Hamiltonian Monte Carlo (HMC) and its dynamic extensions, such as the No-U-Turn Sampler (NUTS), are powerful Markov chain Monte Carlo methods for sampling from complex, high-dimensional probability distributions. Riemannian manifold Hamiltonian Monte Carlo (RMHMC) extends HMC by allowing the mass matrix to depend on position, which can substantially improve mixing but also makes implementation considerably more challenging. In this paper, we study an adaptive hierarchical version of RMHMC that is well suited to many hierarchical sampling problems. A key feature of hierarchical RMHMC is that, unlike general RMHMC, it admits a closed-form explicit leapfrog integrator, enabling efficient implementation and direct use within dynamic HMC methods such as NUTS. We introduce an adaptive scheme that automatically tunes the parameters of the hierarchical mass matrix during simulation. Importantly, the target density need not exhibit any hierarchical or block structure; the hierarchy is instead imposed on the mass matrix as a modeling device to capture the local geometry of the target distribution. Numerical experiments demonstrate appealing empirical performance in high-dimensional Bayesian inference problems.

We prove that every ordinal $α<ω_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive answer to a problem posed by Nicolas Luzin in 1935.

This paper presents a framework for local solutions to time-varying linear differential-algebraic equations (DAEs) with real meromorphic coefficients. The local solutions on compact intervals form a sheaf. This permits a simple definition of controllability in the sense of Jan C. Willems. We prove that this notion is equivalent to the established global notion by giving an algebraic characterization based on the Teichmüller-Nakayama form. Finally, we study conditions under which local solutions admit extension, which is necessary for controllability.

Scanning Tunneling Microscopy (STM) has revolutionized our atomic scale understanding of surfaces and accelerated progress in nanotechnology. This technique, however, is restricted to metal or semiconducting samples, as it requires a tiny current to stabilize the tip-sample distance with atomic scale precision. We developed a new imaging and feedback method that relies on true alternating current (AC) without any direct current (DC) component. This technique does not only enable the imaging on non-conducting surfaces with atomic resolution, like (thin) glass and oxides, it provides also access to high-frequency electronic sample information. We demonstrate that it is possible to measure on 25nm thick silicon oxide with 10 MHz tunneling current.

We study the sensitivity of a future muon collider to exotic Higgs decays in a minimal scenario of Standard Model (SM) augmented with a light singlet scalar $S$. We consider the decay $h\to SS$ and $S$'s subsequently decay back to SM. In particular, we focus on final states with four bottom quarks ($4b$), or two bottom quarks and two muons ($2b2μ$). Analyses are performed for two muon collider benchmark configurations: center-of-mass collision energy $\sqrt{s}=3~\mathrm{TeV}$ with $1~\mathrm{ab}^{-1}$ data and $\sqrt{s}=10~\mathrm{TeV}$ with $10~\mathrm{ab}^{-1}$ data. Machine-learning techniques are applied to suppress backgrounds and mitigate jet-combinatorics effects in both channels. We find that the $4b$ mode could be sensitive to the branching ratio, BR$(h \to SS \to 4b)$, of ${\cal O}(10^{-2})$ at 3 TeV and ${\cal O}(10^{-3})$ at 10 TeV, significantly improving upon high-luminosity LHC projections. In the Higgs-portal model with $S$ coupling to SM only through mixing with the Higgs, the sensitivities to BR$(h \to SS)$ remain at the same level given ${\cal O}(1)$ branching fraction of $S$ decaying into $b$-quarks. The $2b2μ$ mode benefits from a clean dimuon resonance and can probe BR$(h\to SS\to 2b2μ)$ down to $10^{-5}$ level at a 10 TeV muon collider. But the sensitivity to BR$(h \to SS)$ will be significantly reduced due to the small branching fraction of $S$ decaying into muons in the Higgs portal model.

The first detection of supernova burst neutrinos was achieved through the observation of SN1987A, almost four decades ago. However, neutrinos produced during the burning stages of a star prior to core collapse are yet to be detected. Detection of pre-supernova neutrinos could provide an early warning of an imminent supernova and allow the scientific community time to focus their resources on the observation and study of such an event leading to better understanding of these rare phenomena. Integrating pre-supernova models into a neutrino event generator would help to provide a unified framework for studying these neutrinos in current and next generation detectors. sntools is a neutrino event generator for supernova burst neutrinos, originally developed to study supernova model discrimination with Hyper-Kamiokande. Work to add support for pre-supernova event generation to sntools is presented, detailing the adaptations and additions to the code, with emphasis on how time binning can be optimised for a robust simulation, and also detailing the status of the validation process. The current status and capabilities of the package will be explained alongside plans for any further work and the intended use for the new functionality within the Hyper-Kamiokande Collaboration.

Spontaneous emission of a quantum emitter, such as an excited atom, is a fundamental process in quantum electrodynamics (QED), typically associated with exponential decay to the ground state accompanied by irreversible photon emission. This simple Markovian picture, however, is profoundly modified in the presence of time-delayed feedback, structured continua, or cooperative emission, as occurs when an emitter radiates in front of a mirror, when several emitters radiate collectively, or in the case of a giant atom. In such regimes, strong non-Markovian dynamics arise from photon reabsorption and interference effects, leading to pronounced deviations from exponential decay. Here we demonstrate the emergence of exceptional points (EPs) in these highly non-Markovian waveguide-QED environments, i.e., non-Markovian EPs. These EPs appear directly in the relaxation dynamics as sharp transitions to oscillatory behavior, manifested by the appearance of real zeros in the excited-state amplitude. We analyze in detail the spontaneous emission of giant atoms with two or more coupling points, highlighting the mechanisms leading to non-Markovian EPs, and show that similar phenomena arise in other waveguide-QED settings, such as the collective spontaneous emission of spatially separated point-like emitters. Our results reveal waveguide-QED systems as experimentally accessible platforms for realizing and exploring non-Markovian EP physics.

This paper investigates mean field games and control on sparse networks. In the case of large expander graphs, the limit topologies are analyzed using the graphexon framework, which characterizes both dense network limits and sparse connections. We prove that the sequence of empirical graphexon measures defined on finite graphs converges weakly to a limit graphexon measure on a continuous state space. Furthermore, the associated sequence of discrete averaging operators converges strongly to a continuous operator. These properties enable the formulation of a linear-quadratic mean field game in which each agent is identified by a spatial network label $α\in X$ and only interacts with the neighborhood average defined by the operator $\mathcal{G}$ characterized by large expander graphs. In Section 5, algebraic conditions for the global asymptotic stability of the closed-loop system are established. The analysis identifies parameter thresholds that gives rise to a Turing-type topological instability, where the homogeneous mean state remains stable while the spatial deviation field diverges over the continuous spectrum of the limit operator.

Architecture Decision Records (ADRs) play a critical role in preserving the rationale behind system design, yet their creation and maintenance are often neglected due to the associated authoring overhead. This paper investigates whether Large Language Models (LLMs) can mitigate this burden and, more importantly, how different strategies for presenting historical ADRs as context influence generation quality. We curate and validate a large corpus of sequential ADRs drawn from 750 open-source repositories and systematically evaluate five context selection strategies (no context, All-history, First-K, Last-K, and RAFG) across multiple model families. Our results show that context-aware prompting substantially improves ADR generation fidelity, with a small recency window (typically 3-5 prior records) providing the best balance between quality and efficiency. Retrieval-based context selection yields marginal gains primarily in non-sequential or cross-cutting decision scenarios, while offering no statistically significant advantage in typical linear ADR workflows. Overall, our findings demonstrate that context engineering, rather than model scale alone, is the dominant factor in effective ADR automation, and we outline practical defaults for tool builders along with targeted retrieval fallbacks for complex architectural settings.

For a one-parameter variation of biextension mixed Hodge structures, Brosnan and Pearlstein showed that the limit of the asymptotic height of the variation is given by a certain limit height of the nilpotent orbit. This limit height depends on the choice of a parameter. In the case of a variation of geometric origin related to Ceresa cycles associated with curves of genus three, after fixing a parameter, we show that this limit height is given by the Deligne splitting of a biextension mixed Hodge structure associated with cycles in the boundary.

As AI becomes more common in students' everyday experiences, a major challenge for K-12 AI education is designing learning experiences that can be meaningfully integrated into existing subject-area instruction. This paper presents the design and implementation of an AI4K12-aligned curriculum that embeds AI learning goals within a rural middle school science classroom using Breadth-First Search (BFS) as an accessible entry point to AI problem-solving. Through unplugged activities and an interactive simulation environment, students learned BFS as a strategy for exploring networks and identifying shortest paths, then applied it to science contexts involving virus spread and contact tracing. To examine engagement and learning, we analyzed pre- and post-assessments, student work artifacts, and a teacher interview. Results suggest that students engaged productively with the curriculum, improved their understanding of BFS and AI problem-solving, and benefited from learning these ideas within ongoing science instruction. Teacher feedback further indicated that the module fit well within the science curriculum while supporting intended science learning outcomes. We conclude with curriculum and design considerations for broadening access to learning about problem-solving with AI in education.

Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of geodesics can cease to be geodesic at a finite time. This implies that the conventional point-particle approximation is not the primary issue; rather, the breakdown of geodesic flow restricts a consistent description across scales. We develop a covariant multi-scale framework that resolves this problem by decomposing spacetime into hierarchical regions separated by matter horizons. We show how to match shared boundary consistently at the level of the action, leading to a covariant backreaction contribution. The resulting construction provides a first-principles theoretical foundation for cosmological zoom-in simulations and yields an effective energy-momentum tensor capturing the impact of the geometric backreaction effect. As an application, we demonstrate that this backreaction naturally produces flat galaxy rotation curves without invoking an additional dark matter component. Our results establish a new perspective on nonlinear structure formation, in which long dynamical range is resolved through a hierarchy of discrete geodesic domains.

Motivated by recent experimental advances in the corresponding measurements, non-leptonic hyperon decays are calculated, for the first time in a relativistic manner, in Chiral Perturbation Theory at next-to-leading order (NLO). On the one hand, relativistic loop corrections are computed explicitly based on the ground-state octet and decuplet fields. On the other hand, the NLO weak-transition low-energy constants are estimated by resonance saturation, inspired by the non-relativistic tree-level computation of Ref. [1]. In particular, the $1/2^-$ and the (excited) $1/2^+$ resonance octets are utilized. The remaining unknown parameters are fitted to the decay amplitudes. A good combined fit to both $s$- and $p$-wave amplitudes is achieved with the caveat of not being very tightly constrained. The role of the resonances is found to be crucial. Consequences for further investigations and open questions are addressed.

In one dimension, strongly correlated gapless systems are highly constrained due to conformal invariance, leading to the decoupling of low energy degrees of freedom corresponding to different symmetry sectors. The most familiar example of this is spin-charge separation. Here, we extend this mechanism to the non-Hermitian realm by demonstrating that skin effects corresponding to different symmetry sectors exhibit an emergent decoupling. We establish this for $N$ flavor fermions and demonstrate it numerically for the special case of the Hubbard model, in which spin and charge skin effects separate at low energies. Finally, we construct an interaction-enabled $E_8$ skin effect with no free fermion counterpart.

We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world, and derive a representation theorem for countable frames. The orbit decomposition of the centered symmetry group governs the within-orbit structure: worlds in the same orbit are conditionally identically distributed, and on orbits satisfying a richness condition and countable infinitude they are conditionally i.i.d. given a rigid orbit-specific directing measure. Point-homogeneous S5 frames yield a single de Finetti parameter; S4 frames may admit multiple orbits, with the richer orbits carrying rigid directing measures and the remainder carrying only weaker invariant structure. Two applications follow. First, the orbit decomposition determines whether learning pools globally or remains orbit-local. Second, it supplies a mechanism for structural credal fine-graining indexed to orbit regions, distinct from hyperintensionality in the strict sense of distinguishing coextensive propositions.

Telegram, initially a messaging app, has evolved into a platform where users can interact with various services through programmable applications, bots. Bots provide a wide range of uses, from moderating groups, helping with online shopping, to even executing trades in financial markets. However, Telegram has been increasingly associated with various illicit activities -- financial scams, stolen data, non-consensual image sharing, among others, raising concerns bots may be facilitating these operations. This paper is the first to characterize Telegram bots at scale, through the following contributions. First, we offer the largest general-purpose message dataset and the first bot dataset. Through snowball sampling from two published datasets, we uncover over 67,000 additional channels, 492 million messages, and 32,000 bots. Second, we develop a system to automatically interact with bots in order to extract their functionality. Third, based on their description, chat responses, and the associated channels, we classify bots into several domains. Fourth, we investigate the communities each bot serves, by analyzing supported languages, usage patterns (e.g., duration, reuse), and network topology. While our analysis discovers useful applications such as crowdsourcing, we also identify malicious bots (e.g., used for financial scams, illicit underground services) serving as payment gateways, referral systems, and malicious AI endpoints. By exhorting the research community to look at bots as software infrastructure, this work hopes to foster further research useful to content moderators, and to help interventions against illicit activities.

Quantile regression (QR) relies on the estimation of conditional quantiles and explores the relationships between independent and dependent variables. At high probability levels, classical QR methods face extrapolation difficulties due to the scarcity of data in the tail of the distribution. Another challenge arises when the number of predictors is large and the quantile function exhibits a complex structure. In this work, we propose an estimation method designed to overcome these challenges. To enhance extrapolation in the tail of the conditional response distribution, we model block maxima using the generalized extreme value (GEV) distribution, where the parameters depend on covariates. To address the second challenge, we adopt an approach based on generalized random forests (grf) to estimate these parameters. Specifically, we maximize a penalized likelihood, weighted by the weights obtained through the grf method. This penalization helps overcome the limitations of the maximum likelihood estimator (MLE) in small samples, while preserving its optimality in large samples. The effectiveness of our method is validated through comparisons with other approaches in simulation studies and an application to U.S. wage data.

Solid-state spin defects are promising qubits for quantum network nodes. A key challenge towards larger networks is creating defects with high yield into nanophotonic devices, while maintaining good optical and spin properties. Here, we demonstrate the creation of V2 centers in nanopillars fabricated from commercial bulk-grown 4H-silicon carbide using a pulsed above-bandgap (UV) laser. We observe an eleven-fold increase in the V2 center occurrence after UV laser illumination. These laser-induced V2 centers exhibit narrow optical linewidths and spectral diffusion rates comparable to naturally occurring V2 centers in nanopillars of the same material. Furthermore, we measure a spin coherence time of $T_{2}^{\mathrm{DD}} = 3.6 \pm 0.3~\text{ms}$ under dynamical decoupling, consistent with dephasing by the nuclear-spin bath. This demonstration of the in-situ, post-fabrication generation of coherent V2 centers in nanostructures in widely available bulk-grown 4H-SiC, shows the potential for above-bandgap laser illumination for scalable defect creation in integrated photonic devices.

Sterile neutrinos in the keV mass range are a well-motivated extension of the Standard Model and viable dark matter candidates. Their existence can be probed in laboratory experiments, as the admixture of a sterile state would induce a characteristic kink-like distortion in the $β$-decay electron energy spectrum. The KATRIN experiment is designed to measure the effective electron neutrino mass with sub-eV sensitivity by analyzing the endpoint region of the tritium $β$-decay spectrum. Following the completion of its neutrino mass program, KATRIN will extend its physics reach to the search for keV-scale sterile neutrinos. This effort will be enabled by the TRISTAN detector, a newly developed silicon drift detector array optimized for differential measurements at high rates and energies well below the endpoint. In this article, we present the projected sensitivity of KATRIN to keV-scale sterile neutrinos using a dedicated simulation framework. With four months of detector livetime, KATRIN has the statistical power to probe mixing amplitudes at the level of $|U_{e4}|^2 \sim 10^{-6}$ for sterile neutrino masses in the (4$-$13) keV range, significantly extending the reach of previous laboratory searches. The major experimental systematic uncertainties investigated in this work reduces the sensitivity by a factor of 10$-$50 over the same mass range.

Neuromorphic electronics and spiking neural networks (SNNs) offer energy-efficient data processing, essential for real-time and edge-computing applications. In particular, interfacing and processing biological signals require devices that combine electronic performance with ionic sensitivity, which are capabilities uniquely provided by organic electrochemical transistors (OECTs). However, realizing a simple, fully integrated OECT-based neuron with rich dynamics and adaptability remains challenging. Most reported implementations rely on current-driven operation, which complicates large-scale integration and neuron-neuron coupling due to the need for precise matching of operating currents and bias voltages. Here we present a voltage-driven neuron circuit based on a multivibrator oscillator architecture, entirely fabricated from poly(3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS). The neuron exhibits tunable adaptability through an additional control input, enabling switching between burst latency and length encoding modes. We further demonstrate a hardware-implemented two-neuron unit consisting of an inhibitory and a readout neuron, where readout activity is suppressed depending on the relative timing of the inhibitory input. Finally, we demonstrate that the fabrication process is compatible with polymer dendrite growth, enabling on-chip integration of synaptic elements on the same substrate. Owing to its structural simplicity and compatibility with a single, available material, this approach offers a scalable and accessible route toward integrated OECT-based SNNs.

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

Songwriting has long served as a powerful medium for expressing unconscious emotions and fostering self-awareness in psychotherapy. Due to the auditory-centric nature of traditional approaches, Deaf and Hard-of-Hearing (DHH) individuals have often been excluded from music's therapeutic benefits. In response, this study presents a music psychotherapy tool co-designed with therapists, integrating conversational agents (CAs) and music generative AI as symbolic and therapeutic media. Through a usage study with 23 DHH individuals, we found that collaborative song writing with the CA enabled them to experience emotional release, reinterpretation, and deeper self-understanding. In particular, the CA's strategies -- supportive empathy, example response options, and visual-based metaphors -- were found to facilitate musical dialogue effectively for DHH individuals. These findings contribute to inclusive AI design by showing the potential of human-AI collaboration to bridge therapeutic artistic practices.

The rapid advancement of generative AI (GenAI) is expanding access to songwriting, offering a new medium of self-expression for Deaf and Hard-of-Hearing (DHH) individuals. However, emerging technologies that support DHH individuals in expressing themselves through music have largely been evaluated in single-session settings and often fall short in helping users unfamiliar with songwriting convey personal narratives or sustain engagement over time. This paper explores songwriting as an extended, music-based journaling practice that supports sustained emotional reflection over multiple sessions. We introduce SoulNote, a GenAI system enabling DHH to engage in iterative songwriting. Grounded in user-centered design, including a design workshop, a preliminary study, and a multi-session diary study, our findings show that ongoing songwriting with \textit{SoulNote} facilitated emotional growth across three dimensions: self-insight, emotion regulation, and \revised{everyday attitudes toward emotions and self-care}. Overall, this work demonstrates how GenAI can support marginalized communities by transforming creative expression into a daily practice of self-discovery and reflection.

Strong-to-weak spontaneous symmetry breaking (SWSSB) defines a mixed-state phase of matter--without a pure-state counterpart--in which nonlinear observables such as the Rényi-2 correlator develop long-range order while conventional linear correlations remain short-ranged. Here we study the emergence of SWSSB in one-dimensional open quantum systems governed by Lindbladian evolution, where the transition time diverges with system size and SWSSB appears only asymptotically in the steady state. By tracking the late-time growth of the Rényi-2 correlation length, we uncover a universal dynamical regime controlled purely by the symmetry class of the Lindbladian. Contrary to the conventional expectation that late-time dynamics are governed by the low-lying Liouvillian spectrum, we find that the time dependence of the SWSSB transition--exponential versus algebraic--is dictated solely by symmetry, independent of details of the Lindbladian, including whether the Liouvillian spectrum is gapped or gapless. For $\mathbb{Z}_2$-symmetric dynamics, the Rényi-2 correlation length grows exponentially in time--even when the spectrum is gapless--yielding an effective transition time $t_c \propto \operatorname{ln} L$ and enabling rapid preparation of the $\mathbb{Z}_2$ SWSSB steady state. In contrast, U(1)-symmetric dynamics exhibit algebraic scaling, $t_c \propto L^α$, with a filling-dependent dynamical exponent: ballistic growth ($α\approx 1$) at finite filling crosses over to diffusive scaling ($α= 2$) in the zero-filling limit. These results establish symmetry--rather than spectral gap structure--as the controlling principle for SWSSB late-time dynamical scaling, and open a new route to nonequilibrium symmetry breaking in open quantum systems.

Frøseth (2026; arXiv:2603.05264) shows that a proportional wealth tax on market values is neutral with respect to portfolio choice, Sharpe ratios, and equilibrium prices under CRRA preferences and geometric Brownian motion. This paper investigates the robustness of that result along two dimensions. First, we extend the neutrality frontier: portfolio neutrality -- including all intertemporal hedging demands -- is preserved under stochastic volatility (Heston and general Markov diffusions) and Epstein-Zin recursive utility, but breaks under non-homothetic preferences such as HARA. Second, we identify four channels through which implemented wealth taxes depart from neutrality even under CRRA: non-uniform assessment across asset classes, general equilibrium price effects in inelastic markets, progressive threshold structures, and endogenous labour supply. Each channel is formalised and, where possible, calibrated to the Norwegian wealth tax system. The progressive threshold introduces a tax shield that increases risk-taking near the exemption boundary -- an effect opposite in sign to the HARA distortion -- and, at the extreme, generates a participation margin at which investors exit the tax jurisdiction entirely. We formalise this tax-induced migration as the extreme response at the progressive threshold and examine the Norwegian post-2022 experience as a case study. The full framework is applied to evaluate the Saez-Zucman proposal for a global minimum wealth tax on billionaires and the related French proposal for a national minimum tax above EUR 100 million.

How substructures and disk properties affect dust evolution and the delivery of solids and volatiles into planet-forming regions remains an open question. We present results from tailored dust evolution modeling of the AGE-PRO ALMA large program, a sample of 30 protoplanetary disks spanning different evolutionary stages. Visibility fitting of the AGE-PRO ALMA data (at 1.3\,mm) reveals that approximately half of the disks exhibit radial substructures. Combined with stellar properties, disk inclinations, and gas mass estimates from CO isotopologues and N$_2$H$^+$, this well-characterized set of disks provides an ideal testbed to constrain dust evolution models across different ages and disk morphologies. Using the dust evolution code \texttt{DustPy}, we simulate dust evolution in each disk under four model configurations, varying two key free parameters: the turbulent viscosity ($α= 10^{-4}, 10^{-3}$) and fragmentation velocity ($v_{\rm{frag}} = 1 \mathrm{m\,s^{-1}}, 10 \mathrm{m\,s^{-1}}$). Pressure traps are incorporated by perturbing the gas surface density based on the continuum intensity profiles, and synthetic observations generated with \texttt{RADMC-3D} are compared to these profiles. While no single model fits all disks, nearly half are best reproduced by the configuration with low turbulence and low fragmentation velocity ($α= 10^{-4}, v_{\rm{frag}} = 1\,\mathrm{m\,s^{-1}}$). Models of smooth disks underpredict dust mass, possibly indicating unresolved substructures. Pebble fluxes into inner disk regions correlate more strongly with disk age than with the presence of substructures, highlighting time-dependent dust transport as a key factor in shaping inner disk composition. Our results also provide a comparative baseline for interpreting multiwavelength and JWST water vapor observations.

Violation of Bell inequalities in bipartite systems represented by mutually-commuting von Neumann algebras has pioneered the study of vacuum entanglement in algebraic quantum field theory. It is unexpected that the maximal violation of Bell inequality can discover algebraic structures. In the paper, we establish the mutually-commuting von Neumann algebra model for entanglement swapping networks and Bell-type inequalities on this model. It generalizes the bipartite case to the ternary case. These algebras are all general von Neumann algebras, which provide a natural perspective to investigate Bell nonlocality in quantum networks in the infinitely-many-degree-of-freedom setting. We determine various bounds for Bell-type inequalities based on the structure of von Neumann algebras, and identify the algebraic structural conditions required for their violation. Finally, we show that the maximal violation of Bell-type inequalities in entanglement swapping networks can be used to determine partially the type classification of the underlying von Neumann algebras.

We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-filling-like quotients of various groups, among which mapping class groups of punctured spheres. In particular, we show that the mapping class group of a five-holed sphere (resp. the braid group on four strands) has infinite hyperbolic quotients (strongly) not isomorphic to hyperbolic quotients of any other given sphere mapping class group (resp. any other braid group). These quotients are obtained by modding out suitable large powers of Dehn twists, and we further argue that the corresponding quotients of the extended mapping class group have trivial outer automorphism groups. We obtain these results by studying torsion elements in the relevant quotients.

We report an extremely rich ground state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zig-zag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large inter-chain coupling, via the topological Gaussian transition. Upon decreasing the inter-chain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a non-magnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten $\mathrm{SU(2)}_2$ criticality with a total central charge $c=3$.

Nonlinear Resonant Ultrasound Spectroscopy is a nonlinear ultrasonic technique which allows monitoring small variations in the microstructure of a medium and thus allows materials characterization and monitoring of damage evolution. Application of the technique to monitor Liquid Metal Embrittlement induced by gallium penetration in aluminum is presented here. To define indicators of material degradation, data treatment using the Singular Value Decomposition approach is introduced and discussed. Experimental results show that nonlinear properties are correlated with the state of the liquid metal in the solid matrix, allowing to identify different phases in the process of gallium diffusion along grain boundaries and within the bulk of individual grains. Furthermore, the evolution of gallium damage allows to study correlations between nonlinear, fast and slow dynamic properties.