This article presents a mathematical analysis and numerical strategies for solving the optimization problem of minimizing the quadratic function $J(P) = \text{Tr}(BP)- \frac{1}{2} \text{Tr}(A P A P)$, where $A,B \in \mathbb R^{M \times M}_{\rm sym}$, with $A \succeq 0$, over the Grassmann manifold ${\rm Gr}(m,\mathbb R^M)$. While this problem is non-convex and typically admits non-global local minima - posing challenges for Riemannian optimization and self-consistent field (SCF) algorithms - we identify cases where the global minimizer can be obtained by solving an auxiliary convex problem. When this approach is not directly applicable, the solution to the auxiliary problem still serves as an effective initialization for Riemannian optimization methods and SCF algorithms, significantly improving their performance. This work is motivated by applications in quantum embedding methods, particularly in the construction of bath orbitals, where such optimization problems naturally arise.

This work discusses the broadband X-ray spectral analysis of 11 candidate heavily-obscured active galactic nuclei (AGN) selected based on their infrared and X-ray properties by a recently published machine learning algorithm. This paper is part of a larger work to identify and characterize all AGN in the local universe (z < 0.1) with the largest line-of-sight (los) column densities (NH), the so-called Compton-thick (CT-, NH,los >= 1024 cm-2) AGN. We modeled the X-ray spectra using two physically- motivated models, UXClumpy and RXTorusD. Of the 11 AGN in our sample, we found three to be obscured with 22.7 < LogNH,los <= 23.0, five have 23.0 < LogNH,los <= 23.25, and three have 23.4 < LogNH,los <= 23.9, according to UXClumpy. Meanwhile, according to RXTorusD, we found three AGN to be obscured with 22.7 < LogNH,los <= 23.0, four with 23.0 < LogNH,los <= 23.4, and four with 23.85 < LogNH,los <= 23.96. Additionally, this work served as a comparison between UXClumpy and RXTorusD. We found broad agreement between the two, with 8/11 sources agreeing on the value of the photon index Gamma, while only 5/11 sources agreeing on the NH,los value within the 90% confidence level.

Breakloose friction, the transient force peak at the onset of sliding, is often pronounced in nanoscale contacts but weak or absent in macroscopic systems. Although this behavior is commonly associated with rupture fronts and process-zone effects, how the stiction peak is controlled by system size, temperature, driving rate, and loading geometry, and what mechanisms underlie its emergence or suppression, remains incompletely understood. Here we investigate this problem using three minimal friction models with distinct loading geometries: a multi-particle Prandtl-Tomlinson system with independently driven particles, an end-driven Frenkel-Kontorova chain with elastic stress transmission along the interface, and a uniformly driven FK chain in which each site is coupled locally to the driving stage. We show that similar macroscopic suppression of breakloose friction can arise from fundamentally different mechanisms. In multi-particle PT systems, increasing system size or temperature promotes statistical dephasing of local depinning events, smoothing the global response. In end-driven FK chains, internal elasticity redistributes stress along the interface, delaying sliding onset and, together with higher temperature or slower driving, enabling progressive relaxation during loading. In uniformly-driven FK chains, the stiffness of the driving springs controls the synchronization of slip events and thereby the character of the sliding response. These results demonstrate that the presence or absence of a breakloose peak does not uniquely identify a single physical mechanism, but instead reflects the interplay of local pinning, elastic coupling, and contact architecture.

The Laser Interferometer Space Antenna (LISA) will enable precision studies of Extreme and Intermediate Mass Ratio Inspirals (EMRIs/IMRIs), providing unique probes of astrophysical environments of galactic nuclei and strong-field gravity. Using a fully relativistic pipeline across primary masses $m_1 \in [5\times10^4, 10^7]\,M_\odot$ and secondary masses $m_2 \in [1, 10^4]\,M_\odot$, we map instrumental performance directly to detection horizons and parameter measurement precision. EMRIs with $m_1 = 10^7\,M_\odot$ and $m_2 \sim 1\,M_\odot$ are the most sensitive to instrument degradation, with redshift horizons at $z \sim 0.01$, while IMRIs are the least sensitive to degradation and reach redshifts $z \sim 1-3$. All prograde systems considered achieve sub-percent spin precision within three months of observation. The full 4.5-year mission increases the horizon of systems with $m_1 = 10^7\,M_\odot$ and $m_2 \sim 1\,M_\odot$ by a factor of $\sim 4$ and improves sky localization by one to two orders of magnitude reaching $ < 10\,\mathrm{deg}^2$. IMRI detection is robust against degradation, but their parameter estimation is more vulnerable due to fewer cycles in band. With the full baseline, EMRI observations constrain scalar dipole emission and Kerr quadrupole deviations below ground-based bounds by one to two orders of magnitude. We release the accompanying software and an interactive website to enable the community to rapidly quantify the scientific potential of EMRIs and IMRIs.

The dynamical generation of quantum resources, such as many-body entanglement or Bell correlations, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-$\tfrac12$ chain models -- a staggered nearest-neighbor XXX chain and a long-range XXZ chain -- develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators

We develop estimators that improve precision of heterogeneous treatment effect estimates that allow borrowing information from observational studies when the available covariates in each data source do not perfectly match. Standard data-borrowing methods often assume perfectly matched covariates. We propose MR-OSCAR, an RCT-calibrated, two-stage estimation approach that first predicts the trial-missing variables using the observational data via imputation and then calibrates observational outcome predictions to the randomized trial, preserving the causal contrast, unlike the results for generalization, where imputation does not improve performance. Our theory gives finite-sample guarantees with a transparent error decomposition including an imputation error that shrinks as the observational mapping becomes more predictable. Simulations show that imputation almost always outperforms naively using only the shared covariates and clarifies when borrowing helps (strong predictability of the missing block, moderate trial size) and when it does not (poor predictability or dominant trial-only moderators). We motivate the approach with the Greenlight Plus trial on early childhood obesity and outline a forthcoming EHR analysis at Vanderbilt, highlighting the use of our method in common scenarios where data do not perfectly align.

Radio-loud active galactic nuclei (AGN) are among the most luminous objects in the Universe, emitting radiation from low-energy radio waves to high energy $γ$-rays. They are well known to exhibit flux variations at nearly all accessible wavelengths. However, their variability properties in the ultraviolet (UV) band remain relatively less explored compared to other wavebands. Here, we present the results of a systematic investigation of the UV flux and spectral variability characteristics of 24 radio-loud AGN spanning the redshift range 0.018 $\le$ $z$ $\le$ 2.218. The sample comprises 17 BL Lac objects, 6 flat spectrum radio quasars (FSRQs) and one radio-loud narrow line Seyfert 1 galaxy. We used observations obtained with the Ultra-Violet Imaging Telescope (UVIT) onboard AstroSat during its first ten years of operation, covering both the far-UV (FUV; 1300$-$1800 Å) and near-UV (NUV; 2000$-$3000 Å) bands. Of the 24 sources analysed, 18 showed significant UV variability on hour timescales. We found a bluer when brighter (BWB) spectral trend in two sources: the FSRQ CTA 102 and the BL Lac PKS 0447$-$439. The observed UV variability in our sample of radio-loud AGN, together with the BWB trend detected in these two sources, supports a scenario in which the hour timescale UV variations are driven by intrinsic processes within their relativistic jets.

The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations of the variational coefficients for determining time evolution are solved via classical simulations with a time discretization method. We here present a full-quantum approach, in which ordinary differential equations of the variational coefficients are transformed into static linear equations via the Chebyshev spectral discretization method and then solved via the quantum singular value transformation algorithm. Our full quantum algorithm avoids classical feedback, achieves exponential convergence for smooth Hamiltonians, and yields a quantum circuit depth that is independent of the number of time steps. We demonstrate two implementation strategies, with a global formulation designed for fault-tolerant architectures and a sequential formulation tailored to near-term devices, and validate the approach through numerical simulations of proton-hydrogen charge-transfer dynamics, a prototypical time-dependent quantum chemistry problem. This work establishes a systematic pathway from quantum-classical hybrid variational quantum algorithms to full-quantum solvers for general time-dependent Hamiltonians, particularly those whose dynamics admit compact variational descriptions, opening a route toward full quantum computational advantages in time-dependent simulations.

Collecting everyday speech data for prosodic analysis is challenging due to the confounding of prosody and semantics, privacy constraints, and participant compliance. We introduce and empirically evaluate a content-controlled, privacy-first smartphone protocol that uses scripted read-aloud sentences to standardize lexical content (including prompt valence) while capturing natural variation in prosodic delivery. The protocol performs on-device prosodic feature extraction, deletes raw audio immediately, and transmits only derived features for analysis. We deployed the protocol in a large study (N = 560; 9,877 recordings), evaluated compliance and data quality, and conducted diagnostic prediction tasks on the extracted features, predicting speaker sex and concurrently reported momentary affective states (valence, arousal). We discuss implications and directions for advancing and deploying the protocol.

In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities involving operator monotone functions and matrix means for the $q$-numerical radius of sectorial matrices are obtained.

Reliable and resilient communication is essential for disaster recovery and emergency response, yet terrestrial infrastructure often fails during large-scale natural disasters. This paper proposes a High-Altitude Platform Station (HAPS) and Reconfigurable Intelligent Surfaces (RIS)-assisted Internet of Things (IoT) communication system to restore connectivity in disaster-affected areas. Distributed IoT sensors collect critical environmental data and forward it to nearby gateways via short-range links, while the HAPS-RIS system provides backhaul to these gateways. To overcome the severe double path loss of passive RIS at high altitudes, we propose a dynamically adjustable sub-connected active RIS architecture that can reconfigure the number of elements connected to each power amplifier through switching mechanisms. Simulation results demonstrate substantial gains in downlink and uplink data rates, as well as system energy efficiency, compared with conventional passive RIS schemes. Moreover, a 1 dB increase in ground-station transmit power yields approximately 20-30 Mbps improvement in gateway data rates. These findings confirm that HAPS-RIS technology offers an effective and energy-efficient approach for resilient IoT backhaul in 6G non-terrestrial networks, particularly in line-of-sight (LoS)-dominant HAPS-ground backhaul scenarios.

Baryon number violation is our most sensitive probe of physics beyond the Standard Model. Its realization through heavy new particles can be conveniently encoded in higher-dimensional operators that allow for model-agnostic analyses. The unparalleled sensitivity of nuclear decays to baryon number violation makes it possible to probe effective operators of very high mass dimension, far beyond the commonly discussed dimension-six operators. To facilitate studies of this ginormous and scarcely explored testable operator landscape we provide the exhaustive set of tree-level UV completions consisting of scalars, fermions, and vectors for non-derivative baryon-number-violating operators in this Standard Model effective field theory up to mass dimension 15, which corresponds roughly to the border of sensitivity. In addition to the known Standard Model fields we also include right-handed neutrinos in our operators. Our public code can be used to UV-complete any non-derivative operator and match it onto an operator basis.

Physical selectors (lasers choosing a mode, Ising machines settling on a ground state, condensates occupying a spin state) produce high-dimensional signatures at the moment of decision: full field amplitudes, multimode interference patterns, or scattering responses. These signatures are richer than the winner's index, yet they are routinely discarded. We show that when the signatures are repeatable across trials (stereotyped) and linearly independent across routes, a single linear decoder compiled from calibration data maps them to arbitrary payloads, merging selection and memory access into one event and eliminating the fetch that dominates latency and energy in sparse routing architectures. The construction requires one SVD of measured device responses, which certifies capability and bounds worst-case error for any downstream payload before the task is chosen. Runtime error separates into two independently diagnosable channels, decoding fidelity (controlled by dictionary conditioning $σ_{\min}(Φ)$) and routing reliability (controlled by the margin-to-noise ratio $Δ/T_{\mathrm{eff}}$), each with a distinct physical origin and targeted remedy. We derive the full error decomposition, give Ising-machine selector constructions, and validate the predicted scalings on synthetic speckle-signature simulations across three measurement modalities. No hardware demonstration exists; we provide a falsifiable four-step experimental protocol specifying what a first experiment must measure. Whether real device signatures satisfy stereotypy is the central open question.

We study $(α,β)$-spanners for weighted graphs. We propose a simple greedy completion procedure which starts from a sparse initial graph, and repeatedly fixes pairs of vertices with a bad stretch, generalizing Kunedsen's additive completion [SWAT '14]. As an application, we construct $(k,k-1)$-spanners for weighted graphs of size $\tilde{O}(n^{1+1/k})$, which were previously unknown.

Low-ionisation state (LIS) absorption lines, such as SiII 1526, are widely used to trace the properties of the interstellar medium (ISM) in galaxies. These lines provide crucial insights into galaxy evolution, including feedback mechanisms, metal enrichment, and the escape fraction of ionising photons ($f_{\rm{esc}}$). We expand our understanding of LIS absorption lines as diagnostic tools for ISM properties and $f_{\rm{esc}}$. Using the SPHINX20 cosmological radiation-hydrodynamics simulation, we generated a comprehensive synthetic dataset of LIS absorption lines and tested their predictive power for $f_{\rm{esc}}$ in star-forming galaxies. Synthetic SiII 1260 and SiII 1526 lines were computed with the radiative transfer code RASCAS, incorporating resonant scattering of photons, fluorescent emission, and interactions with dust grains. The simulated data enhance the public SPHINX20 dataset with high-resolution LIS lines for the full 1380 galaxies and ten viewing angles per galaxy. We analysed correlations between line properties, dust attenuation, and $f_{\rm{esc}}$. We also tested our predictions on observed data using the LzLCS and CLASSY surveys. We found a strong correlation between the dust-corrected residual flux of SiII 1526, $\tilde{R} \equiv \rm{R_{flux}^{1526}} \cdot 10^{-0.4A_{1500}}$, and $f_{\rm{esc}}$. We found $f_{\rm{esc}} \approx 1.041\tilde{R}^{1.887} - 0.002$, with small error bars. When we applied observational conditions, the error increased, but the escape fraction was still well recovered. We show by applying common tools for fitting the spectral energy distribution to our mock data that the inferred dust attenuation is often far from the correct value, with an underestimation of the attenuation when the effect of dust is strongest. Our results demonstrate that the residual flux of SiII 1526 is a powerful predictor of the escape fraction of ionising photons.

Functional materials with high electrical conductivity and optical transmittance are vital for thermally tunable free-space photonic systems. Conventional transparent conductors such as graphene and indium tin oxide are limited by high contact resistance, poor mechanical stability, or complex fabrication. Ultra-thin metals, such as pure silver, have also been explored with limited success due to thermal instability and dewetting. Here, we propose an ultra-thin Al-doped Ag film to tackle these challenges. Aluminum promotes heterogeneous nucleation of silver, enabling the formation of continuous, smooth films that are thermally stable at reduced thicknesses while maintaining excellent electrical conductivity and transparency. We find that a 12 nm Al-doped Ag film exhibits an average transmittance of 80% across the visible range with a sheet resistance of 8.3$\pm$1.16 $Ω$cm$^2$. Moreover, on-chip Al-doped Ag microheaters exhibit uniform, rapid thermal response, and stable electrical performance, maintaining functionality for over $10^7$ ON and OFF cycles at temperatures below 400$°$C. Furthermore, as a benchmark, we demonstrate reversible phase-change switching in Ge$_2$Sb$_2$Se$_4$Te (GSST) and VO$_2$. 30$\times$30 $μ$m$^2$ GSST cells exhibited complete crystallization and amorphization under 2.2 V - 200 ms and 4.1V - 50$μ$s pulses, respectively, resulting in a 40% transmission contrast at 780 nm and a tenfold improvement in power consumption compared to similar devices. Additionally, VO$_2$ films displayed reversible insulator-to-metal transitions near 65°C with reflectance and transmittance modulation in the visible and the near-infrared at frequencies up to 25 Hz with room for improvement. These results establish Al-doped Ag as a robust transparent metallic heater for integration in dynamic metasurfaces, optical coatings, and more.

Several dozen binary ultracool and brown dwarf systems have been identified to date. These systems represent valuable probes of star and planet formation at the lowest mass scales. To date, the study of these ultracool binaries has been constrained to the non-interacting case. In this paper, we investigate the dynamics, stability, and evolution of mass transferring ultracool binaries using numerical simulations with accepted equations of state for brown dwarfs. We find that there exists a donor mass inversion, above which the donor dwarf is more massive than the accretor, but below which the accretor is more massive than the donor. Below the hydrogen burning limit, objects with mass ratios $q \sim 1$ are unstable, but slight deviations from this mass ratio are stable at the onset of mass transfer and remain stable throughout extended periods. We compute theoretical mass transfer rates using several angular momentum loss prescriptions and predict lifespans of $\sim 100$ Myrs. We predict that all mass transferring ultracool binaries are tidally locked and possess orbital periods ranging from just under $1$ hour to $3.5$ hours. We find that mass transfer proceeds via direct impact onto the accretor forming a UV or optically bright hotspot on the surface of the accretor.

Substellar objects such as brown dwarfs and planets are generally expected to remain detached from their main-sequence host stars unless orbital decay or stellar expansion brings them into contact, leading to rapid engulfment and destruction. Such a fate is predicted for the Earth and other rocky planets in our solar system; however, in certain cases, theory also allows for stable long-lived mass transfer from a substellar object onto its main-sequence host, though such accretion has never been directly observed. Here we report the first direct observations of stable mass transfer from a substellar object onto a main-sequence star. In particular, we identify two binaries, ZTF J0440+2325 and ZTF J1444+4820, with orbital periods of just 87 and 67 minutes, respectively, in which a brown dwarf stably transfers mass onto an M dwarf companion. These systems demonstrate that the fate of some substellar objects is not rapid engulfment and destruction, but instead gradual consumption for potentially billions of years.

Neutron scattering experiments on the spin-triplet superconductor UTe$_2$ have established that the dominant low-energy magnetic response is along Brillouin zone boundaries, resembling the magnetic susceptibility of narrow-gap interband excitations. We report a study of the sensitivity of these excitations to magnetic field along the crystallographic $\hat{a}$-axis. Up to fields of $μ_0 H$=13 T, the maximal inelastic neutron spectral weight increases in energy transfer, with a pronounced increase in $d\hbarω_{peak}/dH$ near $μ_0 H$=7 T. This behavior parallels the field and temperature dependent features of the electrical resistivity that are associated with Kondo hybridization. Our measurements suggest that $\hat{a}$-axis fields near $μ_0 H$=7~T induce a change in the hybridization between heavy $f$-electrons and the bare conduction band.

The symmetric $p$-Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this work, second-order differentiability properties of solutions to the symmetric $p$-Laplace system are established. They are formulated as maximal Sobolev regularity of the nonlinear stress tensor for locally square integrable right-hand sides.

We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an external drive. We analyze the quantum dynamics of a driven open system described by a time-dependent spin-boson Hamiltonian modeling a particle in a metastable double-well potential with controllable asymmetry. We explore how the work provided by the dynamic potential is related to the transition probability between the two ground states of the double well. These studies motivate further investigations of the driven spin-boson model toward an understanding of the system's evolution and its thermodynamic implications.

Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical framework for inverse optimization in parametric convex models. We first establish that non-identifiability is the generic case: even with normalization and multiple observations, the parameter set compatible with data is generically multi-dimensional, and regularization does not resolve this. We derive necessary and sufficient conditions for identifiability. Motivated by these negative results, we introduce the Inverse Learning (IL) framework, which shifts the inferential target from the unknown parameter to the latent optimal solution, achieving a complexity reduction that is independent of the number of observations. IL explicitly characterizes the full set of compatible parameters rather than returning an arbitrary element. To address the tension between observational fidelity and constraint adherence, we formalize the Observation-Constraint Tradeoff and develop Goal-Integrated Inverse Learning models that enable structured navigation of this spectrum with guaranteed monotonicity. Numerical experiments demonstrate superior solution accuracy, higher parameter recovery rates, and significant computational speedups. We apply the framework to personalized dietary recommendations using NHANES data, proof-of-concept demonstrating improved glycemic control in a prospective feasibility study.

We present an efficient Monte Carlo algorithm for the simulation of the two-dimensional Random Field Ising Model (RFIM). The method combines the event-driven, rejection-free character of the Bortz Kalos-Lebowitz (BKL) algorithm with Glauber transition probabilities, introducing hierarchical probabilistic counters to perform spin selection in O(log N) operations. This enables efficient sampling of the system's dynamics, especially in the low-temperature and low-disorder regime, where traditional Metropolis updates suffer from critical slowing down. Furthermore, this approach allows a proper dynamical simulation of the Ising system's behavior even in the presence of a Random Field (RF), unlike the BKL method. RFIM simulations with Gaussian field distributions reproduce the expected reduction of the pseudo-critical temperature with increasing disorder. Benchmarking shows speedups exceeding two orders of magnitude compared to the Metropolis algorithm in the low-temperature regime. The proposed method provides an efficient and dynamically faithful tool for studying both equilibrium and non-equilibrium phenomena in disordered spin systems.

Randomized experiments (often known as "A/B tests") are widely used to evaluate product and service innovations. We study how to allocate limited experimentation resources across M concurrent experiments in an experiment-rich regime. Existing work on allocation has predominantly focused on minimizing the worst-case mean squared error (MSE) of estimated treatment effects, which favors experiments with larger (and typically unknown) outcome variance. While appropriate for controlling estimation accuracy, this objective does not directly capture a common managerial priority in screening stages: detecting practically meaningful treatment effects with high probability. Motivated by this, we consider the objective of minimizing the worst-case Type II error across all experiments. When the standard deviations are known, we characterize the power-optimal allocation and show that MSE-based allocations can be highly inefficient for detection, even though the two objectives align asymptotically. When the standard deviations are unknown and must be learned from pilot data, we show that a naive plug-in approach, treating pilot standard deviations as truth, can suffer substantial power loss. We propose inflating pilot estimates via correction factors and develop three optimization-based frameworks for selecting them, each reflecting a different risk criterion with distinct managerial implications. Although the resulting stochastic programs are computationally challenging at scale, we derive tractable surrogate reformulations inspired by robust optimization and establish favorable theoretical properties. We further propose Surrogate-S, a fully data-dependent and implementable procedure that computes correction factors using only pilot variance estimates and achieves near-oracle performance in numerical experiments.

In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. This arises naturally when outcomes are difficult to characterize. For instance, if measurements yield smells, it may be impractical to process them individually, while still being reasonable to judge whether two smells are identical or not. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator inequalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural properties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.

A Neumaier graph is an edge-regular graph with a regular clique. Such a graph is said to have parameters $(v,k,λ;e,s)$ if it is a $k$-regular graph on $v$ vertices having a clique of size $s$ such that every edge is contained in $λ$ triangles and every vertex outside $C$ is adjacent with exactly $e$ vertices inside $C$. It was an open problem whether Neumaier graphs can exist with exactly five eigenvalues. In the present paper, we describe a family of Neumaier graphs, and show that inside this family there are 1063 nonisomorphic Neumaier graphs with parameters $(v,k,λ;e,s)=(48,14,2;1,4)$, among which 25 have exactly five eigenvalues. These 1063 graphs are also the first known examples of Neumaier graphs for the mentioned parameters.

Microscopy combined with local spectroscopy is widely used to correlate nanoscale structure with functional properties in materials, but conventional measurements rely heavily on human-selected sampling locations and predefined targets, limiting dataset diversity and the potential for discovery. Here, we present a framework that integrates autonomous microscopy with a dual-novelty deep kernel learning (DN-DKL) for adaptive data acquisition and a dual variational autoencoder (VAE) for representation learning. DN-DKL actively guides the microscopy toward structurally and spectroscopically novel regions, enabling efficient collection of large spectral datasets. Dual-VAE embeds local structure and spectroscopic responses into a shared latent manifold that serves as a structure-property relationship map. We applied this framework for the investigation of halide perovskite films using conductive atomic force microscopy. The results reveal distinct hysteresis behaviors that are linked to specific nanoscale structural motifs, including grain boundary junction points that show hysteresis under different bias conditions and asymmetric grain boundaries that suppress charge transport. This framework establishes a general strategy that leverages the complementary strengths of self-driving microscopy, machine learning, and human expertise to accelerate scientific discovery in functional materials.

We study stochastic resetting of a probe particle in a viscoelastic environment where only the probe is reset while the medium retains memory of its past dynamics. Using a minimal model with finite correlation time, we analyze the competition between the resetting timescale and the viscoelastic relaxation timescale. This interplay leads to nonequilibrium steady states that differ qualitatively from those of Markovian Brownian motion with resetting. In particular, strong memory effects produce stationary position distributions with non-exponential tails. For instantaneous resets, we derive the limiting steady-state distributions analytically and compute exactly the time dependent leading non-vanishing moments. We also investigate non-instantaneous resetting via constant-velocity return protocols. In contrast to overdamped Brownian motion, where steady-state fluctuations are independent of the return dynamics, we find that in a viscoelastic medium the fluctuations depend on the reset velocity. This protocol dependence arises from the finite memory of the environment and highlights the role of environmental correlations in resetting-induced steady states.

In this paper we expand the concept of biological speciation by symmetry breaking of Golubitsky and Stewart to the case of three clades in which N populations following the same dynamical laws can separate. The underlying differential equation is based on a fifth order polynomial of a trait variable with first or second order coupling. We present some general strategies to find all possible steady states and their stabilities. Numerical data are given for a specific system. We show the locations of three-clade distributions in dependence on the coupling and an environmental parameter. The results show a decrease of the number of stable states with higher coupling and a higher probability of ending in a three-clade state for larger N. Limits and potentials of the approach if zero roots for the trait variable occur are discussed.

Swift J1727.8$-$1613 is a newly discovered transient low-mass X-ray binary harbouring a stellar-mass ($\sim 10M_\odot$) black hole. We present state-resolved VLT/X-Shooter optical spectroscopy of its 2023 outburst, sampling the luminous hard-to-soft and late soft-to-hard transitions. During the onset of the brightest radio flare, He\,\textsc{ii} flux rises relative to adjacent epochs, with reduced peak-to-peak separation and full-width-half-maximum, consistent with enhanced irradiation shifting line emissivity to larger radii. We detect no contemporaneous change in the line base tracing the inner disc. The most dramatic change occurs at the onset of the dim-hard state, when strong, broad (higher-order) Balmer lines appear in absorption, and He\,\textsc{ii} remains in emission, but becomes highly asymmetric. While the hardening of the X-ray spectrum likely promotes the reappearance of an underlying disc photosphere, the kinematic alignment between the Balmer absorption ($v_w\sim-750\,\mathrm{km\,s^{-1}}$) and the suppressed blue peak of He\,\textsc{ii} suggests a unified origin in a massive, cool ($T\lesssim10^{4}\,\mathrm{K}$) accretion disc wind. Radiative transfer simulations demonstrate that such asymmetric He\,\textsc{ii} profiles are naturally produced in a rotating and accelerating outflow. Using the Sobolev approximation, we estimate the wind mass-loss rate to be $\dot{M}_w\gtrsim10^{-9}\,M_\odot\,\mathrm{yr^{-1}}$, comparable to the instantaneous accretion rate and a significant fraction of the secular mass-transfer rate from the donor. If persistent at quiescent-level X-ray luminosities, this outflow could strongly impact the system's secular evolution.