A number of upper bounds are proved relating to the triple product property (TPP) for subgroups of finite nilpotent groups of class $2$. The TPP is the property defined for three non-empty subsets $S, T, U$ of a group $G$ that the group equation $s's^{-1}t't^{-1}u'u^{-1} = 1$, over pairs of elements $s', s \in S$, $t', t \in T$, $u', u \in U$, is satisfied if and only if $s' = s$, $t' = t$, $u' = u$. When $G$ is finite, and the parameter $ρ_0(G)$, called \emph{subgroup TPP ratio}, is defined as $ρ_0(G) := \max\frac{|S||T||U|}{|G|}$, where the maximum is over the collection of all triples of subgroups $S, T, U$ of $G$ satisfying the TPP, this paper proves that \textup{(1)} $ρ_0(G) < \sqrt{|G:Z(G)}$} for (all) groups of nilpotency class $2$, \textup{(2)} $ρ_0(G) \leq p$ for $p$-groups with a cyclic commutator subgroup of order $p$, \textup{(3)} $ρ_0(G) = 1$ for $p$-groups of nilpotency class $2$ with a "large" centre, loosely defined as those satisfying $p^2 \leq |G:Z(G)| \leq p^3$, \textup{(4)} and $ρ_0(G) = 1$ for $p$-groups of nilpotency class $2$ with "small" (irreducible, complex) character degrees of $1$ or $p$.

Understanding how polymer architecture governs transport through nanopores is essential for nanocomposite fabrication, membrane design, and polymer upcycling. However, the effect of the nanoscale structure of copolymers on chain transport through nanoporous media remains poorly understood. In this study, we demonstrate that simply inverting the surface orientation of lamellar poly(styrene-block-2-vinylpyridine) (PS-b-P2VP) diblock copolymers, composed of two monomers with strongly contrasting affinities for SiO2, at the entrance of nanoporous silica significantly alters the kinetics of capillary rise infiltration. Using in situ spectroscopic ellipsometry, we find that infiltration of symmetric PS-b-P2VP into silica nanoparticle (SiO2 NP) packings is significantly faster when the P2VP domain is the top layer of the film and first contacts the nanoparticles, compared to when the PS domain is the top layer. Coarse-grained molecular dynamics simulations reveal that this difference originates from block-specific adsorption pathways that reorganize the nanophase structure around nanoparticles: P2VP-first infiltration forms thin adsorbed layers that drive PS into the pore interiors, generating continuous interfacial pathways that enable rapid, interface-mediated transport. In contrast, PS-first infiltration produces thicker P2VP layers that isolate PS domains and disrupt pathway connectivity, forcing chains to rely on a slower, connectivity-limited transport mechanism through P2VP-rich interstitial regions. Above the order-disorder transition, or upon silanizing nanoparticles to neutralize surface affinity, the rate difference disappears. These findings demonstrate how the interplay between nanoscale domain configuration and polymer-surface affinity governs infiltration dynamics, providing mechanistic insight into tuning transport in nanostructured block copolymers.

The Computing Continuum (CC) integrates different layers of processing infrastructure, from Edge to Cloud, to optimize service quality through ubiquitous and reliable computation. Compared to central architectures, however, heterogeneous and dynamic infrastructure increases the complexity for service orchestration. To guide research, this article first summarizes structural problems of the CC, and then, envisions an ideal solution for autonomous service orchestration across the CC. As one instantiation, we show how Active Inference, a concept from neuroscience, can support self-organizing services in continuously interpreting their environment to optimize service quality. Still, we conclude that no existing solution achieves our vision, but that research on service orchestration faces several structural challenges. Most notably: provide standardized simulation and evaluation environments for comparing the performance of orchestration mechanisms. Together, the challenges outline a research roadmap toward resilient and scalable service orchestration in the CC.

Aimed at the simulation, design, and interpretation of advanced pulse experiments crossing the boundaries between nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), including the rapidly emerging, hybrid discipline of pulsed dynamic nuclear polarisation (DNP), we present a host of novel features in the widely used SIMPSON software package addressing these aspects. Along with this come new features for advanced pulse sequence evaluation in terms of propagator splitting, high-order spin operator cross terms, and pulse phase transients. These fundamental new tools are introduced in a C++-based next generation of the SIMPSON software, which improves calculations speed in some aspects, is better prepared for further developments, and facilitates easier community contributions to the open-source software package.

Molecular gas is crucial to understanding star formation and galaxy evolution, but the giant molecular clouds (GMCs) of early-type galaxies (ETGs) have rarely been studied. Here, we present analyses of the spatially resolved GMCs of the lenticular galaxy NGC 1387, exploiting high spatial resolution (0.15" or 14 pc) 12CO(2-1) line observations from the Atacama Large Millimeter/submillimeter Array. We identify 1285 individual GMCs and measure the fundamental properties (radius, velocity dispersion, and molecular gas mass) of each with a modified version of the CPROPStoo package. Unusually for an ETG, the GMCs of NGC 1387 follow scaling relations very similar to those of the Milky Way disc and Local Group galaxy clouds, and most are virialised. GMCs with large masses and radii and/or small galactocentric distances have their angular momenta aligned with the large-scale galactic rotation, while other GMCs do not. These results show that ETGs have more diversified GMC properties than previously thought. We discuss potential reasons for such diversity, and viewing-angle dependency is a plausible candidate.

In this work, we provide an overview of general solutions for displacement fields in static problems of isotropic strain gradient elasticity (SGE). We not only review existing solutions but also derive new representations, showing that all classical elasticity solutions - including those of Boussinesq-Galerkin, Papkovich-Neuber, Naghdi, Lame, Love and Boussinesq - can be simply generalized to SGE framework. In general, it is shown that SGE enables the use of any classical general solution representation combined with a Helmholtz decomposition for the gradient part of the displacement field. Consistency is also established between the presented Papkovich-Neuber representation and the general solutions of SGE proposed previously by Mindlin (1964), Lurie et al. (2006) and Charalambopoulos et al. (2020). Furthermore, we establish the relationships between the stress functions of different general solutions and show their completeness.

Synaptic transmission must balance the need for reliable signalling against the metabolic cost of achieving that reliability. How energetic constraints shape synaptic precision and its regulation during plasticity remains unclear. Here we develop an energy--constrained framework in which synapses minimise postsynaptic response variance subject to a fixed mean and an effective energy budget. Combinations of candidate physiological costs are used to estimate an energy cost for synaptic transmission; this cost is then inferred from quantal statistics. Analysing five published pre- and post-plasticity datasets, we find that observed synaptic mean--variance pairs cluster near a minimal-energy boundary, indicating that precision is limited by energetic availability. Model comparison identifies a dominant calcium pump-like cost paired with a smaller vesicle turnover-like cost, yielding a separable precision--energy relationship, $σ^{-2} \propto E^5$. We further show that plasticity systematically updates synaptic energy budgets according to the scale-free magnitude of mean change, enabling accurate prediction of post-plasticity variance from energy allocation alone. These results provide direct experimental support for the hypothesis that synaptic precision is governed by energy budgets, establishing energy allocation as a fundamental principle linking metabolic constraints, synaptic reliability, and plasticity.

We establish results on the dynamics of interacting charged null fluids in general relativity, specifically in the context of the bouncing continuation proposed in [Ori91]. In this model - the setting for a number of prominent case studies on black hole formation - charged massless particles may instantaneously change direction (bounce) after losing all their 4-momentum due to electrostatic repulsion. We initiate the study of timelike bounce hypersurfaces in spherical symmetry: scenarios in which an incoming beam of charged null dust changes direction along a timelike surface $\mathcal{B}$, which is the (free) boundary of an interacting 2-dust region. We identify a novel decoupling of the equations of motion in this region. First, it is shown that every timelike curve segment $γ$ in the spherically symmetric quotient of Minkowski or Reissner-Nordström spacetimes arises as the bounce hypersurface $\mathcal{B}$ of a charged null dust beam incident from past null infinity $\mathcal{I}^-$. We construct a spacetime $(\mathcal{M},g_{μν})$ describing the full trajectory of the beam, which includes gluing to Reissner-Nordström and Vaidya regions. Across $\mathcal{B}$ the metric has regularity $g_{μν}\in C^{2,1}$ and satisfies Einstein's equation classically, while $C^\infty$ gluing may be achieved across all other interfaces. We also obtain examples of timelike bounce hypersurfaces terminating in a null point. Since these constructions are teleological, we secondly consider a given charged incoming beam from past null infinity. We formulate and solve a free boundary problem which represents the formation of a timelike bounce hypersurface. The result is conditional, applying only in the exterior region of a Reissner-Nordström spacetime, and subject to a technical regularity condition.

We present the development of a data-driven, AI-based model of the Point Spread Function (PSF) that achieves higher accuracy than the current state-of-the-art approach, "PSF in the Full Field-of-View'' (PIFF). PIFF is widely used in leading weak-lensing surveys, including the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) Survey, and the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The PSF characterizes how a point source, such as a star, is imaged after its light traverses the atmosphere and telescope optics, effectively representing the "blurred fingerprint'' of the entire imaging system. Accurate PSF modeling is essential for weak gravitational lensing analyses, as biases in its estimation propagate directly into cosmic shear measurements -- one of the primary cosmological probes of the expansion history of the Universe and the growth of large-scale structure for dark energy studies. To address the limitations of PIFF, which constructs PSF models independently for each CCD and therefore loses spatial coherence across the focal plane, we introduce a deep-learning-based framework for PSF reconstruction. In this approach, an autoencoder is trained on stellar images obtained with the Hyper Suprime-Cam (HSC) of the Subaru Telescope and combined with a Gaussian process to interpolate the PSF across the telescope's full field of view. This hybrid model captures systematic variations across the focal plane and achieves a reconstruction error of $3.4 \times 10^{-6}$ compared to PIFF's $3.7 \times 10^{-6}$, laying the foundation for integration into the LSST Science Pipelines.

Non-reference metrics (NRMs) can assess the visual quality of images and videos without a reference, making them well-suited for the evaluation of user-generated content. Nonetheless, rate-distortion optimization (RDO) in video coding is still mainly driven by full-reference metrics, such as the sum of squared errors, which treat the input as an ideal target. A way to incorporate NRMs into RDO is through linearization (LNRM), where the gradient of the NRM with respect to the input guides bit allocation. While this strategy improves the quality predicted by some metrics, we show that it can yield limited gains or degradations when evaluated with other NRMs. We argue that NRMs are highly non-linear predictors with locally unstable gradients that can compromise the quality of the linearization; furthermore, optimizing a single metric may exploit model-specific biases that do not generalize across quality estimators. Motivated by this observation, we extend the LNRM framework to optimize ensembles of NRMs and, to further improve robustness, we introduce a smoothing-based formulation that stabilizes NRM gradients prior to linearization. Our framework is well-suited to hybrid codecs, and we advocate for its use with overfitted codecs, where it avoids iterative evaluations and backpropagation of neural network-based NRMs, reducing encoder complexity relative to direct NRM optimization. We validate the proposed approach on AVC and Cool-chic, using the YouTube UGC dataset. Experiments demonstrate consistent bitrate savings across multiple NRMs with no decoder complexity overhead and, for Cool-chic, a substantial reduction in encoding runtime compared to direct NRM optimization.

The focusing of particle beams for collider experiments is crucial for maximizing the luminosity and thus the discovery potential of these machines. In recent years, plasma wakefield acceleration has emerged as a leading candidate for achieving higher energy collisions with smaller facility footprints due to the large accelerating gradients in the plasma. This higher beam energy poses significant challenges for the final focusing system of the collider. Here, we discuss the various challenges of final focusing for TeV-scale plasma accelerators and propose possible solutions. Finally, we present the first design of a final focusing system for a 10 TeV linear wakefield collider, evaluate its performance, and discuss its shortcomings as well as improvements for future designs.

We propose a minimal tight-binding model for the electronic interface layer of the LaAlO$_3$/SrTiO$_3$ heterostructure with oxygen vacancies. In this model, the effective carriers are subject to oxygen vacancy induced magnetic impurities. Both the effects of random on-site potentials and Zeeman-like exchange interactions between correlated carriers and magnetic impurities are taken into account. By applying the combined coherent potential approximation (CPA) and dynamical mean-field theory (DMFT) for a ferromagnetic state, we uncover a disordered Fermi-liquid regime for the majority-spins and a low energy scale which controls the transport of the minority-spin carriers, both induced by the magnetic impurities.

Transaction flow networks are crucial in detecting illicit activities such as wash trading, credit card fraud, cashback arbitrage fraud, and money laundering. \revise{Our collaborator, Grab, a leader in digital payments in Southeast Asia, faces increasingly sophisticated fraud patterns in its transaction flow networks. In industry settings such as Grab's fraud detection pipeline, identifying fraudulent activities heavily relies on detecting dense flows within transaction networks. Motivated by this practical foundation,} we propose the \emph{\(S\)-\(T\) densest flow} (\SDMF{}) query. Given a transaction flow network \( G \), a source set \( \Src \), a sink set \( \Dst \), and a size threshold \( k \), the query outputs subsets \( \Src' \subseteq \Src \) and \( \Dst' \subseteq \Dst \) such that the maximum flow from \( \Src' \) to \( \Dst' \) is densest, with \(|\Src' \cup \Dst'| \geq k\). Recognizing the NP-hardness of the \SDMF{} query, we develop an efficient divide-and-conquer algorithm, CONAN. \revise{Driven by industry needs for scalable and efficient solutions}, we introduce an approximate flow-peeling algorithm to optimize the performance of CONAN, enhancing its efficiency in processing large transaction networks. \revise{Our approach has been integrated into Grab's fraud detection scenario, resulting in significant improvements in identifying fraudulent activities.} Experiments show that CONAN outperforms baseline methods by up to three orders of magnitude in runtime and more effectively identifies the densest flows. We showcase CONAN's applications in fraud detection on transaction flow networks from our industry partner, Grab, and on non-fungible tokens (NFTs).

We introduce a notion of nondegenerate neck pinch singularity along the Lagrangian mean curvature flow of surfaces in a Calabi-Yau surface. We show that such singularities can occur, are stable under small perturbations, and any neck pinch singularity can be perturbed to such a nondegenerate singularity near the singular time. Using this we answer some questions raised by Neves and Joyce. We also introduce nondegenerate teardrop singularities and show that these cannot occur for embedded flows.

Latent heat flux is a primary pathway for ocean-atmosphere exchange of heat and moisture, yet the influence of sea surface temperature variability at fine scales ($\leq$ 100 km) on latent heat flux variability, particularly over the Southern Ocean, remains poorly understood. Here we quantify the scale-dependent drivers of latent heat flux (LHF) variability using a year-long, global, fully coupled ocean-atmosphere simulation with kilometer-scale resolution. Annual-mean LHF in eddy-rich regions reaches $\approx$ 215 W m$^{-2}$, approximately three times larger than in eddy-poor regions. Spectral analyses show that ocean mesoscale [$\mathcal{O}$(100 km)] and submesoscale [$\mathcal{O}$(1-10 km)] variability accounts for up to $\approx$ 80% of the total LHF variance in eddy-rich sectors, but as little as 10% in eddy-poor regions, and increases proportionally with eddy kinetic energy and sea surface temperature (SST) variance. We also find that strong submesoscale SST fronts ($\approx$ 5 $^\circ$C over 10 km) force a localized secondary circulation that extends well above the marine boundary layer into the mid-troposphere. Comparison with ERA5 shows that fine ocean scales, responsible for about 17% of the ocean-driven LHF variance in the simulation, are largely unresolved in the reanalysis, leading to a muted atmospheric response lacking any secondary circulation. Despite a strong heterogeneity in LHF variability, the atmospheric dynamics are mostly uniform across the domain, suggesting a non local atmospheric response to ocean forcing. These results highlight the potential for ocean meso- and submesoscales, commonly under-resolved in climate models and reanalysis, to influence Southern Ocean air-sea coupling and atmosphere both locally and remotely.

We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $Λ>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $Λ$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,Λ)$ locally in the slow-rotation regime away from $a=0$.

With the rapid adoption of large language models (LLMs) in automated code refactoring, assessing and ensuring functional equivalence between LLM-generated refactoring and the original implementation becomes critical. While prior work typically relies on predefined test cases to evaluate correctness, in this work, we leverage differential fuzzing to check functional equivalence in LLM-generated code refactorings. Unlike test-based evaluation, a differential fuzzing-based equivalence checker needs no predefined test cases and can explore a much larger input space by executing and comparing thousands of automatically generated test inputs. In a large-scale evaluation of six LLMs (CodeLlama, Codestral, StarChat2, Qwen-2.5, Olmo-3, and GPT-4o) across three datasets and two refactoring types, we find that LLMs show a non-trivial tendency to alter program semantics, producing 19-35% functionally non-equivalent refactorings. Our experiments further demonstrate that about 21% of these non-equivalent refactorings remain undetected by the existing test suites of the three evaluated datasets. Collectively, the findings of this study imply that reliance on existing tests might overestimate functional equivalence in LLM-generated code refactorings, which remain prone to semantic divergence.

We show how the micro-focused BLS signal of forward volume spin waves is formed and why it remains observable despite symmetry-based "suppression" expectations. A reciprocity-theorem based model with vectorial diffraction-limited focusing identifies the nonnegligible longitudinal focal-field component as the key element responsible for BLS sensitivity in the forward volume geometry. We further demonstrate that full polarization analysis, implemented through polarizer-analyzer maps of coherently excited spin waves, provides information beyond the conventional crossed polarizer-analyzer readout. In a BiYIG thin film, the measured maps exhibit Stokes/anti-Stokes polarization asymmetries and nontrivial patterns that stem from quadratic magneto-optical coupling terms. Fitting the data with a model including Voigt and Cotton-Mouton contributions yields an effective Cotton-Mouton constant and shows that the quadratic response is comparable to the linear Voigt contribution.

Despite significant advances in lead-free perovskite photovoltaics, achieving a balance among environmental safety and high optoelectronic performance remains challenging. The inorganic double perovskite Cs2AgBiBr6 has emerged as a promising candidate owing to its robust three-dimensional crystal structure and suitable visible-range bandgap. However, best power conversion efficiencies (PCEs) for Cs2AgBiBr6 solar cells reported so far - 6.37% experimentally and 27.78% in numerical studies - remain below the theoretical performance potential, largely due to suboptimal charge transport layers, and interface-related recombination losses. Here, we address this gap using a 3D finite-element method (FEM) implemented in COMSOL Multiphysics, which couples optical simulations with semiconductor drift-diffusion transport. To our knowledge, this work represents the first comprehensive 3D FEM-based study of a double halide perovskite solar cell. Screening of 25 electron transport layer (ETL)-hole transport layer (HTL) combinations identifies CeO2 and P3HT as the optimal ETL and HTL respectively. Device performance is further analyzed through systematic variation of layer thicknesses, doping concentrations and defect densities within the FTO/CeO2/Cs2AgBiBr6/P3HT/Au architecture. Under optimized parameters, the simulated device achieves a PCE of 31.76%, representing the theoretical upper bound predicted by the model. Overall, this work demonstrates 3D physics-based device engineering as a decisive pathway for overcoming efficiency bottlenecks in lead-free double perovskite photovoltaics.

This paper is devoted to the theory of $GL_n({\mathbb Z})$-conjugacy classes of regular integer $n\times n$ matrices. Such a matrix is $GL_n({\mathbb Q})$-conjugate to the companion matrix of its characteristic polynomial. But the set of $GL_n({\mathbb Z})$-conjugacy classes of regular integer matrices with a fixed characteristic polynomial $f$ is usually nontrivial (finite if $f$ has simple roots, infinite if $f$ has multiple roots). It is in 1:1-correspondence to a subsemigroup of a certain quotient semigroup of the commutative semigroup of full lattices in the algebra ${\mathbb Q}[t]/(f)$. In its first part, the paper gives a survey on old and new results on full lattices and orders in a finite dimensional commutative ${\mathbb Q}$-algebra with unit element and on induced semigroups. In its longer second part, the paper applies this theory to many examples, essentially all cases with $n=2$, many cases with $n=3$ and two cases with arbitrary $n$, the case with $n$ different integer eigenvalues and the case of a single $n\times n$ Jordan block.

Shallow ensembles provide a convenient strategy for uncertainty quantification in machine learning interatomic potentials, that is computationally efficient because the different ensemble members share a large part of the model weights. In this work, we systematically investigate training strategies for shallow ensembles to balance calibration performance with computational cost. We first demonstrate that explicit optimization of a negative log-likelihood (NLL) loss improves calibration with respect to approaches based on ensembles of randomly initialized models, or on a last-layer Laplace approximation. However, models trained solely on energy objectives yield miscalibrated force estimates. We show that explicitly modeling force uncertainties via an NLL objective is essential for reliable calibration, though it typically incurs a significant computational overhead. To address this, we validate an efficient protocol: full-model fine-tuning of a shallow ensemble originally trained with a probabilistic energy loss, or one sampled from the Laplace posterior. This approach results in negligible reduction in calibration quality compared to training from scratch, while reducing training time by up to 96%. We evaluate this protocol across a diverse range of materials, including amorphous carbon, ionic liquids (BMIM), liquid water (H$_2$O), barium titanate (BaTiO$_3$), and a model tetrapeptide (Ac-Ala3-NHMe), establishing practical guidelines for reliable uncertainty quantification in atomistic machine learning.

Laser guide stars (LGSs) have been deployed for the last 20-30 years in ground-based astronomical telescopes to overcome the limited sky coverage of classical adaptive optics (AO) systems. Unfortunately, slow altitude drifts of the sodium layer compromise focus measurements, generating the so-called slow focus error, and, consequently, a natural guide star (NGS) is needed to compensate for that error. Our goal is to develop and operationalize a focal plane wavefront sensing (FPWFS) technique for slow focus tracking for the Keck I telescope, which can significantly increase sky coverage and allow slow focus tracking at higher frequencies, reducing the lag error. We develop, characterize, and compare three different FPWFS algorithms, namely Gerchberg-Saxton (GS), linearized focal plane technique (LiFT), and Gaussian fit (Gf). These algorithms were studied for the specific purpose of slow focus sensing in the NIR (H and K bands) using numerical simulations and data collected at Keck in 2025 (bench and on-sky). The three algorithms were studied and characterized against different criteria such as linearity, computational costs, and resistance to low signal-to-noise ratio and/or residuals. From the results obtained, the main candidate for an on-sky deployment was GS. On-sky tests showed promising results, with GS successfully compensating for purposely introduced focus errors, even under the presence of high turbulence conditions. This work can also be extrapolated to other existing 8-10 m class telescopes, or even future 30-40 m class telescopes, where the use of FPWFS can significantly improve sky coverage and reduce the lag error.

Social media platforms have rapidly adopted algorithmic curation with little consideration for the potential harm to users' mental well-being. We present findings from design workshops with 21 participants diagnosed with mental illness about their interactions with social media platforms. We find that users develop cause-and-effect explanations, or folk theories, to understand their experiences with algorithmic curation. These folk theories highlight a breakdown in algorithmic design that we explain using the framework of entanglement, a phenomenon where there is a disconnect between users' actions and platform outcomes on an emotional level. Participants' designs to address entanglement and mitigate harms centered on contextualizing their engagement and restoring explicit user control on social media. The conceptualization of entanglement and the resulting design recommendations have implications for social computing and recommender systems research, particularly in evaluating and designing social media platforms that support users' mental well-being.

An analytical tool is presented to compute the parametric regions of flutter instabilities of a two-dimensional flexible foil elastically mounted. It is based on a new analytical formulation of the unsteady fluid-estructure interaction valid for small-amplitude oscillations and deformations of the foil immersed in an inviscid fluid. The formulation extends a previous analysis by including the effects of gravity and a second flexural mode, increasing its validity range to much smaller rigidities. The analytical results are validated with available numerical results, capturing the first two natural flexural modes down to values of the stiffness parameter $S$ of order $10^{-1}$. When only passive heave, or only passive pitch, is allowed, the rigid foil is stable, existing an upper stiffness bound for the flexural instabilities, wich become coupled with the spring instability mode for small spring constant increasing the growth rate. These coupled spring (linear or torsional) and flexural instability modes occur below a threshold value of $S$ and above a threshold value of $R$, both depending on the corresponding spring constant. Coupled pitch-heave flutter instabilities of a rigid foil occur in a region below a curve of the parametric plane of the two springs constants that depends on $R$, which shrinks to zero as $R$ decreases. For a flexible foil, the flexural unstable modes become coupled with the springs unstable mode as $S$ decreases from infinity, enlarging the mass ratio range for flutter instability and increasing its growth rate, the more so the smaller the springs constants. The parametric regions for flutter instabilities are easily characterized with the present analytical tool, providing the corresponding frequency and critical flutter velocity. The present results can be useful as a guide in the design of future turbines based on flexible oscillating foils.

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.

We investigate critical restricted solid-on-solid models associated to Dynkin diagrams of type $A$, $D$ and $E$, with fixed, periodic and twisted periodic boundary conditions. These models are endowed with an action of the diagrams of the Temperley-Lieb category. For each model, we obtain the decomposition of the state space as a direct sum of irreducible modules over the Temperley-Lieb algebra $\mathsf{TL}_N(β)$ or its periodic incarnation $\mathsf{\mathcal EPTL}_N(β)$. This allows us to recover the known conformal partition functions for these models in the continuum scaling limit. For each irreducible factor arising in the decompositions, we define an associated local operator on the lattice, which behaves like a connectivity operator. Using knowledge from the Temperley-Lieb representation theory at roots of unity, we show that these operators satisfy certain linear difference relations, which are lattice counterparts of the singular-vector relations in conformal field theory.

Integrating artificial intelligence (AI) into wireless channel modeling requires large, accurate, and physically consistent datasets derived from real measurements. Such datasets are essential for training and validating models that learn spatio-temporal channel behavior across frequencies and environments. NYUSIM, introduced by NYU WIRELESS in 2016, generates realistic spatio-temporal channel data using extensive outdoor and indoor measurements between 28 and 142 GHz. To improve scalability and support 6G research, we migrated the complete NYUSIM framework from MATLAB to Python, and are incorporating new statistical model generation capabilities from extensive field measurements in the new 6G upper mid-band spectrum at 6.75 GHz (FR1(C)) and 16.95 GHz (FR3) [1]. The NYUSIM Python also incorporates a 3D antenna data format, referred to as Ant3D, which is a standardized, full-sphere format for defining canonical, commercial, or measured antenna patterns for any statistical or site-specific ray tracing modeling tool. Migration from MATLAB to Python was rigorously validated through Kolmogorov-Smirnov (K-S) tests, moment analysis, and end-to-end testing with unified randomness control, confirming statistical consistency and reproduction of spatio-temporal channel statistics, including spatial consistency with the open-source MATLAB NYUSIM v4.0 implementation. The NYUSIM Python version is designed to integrate with modern AI workflows and enable large-scale parallel data generation, establishing a robust, verified, and extensible foundation for future AI-enabled channel modeling.

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard directional information through symmetrization or produce sparse, implementation-dependent rankings that obscure structural importance. We introduce a unified spectral framework for centrality analysis in directed networks grounded in the Singular value decomposition of the incidence matrix. The proposed approach derives both vertex and edge centralities via the pseudoinverse of Hodge Laplacians, yielding dense and well-resolved rankings that overcome the sparsity limitations commonly observed in betweenness centrality for directed graphs. Unlike traditional measures that require graph symmetrization, our framework naturally preserves directional information, enabling principled hub/authority analysis while maintaining mathematical consistency through spectral graph theory. The method extends naturally to hypergraphs through the same mathematical foundation. Experimental validation on real-world networks demonstrates the framework's effectiveness across diverse domains where traditional centrality measures encounter limitations due to implementation dependencies and sparse outputs.

This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids the use of special functions, for instance, distinguishing it from the widely used gamma KDE, which relies on the gamma function. Despite its simpler form, the GE KDE maintains similar flexibility and shape characteristics, aligning with distributions such as the gamma, which are known for their effectiveness in modelling positive data. We derive the asymptotic bias and variance of the proposed kernel density estimator, and formally demonstrate the order of magnitude of the remaining terms in these expressions. We also propose a second GE KDE, for which we are able to show that it achieves the optimal mean integrated squared error, something that is difficult to establish for the former. Through numerical experiments involving simulated and real data sets, we show that GE KDEs can be an important alternative and competitive to existing KDEs.

Fast directional solidification during Laser Additive Manufacturing (LAM) produces a complex microstructure in nickel-based superalloys, comprising columnar grains with cellular sub-grain structures and carbides. Using non-destructive Scanning 3D X-ray Diffraction (S3DXRD), we reveal spatially complex orientation and intergranular strain relationships that couple strongly to processing-induced cellular sub-grain networks and a primary cubic metal carbide (MC) phase. We have examined 3D orientation and elastic strain tensor fields across 82 $γ$ grains together with the spatial distribution of over 37,000 MC carbides in an ABD-900AM alloy sample manufactured by the Directed Energy Deposition (DED) LAM process. Carbides are spatially associated with the cellular sub-grain network with a weak but present orientation relationship with their parent $γ$ grains. The MC carbides, known to be Ti, Ta and Nb rich, form in regions of high solute segregation, resulting in a significant volumetric lattice parameter patterning in the associated $γ$ phase regions. These chemically distinct solute-rich regions possess a higher associated elastic modulus compared to intercellular regions and determine the local residual stress patterning. These results provide the first non-destructive 3D study of the relationship between rapid solidification-induced segregation, deformation heterogeneity and carbide architectures in an additively manufactured Ni-based superalloy. The insights provide crucial detail to rationalise LAM process parameter optimisation and the coupled spatially governed structural performance.