Web-measurement studies treat commercial VPNs as interchangeable vantage points within a country, assuming that any VPN in a particular country is as good as any other. We show that this assumption does not hold: the same country measured through different VPN providers yields materially different conclusions about where endpoints sit, who hosts them, and which physical replicas serve them. Using large-scale browser-based measurements across fourteen countries and four major VPN providers, complemented by targeted DNS and replica-selection probes, we examine sources of this variability across three layers of the VPN-to-endpoint path: vantage identity, name resolution, and replica selection. We find that the variability is driven primarily by layers below the client: commercial VPN providers operate their own in-country DNS infrastructure, often intercepting queries regardless of client configuration; CDNs steer on the exit network, sending identical queries to different replicas; and peering paths route identical DNS answers to different physical facilities. We distill these findings into a set of reporting practices for VPN-based Web measurement.

An impulse response/equilibrium model (IREM) structure combines a linear convolution model with a nonlinear function that sets the current operating point via an equilibrium variable with integrator dynamics. This model structure is well suited for mildly nonlinear systems and in particular has been applied to battery fast charging control. This paper provides observability conditions for the IREM model structure and bounds on the prediction error. These conditions can be evaluated directly on the system impulse response.

We investigate the interplay between quantum correlations and multiparameter quantum estimation in top--antitop quark pair production through the gluon-fusion channel. Using the spin density matrix formalism, we construct an effective two-qubit quantum state governed by the relativistic parameters associated with the scattering process. Within the framework of quantum metrology, we derive the quantum Fisher information matrix for the simultaneous estimation of the relativistic velocity parameter and the production angle, and we analyze the corresponding quantum precision bounds. Our results reveal highly nontrivial estimation regimes strongly controlled by relativistic spin correlations and scattering geometry. We further characterize the produced state through the concurrence and demonstrate the existence of strong connections between entanglement structures and multiparameter estimation sensitivity. Finally, we discuss the experimental feasibility of probing these effects at the Large Hadron Collider through spin-correlation observables and reconstructed top--antitop density matrices. Our results identify top--antitop production as a unique relativistic platform for exploring quantum information theory and multiparameter quantum metrology in high-energy physics.

Bayesian multidimensional scaling (BMDS) embeds $n$ objects in a low-dimensional space to approximately preserve an observed dissimilarity matrix. Compared to classic MDS, BMDS is more robust to model misspecification and supports posterior uncertainty quantification and joint estimation within hierarchical models. However, standard BMDS inference is computationally prohibitive, requiring $O(n^2)$ operations per MCMC iteration to evaluate the likelihood. We propose Barnes--Hut BMDS (BH-BMDS), which uses a tree-based approximation to the likelihood and a Gibbs sampler that leverages this structure, remaining compatible with hierarchical extensions. BH-BMDS reduces computational complexity to $O(n \log n)$ while preserving the geometric fidelity of the embedding. We further establish consistency for the stationary measure of BH-BMDS, proving that it concentrates around the true latent configuration even as the total error of the surrogate likelihood diverges. Notably, this consistency holds in the infinite-dimensional limit. We evaluate the approximation on datasets with diverse structure, including air traffic networks, arXiv abstracts, MNIST images and neural activity recordings from mouse models of tau pathology. Across all settings, BH-BMDS closely matches BMDS while achieving substantial computational gains, with approximately 10-fold speedups at $n=1{,}000$ and 70-fold speedups at $n=10{,}000$. These gains increase with $n$, demonstrating strong empirical scalability.

Emergent constraints in climate science are empirical relations that link the response to a forcing of a physical observable to the properties of other observables, with the aim of reducing climate change projection uncertainties. Here we use recent results in linear response theory to develop a mathematical framework for dynamic emergent constraints, a class of emergent constraints linking the response of different observables to the same forcing. We show how traditional dynamic emergent constraints are a special case of more general relations, that we call integral dynamic emergent constraints. These relations allow to compute the response of a predictand as the convolution of the response of a predictor and the proxy Green's function of the predictand-predictor pair. The conditions for the existence of integral emergent constraints are related to the causality of the proxy Green's function and the time scales at which the system is observed. We apply this framework to global warming simulations with the MPI-ESM climate model, to study dynamic emergent constraints between different observables. These results allow to put the theory of dynamic emergent constraints on firm mathematical ground, and suggest a protocol to identify necessary conditions for the existence of such relations in climate data.

This paper proposes ideometrics as the foundation for a generalised and potentially testable theory of human progress and civilisational progress, thus linking ideometrics to studies in economics and history. Building on prior work that conceptualises the human brain as a sensor of ideas, human progress is understood not primarily through outcomes such as wealth, health, or technological advancement, but through the dynamic process of the "idea life cycle" that shapes future states. The paper advances a formal definition of human progress as a measurable improvement in the ability of individuals and societies to generate, evaluate, prioritise, and implement ideas in a way that increasingly aligns prioritised ideas with those that truly lead to preferred future states, given available information and uncertainty, and under scarcity of human capacity, energy, time and resources. It introduces the Ideometric Index of Human Progress (IIHP) that captures the quality of idea generation (G), accuracy of their evaluation (E), efficiency of their prioritisation (P), and effectiveness of their implementation (Ie). It shows that the future progress will be realised if there is good alignment between the perceived future value of ideas and their true, realised future value, assessed as outcome monitoring (O). This formulation shifts the analytical focus from static outcomes to the quality of evaluating ideas, thereby offering a novel lens for understanding progress and regress. The concept can also be extended to long periods of history through the Ideometric Index of Civilisational Progress (IICP), where additional parameters of successful documentation of outcomes (D) and successful intergenerational transmission of gathered knowledge (T) are added. By transforming ideas into measurable units of analysis, ideometrics offers a potentially transformative approach to understanding human progress.

The stochastic dynamics of dislocations on a one-dimensional periodic lattice domain are considered. Two models are studied: one without a collision rule, and one which annihilates colliding dislocations if they have opposite orientation. The behaviour of both models is investigated by means of a series of numerical simulations exploring the asymptotic behaviour of these models as the number of dislocations increases. From these simulations, evidence is obtained that the discrete model with annihilation tends to a PDE for the dislocation density that accounts for annihilation. However, the discrete model without a collision rule does not appear to exhibit consistent convergence behaviour; instead, it appears that the expected PDE with conserved dislocation density appears in the limit for some parameters, but that for other parameters the density appears to follow to the evolution of the PDE with annihilation. These findings provide evidence that a careful treatment of dislocation collisions is important in discrete dislocation dynamics models.

In this paper, we study a structural acoustic model consisting of a semilinear wave equation defined on a three-dimensional bounded domain, coupled with a Kirchhoff-Love plate equation acting on a flat portion of the boundary. Primarily for mathematical interest, we impose nonlinear damping terms and logarithmic-type supercritical source terms on the system. We investigate local and global well-posedness, energy decay rates of potential well solutions, and blow-up of solutions under different conditions on the parameters and initial data. The main novelties include the analysis of the interaction between nonlinear damping and logarithmic energy-amplifying source terms, as well as the development of techniques for handling logarithmic source terms within potential well theory. The logarithmic nonlinearities are not homogeneous under scaling, which creates difficulties in studying potential well solutions. The wave-plate coupling through the acoustic pressure also causes technical difficulties in the analysis, especially in the proof of blow-up of weak solutions.

For $(M,g)$ a compact Riemannian surface with Laplace-Beltrami operator $Δ$, and for $λ,δ\geq 0$, let $P_{λ,δ}$ be the spectral projector on the frequency interval $[λ-δ,λ+δ]$ associated to $\sqrt{-Δ}$. For the Euclidean disk, away from its boundary, we improve the upper bound on the $L^2\to L^4$ norm of $P_{λ,δ}$ in the regime where the bandwidth $δ$ is polynomially small compared to the target frequency $λ$. Decomposing on the explicit joint eigenbasis of $\left(\sqrt{-Δ}, \frac{1}{i}\frac{\partial}{\partial θ}\right)$ given in terms of Bessel eigenfunctions, which are well-approximated by oscillatory functions outside of their caustic set, we reduce the analysis to a number of precise quantitative estimates of nonstationary phase oscillatory integrals. We strongly use convexity phenomenon both for these estimates, and then for the summation of the contribution of all eigenfunctions through a new arithmetic estimate. The method extends to other $S^1$-symmetric surfaces satisfying similar conditions on the induced completely integrable structure.

In this work, we extend Goebel-Kirk fixed point theorems to the setting of mappings of asymptotically Hölder-nonexpansive type. By providing several non-trivial examples, we show that this new framework strictly contains its classical counterparts. Furthermore, we prove that if a Banach space contains an isomorphic copy of either $c_0$ or $\ell_1$, then the fixed point property (FPP) for this class of mappings fails. Finally, we show that every infinite-dimensional Banach space contains a compact convex set $K$ admitting a fixed-point free, affine self-mapping $T$ which is of asymptotically Hölder-nonexpansive type and possesses no continuous iterates.

We present an experimental implementation of the multiplayer Quantum Volunteer's Dilemma on noisy intermediate-scale quantum (NISQ) hardware, executed on the ibm_kingston backend via Qiskit Runtime. The game is evaluated for N = 2 to 9 players under four transpiler optimization levels, with 20 independent repetitions per configuration and 2048 shots per circuit, including post-processing readout error correction via mthree. Target-state fidelity decays with system size but remains above 70% (corrected) through N = 9. With readout correction, the global average payoff reproduces the quantum theoretical benchmark exactly for N <= 6 and exceeds the classical Nash equilibrium across the full tested range. Optimization level 2 is selected as the reference configuration after gate count analysis reveals that levels 2 and 3 produce identical transpiled circuits, with level 2 achieving superior fidelity stability. A Hamming distance analysis of raw measurement counts shows that single-qubit errors dominate at small N, with multi-qubit contributions growing beyond N = 6. A calibration-based digital twin captures global payoff trends but exhibits a linear fidelity decay profile that diverges from the hardware behavior at large N, exposing the limits of first-order independent per-qubit noise models. These results demonstrate that aggregate quantum advantage in multiplayer games is robust to NISQ noise conditions across the full tested range, while the practical observability of state-level advantage is constrained to N <= 8 under post-processed readout correction.

Subsampling-based Markov chain Monte Carlo (MCMC) algorithms aim to accelerate Bayesian inference by evaluating the likelihood using only a subset of the data at each iteration. However, in many standard tall-data applications, individual likelihood contributions are inexpensive to evaluate and the resulting reductions in actual computing time are often substantially smaller than the nominal reduction in data size due to computational overhead. We study a different computational regime arising in frequency-domain inference for continuous-time processes observed at equally spaced discrete time points. This gives rise to aliasing, whereby each contribution to the Whittle likelihood requires summation over shifted frequency components, unlike standard discrete-time spectral settings where spectral evaluations do not require such summation. We demonstrate that this structure makes subsampling MCMC, a subsampling-based MCMC approach that estimates the log-likelihood using data subsampling and efficient control variates, particularly effective for reducing computational cost. We illustrate the approach for Bayesian frequency-domain inference in discretely observed continuous-time autoregressive moving average models driven by finite second-moment Lévy processes.

When redeeming open-end funds sell and natural buyers do not step in at once, some limited-capital investor must take the other side and carry the inventory until prices recover. This paper asks what return that investor requires. A continuous-time market-clearing model delivers an expected-return restriction in which the price of residual supply depends on inventory risk, trading costs, funding frictions, and the scarcity of balance sheet available to absorb it. Mapping U.S. mutual fund flows through predetermined holdings over 2003--2024, we measure one observable component of this residual supply. Forced-sale pressure predicts actual fund selling, contemporaneous price declines, and positive returns over the following one to six months. The premium roughly doubles when market-wide absorption capacity is tight, and it concentrates in stocks with thin investor bases and limited trading capacity -- precisely the cross section in which clearing the imbalance should be most costly, and a pattern that mechanical return reversal does not generate.

Large language models are increasingly deployed as intelligent tutors, yet research on aligning them for special education remains absent. Recent work has applied reinforcement learning to LLM tutors, but these methods target a generic learner in a single domain (mathematics) and do not address the cognitive and communicative diversity of learners with disabilities. We introduce \emph{Special-R1}, a framework that extends pedagogical RL to special education through two components: (1) a two-dimensional adaptive system prompt that couples a difficulty-based support level with a disability-specific teaching style across five disability profiles; and (2) a persona-aware Thinking Reward whose judge rubric is conditioned on the learner's disability profile. On a persona-augmented test set of 690 multi-turn dialogues, our full model raises persona-aware Fit from 6.75 (generic baseline) to 8.40 (+1.65) and SPED-rubric Helpfulness from 0.720 to 0.768, leading on the four-component Total (2.911, +0.064 over the runner-up) while remaining within 0.01 of the strongest variant on the out-of-domain OpenLearnLM benchmark (8.53). Ablations show that the Thinking Reward becomes effective only in combination with adaptive prompting, and that residual weakness on specific learning disability in mathematics motivates targeted multimodal extensions.

The present investigation focuses on the improvement of the accuracy of the description of physical observables of interest in moderately sized fermionic basis within the framework of covariant density functional theory. It extends previous study of Ref. [1] to point coupling (PC) covariant energy density functionals (CEDFs) and to excited states. Using as a benchmark the solutions corresponding either to infinite fermionic basis or those extrapolated to such a basis it is shown that the optimization of oscillator frequency $\hbarω_0$ of the harmonic oscillator (HO) basis leads to a substantial improvement in the description of different physical observables in the fermionic basis truncated at $N_F$. Globally optimized scaling factors $f_{opt}(A)$ of the oscillator frequency and the sizes $N_F^{\varepsilon}$ of the HO bases providing the required accuracy $\varepsilon$ in the calculations of the binding energies are generated for the PC functionals. The optimization of the basis also significantly improves the accuracy of the description of potential energy curves, defining the fission barriers and fission isomers in actinides and superheavy nuclei, provided that the size of the basis is at least equal to $N_F=20$. The optimization of the HO basis improves the accuracy of the description of the energies of bound single-particle states: the only exceptions are weakly bound neutron states with low orbital momenta $l=0$, 1 and 2. It is demonstrated for the first time that the halo densities of neutron halo nuclei generated in the coordinate space calculations are well reproduced in the calculations with very large fermionic HO bases.

Aligning large language models (LLMs) as math tutors typically demands costly reinforcement-learning (RL) training and external LLM judges. We ask whether a frozen model's internal reasoning signals can replace both. We propose the Tutoring Effectiveness Index (TEI), a training-free, judge-free four-signal index that combines a Schoenfeld-Verify keyword ratio, a math-step density, an ends-question rate, and a deep-reasoning gate from the Deep-Thinking Ratio (DTR) probe. Selecting from $N$ candidates with TEI (the TEI@$N$ rule) raises the improvement rate on pre-incorrect scenarios from $59.0\%$ to $81.9\%$ at $N{=}8$ on a frozen DeepSeek-R1-8B base, with no training and no external judge. We also measure the alignment tax of pedagogical GRPO. Thinking length drops from $1{,}764$ to $119$ words per turn ($-93\%$), Content-Knowledge and Pedagogical-Knowledge accuracy fall by $-71\%$ and $-80\%$ relative, and the student's $Δ$ Solve Rate crosses from $+0.180$ to $-0.012$. To anchor the behavioural reading, we reproduce an 82-code educational codebook on $119{,}009$ tutor sentences with a one-shot structural classifier. Together, these results offer a cost-effective recipe for building math-tutoring LLMs without RL training or external judges.

In this paper, we perform parameter estimation with an analytical model to simulate the gravitational wave emission during the core bounce phase of a rapidly rotating core collapse supernova progenitor. This approach enables us to estimate the parameter $β$, defined as the ratio of rotational kinetic energy to gravitational potential energy in core collapse supernovae. To verify the reliability of both the analytical model and the inferred value of $β$, we use a numerical template bank constructed from Abylkairovś gravitational waveform catalog and simulate O4 noise, characterized by the interferometers power spectral density. An average fitting factor of 94\% over the interval 0.02 $< β<$ 0.14 shows that our analytical model reproduces the key characteristics of the core-bounce waveform with high accuracy, leading to only a 6\% reduction in the optimal signal to noise ratio. This provides a quantitative measure of how well the analytical model performs. Subsequently, we analyze the error in estimating $β$ using a Matched Filter method and compare it to the corresponding Cramér Rao Lower Bound. The results obtained by considering noise and waveforms at distances of 5, 10, and 50 kpc enable an assessment of how accurately the selected statistical model fits the observed data. From the asymptotic expansion of the variance, we derive a theoretical lower bound for the error that falls below $10^{-1}$ when the parameter $β$ decreases with distance.

We study the repulsive Hubbard model at half filling in the strong-coupling regime, with a staggered magnetic field of strength \(h\). The analysis is carried out in the canonical half-filled ensemble, with temperature measured on the Heisenberg scale \(J_0(U)=4t^2/U\). Uniformly for \(|h|\le h_0\) and \(βJ_0(U)\ge \ell_0\), we prove finite-volume Hubbard--Heisenberg pressure estimates with errors uniform in the system size. These estimates pass to thermodynamic limits whenever the limiting pressures exist. The proof uses a strong-coupling unitary transformation which separates the singly occupied spin sector from sectors containing empty or doubly occupied sites. On the singly occupied sector, the effective Hamiltonian is compared with the Heisenberg reference Hamiltonian; the remaining sectors are controlled through a decomposition of the transformed partition function according to the set of empty or doubly occupied sites. For fixed positive staggered-field windows \(I\Subset(0,h_0]\), the magnetisation comparison is then derived from the pressure comparison by convexity of finite-volume pressures. We also prove charge-sector suppression estimates, uniformly for \(|h|\le h_0\): in the large positive-\(U\) Heisenberg-scale regime, the density of empty or doubly occupied sites and the double-occupancy density are small, and the squared staggered charge divided by \(|Λ|^2\) is small. Thus the results give a quantitative Gibbs-state formulation of the strong-coupling picture in which the half-filled repulsive Hubbard model is described, at the Heisenberg scale, by effective antiferromagnetic spin degrees of freedom, while charge fluctuations are suppressed.

Young equation provides a remarkably successful macroscopic description of wetting, yet its molecular origin (particularly for water) has remained elusive for over two centuries. Here we make the molecular basis of aqueous wetting explicit by reformulating it in terms of a molecular wetting coefficient, omega m, which quantifies how an interface compensates the intrinsic energetic cost of hydrogen-bond defects relative to bulk water. Across a broad and continuous spectrum of hydrophilicities, spanning chemically diverse experimental and model surfaces, macroscopic contact angles collapse onto a single universal master curve when expressed through omega m. This molecular reformulation closes Young and Young-Dupre relations on energetic grounds, establishing a unified and predictive physical link between wetting, adhesion, cavitation, and nanoconfined filling. By anchoring interfacial behavior to waters intrinsic hydrogen-bond energetic scales, our results reveal wetting as an emergent property of water itself, rather than a surface-specific attribute and provide a transferable molecular framework that recalibrates energetic intuition and guides the rational design of aqueous interfaces. (This document is the unedited Author version of a Submitted Manuscript subsequently accepted for publication in J. Am. Chem. Soc. For the published version, which includes a more complete molecular-thermodynamics grounding of the method see the published version)

Materials used in polymer-based additive manufacturing processes, such as Digital Light Processing (DLP) and direct ink writing (DIW), typically exhibit non-Newtonian rheology. Carreau--Yasuda and power-law models describe basic shear-thinning and shear-thickening behavior well, but applying them to a new material requires choosing a functional form, deriving it, and re-implementing it inside the flow solver. We present a deployment workflow in which a neural network trained on experimental rheometry data serves as the viscosity closure inside a Cahn--Hilliard--Navier--Stokes (CHNS) finite element solver. Lipschitz regularization during training produces smooth viscosity predictions, and the trained network is exported in the Open Neural Network Exchange (ONNX) format and queried by the solver at runtime via the ONNX runtime, without solver modification or network reimplementation. The framework is built on a parallel octree-based adaptive mesh refinement infrastructure that concentrates resolution at the fluid interface. We validate the CHNS solver against benchmark shear-thinning bubble-rise cases from the literature, reproducing reported bubble shapes across varying power-law indices and Weber numbers. We characterized two silicone ink formulations, recorded their rise dynamics in perfluorodecalin on high-speed video, and used the resulting data to test the full workflow. Simulated rise velocities fall within the experimentally measured spread, and the simulated steady-state droplet shape agrees with the observed one. This work contributes to a growing body of literature on integrating neural constitutive closures into multiphysics simulations, and demonstrates a practical path for deploying experimentally trained rheological surrogates inside finite element solvers.

Motivated by a high-dimensional regression problem in spatial multimodal omics (SMO), we propose a Bayesian framework for local spatial feature selection, where a random domain partition prior is introduced to divide the spatial domain into several contiguous clusters with flexible shapes and an unknown number of clusters, conditional on which a local feature selection prior is imposed within each cluster. The notion of "feature" is general and may include both covariates and functional bases, allowing the framework to perform both local variable selection and local basis selection, the latter being essential for adaptively approximating spatially varying functions with localized characteristics. We derive coupled hyperparameter conditions linking domain partition and local feature selection priors, under which the consistency theory and posterior contraction rates of both the domain partition and feature selection are established. We develop an efficient informed reversible jump Markov chain Monte Carlo algorithm to address the computational challenges encountered in joint posterior sampling of domain partitions and selected features. Simulation studies demonstrate the effectiveness of the proposed model and algorithm, highlighting its advantages over existing methods. The application of our model to an SMO dataset reveals biologically meaningful spatial patterns within breast cancer tissue.

We study the well-posedness for the intermediate nonlinear Schrödinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-posedness in $H^{s}(\mathbb{T})$ for any $s\geq \frac 12$. We extend this result to global well-posedness under a small $L^2$-norm constraint by exploiting the complete integrability of the continuum Calogero-Moser equation (CCM). We also establish additional results such as the unconditional well-posedness in the energy space and the convergence of solutions to INLS to those of CCM in the infinite-depth limit.

A distance-k dominating set of a graph is a set of vertices such that every vertex lies within distance k of some vertex in the set; its minimum size is the distance-k domination number gamma_k. We study gamma_k for triangular matchstick graphs T_d. Harris et al. (2020) claimed two upper bounds for the cases k=1 and k=2. These bounds are shown to be incorrect and are replaced by a corrected general upper bound for gamma_k(T_d) obtained by refining their tiling method. For k=1 and d=7q+beta, where 0 <= beta <= 6, we further sharpen this construction and prove gamma(T_{7q+beta}) <= 3.5q^2+(beta+4.5)q+(beta-1). Finally, we determine the radius of T_d as r_d = ceil(2d/3), which implies gamma_k(T_d)=1 whenever k >= r_d.

Artificial intelligence is now embedded as a primary decision engine in continuously operated financial AI pipelines spanning training and updating, deployment and inference, and operation with monitoring and feedback. The automation and scale that make these pipelines effective also create novel attack surfaces, where small algorithmic perturbations can amplify into persistent, system-level financial harm. Existing surveys, however, either treat AI as a defensive tool or analyse adversarial machine learning in a domain-agnostic manner, abstracting away finance-specific constraints such as accounting plausibility, non-IID federated data, continuous retraining, and automation-amplified downstream effects. We address this gap with a unified, lifecycle-centric and mechanism-driven framework. We partition financial AI into three lifecycle stages: training and updating, deployment and inference, and operation, monitoring, and feedback. We further propose the Financial AI Security and Robustness Taxonomy, organising seventeen attack subtypes across data and model poisoning, adversarial attacks on decision boundaries, prompt injection in LLM-mediated workflows, and deepfake-driven subversion of KYC verification layers. For each subtype, we analyse algorithmic strategy, feasibility constraints, stealth and persistence, and downstream financial consequences. Finally, we identify open challenges and outline a research agenda toward lifecycle-aware stress testing and finance-relevant robustness benchmarks.

Wave-like dark matter ($ψ$DM) is an elusive dark matter (DM) candidate. The model, often also called fuzzy or ultralight DM, proposes that DM is an extremely light ($m\sim10^{-22}$ eV) boson and thereby has a kpc-scale de Broglie wavelength. Hence, interference of DM gives rise to sub-galactic density fluctuations that can be studied with strong gravitational lensing. In this paper, we use the residual power spectrum, $\mathrm{P}_δ(k)$, as a probe of $ψ$DM, which quantifies deviations from smooth lensing predictions, measured from multiply-imaged galaxies in strong cluster lenses. The key idea is that imprinted in these deviations are lensing distortions from DM substructure, which can be harnessed statistically to distinguish among DM theories. We simulate JWST-quality mock observations of strong gravitational lensing in galaxy clusters, modeling line-of-sight DM substructure within $ψ$DM and the standard cold dark matter (CDM) paradigms. Using mock deep observations ($\sim$ 20 hours), we find that $\mathrm{P}_δ(k)$ is sensitive to both $ψ$DM particle mass and fluctuation amplitude, and can distinguish $ψ$DM fluctuations from CDM subhalos. We demonstrate that $\mathrm{P}_δ(k)$ can be measured directly from data by modeling the smooth lensing with a local Curved Arc Basis formalism. With realistic modeling systematics, we find a statistically significant separation between $ψ$DM and CDM across $1 \lesssim k \lesssim 11\,\mathrm{kpc}^{-1}$ -- offering an independent probe of the wave-like nature of DM complementary to existing constraints.

In this paper, we review the theory of the Fourier-Bessel transform. Many of the standard results for the Fourier-Bessel transform have become folklore results or predate modern functional analysis and rely on hard analysis proofs that miss the elegance of more modern machinery. This review aims to centralize some of the basic theory while providing some new proofs and approaches that can be applied to other integral transforms beyond the Fourier and Fourier-Bessel transform.

We present a method to determine admissible configurations that lead to relative equilibria in the full gravitational N-body problem. The method exploits the SO(3) symmetry by working with its fundamental invariants and does not rely on restrictive assumptions about mass distributions or on truncating the gravitational potential. As a result, it yields necessary conditions that apply to arbitrary rigid-body configurations. This work is presented in two parts. In the first (this) part, we assume every body is axisymmetric to give a clear, pedagogical exposition of the approach; in a forthcoming paper, we remove that restriction and treat general triaxial bodies (the method remains valid, but the number of variables increases). As an illustration, we systematically recover all known relative-equilibrium families for the two-body problem consisting of one sphere and one axisymmetric body, confirm earlier results in the literature, and derive new necessary conditions for certain configurations, including additional constraints for the arrow and non-Lagrangian types. In the special case of a sphere and an axisymmetric body, we also obtain sufficient conditions for relative equilibria under a monotonicity assumption on the potential.

Hit ratio is a common service metric for electronic corporate bond market making, but raw hit-ratio targets can be economically misleading when client flow has heterogeneous adverse-selection content. This paper extends a stochastic-control framework for OTC bond RFQ market making with hit-ratio constraints by replacing raw hit ratio with a residual-quality-adjusted hit ratio. The key modelling distinction is that adverse post-trade markouts are first decomposed into observable credit factors, carry/rolldown, issuer-relative-value effects, index or ETF demand effects, and residual adverse selection. Only the residual component is treated as client-flow toxicity. The resulting control problem remains tractable: after dualizing the quality-hit-ratio penalty, the HJB retains separable Hamiltonians, and the dual variable is the solution of an exact one-dimensional nonlinear fixed point for each targeted tier. Under a quadratic value-function approximation, optimal quotes decompose into a riskless spread, inventory skew, credit-alpha skew, residual-toxicity charge, and quality-hit-ratio subsidy. Synthetic multi-bond simulations with nonlinear dual solves illustrate that raw hit-ratio targeting can subsidize residual-toxic flow, while residual-quality targeting reallocates service toward low-residual-toxicity flow and improves the attained service/economics frontier. A final reduced-form extension studies inventory-recycling value through risk-aware style-aligned client-flow warehousing. Sweep or portfolio-trade opportunities fill randomly, and participation is sized using the same quadratic value approximation as the RFQ quoting problem. A passive/index-demand experiment is reported in the appendix as a special case of forecastable client flow. The numerical evidence is synthetic and mechanism-oriented; no proprietary RFQ data are used.

We study high-dimensional inference problems with tensor-structured data and establish conditions under which their free energy can be approximated by that of a Gaussian comparison model. Our framework applies to models with independent observations and mismatch between the data-generating distribution and the statistical model. The results extend prior work beyond matrix settings and accommodate scaling regimes where the model parameters depend on the dimension. A key technical contribution is the use of generic chaining to control remainder terms arising from likelihood expansions over tensor-structured parameter spaces. As an application, we establish free energy universality for binary hypergraph models under the minimal assumption of diverging average degree, showing that their asymptotic behavior coincides with that of a Gaussian tensor model, even under model mismatch.

In this paper we study dicritical foliations having a family of cusps as invariant curves. We give conditions to assure that all the curves of the family have the same semimodule of differential values. We also give an expression to compute the conductor of a cuspidal semimodule.