We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.

Cherenkov imaging detectors will continue to play a central role for particle identification in future particle and nuclear physics experiments. Growing demands on momentum coverage, timing precision, radiation tolerance, and sustainability have driven extensive R&D in detector concepts, radiator materials, and photon sensors. This article reviews recent efforts, focusing on experiments leading advances in sensor technology, radiator materials, and the exploitation of Cherenkov photon timing to push PID limits, while highlighting synergies across experiments in addressing common challenges.

A graph $G$ is universal for a class of graphs $\mathcal{C}$, if, up to isomorphism, $G$ contains every graph in $\mathcal{C}$ as a subgraph. In 1978, Chung and Graham asked for the minimal number $s(n)$ of edges in a graph with $n$ vertices that is universal for all trees with $n$ vertices. The currently best bounds assert that $n\ln n-O(n)\le s(n) \le C n\ln n+O(n)$, where $C = \frac{14}{5\ln 2} \approx 4.04$. We improve the upper bound to $c n\ln n + O(n)$, where $c = \frac{19}{6\ln 3} \approx 2.88$. In the proof we develop a strategy that, broadly speaking, is based on separating trees into three parts, thus enabling us to embed them in a structure that originates from ternary trees. Our method also applies to graphs with a bound on their treewidth. Let $s_w(n)$ be the minimum number of edges in a $n$-vertex graph that is universal for graphs with treewidth $w$. By performing a blow-up to our universal structure for trees we establish that $nw \ln(n/w) -O(nw) \leq s_w(n) \leq \frac{19}{6\ln3} n (w+1) \ln(n/w) + O(nw)$.

This paper considers a framework for combinatorial variants of perpetual-scheduling problems. Given an independence system $(E,\mathcal{I})$, a schedule consists of an independent set $I_t \in \mathcal{I}$ for every time step $t \in \mathbb{N}$, with the objective of fulfilling frequency requirements on the occurrence of elements in $E$. We focus specifically on combinatorial bamboo garden trimming, where elements accumulate height at growth rates $g(e)$ for $e \in E$ and are reset to zero when scheduled, with the goal of minimizing the maximum height attained by any element. We assume that $g$ is normalized so that it is a convex combination of the incidence vectors of $\mathcal{I}$. Using the integrality of the matroid-intersection polytope, we prove that, when $(E,\mathcal{I})$ is a matroid, it is possible to guarantee a maximum height of at most 2, which is optimal. We complement this existential result with efficient algorithms for specific matroid classes, achieving a maximum height of 2 for uniform and partition matroids, and 4 for graphic and laminar matroids. In contrast, we show that for general independence systems, the optimal guaranteed height is $Θ(\log |E|)$ and can be achieved by an efficient algorithm. For combinatorial pinwheel scheduling, where each element $e\in E$ needs to occur in the schedule at least every $a_e \in \mathbb{N}$ time steps, our results imply bounds on the density sufficient for schedulability.

Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.

The exponential growth of data collection necessitates robust privacy protections that preserve data utility. We address information disclosure against adversaries with bounded prior knowledge, modeled by an entropy constraint $H(X) \geq b$. Within this information privacy framework -- which replaces differential privacy's independence assumption with a bounded-knowledge model -- we study three core problems: maximal per-record leakage, the primal leakage-distortion tradeoff (minimizing worst-case leakage under distortion $D$), and the dual distortion minimization (minimizing distortion under leakage constraint $L$). These problems resemble classical information-theoretic ones (channel capacity, rate-distortion) but are more complex due to high dimensionality and the entropy constraint. We develop efficient alternating optimization algorithms that exploit convexity-concavity duality, with theoretical guarantees including local convergence for the primal problem and convergence to a stationary point for the dual. Experiments on binary symmetric channels and modular sum queries validate the algorithms, showing improved privacy-utility tradeoffs over classical differential privacy mechanisms. This work provides a computational framework for auditing privacy risks and designing certified mechanisms under realistic adversary assumptions.

We embed the covariant, gauge-invariant gravitational radiation criteria of Fernández-Álvarez and Senovilla, based in terms of conformal geometry and the Bel-Robinson tensor, into the hydrodynamic framework of gauge/gravity duality. This construction uncovers a direct correspondence between bulk gravitational waves and dissipative processes in the boundary theory, from which a natural notion of entropy production emerges. We further analyze a smooth flat limit in which the dual fluid becomes Carrollian, with dissipation governed by Carroll-covariant tensors. As an example, we apply our framework to the Robinson-Trautman family of solutions.

The phenomena of induced transparency, with the typical examples of electromagnetically induced transparency (EIT) in atomic media and those based on coupled optical resonators, have attracted tremendous interest since their discoveries. Owing to the limitations of the involved physical elements, however, near-100\% transmissions were reported under highly demanding experimental conditions. With a structure of three linearly coupled optical resonators, an active one carrying optical gain and two passive ones simply with dissipation, we demonstrate that a transmitted light field can become completely transparent through the structure, which displays all properties similar to those of EIT. It is due to a destructive interference mechanism that totally eliminates the intracavity field in the dissipative resonator directly coupled to the transmitted field of any feasible power, when the coupling strength of two other resonators is tuned across a point determined by their associated gain and loss rates. This mechanism works for all possible coupling strengths of the dark resonator with the input field and its neighboring resonator, as well as for any available quality factor from its fabrication. The transparency window size and output field intensity can be freely adjusted by tuning two inter-cavity couplings of wide ranges, without modifying the built-in optical gain which can be just slightly stronger than the dissipation of the active resonator.

GPU-accelerated Inverted File (IVF) index is one of the industry standards for large-scale vector search but relies on static VRAM layouts that hinder real-time mutability. Our benchmark and analysis reveal that existing designs of GPU IVF necessitate expensive CPU-GPU data transfers for index updates, causing system latency to spike from milliseconds to seconds in streaming scenarios. We present SIVF, a GPU-native index that enables high-velocity, in-place mutation via a series of new data structures and algorithms, such as conflict-free slab allocation and coalesced search on non-contiguous memory. SIVF has been implemented and integrated into the open-source vector search library, Faiss. Evaluation against baselines with diverse vector datasets demonstrates that SIVF reduces deletion latency by orders of magnitude compared to the state-of-the-arts. Furthermore, distributed experiments on a 12-GPU cluster demonstrate that SIVF exhibits near perfect linear scalability, achieving an aggregate ingestion throughput of 4.07 million vectors/s and a deletion throughput of 108.5 million vectors/s.

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the analysis of flat $\bar\partial$-connections that define holomorphic structures on line bundles over the quantum projective line. Within this framework, we relate the existence of invertible solutions to the gauge equation associated with holomorphic structures precisely to the existence of fixed points, lying in the open unit ball, of certain nonlinear maps acting on an appropriate Banach space.

We present a rotational velocity (vsini) survey of 32 stellar/substellar objects and giant planets using Keck/KPIC high-resolution spectroscopy, including 6 giant planets (2-7 M$_\mathrm{Jup}$) and 25 substellar/stellar companions (12-88 M$_\mathrm{Jup}$). Adding companions with spin measurements from the literature, we construct a curated spin sample for 43 benchmark stellar/substellar companions and giant planets and 54 free-floating brown dwarfs and planetary mass objects. We compare their spins, parameterized as fractional breakup velocities at 10 Myr, assuming constant angular momentum evolution. We find the first clear evidence that giant planets exhibit distinct spins versus low-mass brown dwarf companions (10 to 40 M$_\mathrm{Jup}$) at 4-4.5 $σ$ significance assuming inclinations aligned with their orbits, while under randomly oriented inclinations the significance is at 1.6-2.1 $σ$. Our findings hold when considering various assumptions about planets, and the mass ratio below 0.8% gives a clean cut for rotation between giant planets and brown dwarf companions. The higher fractional breakup velocities of planets can be interpreted as less angular momentum loss through circumplanetary disk braking during the planet formation phase. Brown dwarf companions exhibit evidence of slower rotation compared to isolated brown dwarfs, while planets and planetary mass objects show similar spins. Finally, our analysis of specific angular momentum versus age of 221 stellar/substellar objects below 0.1 M$_{\odot}$ with spin measurements in the literature indicates that the substellar objects of 5-40 M$_\mathrm{Jup}$ retain much higher angular momenta compared to stellar and substellar objects of 40-100 M$_\mathrm{Jup}$ after 10 Myr, when their initial angular momenta were set.

This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic balance equations for mass, momentum, and energy are obtained, and constitutive equations for the fluxes are determined through a first-order Chapman--Enskog expansion. As for elastic collisions, the transport coefficients are given in terms of the solutions of a set of coupled linear integral equations. Approximate solutions to these equations for diffusion transport coefficients and shear viscosity are achieved by assuming steady-state conditions and considering leading terms in a Sonine polynomial expansion. These transport coefficients are expressed in terms of the coefficients of restitution, concentration, the masses and diameters of the mixture's components, and the system's density. The results apply to moderate densities and are not limited to particular values of the coefficients of restitution, concentration, mass, and/or diameter ratios. As an application, the thermal diffusion factor is evaluated to analyze segregation driven by temperature gradients and gravity, providing criteria that distinguish whether larger particles accumulate near the hotter or colder boundaries.

Distributed sensor networks are commonly operated through coincidence logic: if detector reports overlap within a prescribed time window, an event is declared. While effective for clean, high-significance signals, this approach becomes fragile when detector liveness is intermittent due to deadtime, saturation, vetoes, resets, or asynchronous sampling. In such settings, physically meaningful events may be partially observed yet discarded by binary coincidence rules. We introduce \textit{Synchromodulametry}, a hardware-first framework that promotes \emph{coherence} -- rather than coincidence alone -- to a real-time state variable of the network. The framework is organized around three compact components: a liveness-aware effective observable $Ψ_i^{\mathrm{eff}}(t)$ that preserves information continuity under detector non-idealities, an alignment layer based on relative inter-node delays $τ_{ij}$, and a covariance-based coherence functional $\mathcal{G}(t)$ for triggering and monitoring. Together, these components define a practical pipeline from raw digitized streams to persistent observables, aligned network state, and global coherence estimation. Rather than reducing detector behavior to a binary coincidence flag, Synchromodulametry represents the network as a system capable of entering, maintaining, and losing coherent state in real time.

We study generalizations of Buchdahl's compactness limits for perfect-fluid star solutions of $D$-dimensional Einstein gravity coupled to higher-curvature corrections. We focus on Quasi-topological theories involving infinite towers of terms for which the unique vacuum spherically symmetric solutions correspond to regular black holes. We solve analytically the problem of constant-density stars and find that the space of solutions is bounded by: configurations with divergent central-pressure, corresponding to the most compact stars; configurations which possess zero central-pressure; and configurations for which the sizes of the stars coincide with the inner-horizon radii of the would-be regular black holes. In the more general case of perfect-fluid stars for which the mean density decreases with increasing radius, we show that, for each density profile, maximum compactness is reached when the metric becomes singular at the center. Under certain additional conditions, we find a novel Buchdahl limit for the maximum compactness of stars, attained by a specific constant-density profile. We show, in particular, that stars in these theories may be more compact than in Einstein gravity. While the vacuum solutions of these theories are such that all curvature invariants take mass-independent maximum finite values, we argue that there exist ordinary matter stars with finite central pressures for which such bounds can be violated -- namely, arbitrarily high curvatures can be reached -- unless additional constraints, such as the dominant energy condition, are imposed on the fluid.

We study the behavior of integral transforms under base change. In particular, we establish a yoga of local algebra and fibers to test for derived equivalences or fully faithfulness via integral transforms. This generalizes a result of Orlov to singular varieties and strengthens several results in the literature by allowing arbitrary base fields. Additionally, it provides new insight into fibrations and their singularities in arithmetic settings (e.g.\ projective and flat schemes over a DVR).

We derive the shockwave metric in four-dimensional Einstein-Maxwell effective field theory (EFT) by performing an ultra-relativistic boost of the charged black hole solution accompanied by a rescaling of its mass and charge, including leading order EFT corrections. In contrast to the neutral (Schwarzschild) case, where higher derivative operators leave the shockwave geometry unchanged, we show that electrically charged shockwaves receive nontrivial EFT corrections. We then compute the time delay experienced by a probe photon traversing the resulting charged shockwave. We find that two EFT contributions, the correction to the shockwave geometry and the backreaction induced by the probe photon, are both essential for obtaining a physical time delay that is invariant under field redefinitions of the metric.

We study the one-dimensional S=1 XXZ spin model with single-ion anisotropy. It is known that at the transition points between the Haldane and large-D phases, the model exhibits a quantum criticality described by the Gaussian theory, i.e., a conformal field theory with the central charge c=1. Using the bosonization approach, we investigate various correlation functions at the phase transition and derive their asymptotic forms. This allows us to clarify their peculiar behavior: the longitudinal (transverse) two-point spin correlation function has components that decay algebraically only in the uniform (staggered) sector. These theoretical predictions are verified by the numerical calculations using the density-matrix renormalization group method. The effect of weak bond alternation on the critical ground state at the phase transition is also discussed. It is shown that the bond alternation induces the missing power-law components in the correlation functions.

We study zero-divisors in the $16$-dimensional sedenion algebra from the viewpoint of the determinant of left multiplication. We show that this determinant admits a canonical factorization into the square of a quartic polynomial, obtained via a $G_2$-invariant reduction to a quaternionic normal form and an explicit block computation. The quartic factor recovers the classical characterization of left zero-divisors in terms of the imaginary components. After normalization, the resulting zero-divisor manifold is identified with the Stiefel manifold $V_2(\mathbb{R}^7)$. We also analyze a $3$-dimensional purely imaginary slice, on which the quartic reduces to a simple quadratic form. This yields a concrete geometric model of the zero-divisor locus as a quadratic cone in the slice.

In causal inference, estimating the average treatment effect is a central objective, and in the context of competing risks data, this effect can be quantified by the cause-specific cumulative incidence function (CIF) difference. While doubly robust estimators give a more robust way to estimate the causal effect from the observational study, they remain inconsistent if both models are misspecified. To improve the robustness, we develop a multiply robust estimator for the difference in cause-specific CIFs using right-censored competing risks data. The proposed framework integrates the pseudo-value approach, which transforms the censored, time-dependent CIF into a complete-data outcome, with the multiply robust estimation framework. By specifying multiple candidate models for both the propensity score and the outcome regression, the resulting estimator is consistent and asymptotically unbiased, provided that at least one of the multiple propensity score or outcome regression models is correctly specified. Simulation studies show our multiply robust estimator remains virtually unbiased and maintains nominal coverage rates under various model misspecification scenarios and a wide range of choices for the censoring rate. Finally, the proposed multiply robust model is illustrated using the Right Heart Catheterization dataset.

We study the radiative heat transfer through a Su-Schrieffer-Heeger chain of plasmonic InSb nanoparticles in close vicinity of an InSb substrate. We show how the frequency bands of the in-plane and out-of-plane modes in the chain are deformed by the coupling to the surface waves in the InSb substrate by considering different carrier concentrations. By calculating the Zak phase we show that also in the presence of the substrate there is a topological phase transition and that topologically protected edge modes emerge for finite chains. Finally, we demonstrate the long-range heat transport along the chain due to the coupling to the surface waves of the sample {accompanied by a non-monotonic distance dependence of this effect and we show imprints of the trivial and non-trivial phase in the photonic local density of states.} We find an enhanced heat transfer in the topological non-trivial phase compared to the trivial phase due to the contribution of the edge modes.

Results are presented on $χ_{b1,2}(2P) \to ωΥ(1S)$ transitions from $e^+e^- \to Υ(3S) \to γχ_{b1,2}(2P)$ decays. The data were collected with the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$ collider at SLAC. The integrated luminosity of the data sample is 28.0 fb$^{-1}$, corresponding to $121.3 \times 10^6$ $Υ(3S)$ decays. Signals of $χ_{b1,2}(2P)$ are observed over a negligible background. Improved precision measurements of branching fractions are obtained. First measurements of the $χ_{b1,2}(2P)$ angular distributions are performed. No evidence is found for the presence of a $χ_{b0}(2P) \to ωΥ(1S)$ decay mode.

Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum weak measurement is proposed, where pairwise orthogonal postselected measurement bases with various tiny angles and optimal compositions of measured results are chosen as a decoding rule. The signal to be protected can be retrieved with a minimal distortion after having been transmitted through a noisy channel. Demonstrated by typical examples of encoding signal on two-level superposition state or Einstein-Podolsky-Rossen state transmitted through random telegraph noise and decoherence noises channel, the mean squared error distortion may be close to $0$ and the fault-tolerant capability could reach $1$ with finite quantum resources. To verify the availability of the proposed approach, classic coherent light and quantum coherent state are used for encoding information in the experiment. Potentially, the proposed approach may provide a solution for suppressing noise effects in long-distance quantum communication, high-sensitivity quantum sensing, and accurate quantum computation.

High-resolution range profiles (HRRPs) play a critical role in automatic target recognition (ATR) due to their richinformationregarding target scattering centers (SCs), which encapsulate the geometric and electromagnetic characteristics of thetarget.Under few-shot circumstances, traditional learning-based methods often suffer from overfitting and struggle togeneralizeeffectively. The recently proposed HRRPLLM, which leverages the in-context learning (ICL) capabilities of largelanguagemodels (LLMs) for one-shot HRRP ATR, is limited in few-shot scenarios. This limitation arises because it primarilyutilizesthe distribution of SCs for recognition while neglecting the variance of the samples caused by aspect sensitivity. Thispaperproposes a straightforward yet effective Aspect-Distributed Prototype (ADP) strategy for LLM-based ATRunder few-shotconditions to enhance aspect robustness. Experiments conducted on both simulated and measured aircraft electromagneticdatasets demonstrate that the proposed method significantly outperforms current benchmarks.

Majorana bound states (MBSs), with their non-Abelian statistics and topological protection, are key candidates for fault-tolerant quantum computation. However, their unambiguous identification in solid-state systems remains a fundamental challenge. Here, we present a theoretical study demonstrating that drag transport in a capacitively coupled double quantum dot system offers a robust and nonlocal probe of weakly coupled MBSs. Using the master equation approach, we investigate both steady-state and transient dynamics and uncover a distinctive signature of MBSs, namely the emergence of pronounced split peaks in the drag transconductance, directly linked to inter-MBS coupling. We further show that the dynamics of quantum coherence is correlated with the emergence and enhancement of MBS-induced split peaks in the drag transconductance. A comparative analysis with trivial subgap states reveals key differences, that is, MBS-induced transconductance peaks are symmetric and exhibit characteristic splitting, while trivial-state features are generally asymmetric and lack such robust splitting behavior. These findings establish experimentally accessible criteria for distinguishing MBSs from trivial subgap states and provide a practical framework for probing Majorana physics through nonlocal transport.

Motivated by recent breakthrough studies of wave hyperbolicity in extremely anisotropic natural materials and artificial composites, we investigate the radiation pattern of a localized emitter in a hyperbolic medium. Since the emission of a point source is associated with the Fourier transform of the iso-frequency contours of a medium, we derive and analyze the properties of the Fourier transform of hyperbolic dispersion, which sheds light into the emission properties in the presence of hyperbolic bands. Our analysis leads to a generalized form of Huygens' principle for hyperbolic waves, connecting to the emergence of negative refraction and focusing with hyperbolic media. We also highlight the occurrence of aliasing artifacts in polariton imaging. More broadly, our findings provide analytical tools to model polariton propagation in materials with extreme anisotropy, and may be applied to several other physical platforms featuring hyperbolic responses, from astrophysics to seismology.

We study the emergence of the nonlocal Josephson effect in a system composed of three laterally coupled minimal Kitaev chains and exploit it to realize the nonlocal Josephson diode effect. We find that an imbalance between crossed Andreev reflections and electron cotunneling in the middle Kitaev chain gives rise to an asymmetric $2π$-periodic phase-dependent Andreev spectrum, controlled by the superconducting phases across the left and right junctions. We then show that the asymmetric Andreev spectrum, formed by hybridized Andreev bound states at the left and right junctions, enables a supercurrent across one junction via the phase difference at the other junction, thereby signaling the nonlocal Josephson effect. Notably, these nonlocal Josephson supercurrents exhibit distinct positive and negative critical currents, demonstrating the realization of the nonlocal Josephson diode effect with highly tunable polarity and efficiencies exceeding $50\%$. The nonlocal Josephson diode effect requires breaking local time-reversal and local charge-conjugation symmetries, with the latter being unique to minimal Kitaev chains. Our results establish minimal Kitaev chains as a highly controllable platform for engineering nonlocal Josephson phenomena.

Dynamic obstacle avoidance (DOA) for unmanned aerial vehicles (UAVs) requires fast reaction under limited onboard resources. We introduce the distributionally robust acceleration control barrier function (DR-ACBF) as an efficient collision avoidance method maintaining safety regions. The method constructs a second-order control barrier function as linear half-space constraints on commanded acceleration. Latency, actuator limits, and obstacle accelerations are handled through an effective clearance that considers dynamics and delay. Uncertainty is mitigated using Cantelli tightening with per-obstacle risk. A DR-conditional value at risk (DR-CVaR)based early trigger expands margins near violations to improve DOA. Real-time execution is ensured via constant-time Gauss-Southwell projections. Simulation studies achieve similar avoidance performance at substantially lower computational effort than state-of-the-art baseline approaches. Experiments with Crazyflie drones demonstrate the feasibility of our approach.

We introduce a novel structure-preserving vertex-staggered semi-implicit four-split discretization of a unified first order hyperbolic formulation of continuum mechanics that is able to describe at the same time fluid and solid materials within the same mathematical model. The governing PDE system goes back to pioneering work of Godunov, Romenski, Peshkov and collaborators. Previous structure-preserving discretizations of this system allowed to respect the curl-free properties of the distortion field and the specific thermal impulse in the absence of source terms and were consistent with the low Mach number limit with respect to the adiabatic sound speed. However, the evolution of the thermal impulse and the distortion field were still discretized explicitly, thus requiring a rather severe CFL stability restriction on the time step based on the shear sound speed and the finite, but potentially large, speed of heat waves. Instead, the new four-split semi-implicit scheme presented in this paper has a material time step restriction only. For this purpose, the governing PDE system is split into four subsystems: i) a convective subsystem, which is the only one that is treated explicitly; ii) a heat subsystem, iii) a subsystem containing momentum, distortion field and specific thermal impulse; iv) a pressure subsystem. The three subsystems ii)-iv) are all discretized implicitly, hence a rather mild CFL restriction based on the velocity of the continuum is imposed. The method is asymptotically consistent with the low Mach number limit and the stiff relaxation limits. Moreover, it maintains an exactly curl-free distortion field and thermal impulse in the case of linear source terms or in their absence. The scheme is benchmarked against classical test cases verifying its theoretical properties.

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing formulations based on isotropic kernels often suffer from spurious oscillations in regions with sharp gradients or strong flow anisotropy. This work introduces an anisotropic, gradient-informed, and adaptively sampled extension of the constrained RBF framework for regression of scattered data. Gradient information is estimated via local polynomial regression at collocation points, smoothed, and used to (1) re-sample data, maximizing sampling density near steep gradients while downsampling in smooth regions, and (2) construct a local anisotropic metric that shapes each basis function according to the flow directionality. In addition, a gradient-informed regularization is introduced by embedding observed gradients into the least-squares system as weighted soft constraints. The resulting formulation is fully meshless, linear, and computationally efficient, while significantly improving reconstruction quality in challenging regions. The method is evaluated on both synthetic and experimental datasets, including direct numerical simulation (DNS) data of a turbulent channel and time-resolved particle tracking velocimetry of a turbulent jet. Results show that the proposed approach outperforms isotropic and gradient-free RBF formulations in accuracy, smoothness, and physical consistency -- particularly near shear layers and boundaries -- while reducing the number of bases by an order of magnitude. To support the application, we have created a repository (https://github.com/mendezVKI/SPICY_VKI) that provides access to the investigated datasets.

The problem of subgraph counting asks for the number of occurrences of a pattern graph $H$ as a subgraph of a host graph $G$ and is known to be computationally challenging: it is $\#W[1]$-hard even when $H$ is restricted to simple structures such as cliques or paths. Curticapean and Marx (FOCS'14) show that if the graph $H$ has vertex cover number $τ$, subgraph counting has time complexity $O(|H|^{2^{O(τ)}} |G|^{τ+ O(1)})$. This raises the question of whether this upper bound can be improved for input graphs $G$ from a restricted family of graphs. Earlier work by Eppstein~(IPL'94) shows that this is indeed possible, by proving that when $G$ is a $d$-degenerate graph and $H$ is a biclique of arbitrary size, subgraph counting has time complexity $O(d 3^{d/3} |G|)$. We show that if the input is restricted to $d$-degenerate graphs, the upper bound of Curticapean and Marx can be improved for a family of graphs $H$ that includes all bicliques and satisfies a property we call $(c,d)$-locatable. Importantly, our algorithm's running time only has a polynomial dependence on the size of~$H$. A key feature of $(c,d)$-locatable graphs $H$ is that they admit a vertex cover of size at most $cd$. We further characterize $(1,d)$-locatable graphs, for which our algorithms achieve a linear running time dependence on $|G|$, and we establish a lower bound showing that counting graphs which are barely not $(1,d)$-locatable is already $\#\text{W}[1]$-hard. We note that the restriction to $d$-degenerate graphs has been a fruitful line of research leading to two very general results (FOCS'21, SODA'25) and this creates the impression that we largely understand the complexity of counting substructures in degenerate graphs. However, all aforementioned results have an exponential dependency on the size of the pattern graph $H$.