Extracting 3D atomic coordinates from spectroscopic data is a longstanding inverse problem. We present an equivariant diffusion model that generates site-specific 3D structures directly from near-edge spectra (ELNES/XANES). Trained on Si-O crystals, the model achieves radial accuracy comparable to Extended X-ray Absorption Fine Structure (EXAFS) (RMSD ~0.06 Å) but with superior coordination number precision (errors < 4.3% vs. EXAFS ~20%). Crucially, it reconstructs full 3D geometries including bond angles, overcoming the limitations of 1D radial distribution analysis. The model demonstrates robust out-of-distribution generalization, accurately predicting local structures in amorphous systems despite being trained exclusively on crystalline lattices. Application to experimental O K-edge spectra from α-quartz validates practical applicability. This generative approach outperforms template matching and establishes automated, quantitative 3D structure determination from spectroscopic data.

We consider the one-dimensional nonlinear Schrödinger equation $$ iu_t + u_{xx} + \mathcal{N}(u)u=0, \quad x,t \in \mathbb R, $$ with the nonlinearity term that is expressed as a sum of powers, possibly infinite: $$ \mathcal{N}(u) = \sum d_k |u|^{α_k}, \quad α_k > 0. $$ We first investigate the local well-posedness of this equation for any positive powers of $α_k$ in a certain weighted class of initial data, subset of $H^1 (\mathbb R)$. For that we use an approach of Cazenave-Naumkin [19], thus, avoiding any Strichartz estimates. Then, using the pseudo-conformal transformation, we extend the local result to the global one for the initial data with a quadratic phase. Furthermore, we investigate the asymptotic behavior of such global solutions and prove scattering for data with the quadratic phase $e^{ib|x|^2}$ with sufficiently large positive $b$, in $H^1(\mathbb R)$. One of the advantages of considering an infinite sum in the nonlinearity term is being able to consider exponential nonlinearities, such as $e^{γ|u|^{k}} u$, as well as sine or cosine nonlinearities, and obtain well-posedness in those cases, the first such result for most of those nonlinearities. To conclude, we show numerical simulations for various examples of combined nonlinearities, including the double nonlinearity and an exponential one, then investigate the behavior of solutions with positive or negative initial $b$ in a quadratic phase data. Furthermore, we also show that a ground state in the NLS equation with combined nonlinearities no longer provides a sharp threshold for global behavior such as scattering vs. finite time blow-up, instead the equation has a much richer dynamics.

Interfacial thermal transport between graphene and water plays a critical role in a wide range of thermal and energy applications. Although chemical functionalization can significantly enhance graphene-water interfacial thermal conductance, it often degrades graphene's intrinsic in-plane phonon transport. In this work, we perform a systematic deep neural network molecular dynamics study comparing edge-functionalized graphene nanoribbons with surface-functionalized graphene in aqueous environments. We demonstrate that functionalizing only 10% of the ribbon edges with hydroxyl groups increases the graphene-water interfacial thermal conductance by more than eightfold, primarily due to strengthened interfacial interactions and improved wettability at the edges. In contrast to basal-plane oxidation, edge functionalization largely preserves in-plane thermal conductivity. Importantly, hydroxyl edge groups exert competing effects on phonon transport: they introduce additional boundary scattering that suppresses heat conduction, while simultaneously passivating dangling bonds at bare edges, thereby reducing phonon localization and edge-induced scattering. This competition leads to a non-monotonic dependence of in-plane thermal conductivity on edge functionalization ratio. These results establish edge functionalization as an effective strategy for enhancing graphene-water interfacial thermal transport without sacrificing intrinsic phonon transport properties.

Vibration from an erroneous disturbance harms the manufactured components and lowers the output quality of an FDM printer. For moving machinery, vibration analysis and control are crucial. Additive manufacturing is the basis of 3D printing, which utilizes mechanical movement of the extruder to fabricate objects, and faults occur due to unwanted vibrations. Therefore, it is vital to examine the vibration patterns of a 3D printer. In this work, we observe these parameters of an FDM printer, exemplified by the MakerBot Method X. To analyze the system, it is necessary to understand the motion it generates and select appropriate sensors to detect those motions. The sensor measurement values can be used to determine the condition of the printer. We used an accelerometer and an acoustic sensor to measure the vibration and sound produced by the printer. The outputs from these sensors were examined individually. The findings show that vibration occurs at relatively low levels during continuous motion because it mainly appears at component transition edges. Due to abrupt acceleration and deceleration during zigzag motion, vibration reaches its peak.

In this work, we reformulate the relativistic BDNK (Bemfica-Disconzi-Noronha-Kovtun) diffusion equation in flux-conservative form, and solve the resulting equations in $(1+1)$D using both a second-order Kurganov-Tadmor finite volume scheme and physics-informed neural networks (PINNs). In particular, we introduce the SA-PINN-ACTO framework, which combines the self-adaptive PINN technique with an exact enforcement of initial and periodic boundary conditions through an algebraic transform of the network's raw output, allowing the network to focus solely on minimizing the PDE residual. We test both approaches on smooth and discontinuous initial data, for both trivial and dynamically evolving velocity and temperature BDNK backgrounds, and for two characteristic speeds. The SA-PINN-ACTO method matches the converged Kurganov-Tadmor solutions for smooth profiles, while for discontinuous profiles the errors increase, reflecting an expected limitation of PINNs near sharp gradients.

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole ``sucks in'' the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein--Maxwell--Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship.

Let $μ(r)$ denote the minimal side length of a square inscribed in the curvilinear triangular region formed by two tangent circles of radii $1$ and $r \ge 1$ together with their common tangent line. The problem of finding a closed-form expression for $μ(r)$ was posed in early nineteenth-century Japan by Morikawa. It was proved by Holly and Krumm (2021) that no expression in radicals exists for $μ(r)$. In this article we show that $μ$ is an algebraic function, and consequently real-analytic on $[1,\infty)$ outside a finite explicitly computable set. In particular, although no expression in radicals exists, the function admits convergent Taylor expansions at all non-exceptional values of $r$, whose coefficients may be computed by Newton iteration from the defining algebraic equation. We illustrate the method by explicitly computing the Taylor expansion of $μ(r)$ centered at $r=1$.

Flat-top (FT) solitons are optical pulses that arise from the balance of dispersion and self-phase modulation in media with the competing cubic-quintic nonlinearity. Previously, FT solitons were studied only in the case of the second-order dispersion ($m=2$). Following the recent observation of pure-quartic solitons (corresponding to $m=4$), we here construct families of FT solitons in the setting with pure-high-even-order dispersion (PHEOD), including $m=4,6,8$, and $10$, and address interactions between them. The PHEOD solitons are completely stable, and, unlike the conventional solitons, they feature oscillatory tails. Interactions between the PHEOD solitons are anomalous, featuring repulsion and attraction between in- and out-of-phase solitons, respectively. These results expand the variety of optical solitons maintained by diverse dispersive nonlinear media.

Vehicle dwelling has increased significantly in recent years. While HCI research has explored vehicle dwelling through the lens of digital nomadism and vanlife, it has largely overlooked the complexities of vehicle dwelling as a form of housing insecurity, as well as the unique constraints of living in smaller vehicles. Drawing on a qualitative analysis of posts and comments from an online community, we examine car dwellers' infrastructuring work to manage daily life under social, spatial, and infrastructural constraints. We further explore the motivations and identity negotiations of car dwellers, whose experiences fall between homelessness and nomadism, and highlight how developing infrastructural competence can shape identity. We discuss implications for future HCI research on mobility and dwelling under conditions of uneven access to infrastructure and provide design recommendations for technologies that better account for car dwellers' diverse needs, circumstances, and identities.

Additive manufacturing, particularly fused deposition modeling, is transforming modern production by enabling rapid prototyping and complex part fabrication. However, its layer-by-layer process remains vulnerable to faults such as nozzle clogging, filament runout, and layer misalignment, which compromise print quality and reliability. Traditional inspection methods are costly, time-intensive, and often limited to post-process analysis, making them unsuitable for real-time intervention. In this current study, the authors developed a novel, low-cost, and portable faultdetection system that leverages multimodal sensor fusion and artificial intelligence for real-time monitoring in FDM-based 3D printing. The system integrates acoustic, vibration, and thermal sensing into a non-intrusive architecture, capturing complementary data streams that reflect both mechanical and process-related anomalies. Acoustic and thermal sensors operate in a fully contactless manner, while the vibration sensor requires minimal attachment such that it will not interfere with printer hardware, thereby preserving portability and ease of deployment. The multimodal signals are processed into spectrograms and time-frequency features, which are classified using convolutional neural networks for intelligent fault detection. The proposed system advances Industry 4.0 objectives by offering an affordable, scalable, and practical monitoring solution that improves faultdetection accuracy, reduces waste, and supports sustainable, adaptive manufacturing.

In this work, we investigate the effects of the growth rate scale dependence in the Symmetron modified gravity (MG) model on cosmic structure formation and we analyze the redshift-space distortion (RSD) multipoles, comparing with the Hu-Sawicki $f(R)$ model (specifically the F6) and the standard $Λ$CDM model. The analysis employs a scale-dependent growth equation and utilizes the fk-PT perturbation theory approach, implemented in the FOLPS-nu code, to compute the full 1-loop power spectrum multipoles, in particular, the monopole and quadrupole ($\ell=0,2$, respectively). The results show that at redshift $z=0$, the monopole of both MG models is suppressed compared to $Λ$CDM, with the Symmetron being closer to the standard model, while the quadrupole presents the opposite behavior. To validate the pipeline, we use General Relativity (GR) mock catalogs (EZMocks), since suitable Symmetron simulations are not available. The main result is that the Markov Chain Monte Carlo (MCMC) analysis successfully recovers the expected GR limit (i.e., $β_0 \approx 0$) from the Symmetron model when applied to this mock data, confirming the viability of our methodology for cosmological inference. Then, we conclude that the pipeline is prepared to test MG models against current and near-future galaxy surveys.

Code translation, the automatic conversion of programs between languages, is a growing use case for Large Language Models (LLMs). However, direct one-shot translation often fails to preserve program intent, leading to errors in control flow, type handling, and I/O behavior. We propose an algorithm-based pipeline that introduces a language-neutral intermediate specification to capture these details before code generation. This study empirically evaluates the extent to which structured planning can improve translation accuracy and reliability relative to direct translation. We conduct an automated paired experiment - direct and algorithm-based to translate between Python and Java using five widely used LLMs on the Avatar and CodeNet datasets. For each combination (model, dataset, approach, and direction), we compile and execute the translated program and run the tests provided. We record compilation results, runtime behavior, timeouts (e.g., infinite loop), and test outcomes. We compute accuracy from these tests, counting a translation as correct only if it compiles, runs without exceptions or timeouts, and passes all tests. We then map every failed compile-time and runtime case to a unified, language-aware taxonomy and compare subtype frequencies between the direct and algorithm-based approaches. Overall, the Algorithm-based approach increases micro-average accuracy from 67.7% to 78.5% (10.8% increase). It eliminates lexical and token errors by 100%, reduces incomplete constructs by 72.7%, and structural and declaration issues by 61.1%. It also substantially lowers runtime dependency and entry-point failures by 78.4%. These results demonstrate that algorithm-based pipelines enable more reliable, intent-preserving code translation, providing a foundation for robust multilingual programming assistants.

We study the set of square-free parts of volume polynomials associated with four planar lattice polytopes. This is motivated by the problem of describing possible pairwise intersection numbers of four curves in $(\mathbb{C}^*)^2$ with prescribed Newton polytopes and generic coefficients. It is known that for arbitrary convex bodies in $\mathbb{R}^2$, the corresponding square-free polynomials are characterized by the Plücker-type inequalities. We show that this characterization fails in the lattice setting: the interior of the space defined by the Plücker-type inequalities contains integer polynomials that are and are not realizable by lattice polytopes. This phenomenon arises from additional arithmetic constraints on the mixed areas of lattice polytopes. These constraints become apparent when we study a "discrete diagram", which maps a pair of planar lattice polytopes to their mixed area together with their lattice widths in a given direction.

We derive a set of generators for the rational homology of the desingularised genus one mapping space $\widetilde{\mathcal{M}}_{1,n}(\mathbb{P}^r,d)$ constructed by Vakil--Zinger and qualitatively describe the relations among the generators. The results build on a detailed study of the stratifications of the moduli spaces coming from tropical geometry and the constraints coming from the weight filtration on the Borel--Moore homology groups of strata, extending the techniques from the previous study on $\overline{\mathcal{M}}_{g,n}.$ Our results imply that the even homology of $\widetilde{\mathcal{M}}_{1,n}(\mathbb{P}^r,d)$ is tautological and controlled by genus-zero and reduced genus-one Gromov--Witten theory. We verify the Hodge and Tate conjectures for $\widetilde{\mathcal{M}}_{1,n}(\mathbb{P}^r,d),$ completely describe its rational Picard group, and recover known results on the vanishing of odd cohomology. Our techniques also apply to the pure weight homology groups of genus one stable maps $\overline{\mathcal{M}}_{1,n}(\mathbb{P}^r,d).$

The increasing development of wireless communication bands has motivated the development of compact, low-loss, and frequency adjustable RF filtering technologies. Acoustic resonators are the ideal solution to these requirements, and tunable implementations offer a path toward reconfigurable front ends. In this work, we investigate epitaxial barium titanate (BTO) grown on silicon as a platform for tunable acoustic resonators operating in the sub-GHz regime. We demonstrate lateral excitation of symmetric lamb (S0) modes in X-cut BTO membranes, in contrast to prior thickness-defined ferroelectric resonators. Devices are designed using finite-element simulations and fabricated with laterally patterned electrodes that enable overtone coupling to multiple resonant modes. Under applied DC bias, ferroelectric domains align, allowing electrical excitation, frequency tuning, and quality-factor enhancement of acoustic modes. Resonances near 300 MHz and 700 MHz exhibit electromechanical coupling up to 8% and bias-dependent frequency tuning, with a distinct transition in behavior near 20 V. These results highlight monolithic BTO on silicon as a promising material system for laterally excited, tunable acoustic resonators for reconfigurable RF applications.

With the rapid advancement of large language models (LLMs), efficiently serving LLM inference under limited GPU resources has become a critical challenge. Recently, an increasing number of studies have explored applying serverless computing paradigms to LLM serving in order to maximize resource utilization. However, LLM inference workloads are highly diverse, and modern GPU clusters are inherently heterogeneous, making it necessary to dynamically adjust deployment configurations online to better adapt to the elastic and dynamic nature of serverless environments. At the same time, enabling such online reconfiguration is particularly challenging due to the stateful nature of LLM inference and the massive size of model parameters. In this paper, we propose a dynamic pipeline reconfiguration approach that enables online adjustment of pipeline configurations while minimizing service downtime and performance degradation. Our method allows the system to select the optimal pipeline configuration in response to changing workloads. Experimental results on heterogeneous GPU platforms, including NVIDIA A100 and L40s, demonstrate that our migration mechanism incurs less than 50 ms of service downtime, while introducing under 10% overhead on both time-to-first-token (TTFT) and time-per-output-token (TPOT).

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally intensive to directly embed in the simulation model. Replacing these elements with estimated or learned approximations introduces a form of epistemic uncertainty that we refer to as submodel uncertainty. This paper investigates how submodel uncertainty affects the estimation of system performance metrics. We develop a framework for quantifying submodel uncertainty in stochastic simulation models and extend the framework to digital-twin settings, where simulation experiments are repeatedly conducted with the model initialized from observed system states. Building on approaches from input uncertainty analysis, we leverage bootstrapping and Bayesian model averaging to construct quantile-based confidence or credible intervals for key performance indicators. We propose a tree-based method that decomposes total output variability and attributes uncertainty to individual submodels in the form of importance scores. The proposed framework is model-agnostic and accommodates both parametric and nonparametric submodels under frequentist and Bayesian modeling paradigms. A synthetic numerical experiment and a more realistic digital-twin simulation of a contact center illustrate the importance of understanding how and how much individual submodels contribute to overall uncertainty.

Fidelity-based quantum kernels provide a direct interface between quantum feature maps and classical kernel methods, but they can exhibit exponential concentration: with increasing system size or circuit expressivity, the Gram matrix approaches the identity and suppresses informative similarity structure. We present an empirical study of two mitigation strategies implemented in Qiskit: (i) local (patch-wise) kernels that aggregate subsystem similarities, and (ii) multi-scale kernels that mix local and global similarity across patch granularities. We benchmark baseline, local, and multi-scale kernels under matched preprocessing, splits, and SVM protocols on several tabular datasets, sweeping the feature dimension $d\in\{4,6,\dots,20\}$. We report concentration diagnostics based on off-diagonal kernel statistics, spectral richness via effective rank, and centered alignment with labels. Across datasets, local and multi-scale constructions consistently mitigate concentration and yield richer kernel spectra relative to the global fidelity baseline, while the impact on classification accuracy depends on the dataset and dimension.

We present the discovery and analysis of three microlensing planets identified through brief positive anomalies on the wings of their light curves. The events, KMT-2021-BLG-0852, KMT-2024-BLG-2005, and KMT-2025-BLG-0481, were detected in high-cadence survey data from the KMTNet, OGLE, MOA, and PRIME collaborations. The anomaly morphologies are consistent with major-image perturbations induced by planetary-mass companions located near the peripheral caustic. A systematic exploration of model degeneracies, including binary-source scenarios, higher mass-ratio binary lenses, and the inner--outer caustic degeneracy, firmly establishes the planetary origin of each signal. Measurements of the angular Einstein radius and event timescale, combined with Bayesian priors from a Galactic model, yield the physical parameters of each system. The hosts are low-mass stars (0.12--0.75~$M_\odot$), while the companions are Saturn-mass planets (0.16--0.59 $M_{\rm J}$) projected at separations of 1.1--7.8 au, placing them beyond the snowline of their hosts. These results demonstrate the capability of microlensing to detect and characterize cold giant planets around low-mass stars at kpc distances, populating the critical transition region between ice giants and gas giants.

Lie algebras provide a useful framework for theoretical analysis in quantum machine learning, particularly in hybrid quantum-classical learning. From the viewpoint of function approximation, expectation values of parameterized quantum circuits can be viewed as trigonometric polynomials whose accessible Fourier modes are determined by the spectra of the generators. In this study, we describe: (1) a minimax lower bound on the $ L^{2} $-approximation error over a Sobolev ball when the circuit's effective frequency set is contained in a radius-$K$ ball, which yields a scaling law of the form $ Ω(K^{\frac{d}{2} - r}) $ for $ r > \frac{d}{2} $ (assuming the target function belongs to the Sobolev space $ W_2^{r}(\mathbb{T}^{d}) $), and we also derive a Jackson-type upper bound on the approximation error of quantum circuits under Sobolev regularity of the target function, expressed in terms of an effective bandwidth determined by generator spectral gaps; (2) a generator-selection rule motivated by enlarging the effective frequency set via non-commuting generators; and (3) a simple heuristic metric based on the trace component of generators, aimed at characterizing training behaviors related to barren plateaus. Simulation experiments on toy problems illustrate the practical implications of the frequency-spectrum perspective and the proposed heuristics.

Background: Symbolic models, particularly decision trees, are widely used in software engineering for explainable analytics in defect prediction, configuration tuning, and software quality assessment. Most of these models rely on correlational split criteria, such as variance reduction or information gain, which identify statistical associations but cannot imply causation between X and Y. Recent empirical studies in software engineering show that both correlational models and causal discovery algorithms suffer from pronounced instability. This instability arises from two complementary issues: 1-Correlation-based methods conflate association with causation. 2-Causal discovery algorithms rely on heuristic approximations to cope with the NP-hard nature of structure learning, causing their inferred graphs to vary widely under minor input perturbations. Together, these issues undermine trust, reproducibility, and the reliability of explanations in real-world SE tasks. Objective: This study investigates whether incorporating causality-aware split criteria into symbolic models can improve their stability and robustness, and whether such gains come at the cost of predictive or optimization performance. We additionally examine how the stability of human expert judgments compares to that of automated models. Method: Using 120+ multi-objective optimization tasks from the MOOT repository of multi-objective optimization tasks, we evaluate stability through a preregistered bootstrap-ensemble protocol that measures variance with win-score assignments. We compare the stability of human causal assessments with correlation-based decision trees (EZR). We would also compare the causality-aware trees, which leverage conditional-entropy split criteria and confounder filtering. Stability and performance differences are analyzed using statistical methods (variance, Gini Impurity, KS test, Cliff's delta)

We construct a skew-Hadamard matrix of order 1252 = 2(5^4 + 1) using a bordered skew-Hadamard difference family over GF(5^4), with blocks given as unions of cyclotomic classes of order N = 16. This order has been reported as missing in some widely used open-source computational tables; we provide an explicit instance together with verification artifacts. We prove the structural prerequisites for the bordered construction (skew-symmetry of one block and the constant autocorrelation-sum condition), and we compute algebraic invariants to facilitate classification: the associated tournament adjacency matrix has full rank over GF(2), and the matrix has full rank over GF(3) and GF(5). We also exhibit an explicit affine subgroup of the automorphism group of size 24 375. All claims are supported by a reproducible artifact bundle including the explicit matrix and verification logs.

Active networks composed of biopolymers and motor proteins provide versatile biomimetic systems that have advanced active matter physics and deepened our understanding of cytoskeletal dynamics and self-organization under diverse stimuli. In these systems, activity arises in aqueous solutions where motor proteins cross-link biopolymers and generate active stress driving the emergent network behavior. Here, we establish the active network in the form of a sessile, multi-component droplet on a substrate and investigate how evaporation influences its dynamics. We focus on how mass loss and compositional changes in the droplet reshape the behavior of the active suspension. We show that capillary and Marangoni flows drive the self-organization of microtubules into a distinctive radial arrangement within the droplet. The cross-linking ability of motor proteins gives rise to a striking non-monotonic wetting behavior, where the extensile stresses generated by the motor proteins strongly affect the characteristic timescale of the contact-line retracting and subsequent expansion. Using a combined experimental and theoretical approach, we demonstrate the crucial role of crosslinking in evaporating microtubule networks, and explain how active stresses together with evaporation-induced flows govern the dynamics of reconstituted microtubule systems and their wetting behavior. Evaporating droplets have recently attracted significant attention in the scientific community, and the findings of the setup presented in this study can have broad implications, ranging from self-organization and mechanical pattern formation in biological systems to questions about the origin of life.

The first stars likely formed from pristine clouds, marking a transformative epoch after the dark ages by initiating reionisation and synthesising the first heavy elements. Among these, low-mass Population III stars are of particular interest, as their long lifespans raise the possibility that some may survive to the present day in the Milky Way's stellar halo or satellite dwarfs. As the first paper in a series, we present hydrodynamic evolutionary models for 0.7 - 1 MSun stars evolved up to the white dwarf phase, utilising the MESA software instrument. We systematically vary mass-loss efficiencies, convective transport, and overshooting prescriptions, thereby mapping how uncertain physics influences nucleosynthetic yields; surface enrichment, including nitrogen-rich post-main sequence stars arising from convective shell mergers; remnant properties, such as low-mass helium or carbon-oxygen white dwarfs (M_WD ~ 0.45-0.55 MSun) and transient UV-bright phases; and potential observational signatures, including neutrino emission during shell mergers and helium flashes. These models establish a predictive framework for identifying surviving Pop III stars and their descendants, providing both evolutionary and observational constraints that were previously unexplored.

Dense granular flows exhibit nonlocal effects due to stress transmission in microplastic events, especially in quasi-static or slowly sheared regions. Hence, traditional local rheological models fail to capture spatial cooperativity effects that are prominent in many granular systems. The nonlocal granular fluidity (NGF) model addresses this limitation by introducing a diffusive-like partial differential equation for a fluidity field, governed by a key material-dependent parameter: the nonlocal amplitude A. However, determining A from experiments or simulations is known to be difficult and typically requires extensive calibration across multiple geometries. In this work, we present a data-driven platform based on Physics-Informed Neural Networks (PINNs) embedded with the NGF model, capable of solving granular flows in a forward or inverse manner. We show that once trained on transient flow fields, these non-local PINNs can readily infer the material parameters, as well as the pressure and stress fields. These data-driven frameworks allow for accurate recovery of small variations in the nonlocal amplitude, A, which lead to sharp bifurcation-like transitions in the flow field. This approach demonstrates the feasibility of data-driven parameter inference in complex nonlocal models and opens up new possibilities for characterizing granular materials from sparse experimental observations.

In a number of physically relevant contexts, a quantum system interacting with a decohering environment is simultaneously subjected to time-dependent controls and its dynamics is thus described by a time-dependent Lindblad master equation. Of particular interest in such systems is to understand the circumstances in which, despite the ability to apply time-dependent controls, they lose information about their initial state exponentially with time i.e., their dynamics are exponentially contractive. While there exists an extensive framework to study contractivity for time-independent Lindbladians, their time-dependent counterparts are far less well understood. In this paper, we study the contractivity of Lindbladians, which have a fixed dissipator (describing the interaction with an environment), but with a time-dependent driving Hamiltonian. We establish exponential contractivity in the limit of sufficiently small or sufficiently slow drives together with explicit examples showing that, even when the fixed dissipator is exponentially contractive by itself, a sufficiently large or a sufficiently fast Hamiltonian can result in non-contractive dynamics. Furthermore, we provide a number of sufficient conditions on the fixed dissipator that imply exponential contractivity independently of the Hamiltonian. These sufficient conditions allow us to completely characterize Hamiltonian-independent contractivity for unital dissipators and for two-level systems.

We study the Galerkin approximation of the three-dimensional Navier-Stokes equations. In particular, we examine the convergence of these solutions in a sequence of finite dimensional spaces as the dimension goes to infinity. For any sequence of steady state or, respectively, time dependent Galerkin solutions that converges to a solution of the Navier-Stokes equations, we obtain a subsequence with an intrinsic asymptotic expansion in appropriate nested function spaces. Consequently, an induced asymptotic expansion is obtained in a more standard spatial Sobolev or, respectively, spatiotemporal Sobolev-Lebesgue space. In the case of steady states, we establish certain relations among leading terms of this expansion.

The loss of biodiversity due to the likely widespread extinction of species in the near future is a focus of current concern in conservation biology. One approach to measure the impact of this extinction is based on the predicted loss of phylogenetic diversity. These predictions have become a focus of the Zoological Society of London's 'EDGE2' program for quantifying biodiversity loss and involves considering the HED (heightened evolutionary distinctiveness) and HEDGE (heightened evolutionary distinctiveness and globally endangered) indices. Here, we show how to generalise the HED(GE) indices by expanding their application to more general settings (to phylogenetic networks, to feature diversity on discrete traits, and to arbitrary biodiversity measures). We provide a simple and explicit description of the mean and variance of such measures, and illustrate our results by an application to the phylogeny of all 27 extant Crocodilians. We also derive various equalities for feature diversity, and an inequality if species extinction rates are correlated with feature types.

We compare the ability of a simulated annealing program and an evolutionary algorithm to find molecules with large molecular average hyperpolarizabilities. This property is an important component of nonlinear optical materials. Both optimization programs represent molecules as SMILES strings, a method that is widely used by chemists to describe molecular structure using short ASCII strings. Our results suggest that both approaches are comparable and can be used to solve a variety of more realistic problems of interest to chemists and material scientists.

Bilobate contact binaries comprise a significant fraction of the relict Kuiper Belt, which includes the exemplary contact binary (486958) Arrokoth. The surfaces of its lobes contain similar amounts of highly volatile chemical species and few craters, indicating formation in a homogeneous and gentle environment. Arrokoth's bilobate shape was initially hypothesized to have formed via the direct gravitational collapse of a pebble cloud in the solar system's protoplanetary disk. However, alternative hypotheses have proposed that Arrokoth may be the result of binary planetesimal formation and the subsequent dynamical evolution of the binary components into contact through external perturbations over long timescales. Here, we show that contact binary planetesimals like Arrokoth can form directly from the gravitational collapse of pebble clouds. We used a soft-sphere discrete element method (SSDEM) to discover that planetesimals form a wide variety of shapes, including bilobate contact binaries. This method creates planetesimals as particle-aggregates with particles resting upon each other's surfaces via mutual surface penetration. The formation of contact binaries in our simulations strengthens the hypothesis that Arrokoth, and perhaps many other contact binaries in the Kuiper Belt, formed directly as bilobate objects from gravitational collapse, and so their shapes and surfaces record the era of planet formation.