Many essential biological functions, such as breathing and locomotion, rely on the coordination of robust and adaptable rhythmic patterns, governed by specific network architectures known as connectomes. Rhythmic adaptation is often linked to slow structural modifications of the connectome through synaptic plasticity, but such mechanisms are too slow to support rapid, localized rhythmic transitions. Here, we propose a neuromodulation-based control architecture for dynamically reconfiguring rhythmic activity in networks with fixed connectivity. The key control challenge is to achieve reliable rhythm switching despite neuronal degeneracy, a form of structured variability where widely different parameter combinations produce similar functional output. Using equivariant bifurcation theory, we derive necessary symmetry conditions on the neuromodulatory projection topology for the existence of target gaits. We then show that an adaptive neuromodulation controller, operating in a low-dimensional feedback gain space, robustly enforces gait transitions in conductance-based neuron models despite large parametric variability. The framework is validated in simulation on a quadrupedal gait control problem, demonstrating reliable gallop-to-trot transitions across 200 degenerate networks with up to fivefold conductance variability.

Assume $n=2m\geq 2$ and let $F(x)=x^{d_1}+x^{d_2}$ be a binomial vectorial function over $\F_{2^n}$ possessing the maximal number (i.e. $2^n-2^m$) of bent components. Suppose the $2$-adic Hamming weights $\wt_2(d_1)$ and $\wt_2(d_2)$ are both at most $2$, we prove that $F(x)$ is affine equivalent to either $x^{2^m+1}$ or $x^{2^i}(x+x^{2^m})$, provided that \[ \ell(n):=\min_{γ:~\F_2(γ)=\F_{2^n}} \dim_{\F_2}\F_2[σ]γ>m, \] where $σ$ is the Frobenius $(x\mapsto x^2)$ on $\F_{2^n}$, and $\gcd(d_1,d_2,2^m-1)>1$. Under this condition, we also establish two bounds on the nonlinearity and the differential uniformity of $F$ by means of the cardinality of its image set.

Estimating generation costs from observed electricity market data is essential for market simulation, strategic bidding, and system planning. To that end, we model the relationship between generation costs and production schedules with a latent variable model. Estimating generation costs from observed schedules is then formulated as Bayesian inference. A prior distribution encodes an initial belief on parameters, and the inference consists of updating the belief with the posterior distribution given observations. We use balanced neural posterior estimation (BNPE) to learn this posterior. Validation on the IEEE RTS-96 test system shows that marginal costs are recovered with narrow credible intervals, while start-up costs remain largely unidentifiable from schedules alone. The method is benchmarked against an inverse-optimization algorithm that exhibits larger parameter errors without uncertainty quantification.

Molecular communication (MC) is a communication paradigm in which information is conveyed through the controlled release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside the human body. In this environment, the cardiovascular system ( CVS) acts as the physical channel, which forms a closed-loop network where particle transport is mainly governed by the combined effects of diffusion and flow. Despite the fact that physiological flows in many parts of the human body are inherently pulsatile due to the cardiac cycle, most existing models for dispersive closed-loop MC channels assume a constant flow velocity. In this paper, we present a time-variant one-dimensional (1D ) channel model for dispersive closed-loop MC systems with pulsatile flow. We derive an analytical expression for the channel impulse response (CIR ), which follows a wrapped Normal distribution with time-variant mean and variance. The obtained model reveals the cyclostationary nature of the channel and quantifies the influence of pulsation on the temporal concentration profile compared to steady-flow systems. Finally, the model is validated by three-dimensional ( 3D ) particle-based simulations (PBS s), showing excellent agreement and enabling an efficient analytical characterization of the channel.

Integrated sensing and communication (ISAC) is a key enabler of 6G, supporting environment-aware services. A fundamental sensing task in this setting is reliable multi-target detection and tracking. This paper proposes a temporal graph neural network (TGNN)-based tracking method that exploits delay and Doppler information from the wireless channel. The delay-Doppler map is modeled as a sequence of graphs, and tracking is formulated as a temporal node classification problem, enabling joint clustering and data association of dynamic targets. Using ray-tracing-based channel outputs as ground truth, the method is evaluated across multiple scenes with varying target positions, velocities, and trajectories and is compared with a Kalman filter baseline. Results demonstrate reduced normalized mean squared error (NMSE) in delay and Doppler, leading to more accurate multi-target tracking.

Chirality plays a crucial role in a broad range of processes including light-matter interactions in physics, chemistry and biology, which opens up new applications in nanophotonics, quantum technologies and photochemistry. Quantum tunnelling provides a promising mechanism for light generation at the nanoscale, however the realisation of chiral light emission has remained elusive. Here, by integrating tunnel junctions with chiral plasmonic nanohelicoids, we achieve nanoscale generation of chiral light at a single-particle level. The tunnelling-driven resonant excitation of chiral dipolar modes of the nanohelicoids results in emission of a vortex light beam possessing both spin angular momentum with handedness selectivity of over 0.8 and its orbital counterpart, equal in magnitude and opposite in sign. The developed approach offers a new means for sculpturing photon spin generation at the nanoscale, highlighting its potential for next-generation optical components in display and AR/VR applications, as well as quantum information processing and photochemistry.

We initiate the study of asynchronous quantum distributed systems, focusing on the case of implementing atomic quantum global operations that can be decomposed into a collection of local operations on the components of the system. A simple example of such an operation is a quantum snapshot in which the whole system is instantaneously measured. Based on the classical snapshot algorithm of Chandy and Lamport, we design a quantum distributed algorithm to implement such decomposable global operations, which we call the QGO Algorithm. The analysis of our algorithm shows that arguments based on Lamport's computational causality remain valid in the quantum world, even though, due to entanglement, causality is not manifest from the standard description of the system in terms of a (global) quantum state. Our other contributions include a formal model of quantum distributed computing, and a formal specification for the desired behavior of a global operation, which may be of interest even in classical settings (such as in the setting of randomized algorithms).

Ensuring Large Language Model (LLM) safety is crucial, yet the lack of a clear understanding about safety mechanisms hinders the development of precise and reliable methodologies for safety intervention across diverse tasks. To better understand and control LLM safety, we propose the Expected Safety Impact (ESI) framework for quantifying how different parameters affect LLM safety. Based on ESI, we reveal distinct safety-critical patterns across different LLM architectures: In dense LLMs, many safety-critical parameters are located in value matrices (V) and MLPs in middle layers, whereas in Mixture-of-Experts (MoE) models, they shift to the late-layer MLPs. Leveraging ESI, we further introduce two targeted intervention paradigms for safety enhancement and preservation, i.e., Safety Enhancement Tuning (SET) and Safety Preserving Adaptation (SPA). SET can align unsafe LLMs by updating only a few safety-critical parameters, effectively enhancing safety while preserving original performance. SPA safeguards well-aligned LLMs during capability-oriented intervention (e.g., instruction tuning) by preventing disruption of safety-critical weights, allowing the LLM to acquire new abilities and maintain safety capabilities. Extensive evaluations on different LLMs demonstrate that SET can reduce the attack success rates of unaligned LLMs by over 50% with only a 100-iteration update on 1% of model weights. SPA can limit the safety degradation of aligned LLMs within 1% after a 1,000-iteration instruction fine-tuning on different tasks. Our code is available at: https://github.com/ZJU-LLM-Safety/SafeWeights-ACL.

Dock-based bike-sharing systems exhibit spatial imbalances between bicycle supply and user demand, often addressed through overnight truck-based rebalancing. This work studies static overnight rebalancing under demand uncertainty modeled as a tri-objective optimization problem. The objectives minimize total travel distance, expected unmet demand, and a robustness-oriented unmet demand measure over high-demand scenarios. Route plans are evaluated via a recourse simulation that enforces truck loads and station capacity constraints across multiple demand realizations. The robustness objective supports selecting plans that reduce peak-demand service degradation. Trade-off solutions are approximated with Non-dominated Sorting Genetic Algorithm II using a permutation--partition encoding and domain-specific relocation operators, including a biased best-improvement move for station relocation. Experiments on the real Barcelona Bicing system with 460 stations show well-distributed Pareto sets and substantial contributions to the reference non-dominated set. Greedy constructive baselines mainly yield extreme solutions and are often dominated.

We formulate operating-system vulnerability discovery as a \emph{repeated Bayesian Stackelberg search game} in which a Large Reasoning Model (LRM) orchestrator allocates analysis budget across kernel files, functions, and attack paths while external verifiers -- static analyzers, fuzzers, and sanitizers -- provide evidence. At each round, the orchestrator selects a target component, an analysis method, and a time budget; observes tool outputs; updates Bayesian beliefs over latent vulnerability states; and re-solves the game to minimize the strategic attacker's expected payoff. We introduce \textsc{VCAO} (\textbf{V}erifier-\textbf{C}entered \textbf{A}gentic \textbf{O}rchestration), a six-layer architecture comprising surface mapping, intra-kernel attack-graph construction, game-theoretic file/function ranking, parallel executor agents, cascaded verification, and a safety governor. Our DOBSS-derived MILP allocates budget optimally across heterogeneous analysis tools under resource constraints, with formal $\tilde{O}(\sqrt{T})$ regret bounds from online Stackelberg learning. Experiments on five Linux kernel subsystems -- replaying 847 historical CVEs and running live discovery on upstream snapshots -- show that \textsc{VCAO} discovers $2.7\times$ more validated vulnerabilities per unit budget than coverage-only fuzzing, $1.9\times$ more than static-analysis-only baselines, and $1.4\times$ more than non-game-theoretic multi-agent pipelines, while reducing false-positive rates reaching human reviewers by 68\%. We release our simulation framework, synthetic attack-graph generator, and evaluation harness as open-source artifacts.

Artificial Intelligence (AI)-assisted coding environments operate within finite context windows of 128,000-1,000,000 tokens (as of early 2026), yet existing tools offer limited support for monitoring and optimizing token consumption. As developers open multiple files, model attention becomes diluted and Application Programming Interface (API) costs increase in proportion to input and output as conversation length grows. Tokalator is an open-source context-engineering toolkit that includes a VS Code extension with real-time budget monitoring and 11 slash commands; nine web-based calculators for Cobb-Douglas quality modeling, caching break-even analysis, and $O(T^2)$ conversation cost proofs; a community catalog of agents, prompts, and instruction files; an MCP server and Command Line Interface (CLI); a Python econometrics API; and a PostgreSQL-backed usage tracker. The system supports 17 Large Language Models (LLMs) across three providers (Anthropic, OpenAI, Google) and is validated by 124 unit tests. An initial deployment on the Visual Studio Marketplace recorded 313 acquisitions with a 206.02\% conversion rate as of v3.1.3. A structured survey of 50 developers across three community sessions indicated that instruction-file injection and low-relevance open tabs are among the primary invisible budget consumers in typical AI-assisted development sessions.

In this paper, we consider an image coding process consisting of the following four steps: a direct transformation, a direct quantization, an inverse quantization, and an inverse transformation, where Hadamard transforms are used for the transformation steps and a dead-zone quantizer is used for the quantization. The aim of this paper is to provide a theoretical tool for analyzing this process. We discuss error bounds for this process and bounds on the largest absolute value that the components of the result can attain. In order to obtain these bounds, we use methods of linear algebra and properties of Hadamard matrices. The obtained formulae depend on the size of the matrices, the parameters of the quantizer and the dequantizer, and a bound on the source values. Knowing the error bounds helps control the trade-off between compression efficiency and output quality. Knowing the bounds on the largest absolute value helps decide how many bits are needed to store the result. In addition, we demonstrate a connection between the norm $\|\mathbf{H}\|_{\infty, 1}$ of a Hadamard matrix $\mathbf{H}$ and the maximal excess $σ([\mathbf{H}])$ of the equivalence class containing $\mathbf{H}$.

We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and derive the corresponding reduced observables, brackets, and equations of motion, yielding a Lie--Poisson reduction by a subgroup for field theories. We also address the reconstruction problem, characterizing reconstruction in terms of the flatness of an associated connection. Several examples, including the heavy top, molecular strands with broken symmetry, and affine principal bundles, illustrate the general framework.

The aim of this chapter, focused on relativistic mean-field models and part of the Encyclopedia of Nuclear Physics, is to provide an introductory, self-contained discussion accessible to a broad audience, including advanced undergraduate students. The chapter surveys the fundamental ideas, assumptions, and theoretical framework underlying relativistic mean-field models, and illustrates their wide range of applications across nuclear science. Particular emphasis is placed on the central role that these models play in the construction of equations of state for strongly interacting matter, as well as on the intimate connections between nuclear experiments, astrophysical observations, and theoretical modeling. In this context, relativistic mean-field theory is shown to provide a unified description of bulk nuclear properties and dense neutron-rich matter, enabling the interpretation of the remarkable structural and observational properties of neutron stars in the emerging era of multi-messenger astronomy.

We study complete $3$-manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R}^3$, and that an open handlebody admitting such a metric must have genus at most $1$. The proof uses exhaustions by level sets of harmonic functions and refined average gradient estimates.

The so-called JKO scheme, named after Jordan, Kinderlehrer and Otto, provides a variational way to construct discrete time approximations of certain partial differential equations (PDEs) appearing as gradient flows in the space of probability measures equipped with the Wasserstein metric. The method consists of an implicit Euler scheme, which can be implemented numerically. Yet, in practice, evaluating the Wasserstein distance can be numerically expensive. To address this problem, a common strategy introduced by Peyré in 2015 and which has been shown to produce faster computations, is to replace the Wasserstein distance with its entropic regularization, also known as the Schrödinger cost. In 2026, the first author, Hraivoronska and Santambrogio, proved that if the regularization parameter $\varepsilon$ is proportional to the time step $τ$, that is, $\varepsilon = ατ$ for some $α> 0$, then as $τ\to 0$, this change results in adding to the limiting PDE the additional linear diffusion term $\fracα{2} Δρ$. Our goal in this article is to provide a convergence rate under convexity assumptions between the entropic JKO scheme and the solution of the initial PDE as both $α$ and $τ$ tend to zero. This will appear as a consequence of a new bound between the classical and entropic JKO schemes.

This paper presents SPIROS (Streamlined, Precise, Intuitive, and Rapid Optical Simulator), a dedicated optical simulation tool developed for the design and analysis of particle physics detectors. Unlike general-purpose frameworks such as GEANT4, SPIROS offers a lightweight simulation engine and a user-friendly interface optimized for optical processes, including scintillation, Cherenkov emission, and photon transport with reflection, refraction, scattering, absorption, and detection. Detector geometries can be directly imported from 3D CAD models, and all configurations including materials, surfaces, sources, and sensors are specified via a single human-readable input file. Validation against GEANT4 shows excellent agreement in photon generation and propagation behaviors, while benchmark tests demonstrate that SPIROS runs more than two times faster for typical detector configurations. The software has already been applied to multiple neutrino experiments, including T2K, NINJA, and AXEL, for detector design, performance studies, and optimization. SPIROS is open-source and freely available at https://github.com/tkikawa/spiros.

We show how to construct unitary dual $2$-cocycles for a class of semidirect products that exhibit many similarities with the affine group ${\rm Aff}(V)=\GL(V)\ltimes V$ of a finite dimensional vector space over a local skew field. The primary source of examples comes from Lie groups whose Lie algebras are Frobenius seaweeds. The construction builds on our earlier results and relies heavily on representation theory and an associated quantization procedure of Kohn--Nirenberg type. On the technical side, the key point is the observation that any semidirect product $G=H\ltimes V$ in our class can be presented as a double crossed product $G=P\bowtie N$ with respect to which the unique square-integrable irreducible representation of $G$ takes a particularly nice form. The Kohn--Nirenberg quantization that we construct is intimately related to a scalar Fourier transform $\CF\colon L^2(N)\to L^2(P)$ intertwining the left regular representations of $P$ and $N$ with representations defined by the dressing transformations.

We study the design of an offloaded model predictive control (MPC) operating over a lossy communication channel. We introduce a controller design that utilizes two complementary bandwidth-reduction methods. The first method is a multi-horizon MPC formulation that decreases the number of optimization variables, and therefore the size of transmitted input trajectories. The second method is a communication-rate reduction mechanism that lowers the frequency of packet transmissions. We derive theoretical guarantees on recursive feasibility and constraint satisfaction under minimal assumptions on packet loss, and we establish reference-tracking performance for the rate-reduction strategy. The proposed methods are validated using a hardware-in-the-loop setup with a real 5G network, demonstrating simultaneous improvements in bandwidth efficiency and computational load.

Compact, low-noise coherent light sources in the visible remain challenging due to limited gain platforms and inefficient pumping. We report a new route to visible microlasing based on direct, one-photon blue pumping and an amorphous fluoride gain material platform. Dysprosium doped fluoride microspheres are fabricated via plasma-torch-induced, pressureless amorphization of single crystals, enabling compositions beyond conventional glass-forming limits while ensuring ultrasmooth morphology, low phonon energy, and homogeneous dopant distribution. We demonstrate the first fiber-coupled whispering-gallery-mode lasing from an amorphous fluoride microsphere in the yellow (573 nm), with an ultralow threshold of $190 μ$W despite spin-forbidden Dy$^{3+}$ transitions. Lasing is evidenced by characteristic light-light curve indicating a low spontaneous emission factor, narrow-linewidth emission, and relaxation oscillations yielding a loaded quality factor of $Q = 3.5 \times 10^6$. This platform is readily extendable to other rare-earth emitters, enabling entire visible spectral coverage beyond the limitations of upconversion pumping, with prospects for color-tunable and white-light emission. Finally, fiber-based amplification of the WGM signal demonstrates a pathway toward compact, fiber-integrated visible microlasers with controllable noise and linewidth.

We report the discovery of six faint millisecond pulsars (MSPs) in the globular clusters NGC 6517 and NGC 7078 (M15) using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). These discoveries were enabled by stacking power spectra from multiple observations, a method that effectively boosts the signal-to-noise ratio of faint sources. In NGC 6517, we identified four new MSPs (NGC 6517S-V) with spin periods ranging from 3.68 to 6.02 ms and dispersion measures (DMs) between 182.45 and 182.85 pc cm^-3. In M15, two additional MSPs (M15M and M15N) were discovered, with spin periods of 4.83 and 9.28 ms, and DMs of 67.89 and 66.65 pc cm^-3, respectively. A phase-coherent timing solution has been obtained for M15M; however, sparse detection rates currently preclude phase-connected solutions for the remaining five pulsars. Current timing parameters suggest all six MSPs are isolated, which is consistent with the expected pulsar populations in core-collapsed globular clusters. Notably, pulsars M15N, NGC 6517U, and NGC 6517V eluded detection by standard frequency-domain searches (e.g., PRESTO-based) and the Fast Folding Algorithm, demonstrating that the stack search technique significantly enhances detection sensitivity to inherently faint pulsar signals.

We develop a local Lie theory for Lie algebras equipped with a quasi-norm, i.e., complete topological vector spaces satisfying a relaxed triangle inequality $\|x+y\|\le \Ctri(\|x\|+\|y\|)$ with $\Ctri\ge 1$. We prove that the Baker--Campbell--Hausdorff (BCH) series converges in a neighborhood of the origin, provided the quasi-norm admits a continuous Lie bracket with finite continuity constant $\Cbracket$. The proof relies on the Aoki--Rolewicz theorem to construct an equivalent $p$-norm satisfying $p$-subadditivity, enabling rigorous Cauchy-sequence arguments in the complete quasi-metric space $(E, d_p)$. This yields a well-defined local Lie group structure via the exponential map. We analyze the geometric deformation induced by the quasi-norm exponent $p\in(0,1]$, showing that it modifies metric properties while preserving the underlying Lie algebraic structure. Numerical estimates of BCH coefficients up to degree $20$, with coefficients defined precisely via Hall--Lyndon basis projection, demonstrate that classical combinatorial bounds are conservative in the presence of algebraic cancellations, allowing significantly larger practical convergence radii in structured algebras. Applications include weak Schatten ideals $\mathcal{L}_{p,\infty}(H)$ for $0<p<1$ and certain Hardy-space operator algebras. \smallskip\noindent\textbf{Remark on the convergence radius.} The Catalan-majorant method yields convergence for $\|x\|+\|y\| < 1/(4\Cbracket)$; the additional factor $\Ctri$ appearing in the combined constant $\Ctotal = \Ctri\Cbracket$ is an artefact of switching to the $p$-norm to establish Cauchyness of partial sums. When the quasi-norm itself is directly a $p$-norm ($\Ctri=1$), no such penalty arises and the radius reduces to $1/(4\Cbracket)$.

Let $f:\mathbb C\to \widehat{\mathbb C}=\mathbb C \cup\{\infty\}$ be a transcendental meromorphic function (possibly without any pole) with a single essential singularity, and that is chosen to be at $\infty$. The set of points $z\in\mathbb{\widehat{C}}$ such that the family of iterates $\{f^n\}_{n\geq 0}$ is defined and forms a normal family in a neighborhood of $z$ is known as the Fatou set of $f$. For a Fatou component $W$, let $W_j$ denote the Fatou component containing $f^j(W)$. A Fatou component $W$ is called wandering if $W_m\bigcap W_n=\emptyset$ for all $m \neq n$. A wandering domain $W$ of $f$ is called a Baker wandering domain, if each $W_n$ is bounded, multiply connected, and $W_n$ surrounds $0$ for all large $n$ and, dist$(W_n,0)\to\infty$ as $n\to\infty$. This paper surveys the current state of knowledge on Baker wandering domains. We revisit the first example of the Baker wandering domain followed by other examples. The influence of Baker wandering domain on the singular values and dynamics of the function is presented. We also discuss some classes of functions that do not possess any Baker wandering domain. Several problems are proposed throughout the article at relevant places.

An exact magnetic system over a closed manifold $M$ consists of a pair $(g,α)$, where $g$ is a Riemannian metric and $α$ is a 1-form encoding a magnetic field. In this context, we consider a generalization of the marked length rigidity conjecture: does the marked magnetic action spectrum of magnetic systems with Anosov magnetic flow determine the metric and the 1-form, up to a natural obstruction? In this article we answer this question in two settings: 1) locally for systems with close metrics and 1-forms and 2) for metrics in the same conformal class.

The T2K long-baseline neutrino oscillation experiment in Japan continues to lead the search for leptonic charge-parity violation while providing precision measurements of mixing and mass splitting parameters. Central to this programme is the mitigation of systematic uncertainties through the near detector complex, which provides high-statistics neutrino-nucleus interaction cross-section measurements across various targets. This contribution presents the latest T2K oscillation results, incorporating the first data with a gadolinium-loaded far detector, and highlights several recent cross-section measurements, including several world-first measurements of rare interaction channels. Together, these results demonstrate the vital synergy between interaction modelling and oscillation analysis in the search for charge-parity violation in the T2K-II era.

The integration of sonocatalysis with photocatalysis offers a powerful strategy for advanced wastewater treatment by overcoming rapid charge carrier recombination in conventional photocatalytic systems. Although these processes are often treated separately due to their distinct mechanisms, their combination creates a highly efficient synergistic system. In this study, we investigate the sonophotocatalytic degradation of methyl orange (MO) using Cu-doped LaFeO3 perovskite nanoparticles. The Cu doped catalyst demonstrated excellent performance, achieving a degradation rate of 0.0455 min-1 and complete removal of MO within 120 minutes under combined ultrasonic and light irradiation. A strong synergistic effect was observed, with a synergy index of approximately 10, highlighting the enhanced interaction between sonocatalysis and photocatalysis. The catalyst also exhibited good stability and reusability, maintaining high efficiency over four consecutive cycles. Mechanistic studies using scavenger experiments revealed that hydroxyl radicals and photogenerated holes are the main reactive species responsible for degradation. A plausible reaction pathway is proposed based on these findings. Overall, Cu doped LaFeO3 shows superior sonophotocatalytic activity compared to the undoped material, demonstrating the potential of synergistic sonophotocatalytic processes for efficient pollutant removal.

Whispering-gallery-mode (WGM) microsphere resonators have emerged as a versatile platform across various photonic applications. Despite significant progress, their performance at short wavelengths is fundamentally limited by scattering-induced optical losses that restrict achievable quality factors (Q-factor). Although surface roughness has long been recognised as the leading cause of these losses, its physical origin has remained unclear, with current understanding attributing it to unavoidable fabrication imperfections. Here, we show that thermally excited capillary waves are the fundamental source of scattering losses in microsphere cavities. Using high-resolution atomic force microscopy (AFM) combined with rigorous statistical analysis, we quantitatively identify the characteristic signatures of frozen capillary fluctuations at the sub-nanometre level. The experimentally extracted roughness parameters show close agreement with theoretical predictions based on capillary wave theory. These findings fundamentally revise the prevailing interpretation of surface scattering losses and establish thermodynamic fluctuations, rather than fabrication defects, as the limiting roughness mechanism. By identifying frozen capillary waves as the limiting factor, this work opens new pathways for engineering ultra-high-Q microsphere resonators through fabrication management strategies, particularly for visible- and ultraviolet-photonic applications where scattering losses are most severe.

The state space is a fundamental concept for describing the trajectory of a dynamic system. Depending on its form, it can highlight certain changes over time while ignoring others. This is particularly the case for the spaces associated with theoretical ecology models, notably the generalized Lotka-Volterra (gLV) model, which allows the modeling of interacting populations. The fixed-dimension state space classically used in gLV models does not account for the effective renewal of species through addition, removal, or mutation. To address this limitation, we propose a new variable-base state space, introduced in a previous study. This framework leads to a reformulation of the gLV model within the context of hybrid dynamical systems. To illustrate the approach, we apply the proposed model to the gut microbiota, particularly in the context of bacteriotherapy following antibiotic treatment.

High-precision predictions of nuclear properties are a central objective of ab initio nuclear structure theory. However, state-of-the-art many-body methods rely on truncated model spaces to render the nuclear many-body problem tractable, which remains a major source of theoretical error in computations of nuclear observables. In recent years, machine learning, and artificial neural network approaches in particular, have emerged as a powerful data-driven framework for learning convergence patterns directly from ab initio calculations and enabling precision extrapolations beyond the reach of conventional schemes. This review focuses on model-space extrapolation methods developed for the no-core shell model and related many-body methods. We discuss machine learning extrapolation frameworks in comparison to conventional methods and assess their performance for energy spectra, radii, and electromagnetic observables, with particular emphasis on achievable precision and uncertainty estimates through statistical and correlation-based strategies. These developments establish machine learning as an increasingly important component of the precision toolbox in ab initio nuclear theory, enhancing the reliability and predictive power of ab initio nuclear structure calculations.

The rapid expansion of remote work following the last pandemic has renewed interest in whether spatial decoupling of residence from workplace can contribute to rebalancing regional development across the European Union. This paper examines four interrelated dimensions of remote work-induced residential mobility using the R-MAP survey dataset, a large-scale cross-sectional survey of over 7,400 remote workers across Europe collected in 2024. First, the spatial direction of post-2020 relocations is analysed, revealing that mobility occurs overwhelmingly within the same urbanisation tier, with urban-to-urban moves accounting for 67% of all relocations. Counter-urban flows to- ward rural areas remain marginal at just 2% of moves, though their relative demograph- ic impact on small rural populations is non-trivial. Second, the motivational structure of relocation decisions is examined, showing that quality-of-life considerations dominate (cited by 78% of movers), followed by economic and housing factors (70%), while digital infrastructure ranks among the least cited reasons. Third, amenity preferences are compared across residential contexts, documenting striking convergence between urban and rural remote workers, with statistically significant differences emerging only for public transport and restaurant access. Fourth, logistic regression models reveal that remote work intensity is a consistent positive predictor of relocation probability, with a transition from 50% to fully remote work associated with a 6.5 percentage point in- crease in relocation likelihood. Age, education, and industry sector also shape mobility patterns. Overall, the findings suggest that remote work primarily stretches metropolitan systems and reinforces peri-urban zones rather than triggering large-scale redistribution toward structurally weaker peripheral regions.