This contribution presents an alternative stabilization technique for the virtual element method (VEM) based on reduced integration combined with a scaled boundary parametrization. To this end, a Taylor series expansion of the constitutive quantities with respect to the sectional center is carried out, enabling analytical integration of the weak form and reducing the need for integration points to only one per section. The accuracy of the proposed formulation is shown by several numerical examples, including a non-linear patch test. Different loading, e.g. compression under large deformations, and material conditions, such as hyperelastic anisotropy and elasto-plasticity, are considered. The biquadratic serendipity finite element formulation (Q2) and the low-order finite element formulation with hourglass stabilization (Q1STc+) are used for comparison. While the patch test was not fulfilled using higher order shape functions, the formulation led to good results and was able to capture the structure's response accurately. Furthermore, the formulation performed better when the physical element resembled the pre-assigned parent elements. The example of the asymmetrically notched specimen under elasto-plastic material behavior showed that the proposed formulation is able to capture inelasticities.

The Traveling Salesman Problem (TSP) is a classical NP-hard combinatorial optimization problem that aims to find the shortest Hamiltonian cycle visiting each city exactly once and returning to the starting point. This paper proposes a hybrid metaheuristic for the TSP by combining the Dragonfly Algorithm (DA), a swarm-intelligence-based global search method, with Tabu Search (TS), a memory-based local search technique. The proposed method follows a High-Level Relay Hybridization (HRH) scheme, in which DA is first used to explore the solution space and generate a promising initial tour, while TS subsequently refines this solution through neighbourhood-based improvement and tabu memory. The hybrid approach is evaluated on standard TSPLIB benchmark instances, including burma14, att48, and ch150, and compared with standalone DA, standalone TS, and several classical metaheuristics such as Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, and Random Search. A systematic grid-search procedure is also conducted to study the influence of the main hyperparameters on solution quality and execution time. The experimental results indicate that the proposed hybrid can improve tour quality compared with the standalone DA and TS on the tested instances, highlighting the benefit of combining global exploration with local exploitation. However, the results also suggest that performance remains sensitive to parameter settings and problem size, motivating further validation on larger benchmarks and stronger TSP-specific baselines.

Dynamic analysis of Android's application layer typically relies on physical devices, limiting scalability and reproducibility. To compensate, we introduce a systematic re-hosting method that relocates the Android framework and pre-installed software from real device firmware into a fully emulated environment. Our approach integrates vendor-specific components into the Android Open Source Project (AOSP) build system using tailored extraction and injection strategies, producing vendor-flavoured emulator images that preserve system integrity and runtime compatibility. This enables dynamic execution of real-world framework and application-layer components, including proprietary binaries and pre-installed apps, across multiple SDK versions. We evaluate our method on 184 firmware samples from SDK 31-33. It achieves high build and boot success rates, with residual failures primarily occurring during core-service initialization due to baseline strategy limitations, missing dependencies, device-protection checks, or emulator constraints. However, the modular design allows injection strategies to be extended for specific firmware, supporting broader compatibility and future research on automated, adaptive re-hosting. Though we identified potential for optimization through engineering vendor-specific solutions, our research demonstrates the feasibility of vendor-flavoured emulators for scalable, reproducible dynamic analysis.

Multicomponent vapor-deposited organic glasses are essential in organic electronic applications, but achieving controlled component segregation at the nano- and mesoscale remains a challenge, hindering the rational development of high-performance devices. In this study, we investigate binary organic semiconductor mixtures of TPD (N,N'-Bis(3-methylphenyl)-N,N'-diphenylbenzidine) and TCTA (Tris(4-carbazoyl-9-ylphenyl)amine). Despite being miscible in the bulk liquid state, the co-deposited glassy films of these two organic semiconductors exhibit a range of segregation behaviors, from homogenous to clearly phase-separated structures. We employed differential scanning calorimetry and resonant soft X-ray scattering (RSoXS) to study the component segregation behavior and used the National Institute of Standards and Technology RSoXS Simulation Suite, paired with Atomic Force Microscopy, to interpret the energy-dependent RSoXS spectra. Our results indicate that component segregation in co-deposited TPD-TCTA films is due to a kinetically-arrested nucleation-and-growth mechanism, in contrast to the segregation mechanism of a previously reported TPD-DO37 (disperse orange 37) mixture which is strongly immiscible in bulk. This work provides a demonstration of tunable molecular aggregation in organic semiconductor glasses, enabling access to a continuum of morphologies from homogeneously mixed to segregated phases.

We introduce a novel intersection type system for a $λ$-calculus with algebraic effects and handlers. The system, inherently behavioral in nature, enjoys the classical properties of intersection type systems, in particular subject reduction and expansion. It thus characterizes the set of terms whose evaluation process terminates and, at the same time, allows reducing the reachability problem to type inference. This new system, the first with these features for a calculus with handlers, induces a system of simple types which, although not guaranteeing termination, is type sound and admits a decidable HOMC problem, unlike similar type systems like Dal Lago and Ghyselen's HEPCF.

A finite group is said to be quartic-free if its order is not divisible by $p^4$ of any prime $p$. A finite group is called an $A$-group if all of its Sylow subgroups are abelian. Objective of this paper is to provide explicit structure of a quartic-free $A$-group. Further in the process of providing the explicit structure we also determine the derived length of a solvable quartic-free $A$-group.

We introduce a unified theoretical framework for single-plasmon transport in one-dimensional nanowires, bridging the quantized electromagnetic Green's tensor formalism with effective non-Hermitian Hamiltonian models. This approach naturally incorporates propagating surface plasmon polaritons, high-order modes dissipative channels, and intrinsic losses. We investigate both the stationary regime and the spatio-temporal dynamics of a single-plasmon pulse travelling through an atomic chain coupled to a dispersive nanowire. We analyze modal contributions to reflection and transmission spectra for quantum emitter coupled to a silver nanowire, a configuration proposed as a single-plasmon transistor, and we demonstrate that optimized multi-emitter systems offer significant advantages. In case of one quantum emitter coupled to a silver nanowire at telecom wavelengths, we predict a single-plasmon transmittivity down to 7\% under realistic conditions, and an atomic qubit population of 12\%. Extension to multi-emitter systems using a Löwdin orthogonalization procedure enables a consistent treatment of collective interactions. We show that optimized positioning with just five emitters enhances plasmon modulation, achieving a transmittivity of 2\% but also reduces coupling losses to one-third compared to the single-emitter case. Our results establish a robust foundation for analyzing and designing plasmonic waveguide quantum electrodynamics systems.

Classical $(r,δ)$ locally recoverable codes (LRCs) play a central role in distributed data storage systems as they enable an efficient recovery from erasures by accessing a small number of surviving symbols. Motivated by their prospective use in future quantum data storage and by recent theoretical progress on quantum locally recoverable codes (qLRCs), we investigate the construction of qLRCs from classical cyclic $(r,δ)$-LRCs. Our approach identifies cyclic LRCs whose defining sets satisfy a dual-containing condition, allowing them to serve as valid CSS ingredients. We present three explicit families of $(r,δ)$-qLRCs, two of which are optimal with respect to the quantum Singleton-like bound, whenever the codes are pure, thereby providing optimal examples. Additionally, the codes presented in Constructions 2 and 3 have no bound on their lengths with respect to the field size required to obtain these codes.

We study an initial-boundary value problem for a Zakharov type system in three space dimensions in a general domain. Under a smallness assumption on the initial data, we construct a unique global strong solution. The solution is obtained by a direct approach based on higher-order energy estimates and the construction of a Cauchy sequence in suitable Banach spaces, without employing compactness methods. Furthermore, we obtain estimates on the growth of higher-order Sobolev norms of solutions.

For a graph $F$, let $h_F(n,q)$ be the minimum number of copies of $F$ in an $n$-vertex graph with $\mathrm{ex}(n,F)+q$ edges, where $\mathrm{ex}(n,F)$ is the maximum number of edges in an $n$-vertex $F$-free graph. Let $c(n,F)$ be the minimum number of copies obtained by adding one edge to an extremal $F$-free graph. Mubayi's supersaturation conjecture predicts, under a stability hypothesis, that $h_F(n,q)\ge q\,c(n,F)$. Ma and Yuan recently constructed stable graph counterexamples for every fixed $q\ge4$; they asked whether the one-edge equality $h_F(n,1)=c(n,F)$ might still hold for every graph $F$ containing a cycle. We give a negative answer to their question. For each integer $t\ge6$, let $H_t$ be obtained from the $t$-vertex path by replacing each edge with a $3t$-page book, using disjoint page vertices for different path edges. Then $h_{H_t}(n,1)<c(n,H_t)$ for infinitely many values of $n$. Moreover, by taking $t$ large, the ratio $h_{H_t}(n,1)/c(n,H_t)$ can be made arbitrarily small along infinitely many values of $n$.

Millimeter-wave Adaptive Optics (MAO) is essential for high-precision large-aperture submillimeter telescopes, requiring real-time compensation of wavefront errors by capturing them as spatially-discrete excess path length (EPL) fluctuations. This paper presents a unified control-theoretic framework for the EPL compensation problem. We first model the optical drive system as a plant where input commands relate to measured EPL through a first-order system representing mechanical response delay and a measurement matrix characterizing the actuator-to-sensor coupling. We mathematically formulate the control task as an asymptotic disturbance suppression problem, specifically targeting low-frequency disturbances such as thermal and wind-induced deformations. Second, we propose an Anti-Windup Proportional-Integral (AWPI) control law. By employing a decoupling strategy, the design is reduced to a loop-shaping problem for decoupled scalar sensitivity functions, ensuring both stability margins and asymptotic disturbance suppression of constant-valued disturbances. The anti-windup mechanism is integrated to maintain control continuity during the recovery from saturation, preventing undesirable discontinuities in the drive command. Third, we introduce practical operational tools: a manual focus adjustment scheme that allows observer intervention without interfering with the feedback loop, and the cosine similarity index to quantify the suppressibility of specific Zernike modes. Numerical simulations, incorporating a three-axis secondary reflector drive and five-point EPL measurements, demonstrate direction-dependent disturbance rejection and the suppression of von Karman-modeled wind turbulence, validating the effectiveness of the proposed framework for real-world telescope applications.

A unitarily invariant complete Nevanlinna--Pick (CNP) kernel $k$ on the Euclidean ball gives rise to a natural class of operator tuples on Hilbert spaces, known as $1/k$-contractions. We establish a lower estimate for the Taylor joint spectrum of $1/k$-contractions with finite defect in terms of the associated characteristic function. Under the additional assumption that $k$ satisfies the Corona property, this lower estimate coincides with an upper estimate due to Clouâtre--Timko [Adv. Math., 2023], yielding an exact characterization of the Taylor joint spectrum in terms of the characteristic function. As an application, we determine the Taylor joint spectrum of quotient modules of CNP spaces. A key ingredient in the proof is a Beurling--Lax--Halmos theorem for these spaces, established in terms of characteristic functions.

We describe the construction of a database of roughly half a million abelian surfaces over Q of small conductor arising as Pryms associated to a genus 3 double cover of a genus 1 curve. Our construction uses a method that provides a degree of control over the primes of bad reduction.

We revisit the effective coupling of the scalaron to gauge fields in $f(R)$ gravity minimally coupled to the Standard Model, focusing on the scalaron decay into two photons. Treating the scalaron as an intrinsic component of the Jordan-frame metric, we analyse quantum effects arising from its coupling to the energy--momentum tensor. In this framework, the trace anomaly contributes to the scalaron--gauge boson interaction. Using Fujikawa's method, we derive the anomaly-induced contribution, associated with the transformation of matter fields between the Jordan and Einstein frames, first in QED and then in the full Standard Model. The resulting effective scalaron--photon interaction agrees with direct perturbative calculations that include the trace anomaly and differs from the result obtained when only the classical trace of the energy--momentum tensor is taken into account. In the limit where the scalaron mass is much smaller than the masses of particles circulating in the loop, the diagrammatic contribution cancels the anomaly-induced term, leading to a vanishing effective coupling and a strong suppression of the scalaron decay rate into photons. These results clarify the origin of discrepancies in the literature concerning the effective scalaron coupling to massless gauge fields. The discrepancies arise from inequivalent prescriptions for implementing quantum loop effects in $f(R)$ gravity, leading to different scalaron--gauge field interactions with direct implications for scalaron dark-matter phenomenology.

Local search is a well-known heuristic method used in optimization. In this thesis, we explore its capabilities on the vertex coloring problem, an $NP$-hard problem with relevance in both theoretical analysis and practical application. To recognize limitations in the applicability of local search of the vertex coloring problem, we analyze local search landscapes on differently-structured bipartite graphs. We identify structures that ensure only global optima can exist as well as ones that enable the existence of non-global local optima, showing that on general bipartite graphs, it is possible for local search to return arbitrarily bad results. Further, we analyze the capabilities of local search on graphs where a local optimum can be found. To do so, we introduce a gray-box local search mutation operator that removes less frequent colors with higher probability and prove that it finds an optimal coloring on complete bipartite graphs in an expected run time of $Θ(n \log n)$. This is a drastic improvement to the exponential tun time of the black-box Random Local Search, showing that gray-box mutation operators can improve the run time of local search.

The planar Hall effect (PHE) is an anisotropic magnetotransport response generated by coplanar electric and magnetic fields. We investigate the PHE in single- and bilayer two-dimensional electron gases (2DEGs) with Rashba spin-orbit coupling and identify two distinct mechanisms: Zeeman coupling and a band geometric channel. In the Zeeman channel, an in-plane magnetic field distorts the Rashba spin-orbit-coupled band dispersion and generates anisotropic carrier velocities, producing a finite PHE. In an asymmetric Rashba bilayer, interlayer electronic delocalization generates finite planar Berry curvature and orbital magnetic moment components, giving rise to a band geometric PHE channel. Using semiclassical Boltzmann transport theory, we calculate the chemical potential and angular dependence of the planar Hall conductivity for both mechanisms. Symmetry analysis shows that the leading response is quadratic in the magnetic field and exhibits the characteristic $π$-periodic angular dependence. For the parameter regime considered here, the Zeeman-induced contribution dominates, while the band geometric channel provides a distinct symmetry-allowed contribution unique to asymmetric Rashba bilayers. Our results reveal microscopic origins of anisotropic magnetotransport in spin-orbit-coupled two-dimensional materials.

The split covariance intersection filter (Split CIF) is a useful tool for general data fusion and has the potential to be applied in a variety of engineering tasks. The w-optimization problem involved in the Split CIF concerns the performance and implementation efficiency of the Split CIF. It is known that the w-optimization problem enjoys the desirable property of convexity (or more clearly, the second-order convexity in this paper's context). This paper proves that the w-optimization problem further enjoys a more desirable property namely the fourth-order convexity, thanks to which a guaranteed fast implementation of the Split CIF can be realized. The new implementation is coined as the nested Newton method, which is also presented in this paper.

Distributed radio frequency sensing in contested tactical environments demands collaborative learning across mobile nodes. In ad-hoc networks, learning must occur without persistent backhaul, ground truth labels, or reliable communication links. Traditional federated learning approaches assume either ideal link conditions or supervised training objectives, neither of which holds in practice for deployed MANET platforms. This paper presents a hierarchical federated learning framework for unsupervised waveform classification over tactical MANETs subject to Rayleigh fading, random waypoint mobility, and multi-hop routing loss. Each node trains a local denoising convolutional autoencoder on raw IQ observations without label exchange, learning compact representations through a self-supervised reconstruction objective. A two-stage aggregation protocol elects connectivity-based relay aggregators consistent with OLSR multipoint relay selection, compressing cluster-level model updates before forwarding to a mobile server proxy. Simulation results demonstrate that in-network aggregation reduces attempted transmission bits relative to relay-forward federated averaging by around 12% at equivalent classification performance. Notably, stochastic channel-driven subsampling under non-IID data acts as an implicit regularizer, with both MANET conditions matching or exceeding ideal federated averaging on unsupervised representation quality. This suggests that moderate link loss can partially compensate for client drift in heterogeneous networks. Performance is assessed on analysis of the learned latent embeddings using KMeans normalized mutual information and linear probe accuracy.

The production of a top-antitop quark pair in association with a $W$ boson constitutes one of the heaviest final states currently studied at the Large Hadron Collider (LHC) at CERN. Measurements of its production rate have consistently exceeded Standard Model predictions. Owing to the complexity of the two-loop amplitudes entering the double-virtual correction, next-to-next-to-leading-order (NNLO) QCD calculations for this process have so far employed dynamical approximations for the two-loop contribution. We present NNLO QCD predictions based, for the first time, on a direct computation of the required two-loop amplitudes in the generalised leading-colour limit.

This paper is devoted to the numerical analysis of a second-order bulk--surface splitting scheme for the semi-linear wave equation with kinetic boundary conditions. The construction is based on the interpretation of the equations as coupled system and the implementation of different difference formulae for the discrete states depending on their exact position in the system equations. This results in a 4-step scheme which decouples bulk and surface dynamics. We prove energy stability and second-order convergence under a weak CFL condition and validate these results also numerically.

Understanding quantum dynamics in curved spacetime is a central challenge at the intersection of quantum mechanics and gravity. Anti-de-Sitter (AdS) spacetime plays a pivotal role in the context of the AdS/CFT correspondence, which relates gravitational dynamics in the AdS bulk to a conformal field theory (CFT) living on its boundary. Despite its foundational importance, direct experimental access to dynamical quantum phenomena in Lorentzian AdS spacetime has so far remained out of reach. Here, we report the first experimental emulation of fermionic wave packet dynamics in Lorentzian AdS spacetime using a photonic platform. By mapping the Dirac equation in curved spacetime onto the propagation of light in engineered wave\-guide arrays, we directly observe gravitational confinement of relativistic wave packets and resolve their center-of-mass motion in real time. We identify a characteristic superposition of slow geodesic oscillations governed solely by spacetime curvature and fast Zitterbewegung arising from relativistic particle--antiparticle interference. While the geodesic frequency is independent of fermion mass, the Zitterbewegung frequency exhibits a distinct joint dependence on mass and curvature, revealing a curvature-induced modification of relativistic quantum dynamics. Our results provide the first quantitative experimental access to fermionic bulk dynamics in emulated AdS$_2$ spacetime with Lorentzian signature. This establishes a scalable analog platform that may potentially be used for exploring dynamical aspects of holography.

Accurate acoustic modelling of the skull is essential for simulation-guided transcranial focused ultrasound (tFUS), but commonly used skull parameterisation strategies differ in complexity and reported accuracy. This study experimentally compared five k-Wave skull models: two voxel-wise linear mapping models, two three-layer models, and one single-layer fixed-parameter model. Nineteen regions of interest from five historical and two Thiel-embalmed human skulls were tested at 220 kHz, 680 kHz, and 1000 kHz. Bowl-surface source fields were reconstructed using acoustic holography, and simulated intracranial pressure fields were benchmarked against needle-hydrophone measurements. Across frequencies, mean peak-pressure errors ranged from 20% to 31%, whereas intensity errors reached 41% to 77%. Errors in -6 dB focal volume ranged from 11% to 67%, and focal-position discrepancies were typically several millimetres. Simulations generally predicted smaller insertion losses than measured, indicating a tendency to underestimate skull-related attenuation and overestimate transmitted intracranial exposure. The linear mapping model with fixed attenuation gave the lowest frequency-averaged pressure error, but no model showed a consistent advantage across all metrics. These results show that current skull models can reproduce gross intracranial beam patterns while retaining substantial quantitative uncertainty in exposure, focal coverage, and target localisation.

We study an idealized information model for Doppler-only positioning with low earth orbit (LEO) signals of opportunity from a stationary receiver. Motivated by the observation that Doppler measurements from a satellite pass provide information primarily within the associated orbital plane, we model each satellite contribution as a weighted projection onto that plane. Under this model, the combined information matrix from multiple satellites is a sum of orbital-plane projection operators. Closed-form expressions are derived for the eigenvalues, condition number, and worst-case Cramer-Rao lower bound. For two satellites, the conditioning is governed by the dihedral angle between orbital planes and the relative information strengths of the two links. Monte Carlo evaluation of pass-integrated Doppler Fisher information matrices demonstrates that the proposed surrogate captures the dominant conditioning trends associated with orbital-plane diversity. The results provide a simple geometric framework for understanding the role of constellation geometry in Doppler-only positioning systems.

Ecological communities with structured interactions exhibit collective phenomena such as percolation and clustering of occupied sites. While these effects have been documented in experiments and simulations, systematic analytical understanding has remained limited. In this paper, we develop a dynamical theory of these phenomena for competitive ecological systems defined on random interaction graphs. We introduce a discrete version of the generalized Lotka-Volterra model that preserves key macroscopic features of continuous ecological dynamics while enabling analytical treatment. Within this framework, we characterize the emergence of percolating clusters and describe the spatial organization of surviving sites. Our analysis uncovers which equilibria can be reached by the dynamics and shows how this dynamical accessibility governs the onset of clustering and percolation. In doing so, our framework complements classical Lotka-Volterra theory by providing a dynamical perspective on the collective organization of structured communities.

We investigate collisionless power absorption in resonant, low$-$pressure capacitively coupled plasmas (CCPs). In these radio-frequency (RF) discharges, the sheath capacitance almost exactly balances the plasma inductance, driving the total RF discharge voltage down to just a few volts. However, plasma persists not only in this ultra$-$low$-$voltage regime; it also generates ions that strike the electrodes with kinetic energies substantially exceeding the amplitude of the applied RF voltage. This counterintuitive behavior arises from the presence of a pronounced electrostatic potential well of approximately 40 V within the plasma bulk, which confines electrons while simultaneously accelerating ions toward the electrodes. We show that, under these resonant conditions, collisionless electron heating exhibits a fundamentally different behavior from the conventional paradigm of stochastic sheath heating mediated by electron$-$sheath interactions. Instead, the predominant energy transfer mechanism is bulk electron heating in RF electric fields via a primarily collisionless process that emerges from the synergistic action of: (i) a strongly amplified RF electric field within the plasma bulk, (ii) electron oscillatory motion (bouncing) within the plasma potential well, and (iii) electron scattering resulting from collisions with neutral atoms. Collectively, these phenomena give rise to a pronounced high$-$energy tail in the electron energy distribution function and thereby lead to a substantial enhancement of the ionization rates. As the gas pressure rises, the resonance is disrupted. At the same time, the region of maximum power absorption moves from the plasma core toward the edges and the sheath, which is accompanied by the disappearance of the high$-$energy electron population and a corresponding decrease in ionization rates

We develop an inhomogeneous form of Edwards' Jensen-measure duality for Perron envelopes constrained by Monge--Ampère lower bounds. The admissible subsolution families are convex but not cones; nevertheless, the dual measures remain the homogeneous Jensen measures, and the right-hand side enters through a scalar Jensen deficit \[ B_{\mathcal{A}}(x,μ) = \inf_{u\in\mathcal{A}} \left(\int_{\partialΩ}u\,dμ-u(x)\right). \] Under natural structural hypotheses we prove a boundary dual formula \[ \sup\{u(x):u\in\mathcal{A},\ u\leqφ\text{ on }E\} = \inf_{μ\in J_x^\partial} \left( \int_{\partialΩ}φ\,dμ - B_{\mathcal{A}}(x,μ) \right). \] We apply the theorem to real Alexandrov subsolutions and to complex Bedford--Taylor plurisubharmonic subsolutions with continuous density. In one real dimension the deficit is the Green-potential correction; in higher dimensions it has intrinsic stress and current interpretations. On B-regular domains, a bounded Bedford--Taylor approximation theorem identifies bounded and continuous competitors and yields a duality proof of continuity for the corresponding Dirichlet solution. Finally, for smooth strictly elliptic solutions, optimal Jensen measures are the harmonic measures of the linearized Monge--Ampère operators, equivalently the boundary derivatives of the nonlinear solution map.

Dark photons are a gauge boson of a hypothetical dark sector, representing one of the most-studied minimal extensions of the Standard Model, with wide-ranging theoretical and observational implications. Here, we consider scenarios in which an initially unpopulated dark photon sector is populated via resonant photon to dark photon conversions. This process leads to observable spectral distortions in the cosmic microwave background (CMB), that can be used to constrain these models. We extend previous spectral distortion studies of the monopole spectrum to anisotropic spectral distortions, using the newly developed Frequency Hierarchy (FH) framework of CosmoTherm. We illustrate the physics by presenting detailed computations of the photon transfer functions and distortion cross power spectra throughout the dark photon parameter space. We find that the dark photon mass explicitly controls the shape (i.e., multipole-dependence) of the signal power spectra, while the overall amplitude of the signal is determined by the kinetic mixing parameter of the model. Using these results, we place complementary limits on the minimal dark photon model using data from Planck, finding that the constraints are only marginally weaker than those obtained with COBE/FIRAS data for the average (monopole) distortion. In addition, we compute the corrections to the standard temperature field, arguing that conversions at redshifts larger than $2\times 10^6$ may add iso-curvature type perturbations, which could lead to novel constraints in regimes where distortion anisotropies thermalize.

In the presence of stratification, turbulent flows exhibit intermittency not only at small scales but also at large scales, comparable to the mean flow, as observed in the atmosphere and oceans. We study such flows through a large parametric exploration using direct numerical simulations of the Boussinesq equations with different forcing types. We examine two Prandtl numbers (1 and 6) and vary the Froude number ($Fr$) over a range of geophysical interest values, $0.01\le Fr \le 1$, corresponding to a variation in terms of the buoyancy Reynolds number ($R_{IB}$) of $0.06\le R_{IB} \le 2300$. We analyze the dependence on $R_{IB}$ of the buoyancy flux ($B_f$), the mixing efficiency, the shear parameters, and the vertical momentum flux. Strongly non-Gaussian tails in the spatio-temporal distribution of the $B_f$ are observed, with kurtosis reaching $\approx 10^2$, indicating the potential for stratified geophysical flows to be characterized by highly variable transport properties along the direction of gravity even under stable stratification. This is associated with long-time intermittent behavior of vertical velocity and temperature at large scale, which produces local turbulence and enhances dissipation and transport. We present evidence that the skewness of $B_f$ increases with $R_{IB}$ as a power-law and saturates in the passive-scalar limit. We also show that the domain-averaged $B_f$ exhibits two distinct trends: logarithmic growth with $R_{IB}$ and approach to a small offset as stratification strengthens. A simple model for the temporal evolution of energy and $B_f$ indicates that the defect between vertical and potential energy drives strong $B_f$ events. This trend directly leads to convective instabilities, the formation of two-dimensional and three-dimensional eddies, and rapid dissipation on a turnover timescale, allowing the energetic cycle to restart-also occurring in bursts.

Motivated by the need to understand infection spreading in inhomogeneous populations, we consider a \emph{temporal} version of the stochastic block model, where each edge is equipped with a random label, interpreted as a timestamp. We study the size and structure of reachable sets via increasing paths (that is, paths whose edge timestamps are strictly increasing) where the connections per node are of the order of $\log n$. We prove tight results for the first order asymptotics of the size of the reachable set from a typical vertex, and the proportions of reached vertices in each community. We also determine the typical length of the shortest and longest increasing paths with one or two fixed endpoints. In the regime where the reachable set $S$ of a typical vertex is of sublinear size, we describe the structure of the subgraph induced by $S$ by identifying an almost spanning tree (i.e., spanning all but $o(|S|)$ vertices), that is distributed as a weighted random recursive tree, whose height, profile and degree sequence are known. In particular, when $|S|\ll \sqrt{n}$, the subgraph induced by $S$ is itself distributed as this well-understood weighted random recursive tree.

Magnetic equilibrium reconstruction provides the plasma state estimate required for real-time shape control in tokamaks. We present a fast, physics-informed neural network surrogate of the \texttt{liuqe} equilibrium reconstruction code \cite{liuqe1} for the TCV tokamak at EPFL, achieving inference times below 100~$\bmμ$s and enabling 10~kHz shape control. The model is trained on around 10,000 TCV discharges spanning the full operational range of plasma shapes. Its modular branch/trunk architecture decouples magnetic measurement encoding from spatial coordinate processing, enabling physics-informed regularization via automatic differentiation of the predicted flux map. The surrogate has been compiled and deployed on the TCV real-time control system, and validated both offline and in real time against the models \texttt{liuqe-rt} and \texttt{lih}, showing comparable accuracy. Closed-loop performance assessed with the real-time software in-the-loop \texttt{fge} \cite{fge1} demonstrates control-equivalent behavior across multiple control strategies.