respectively. Using very conservative assumptions, the UV-absorbing outflow alone has an estimated mass loss of $>0.82~M_\odot~{\rm yr}^{-1}$ and a kinetic luminosity ratio $L_{kin}/L_{bol}\geq0.75$%. The lower limit is just above the threshold usually cited for significant feedback on the host galaxy. Comparison to PDS 456, the only other known quasar with a UV-absorbing outflow at $0.3c$, suggests that the true $\dot{M}$ and $L_{kin}/L_{bol}$ could be up to two orders of magnitude larger.

Let $d$ be the smallest positive integer, not divisible by $3$, for which there exists an algebraic number over $\mathbb{Q}$ of degree $d$ whose some three algebraic conjugates sum to zero. Employing the classification of vertex-transitive graphs on 16 vertices of degree 6, we prove that $d\neq 16$. This, combined with results obtained by Dubickas, Smyth and Stong \cite{DubickasSmyth2006}, Dubickas and Jankauskas \cite{DubickasJankauskas2015} and Virbalas \cite{Virbalas2025a}, implies that $d=20$.

We investigate dynamical mass generation in a geometrically constructed gauge theory based on the super Lie algebra $su(2,2|3)$, in which gravity, Yang-Mills fields, and fermions are unified as components of a single gauge connection. The model contains no elementary scalar fields and no ad hoc four-fermion interactions. Instead, fermionic self-interactions arise unavoidably from the geometric structure of the theory, through nonminimal couplings and torsion associated with the unified connection. Upon reduction to an effective low-energy description, these interactions generate a Nambu-Jona-Lasinio--type potential that triggers chiral symmetry breaking and the formation of a fermion mass gap. In this framework, mass generation emerges as a direct consequence of the underlying gauge-geometric and algebraic structure, rather than as an independent dynamical assumption.

We study the de Rham cohomology of three families of completely solvable almost abelian solvmanifolds (called basic, complex, and hypercomplex) constructed from a monic integer polynomial with positive distinct roots whose product equals 1, following the work of Andrada and Barberis. Under two algebraic restrictions on such polynomials (the full rank and quasi full rank conditions) we compute the Betti numbers and Poincaré polynomials of these manifolds. Moreover, we study the Dolbeault cohomology of the complex solvmanifolds by identifying them with generalized Nakamura manifolds recently introduced by Cattaneo and Tomassini. Assuming a suitable condition on the lattice, we compute their Hodge numbers, which exhibit a combinatorial structure related to Pascal's triangle in the full rank setting, and are described by explicit generating polynomials in the quasi full rank case.

Assume $G$ is a graph and $k$ is a positive integer. Let $f:V(G)\to \mathbb{N}$ be defined as $f(v)=\min\{k,d_G(v)\}$. If $G$ is $f$-choosable, then we say $G$ is degree-truncated $k$-choosable. The degree-truncated choice number of $G$ is $\operatorname{ch}^{\text{\st{d}}}(G) = \min\{k: G \text{ is degree-truncated $k$-choosable}\}$. For a family $\mathcal{G}$ of graphs, $\operatorname{ch}^{\text{\st{d}}}(\mathcal{G}) = \max\{\operatorname{ch}^{\text{\st{d}}}(G):G \in \mathcal{G}\}$. Let $\mathcal{P}$ denote the family of 3-connected non-complete planar graphs. Richter asked in 2008 whether $ch^{\text{\st{d}}}(\mathcal{P}) \le 6$. In 2025, Zhou, Zhu and Zhu answered this question in negative and proved that $8 \le ch^{\text{\st{d}}}(\mathcal{P}) \le 16$. This result was improved by Jiang, Xu, Xu, and Zhu, who proved that $9 \le ch^{\text{\st{d}}}(\mathcal{P}) \le 12$. In this paper, we further improve the result and prove that $10 \le \operatorname{ch}^{\text{\st{d}}}(\mathcal{P}) \le 11$. We conjecture that $\operatorname{ch}^{\text{\st{d}}}(\mathcal{P}) =10$, and we confirm this conjecture for those planar graphs $G \in \mathcal{P}$ for which the subgraph induced by vertices of degree at least 11 is 4-choosable.

Fluid-structure interactions at low Reynolds number can lead to a much richer phenomenology than previously expected. Here, we study the dynamics of a freely suspended, thin elastic disk in a shear flow, where the plane of the disk is initially parallel to the flow plane. Using a combination of experiments and simulations, we demonstrate that beyond a critical flow strength the disk deforms, performing flapping dynamics, in which the disk curves up and down periodically relative to the horizontal shear plane. The bifurcation diagram obtained by simulation reveals several oscillatory solutions, including a wiggling motion that is predicted by a linear stability analysis. The flapping dynamics is shown to be a subcritical instability whose key ingredient is the finite extensibility of the disk. The behavior we observe has implications for emerging investigations on the flow dynamics of sheet-like particles, such as 2D polymers and 2D crystalline materials immersed in viscous fluids.

With the advent of the Einstein Probe (EP) mission, we are entering a new era in the study of gamma-ray bursts (GRBs), enabling the detection of faint, low-luminosity transients that would previously have gone undetected. EP250304a was an event discovered by EP associated with the broad-lined type Ic supernova (SN) SN 2025fhm located at z = 0.2. Despite no gamma-ray emission being detected at the time of the EP trigger, we identify evidence for a relativistic outflow consistent with a GRB-like jet across multiple wavelengths. We present a detailed spectral and photometric analysis of EP250304a/SN 2025fhm, including multi-band light curve modelling performed with the Redback Python package. We find that this event closely resembles low-luminosity GRB-SNe (llGRB-SNe) such as GRB 060218/SN 2006aj, GRB 100316D/SN 2010bh, and GRB 171205A/SN 2017iuk, all of which exhibit early-time emission consistent with a thermal shocked cocoon. These similarities suggest that EP250304A/SN 2025fhm may belong to an emerging subclass of shocked cocoon-dominated llGRB-SNe, representing the low-luminosity end of a broader continuum of engine-driven GRB-SN explosions.

We present a physics-guided, decoupled dual-branch surrogate model to predict continuous proton energy spectra from laser-driven ion acceleration. Integrating a $β$-VAE for spectral feature extraction with a parallel multi-layer perceptron for scalar boundary enforcement, the framework achieves a predictive accuracy of $R^2 = 0.94$ for the maximum cutoff energy and $R^2 = 0.94$ for the total particle flux, with a median per-sample spectral $R^2 = 0.985$ (in $\log_{10}$ space) across the full 2000-bin energy distribution. The model incorporates uncertainty quantification via deep ensembles, serving as a quantitative probabilistic diagnostic tool with calibration errors below 6.2\%. Within the 1D longitudinal framework, the surrogate reproduces spectral signatures consistent with the transition from Target Normal Sheath Acceleration (TNSA) to the volumetric heating dynamics of Relativistically Induced Transparency (RIT) and Breakout Afterburner (BOA) regimes, as validated against kinetic diagnostics from 1D particle-in-cell simulations. This approach establishes a computationally efficient baseline for future multi-fidelity optimization and provides an engine for closed-loop parameter control in high-repetition-rate laser facilities.

A decade after the first direct detection of gravitational waves, the growing catalog of over one hundred confirmed events is revealing new insights into the spins of stellar-mass black holes. Spin measurements have long been heralded as a promising tracer of compact-object binary formation and evolution, as different formation channels predict unique spin signatures on a population level. In this review, we summarize the astrophysics, phenomenology, and current measurements of black hole spins. We begin with an overview of the predictions for black hole spin magnitudes and orientations from leading formation channels--isolated binary evolution, dynamical formation in clusters, formation in AGN disks, and hierarchical triples. We then describe the imprint of spin effects on the gravitational waveform and the measurability of spin in individual events. Finally, we review current population-level constraints on spin magnitudes, orientations, and effective spin parameters, including correlations with mass and redshift, and discuss their astrophysical implications. We conclude by highlighting open questions and future prospects, emphasizing how improved detector sensitivity will enable increasingly precise spin measurements for both individual events and the binary black hole population as a whole.

We study non-trivial intersection problems for multi-part hypergraphs, excluding the usual extremal examples determined by fixed vertices or fixed coordinates. Our first result determines the exact value of the non-trivial $t$-intersection problem in the symmetric product $[n]^r$ for $1\le t\le r-2$ and all $n\ge2$. Frankl and Nie proved a two-candidate formula for sufficiently large $n$ and conjectured it for all $n\ge 2$; our formula shows that the conjectured expression must be enlarged, in small ranges of $n$, by additional Ahlswede--Khachatrian ball-type terms. Our second result concerns intersecting families in general products $X_1\times\cdots\times X_r$, where $|X_i|=n_i$, with no common vertex. Let $m_0(1,n_1,\ldots,n_r)$ denote the largest size of such a family. We show that this number is equal to the maximum of $\sum_{X\in \mathcal{D}}\prod_{i\in X}(n_i-1)$ over all downsets $\mathcal{D}\subseteq 2^{[r]}$ such that $\bigcup_{X\in \mathcal{D}}X=[r]$ and no two members of $\mathcal{D}$ have union $[r]$. This finite reduction separates the intersection obstruction from the part sizes and yields explicit fully asymmetric formulas for $r=4,5,6$.

We study some local and global properties of solutions of $-Δu- m\abs{\nabla u}^q-e^{u}=0$ in a punctured domain $Ω\setminus\{0\}$, or in an exterior domain of $R^N$, $N\geq 2$, where $m$ is a positive parameter and $q>1$. We study particularly the local behaviour of solutions with an isolated singularity or the asymptotic behaviour for solutions defined in an exterior domain, and also the existence of solutions with the behaviours previously described. These behaviours change drastically according $q$ is smaller or larger than $2$. Many results are obtained by introducing various dynamical systems associated to the equation.

Identifying whether a state family admits an irreducible quantum advantage is a fundamental task in quantum resource theory and quantum information processing. Here we study classically simulable state families, namely those residing within the convex hull of pairwise commuting families and therefore admitting a classical explanation. We develop a complete semidefinite-programming (SDP) hierarchy characterizing the set of classically simulable state families in arbitrary finite dimension. The key step is to reformulate classical simulability as a feasibility problem over deterministic response functions and auxiliary positive-operator-valued measures (POVMs) simulable by rank-one projective measurements. We establish a complete SDP hierarchy for rank-one projectively simulable POVMs and transfer the resulting characterization to state families, yielding both primal feasibility tests and dual affine witnesses certifying failure of classical simulability. Applying the hierarchy to state families mixed with depolarizing noise gives computable upper bounds on the critical classical visibility, which are matched by explicit classical simulations in several symmetric examples. These results provide a systematic convex-optimization framework for certifying classical simulability of quantum state families.

For a finite graph $H$ and a positive integer $h$, the $h$-blowup $H^{(h)}$ of $H$ is the graph obtained by replacing each vertex of $H$ by a set of size $h$ and each edge by a complete bipartite graph between the corresponding sets. We prove that, for every $H$, there exists a constant $h_*(H)$ such that whenever $h\ge h_*(H)$ and $n$ is sufficiently large, every $n$-vertex graph maximizing the number of induced copies of $H^{(h)}$ is a blowup of $H$. This refines the asymptotic result of Hatami, Hirst and Norine and settles the question posed by Bollobás, Egawa, Harris and Jin in 1995.

Finding manifold structures in noisy and high-dimensional point clouds is a challenging but important problem. In astronomical observation survey and simulation data the detection of filaments, streams (1D), walls (2D) and clusters (3D) gives rise to deeper understanding of the evolution of our universe. The Locally Aligned Ant Technique (LAAT) uses biologically inspired agents to efficiently recover faint and multidimensional structures. However, very dense hubs (e.g. nodes or globular clusters) dominate the ants' activity, creating unnecessary computational overheads. In this paper we propose a two-stage solution. First a fast preprocessing step locates the hubs and replaces them with a tailored likelihood model. Subsequently, a mixed likelihood-pheromone strategy guides the ants to efficiently bridge the dense regions. We demonstrate improvements in detection efficiency and robustness of LAAT with synthetic and a large-scale astronomical N-body simulation of the cosmic web.

Wave propagation in a medium differs depending on whether this medium is at rest or moving with respect to an observer. Motion can notably lead to modifications of the wave trajectory, of its polarization, or of its transverse structure. Although these effects are well documented in isotropic dielectrics, they remain largely unexplored and unaccounted for in plasmas, despite the fact that simple models suggest they could in fact be large under certain conditions, as well as recent experimental observations. Here we first review existing models for motion effects on plasma waves, then identify a number of basic challenges that lie in the way of using these models to quantify motion effects in realistic configurations, and finally discuss possible workarounds.

We study a stochastic optimal control problem for McKean-Vlasov stochastic differential equations (SDEs) with common noise, where the dynamics depend on the conditional law of the state. We derive a stochastic maximum principle of Peng type without imposing convexity assumptions on the control domain. In comparison to the standard McKean-Vlasov case, the maximum principle for the common noise case contains a third adjoint state, which is needed to dualize all second-order Lions derivatives in the Taylor expansion of the cost functional. The additional adjoint state is given by a conditional McKean-Vlasov backward SDE. All three adjoint states together allow for a complete linearization of all contributions in the second-order expansion, including interactions between conditionally independent copies of the first variational process. As part of our analysis, we also prove a general well-posedness result for conditional McKean-Vlasov backward SDEs.

The goal of this short note is to prove a unified abstract regularity lemma which recovers Szemerédi's graph regularity lemma, Green's arithmetic regularity lemma, and a regularity lemma for Boolean functions as direct corollaries.

Deep reinforcement learning (DRL) applied to thermal convection control consistently produces \textit{degenerate actuation}: wall-temperature policies whose outputs are saturated, pseudo-random, or spatially incoherent. Two compounding deficiencies are responsible: multilayer-perceptron policies that discard spatial flow structure, and memoryless policies that cannot distinguish self-induced flow changes from background evolution. Together they prevent the discovery of physically meaningful control laws even when cell coalescence (the merging of convection rolls into fewer, larger structures), which would reduce $\mathrm{Nu}$, is accessible to boundary actuation. The present framework addresses both causes through four targeted design choices: convolutional policy networks, Gated Recurrent Unit (GRU) memory, off-policy training (TD3/MADDPG), and action-smoothness constraints. A systematic $2\times2$ factorial design isolates the contribution of each component. On Rayleigh--Bénard convection at $\mathrm{Ra}=10{,}000$, all four configurations achieve cell coalescence and reduce $\mathrm{Nu}$ to as low as $1.83$ ($26\%$ below the uncontrolled baseline) in 350 episodes, without the full-field data augmentation required by prior work. Crucially, coalescence is achieved even by the single-agent configuration, demonstrating that the multi-agent formulation is not a prerequisite once the policy architecture is sufficiently expressive. Applied to double-diffusive convection in the salt-finger regime, the framework spontaneously discovers a travelling-wave actuation whose phase speed adapts to the evolving mixing state of the flow, enhancing heat transfer by $19.1\%$ and reducing salinity variance by $21.0\%$.

Financial volatility exhibits substantial non-stationarity, making single-regime models inadequate for characterising changing market conditions. This paper proposes a triple-timeframe Markov-Switching GARCH (MS-GARCH) framework for volatility regime detection in EUR/USD across daily, four-hour, and hourly horizons. Three independent AR(1)-MS-GARCH models are estimated to capture macro, meso, and micro regime dynamics, while Filardo-style time-varying transition probabilities (TVTP) are incorporated at the shorter horizons through composite stress indicators. The resulting regime probabilities are combined through an outer-product construction into a 27-state cross-scale probability tensor. Using EUR/USD data from 2015-2025, the framework produces statistically distinct Calm, Turbulent, and Crisis regimes and achieves superior out-of-sample volatility forecasting performance relative to a conventional GARCH benchmark. The results suggest that volatility dynamics contain meaningful structure across multiple timescales and that modelling these scales separately provides a more informative representation of market conditions than a single-timescale approach.

Demand-responsive transit (DRT) is a flexible alternative to traditional, fixed-route mass-transit networks. Although DRT can function well in low-density communities, high operating costs and low reliability are common issues. We propose that these issues can be mitigated by moving from a centralized, manually-scheduled scheme to a distributed system capable of dynamically routing multiple vehicles using a slime-mold-inspired routing algorithm to maximize network effectiveness. We additionally introduce the method of dynamic transfers to further optimize transit network efficiency. All passenger allocation and dynamic transfers are handled via a continual cooperative bidding process by the buses. In this paper, we present simulated results for a swarm-driven transit network in suburban, urban, and semi-rural scenarios, using map networks pulled from OpenStreetMap. We show that our approach increases passenger delivery rates relative to a fixed-network approach by 28%, 49%, and 101%, respectively, and results in over 75% reduction in walking time in all cases.

We survey a line of works studying semimartingale reflected Brownian motion in a quadrant, covering both the non-degenerate and degenerate settings. Two main situations are emphasized: the recurrent case, where an invariant measure exists, and the transient case, where the central objects are Green's functions (potential measures). These measures typically arise from Kolmogorov forward equations. For transient or killed models one is also interested in the Martin boundary of the process and, consequently, in all positive harmonic functions, which satisfy Kolmogorov backward equations. Depending on the geometry and parameters of the model, these harmonic functions often admit probabilistic interpretations in terms of absorption, escape, or drift to infinity. All these measures and functions are studied through kernel functional equations satisfied by their Laplace transforms. Several ways of solving these equations are reviewed, each leading to different types of results. Following the analytic approach developed for quarter-plane random walks by Fayolle, Iasnogorodski and Malyshev, a key preliminary step is the analytic continuation of the relevant Laplace transforms onto the complex algebraic curve defined by the zero set of the kernel. Carleman boundary value problem techniques then yield explicit contour-integral representations for the Laplace transforms. In special parameter regimes, Tutte's invariant method provides integral-free formulas and a sharp classification of the transforms according to their algebraic-differential complexity. Singularity analysis combined with saddle-point methods carried out on the kernel algebraic curve, produces precise two-dimensional asymptotics. Finally, in the degenerate setting, the compensation approach provides an alternative constructive method, allowing one to build the densities as an infinite series through explicit iterative corrections.

We derive the first-principles Ehrenfest molecular dynamics describing non-adiabatic processes with the inclusion of the nuclear-velocity-dependent phases (also known as electron-translation factors) on the atomic-orbital basis. These phases, appearing when nuclei are treated dynamically, affect effective Hamiltonians constructed from localised orbitals. In this work, we focus on the effects in the first-principles pseudo-potential Hamiltonian, both for the norm-conserving and ultra-soft cases, derived within the Projector-Augmented-Wave (PAW) method framework. Peierls-like phases depending on the nuclear velocities appear in the non-local part of the potential, while additional nuclear velocity and acceleration-dependent corrections appear in the ultra-soft pseudo-potential case. The use of velocity-including atomic orbital basis enables a Galilean-invariant description of the non-adiabatic Ehrenfest molecular dynamics, removing spurious non-adiabatic couplings that arise from neglecting the nuclear velocity phases in the atomic orbitals.

This manuscripts has two goals. The first goal is to show that the interaction in the Dual Model of Liquids between the solidlike molecule aggregates and the lattice excitations is appropriate to represent the link between the behaviour at macroscopic scale of normal liquids and the physical processes characterizing those systems at mesoscopic scale. The second goal is to show that the duality allows identifying a time arrow on the mesoscopic scale in liquids. The interaction of quanta of elastic energy with the molecular clusters introduces a privileged direction, which is relevant in time dependent and dissipative macroscopic processes, although the interaction remains temporally reversible

We characterize products of Volterra-type integral operators and composition operators acting between quaternionic Fock spaces for the full range \(0<p,q<\infty\), allowing general slice regular composition symbols without any slice-preserving assumption. The criteria are formulated in terms of a Berezin-type testing quantity. Using a fixed-slice matrix realization of the \(\star\)-product, we express slice composition through a matrix functional calculus and relate the testing quantity to complex Berezin-type estimates associated with the eigenvalue maps of the matrix symbol. We also show that the natural affine restrictions are imposed on these eigenvalue functions rather than on the composition symbol itself.