We present an iterative method for generating the complete set of self-energy Feynman diagrams at arbitrary order for the single-polaron problem with arbitrary linear coupling to the lattice. The approach combines a combinatorial representation of noncrossing diagrams, based on Dyck paths associated with Stieltjes-Rogers polynomials, with the constraints of the Ward-Takahashi identity to systematically incorporate vertex corrections. This construction yields a one-to-one correspondence between terms in the expansion based on Stieltjes-Rogers polynomials and diagrammatic contributions, and provides, through a sequence of simple steps, a closed, algorithmic framework for generating all diagrams of a given order, together with their relative weights. The method enables efficient, unbiased evaluation of diagrammatic series and improves the convergence of diagrammatic Monte Carlo by eliminating the need for stochastic weighting between different topologies. We further outline how the construction can be generalized to finite-density electron systems.

We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in problems where the energy landscape is dominated by isolated solutions. We apply this new device to the symmetric binary perceptron model (SBP), and study how its manifold of connected solutions behaves. We choose this particular problem because, while its typical solutions are isolated, it can be solved using local algorithms for a certain range of constraint density $α$ and threshold $κ$. With this new ensemble, we unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold $κ^{\rm no-mem}_{\rm loc.\, stab.}$ (dependent on $α$). This transition appears as paths of solutions shatter, a phenomenon that more conventional statistical mechanics approaches fail to grasp. Finally, we compared our predictions to simulations. For this, we used a modified Monte-Carlo algorithm, designed specifically to target these delocalized solutions. We obtained, as predicted, that the algorithm finds solutions until $κ\approxκ^{\rm no-mem}_{\rm loc.\, stab.}$.

Recent advances in Structural Health Monitoring (SHM) have attracted industry interest, yet real-world applications, such as in ship structures remain scarce. Despite SHM's potential to optimise maintenance, its adoption in ships is limited due to the lack of clearly quantifiable benefits for hull maintenance. This study employs a Bayesian pre-posterior decision analysis to quantify the value of information (VoI) from SHM systems monitoring corrosion-induced thickness loss (CITL) in ship hulls, in a first-of-its-kind analysis for ship structures. We define decision-making consequence cost functions based on exceedance probabilities relative to a target CITL threshold, which can be set by the decision-maker. This introduces a practical aspect to our framework, that enables implicitly modelling the decision-maker's risk perception. We apply this framework to a large-scale, high-fidelity numerical model of a commercial vessel and examine the relative benefits of different CITL monitoring strategies, including strain-based SHM and traditional on-site inspections.

Let F be a non-archimedean local field of characteristic zero whose residue field has at least three elements. Let G be an almost simple linear algebraic group over F, with rank_F(G) >= 2. Let X be a simply connected symmetric space of infinite dimension and finite rank, with non-positive curvature operator. We prove that every continuous action by isometries of G on X has a fixed point. If the group G contains SL_3(F), the result holds without any assumption on the non-archimedean local field F. The result extends to cocompact lattices in G if the cardinality of the residue field of F is large enough, with a bound that depends on rank_F(G).

Scattering experiments using ultrashort X-ray free electron laser (XFEL) pulses have opened a new path for structure determination of a wide variety of specimens, including nano-crystals and entire viruses, approaching atomistic spatial and femtoseconds time resolution. However, random and unknown sample orientations as well as low signal to noise ratios have so far prevented a successful application to smaller specimens like single biomolecules. We here present resolution-annealed stochastic gradient ascent (RASTA), a new approach for direct atomistic electron density determination, which utilizes our recently developed rigorous Bayesian treatment of single-particle X-ray scattering. We demonstrate electron density determination at 2Å resolution of various small proteins from synthetic scattering images with as low as 15 photons per image.

We show that a vector field non-minimally coupled to gravity reproduces exactly the dynamics of an Einstein cluster -- a large ensemble of non-interacting particles moving on circular geodesics under their collective gravitational field. Since Einstein clusters are known to be able to account for flat galactic rotation curves, our results suggest that such rotation curves may arise as a manifestation of modified gravity.

The logarithmic corotational derivative is a key concept in rate-type constitutive relations in continuum mechanics. The derivative is defined in terms of the logarithmic spin tensor, which is a skew-symmetric tensor/matrix given by a relatively complex formula. Using a newly developed commutator based functional calculus, we derive a new representation formula for the logarithmic spin tensor. In addition to the result on the logarithmic corotational derivative we also use the newly developed functional calculus to answer some problems regarding the matrix logarithm and the monotonicity of stress-strain relations. These results document that the commutator based functional calculus is of general use in tensor/matrix analysis, and that the calculus allows one to seamlessly work with tensor/matrix valued functions and their derivatives.

We propose CRAVE (Cluster-based Retrieval Augmented Verification with Explanation); a novel framework that integrates retrieval-augmented Large Language Models (LLMs) with clustering techniques to address fact-checking challenges on social media. CRAVE automatically retrieves multimodal evidence from diverse, often contradictory, sources. Evidence is clustered into coherent narratives, and evaluated via an LLM-based judge to deliver fact-checking verdicts explained by evidence summaries. By synthesizing evidence from both text and image modalities and incorporating agent-based refinement, CRAVE ensures consistency and diversity in evidence representation. Comprehensive experiments demonstrate CRAVE's efficacy in retrieval precision, clustering quality, and judgment accuracy, showcasing its potential as a robust decision-support tool for fact-checkers.

We formulate the Dirac oscillator covariantly in the presence of external non-Abelian gauge fields. More precisely, the matter field is written as $Ψ_{αA}(x)$, where $α$ denotes the Dirac index and $A$ the isospin index, so that the Hamiltonian acts on the tensor-product space $\mathbb{C}^{4}\otimes\mathbb{C}^{2}$ in the fundamental representation. Starting from the gauge-covariant Dirac equation, we then implement the oscillator interaction through the standard non-minimal substitution and promote the construction to an $\mathrm{SU}(2)$ background. In this way, we derive the associated non-Abelian field-strength tensor and isolate the commutator contribution, which has no Abelian analogue. Consequently, the generalized Pauli interaction $σ^{μν}\mathcal{F}_{μν}$ produces matrix-valued spin--isospin couplings. At the same time, the Abelian sector reduces to the conventional Moshinsky--Szczepaniak Dirac oscillator, whose exactly solvable spectrum provides a natural benchmark for the extended theory.

Kondo screening of local moments in normal metals typically leads to hybridized conduction and valence bands separated by a Kondo gap, resulting in an insulating state at half-band filling. We show a dramatic change of this scenario in a Dirac-semimetal-based correlated system -- a bilayer honeycomb lattice heterostructure where a local moment lattice is stacked on a Dirac semimetal breaking the inversion symmetry. This system is modeled by an extended Anderson honeycomb lattice involving the real-space dependence of major interlayer hybridization parameters on the relative sliding distance along the armchair direction. First, we unveil multiple Kondo scales and successive Kondo breakdown transitions in this correlated heterostructure under sliding. Second, we demonstrate the existence of a genuine selective Kondo screening phase which is stabilized near the A-B stack pattern and is accessible by applying interlayer voltage. Third, we find a nearly flat hybridized band located concomitantly within the Kondo gap, resulting in an unprecedented metallic state at half-band filling. This unconventional heavy fermion state is characterized by violation of Luttinger theorem and appearance of a Van Hove singularity at the Fermi energy. The general sliding-driven band structure landscape and the implications of our results for the broad context of multiorbital Kondo physics are briefly discussed.

Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a high-dimensional point cloud together with a real-valued function defined on it, a mapper graph summarizes the induced topological structure: each node represents a local neighborhood, and edges connect nodes whose corresponding neighborhoods overlap. Our focus is the interleaving distance for mapper graphs, arising as a discretized analogue of the interleaving distance for Reeb graphs-a quantity known to be NP-hard to compute. This distance measures how similar two mapper graphs are by quantifying how much they must be ``stretched'' to be made comparable. Recent work introduced a loss function that gives an upper bound on this distance. The loss evaluates how far a given collection of maps, called an assignment, is from being a true interleaving. Importantly, it is computationally tractable, offering a practical way to bound the distance, however the quality of the bound is dependent on the choice of assignment. In this paper, we develop the first framework for bounding the interleaving distance on mapper graphs. We present the bound in two ways: first, by formulating an integer linear program (ILP) that determines whether an $n$-interleaving exists for a given $n$; and second, by constructing an ILP that identifies an assignment with minimal loss for that $n$. We also evaluate the method on small examples where the interleaving distance is known, and on benchmark and simulated datasets, demonstrating the utility of the approach for classification tasks based on mapper graphs.

In this work, we explore two-dimensional attractive Fermi gases at the microscopic level by probing spatial charge and spin correlations in situ. Using atom-resolved continuum quantum gas microscopy, we directly observe fermion pairing and study the evolution of two- and three-point correlation functions as inter-spin attraction is increased. The precision of our measurement allows us to reveal nonlocal anticorrelations in the pair correlation function, fundamentally forbidden by the mean-field result based on Bardeen-Cooper-Schrieffer (BCS) theory but whose existence we confirm in exact auxiliary-field quantum Monte Carlo calculations. We demonstrate that the BCS prediction is critically deficient not only in the superfluid crossover regime but also deep in the weakly attractive side. Guided by our measurements, we find a remarkable relation between two- and three-point correlations that establishes the dominant role of pair-correlations. Finally, leveraging local single-pair losses, we independently characterize the short-range behavior of pair correlations, via the measurement of Tan's Contact, and find excellent agreement with numerical predictions. Our measurements provide an unprecedented microscopic view into two-dimensional Fermi gases and constitute a paradigm shift for future studies of strongly-correlated fermionic matter in the continuum.

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, we show that the category of Lubin-Tate bundles on the $(n-1)$-dimensional Drinfeld symmetric space is equivalent to the category of finite-dimensional smooth representations of the group of units of the division algebra of invariant $1/n$ over $F$.

It is known that an entanglement-based witness of non-classicality can be applied to testing quantum effects in gravity. Specifically, if a system can create entanglement between two quantum probes by local means only, then it must be non-classical. Recently, claims have been made that collapse-based models of classical gravity, i.e. Diósi-Penrose model, can predict gravitationally induced entanglement between quantum objects, resulting in gravitationally induced entanglement is insufficient to conclude that gravity is fundamentally quantum, contrary to the witness statement. Here we vindicate the witness. We analyze the underlying physics of collapse-based models for gravity and show that these models have nonlocal features, violating the principle of locality.

Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized non-orthogonal determinants can achieve energy accuracies comparable to the state of the art. This is obtained by introducing an optimization method that leverages the quadratic dependence of the variational energy on the orbitals of each determinant, enabling an exact iterative optimization, and uses an efficient tensor-contraction algorithm to evaluate the effective Hamiltonian with a computational cost that scales as the fourth power of the number of basis functions. We benchmark the accuracy of the proposed method with exact full-configuration interaction results where available, and we achieve lower variational energies than coupled cluster (CCSD(T)) for several molecules in the double-zeta basis.

We introduce an active-space embedding framework for core-level spectroscopies that connects localized atomic multiplets to continuum resonances within a plane-wave DFT/PAW description. The approach is complementary to widely used core-level Bethe--Salpeter implementations based on a two-particle (core-exciton) picture with typically static screening: here a correlated multiplet manifold of the absorber (including the core hole and open-shell configurations) is coherently coupled to a plane-wave photoelectron, enabling a unified treatment of localized multiplet structure and continuum lineshapes. Spectra are computed in a general time-domain formulation equivalent to Fermi's golden rule: a transition operator tailored to the specific spectroscopy technique is applied to the correlated ground state to generate an excited wavepacket, and the corresponding wavepacket autocorrelation function is evaluated without explicit real-time propagation, using Lanczos tridiagonalization or the kernel polynomial method; the spectral intensity follows from its Fourier representation. We validate the method at the Ce \(N_{4,5}\) edges, reproducing in quantitative agreement with experiment both high-\(Q\) multiplet features and the low-\(Q\) giant dipole resonance continuum, including a characteristic low-energy shoulder relevant for robust Ce valence assignments. The implementation is available open-source within the Quantum ESPRESSO XSPECTRA package (xspectruplet mode), together with reproducible inputs and scripts.

These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we motivate from fundamental open problems in the field of quantum computing. The rigorous construction is non-Lagrangian and non-perturbative, based on previously neglected global completion of the M5-brane's tensor field by flux-quantization consistent with its non-linear self-duality and its twisting by the bulk C-field. This exists only in little-studied non-abelian generalized cohomology theories, notably in a twisted equivariant (and "twistorial") form of unstable Cohomotopy ("Hypothesis H"). As a result, topological quantum observables form Pontrjagin homology algebras of mapping spaces from the orbi-fixed worldvolume into a classifying 2-sphere. Remarkably, results from algebraic topology imply from this the quantum observables and modular functor of abelian Chern-Simons theory, as well as braid group actions on defect anyons of the kind envisioned as hardware for topologically protected quantum gates.

Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs) have sparked considerable interest due to the presence of several intertwined symmetry-breaking phases within a single material. Interestingly, in a recent experiment, magnetic hysteresis was observed in the superconducting state through magnetoresistance measurements in RbV$_{3}$Sb$_{5}$ [Nature Comm \textbf{17}, 1310 (2026)], providing strong evidence of a spontaneous time-reversal symmetry breaking superconducting state. The magnetic hysteresis, combined with crystalline symmetry, imposes strong constraints on the possible pairing symmetries of the superconducting state. In this work, we propose that RbV$_3$Sb$_5$ is a nodal topological superconductor with pseudo-spin-polarized Cooper pairs. The pseudo-spin-polarized superconducting domains resemble the properties of ferromagnetic domains and induce hysteresis. Moreover, the nodal topological superconducting state possesses Majorana flat band modes at the sample boundary, which can be detected by tunneling experiments.

We present a high-precision study of the topological susceptibility in $SU(3)$ pure gauge theory in four space-time dimensions. The result is based on ensembles at seven lattice spacings and in seven physical volumes to facilitate a controlled continuum and infinite-volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support the idea that both strategies yield a universal continuum limit; we find $χ_\mathrm{top}^{1/4}r_0=0.4775(14)(11)$ or $χ_\mathrm{top}^{1/4}=198.1(0.7)(2.7)\,\mathrm{MeV}$. Our appendix data suggest that the excess kurtosis $\langle q^4 \rangle / \langle q^2 \rangle^2-3$ decreases $\propto L^{-2}$ for large box sizes $L$.

We prove parabolic versions of several known gap theorems in classical Yang-Mills theory. On an $\mathrm{SU}(r)$-bundle of charge $κ$ over the 4-sphere, we show that the space of all connections with Yang-Mills energy less than $4 π^2 \left( |κ| + 2 \right)$ deformation-retracts under Yang-Mills flow onto the space of instantons, allowing us to simplify the proof of Taubes's path-connectedness theorem. On a compact quaternion-Kähler manifold with positive scalar curvature, we prove that the space of pseudo-holomorphic connections whose $\mathfrak{sp}(1)$ curvature component has small Morrey norm deformation-retracts under Yang-Mills flow onto the space of instantons. On a nontrivial bundle over a compact manifold of general dimension, we prove that the infimum of the scale-invariant Morrey norm of curvature is positive.

Monitored quantum circuits have attracted significant interest as an example of synthetic quantum matter, intrinsically defined by their quantum information content. Here, we propose a multipartite entanglement perspective on monitored phases through the lens of quantum Fisher information. Our findings reveal that unstructured monitored random circuits fail to exhibit divergent multipartite entanglement even at criticality, highlighting their departure from standard quantum critical behavior. However, we demonstrate that genuinely multipartite entangled phases can be realized through two-site measurements, provided a protection mechanism is in place. This work positions multipartite entanglement as a valuable perspective for the study of interacting monitored circuits and broader frameworks of noisy quantum dynamics.

This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve this, we enable first-order methods to utilize computational oracles for solving diagonal quadratic programs in subproblems. For problems where the optimal value $f^*$ is known, such as those in overparameterized models and feasibility problems, we propose an accelerated first-order method that incorporates a modified Polyak step size and Nesterov's momentum. Notably, our method does not require knowledge of smoothness levels, Hölder continuity parameter of the gradient, or additional line search, yet achieves the optimal oracle complexity bound of $\mathcal{O}(\varepsilon^{-2/(1+3ρ)})$ under Hölder smoothness conditions. When $f^*$ is unknown, we reformulate the problem as finding the root of the optimal value function and develop inexact fixed-point iteration and secant method to compute $f^*$. These root-finding subproblems are solved inexactly using first-order methods to a specified relative accuracy. We employ the accelerated prox-level (APL) method, which is proven to be uniformly optimal for convex optimization with simple constraints. Our analysis demonstrates that APL-based level-set methods also achieve the optimal oracle complexity of $\mathcal{O}(\varepsilon^{-2/(1+3ρ)})$ for convex function-constrained optimization, without requiring knowledge of any problem-specific structures. Through experiments on various tasks, we demonstrate the advantages of our methods over existing approaches in function-constrained optimization.

Superconductivity in a partially filled flat band presents a vexing conceptual hurdle because the absence of a Fermi surface precludes a weak-coupling regime where one can extend insights from the Bardeen-Cooper-Schrieffer picture of a Fermi surface instability. We approach the strongly correlated problem of flat band superconductivity from the strong coupling limit of local attractive interactions on line-graph lattices, whose non-interacting bandstructures host exactly flat bands. In this limit, the pair kinetic energy which sets the superfluid stiffness is expected to scale inversely with the pair binding interaction. Here we demonstrate a striking counterexample. We show that when doped charges propagate on the line-graph of a lattice with strong pairing interaction, they bind into obstructed Cooper pairs whose motion is frustrated by destructive interference. As a result, the leading-order pair kinetic energy vanishes identically in the strong-coupling expansion, producing a flat bosonic band of compact localized pair states, zero superfluid stiffness at leading order, and an extensively degenerate many-body ground state manifold. At quarter filling, the frustrated pair dynamics maps onto a quantum dimer model with a $d$-wave resonating-valence-bond spin liquid ground state, which becomes exact at the analytically solvable Rokhsar-Kivelson point. The pairing Hamiltonian in this limit thus has a topologically ordered ground state with long-range entanglement and deconfined holon excitations. Interestingly, we find exact compact localized eigenstates and extensive degeneracies in the many-body eigenstates of this emergent dimer model. Our results establish a disorder-free mechanism for interaction-driven localization, in which strong pairing collapses the kinetic energy of Cooper pairs.

In the digital era, accidental exposure of sensitive information such as API keys, tokens, and credentials is a growing security threat. While most prior work focuses on detecting secrets in source code, leakage in software issue reports remains largely unexplored. This study fills that gap through a large-scale analysis and a practical detection pipeline for exposed secrets in GitHub issues. Our pipeline combines regular expression-based extraction with large language model (LLM)-based contextual classification to detect real secrets and reduce false positives. We build a benchmark of 54,148 instances from public GitHub issues, including 5,881 manually verified true secrets. Using this dataset, we evaluate entropy-based baselines and keyword heuristics used by prior secret detection tools, classical machine learning, deep learning, and LLM-based methods. Regex and entropy based approaches achieve high recall but poor precision, while smaller models such as RoBERTa and CodeBERT greatly improve performance (F1 = 92.70%). Proprietary models like GPT-4o perform moderately in few-shot settings (F1 = 80.13%), and fine-tuned open-source larger LLMs such as Qwen and LLaMA reach up to 94.49% F1. Finally, we also validate our approach on 178 real-world GitHub repositories, achieving an F1-score of 81.6% which demonstrates our approach's strong ability to generalize to in-the-wild scenarios.

Non-invasive morphological assessment is the cornerstone of oocyte and embryo selection in assisted reproductive technology, yet clinical practice remains limited by two-dimensional, qualitative microscopy. While three-dimensional (3D) fluorescence imaging provides cellular insights, its inherent phototoxicity precludes routine clinical use. Conversely, existing label-free modalities fail to resolve subcellular structures in thick specimens due to two distinct physical barriers: large-scale refractive index heterogeneities, such as the cumulus cells surrounding oocytes, that induce severe aberrations; and short-scale fluctuations, primarily from cytoplasmic lipids, that generate a multiple scattering ``fog''. Here, we report an ultra-fast Reflection Matrix Imaging (RMI) platform designed to overcome these depth and resolution limits. By capturing the back-scattered electromagnetic field for a set of plane-wave illuminations at multiple wavelengths, we record a multi-spectral reflection matrix. From this matrix, we leverage digital adaptive focusing algorithms to computationally compensate for sample-induced aberrations while realigning forward multiple scattering trajectories with the single-scattering contribution. This approach enables label-free 3D visualization of oocytes and blastocysts with an unprecedented subcellular resolution of 300 nm throughout the entire specimen volume. We demonstrate the reliable identification of germinal vesicles and nuclear status in stages previously inaccessible to conventional optics, including imaging through dense cumulus cells. Our method provides a powerful, non-invasive tool for objective grading across all pre-implantation stages, potentially transforming decision-making in clinical IVF.

Developers rely on third-party library Application Programming Interfaces (APIs) when developing software. However, libraries typically come with assumptions and API usage constraints, whose violation results in API misuse. API misuses may result in crashes or incorrect behavior. Even though API misuse is a well-studied area, a recent study of API misuse of deep learning libraries showed that the nature of these misuses and their symptoms are different from misuses of traditional libraries, and as a result highlighted potential shortcomings of current misuse detection tools. We speculate that these observations may not be limited to deep learning API misuses but may stem from the data-centric nature of these APIs. Data-centric libraries often deal with diverse data structures, intricate processing workflows, and a multitude of parameters, which can make them inherently more challenging to use correctly. Therefore, understanding the potential misuses of these libraries is important to avoid unexpected application behavior. To this end, this paper contributes an empirical study of API misuses of five data-centric libraries that cover areas such as data processing, numerical computation, machine learning, and visualization. We identify misuses of these libraries by analyzing data from both Stack Overflow and GitHub. Our results show that many of the characteristics of API misuses observed for deep learning libraries extend to misuses of the data-centric library APIs we study. We also find that developers tend to misuse APIs from data-centric libraries, regardless of whether the API directive appears in the documentation. Overall, our work exposes the challenges of API misuse in data-centric libraries, rather than only focusing on deep learning libraries. Our collected misuses and their characterization lay groundwork for future research to help reduce misuses of these libraries.

A policymaker often wants to steer a decision-maker toward one of two actions, but lacks reliable knowledge of how the decision-maker perceives uncertainty or evaluates risk. We formalize a notion of robust paternalism: a modification a' of a desired action a is robustly more attractive than a relative to b if, for every belief over states and every increasing concave utility function, whenever the decision-maker prefers a to b, she also prefers a' to b. We characterize all such modifications directly in terms of state-dependent payoffs and discuss applications to political competition, bilateral trade, insurance, and information acquisition.

This book studies ultrafilters on connectivity systems, that is, on pairs \((X,f)\) where \(X\) is a finite set and \(f:2^{X}\to \mathbb{N}\) is a symmetric submodular function. Ultrafilters, which play a fundamental role in topology and set theory, are considered here in this broader setting, with particular emphasis on their connections to graph width parameters and to the structural analysis of graph complexity. We develop several results on ultrafilters on connectivity systems and examine related notions such as prefilters, ultra-prefilters, and filter subbases. We also discuss additional width-, length-, and depth-type parameters that naturally arise in this framework, thereby broadening the perspective from which graph structure may be studied. In addition, the book compares a wide range of graph width parameters and related concepts, with the aim of providing a unified viewpoint and a useful point of departure for further research in graph theory and computational complexity. More broadly, the book highlights connections with several neighboring areas of mathematics, including set theory, lattice theory, and matroid theory. It also contains survey-style material intended to clarify the current landscape of graph width theory and to stimulate further developments in the subject.

Relativistic effects strongly influence the electronic structures of the heaviest elements, thereby shaping their chemical and physical properties. Studying ion mobility within a noble gas environment reveals how the ion-neutral interactions depend on the ion's electronic configurations, thus providing an avenue for exploring these effects. An ion mobility spectrometer with a cryogenic drift tube was developed to precisely measure the low-field reduced mobility of heavy lanthanide and actinide cations. The apparatus was characterized by optimizing the bunching operation of ions with a miniature RF coulomb buncher and evaluating the chromatography performance of the drift tube operated with helium buffer gas at a temperature of 298K. Systematic ion mobility measurements of lutetium cations (Lu$^{+}$) drifting in helium gas were carried out as a case study. The electronic state chromatography of Lu$^{+}$ has been demonstrated. The low-field reduced ion mobility for the ground and lowest meta-stable state of Lu$^{+}$ have been examined. In addition, the variation of both states' reduced mobility and the quenching of meta-stable population has been investigated under different reduced electric fields ($E/n_0$), the ratio of an electric field to neutral gas number density.

This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process that evolves jointly in the space of parameters and latent variables and show that the stationary distribution of this diffusion concentrates around the maximum marginal likelihood estimate of the parameters. We then provide two explicit discretisations of this diffusion as practical algorithms to estimate parameters of statistical models. For each algorithm, we obtain nonasymptotic rates of convergence in Wasserstein-2 distance for the case where the joint log-likelihood is strongly concave with respect to latent variables and parameters. We achieve accelerated convergence rates clearly demonstrating improvement in dimension dependence. To demonstrate the utility of the introduced methodology, we provide numerical experiments that illustrate the effectiveness of the proposed diffusion for statistical inference. Our setting covers a broad number of applications, including unsupervised learning, statistical inference, and inverse problems.