We develop quantitative error estimates connecting microscopic fluctuation of interacting particle systems with the mobilities of their hydrodynamic limits. Focusing on the Symmetric Simple Exclusion Process and systems of independent Brownian particles, we provide explicit bounds for the discrepancy between the quadratic variation of fluctuation fields and the corresponding mobilities, in terms of time and spatial discretization parameters. In addition, we establish analogous error estimates for a class of fluctuating hydrodynamic stochastic PDEs with regularized coefficients. For stochastic PDEs with irregular square-root type coefficients, including Dean-Kawasaki type equations, we further identify the asymptotic behavior of the associated fluctuation structures within the framework of renormalized kinetic solutions. Our results provide quantitative insights into the relationship between microscopic fluctuation mechanisms and macroscopic mobilities, and contribute to a structured comparison between discrete particle systems and continuum fluctuating hydrodynamic descriptions.

Edge transport serves as a powerful probe of remarkable low-energy properties of fractional quantum Hall states, including the anyonic character of their excitations. Here, we develop a theory of fractional quantum Hall edges driven out of equilibrium, which is based on the Keldysh action for the bosonized chiral Luttinger liquid. With this non-equilibrium FQH bosonization framework, we first consider a single-mode Laughlin edge and analyze the full counting statistics of charge, the quasiparticle Green's functions, and tunneling transport properties through a quantum point contact, allowing for generic edge excitations. We then extend the formalism to multi-mode edges with inter-mode interactions, and explore, with focus on the $ν=4/3$ and $ν=2/3$ edges as paradigmatic examples, how interaction-induced fractionalization of anyons modifies the edge dynamics and the associated transport observables. While the full counting statistics probes the fractionalized charge of the excitations, the Green's functions and tunneling transport are governed by mutual braiding phases of fractionalized excitations and tunneling quasiparticles. We emphasize in particular the effect of interaction-induced fractionalization on the Fano factor $F$ and the differential Fano factor $F_d$, observables that can be measured experimentally. Our formalism, which provides a unified framework for non-equilibrium transport in FQH edges and Luttinger liquids, permits extracting anyonic braiding information from non-equilibrium edge-transport experiments, and paves the way to various extensions, including more involved experimental geometries and edge structures.

Prompt tuning has become a prominent strategy for enhancing the performance of Large Language Models (LLMs) on downstream tasks. Many IT enterprises now offer Prompt-Tuning-as-a-Service to fulfill the growing demand for prompt tuning LLMs on downstream tasks. Their primary objective is to satisfy users Service Level Objectives (SLOs) while reducing resource provisioning costs. Nevertheless, our characterization analysis for existing deep learning resource management systems reveals that they are insufficient to optimize these objectives for LLM prompt tuning workloads. In this paper, we introduce PromptTuner, an SLO-aware elastic system to optimize LLM prompt tuning. It contains two innovations. (1) We design a Prompt Bank to identify efficient initial prompts to expedite the convergence of prompt tuning. (2) We develop aWorkload Scheduler to enable fast resource allocation to reduce the SLO violation and resource costs. In our evaluation, PromptTuner reduces SLO violations by 4.0x and 7.9x, and lowers costs by 1.6x and 4.5x, compared to INFless and ElasticFlow respectively.

At muon colliders, muon decays naturally produce intense electrons and positrons with unique features, namely high energies, high repetition rates, and small intrinsic uncertainties, that are unavailable at existing accelerator facilities. We quantitatively study the feasibility of extracting such particles in two representative future muon collider designs, IMCC and $μ$TRISTAN. Using Monte Carlo simulations with the corresponding design parameters, we study the spatial, angular, and energy distributions of decay electrons and positrons in the curved sections of the collider ring. We find that typical deflections of $0.1-10~\mathrm{mrad}$ can be achieved even for high-energy electrons carrying large energy fractions ($\simeq 0.6 - 1.0$) of the muon beam energy, with the ring bending magnets (or magnets providing an equivalent field) effectively serving as a pre-septum magnet, that partially deflects the beam before the main septum magnet, suggesting that the extraction scheme could be practically feasible. Exploiting the distinct beam properties of IMCC and $μ$TRISTAN, we propose complementary search strategies, missing energy and momentum searches for dark matter at $μ$TRISTAN and visible-decay searches for axion-like particles and light scalars at IMCC, which probe parameter space beyond the reach of current and other proposed experiments.

The increasing popularity of microcontroller platforms like Arduino enables diverse end-user developers to participate in circuit prototyping. Traditionally, follow-along tutorials serve as an essential learning method for makers, and in fact, several prior toolkits leveraged this format as a way to engage new makers. However, literature and our formative study (N=12) show that makers have unique preferences regarding the construction of their circuits and idiosyncratic ways to assess and debug problems, which contrasts with the step-by-step instructional nature of tutorials and those systems leveraging this method. To address this mismatch, we present a prototyping platform that supports personalized circuit construction and debugging. Our system utilizes an augmented breadboard, which is circuit-aware and supports on-the-fly hardware reconfiguration via contextualized guidance and in-situ circuit validation through interactive tests. Through a usability study (N=12), we demonstrate how makers leverage circuit-aware guidance and debugging to support individual building patterns.

Quantum code surgery offers a flexible, low-overhead framework for executing logical measurements within quantum error-correcting codes. It encompasses several fault-tolerant logical computation schemes, including parallel surgery, universal adapters and fast surgery, and serves as the key primitive in extractor architectures. The efficiency of these schemes crucially depends on constructing low-overhead ancilla systems for measuring arbitrary logical operators in general quantum Low-Density Parity-Check (qLDPC) codes. In this work, we introduce a method to construct an ancilla system of qubit size $O(W \log W)$ to measure an arbitrary logical Pauli operator of weight $W$ in any qLDPC stabilizer code. This new construction immediately reduces the asymptotic overhead across various quantum code surgery schemes.

Salt precipitation near injection wells can reduce permeability, induce excess pressure buildup, and reduce injectivity within days to weeks of CO2 injection, yet the pore-scale mechanisms coupling multiphase flow, evaporation, and crystallization warrant further detailed quantification across variable phase states and flow regimes. We present high-resolution microfluidic experiments that systematically quantify the dynamics of halite crystallization during CO2-driven brine evaporation across liquid, gaseous, and supercritical phases (50-80 bar, 20--60 C, Pe = 50--1440). Crystallization kinetics are controlled by transport, with the Avrami rate constant (K) increasing by two orders of magnitude with the Peclet number and exhibiting the dependence of the temperature of Arrhenius (Ea = 58.6 kJ/mol. Supercritical CO2 achieves superior displacement efficiency (residual saturation 0.22-0.36, fractal dimension D = 1.79-1.82) and the fastest evaporation (Sherwood numbers 2-3x higher than the liquid phase), reducing the nucleation time from 57 min (20C, liquid) to <1 min (40-60 C, gas/supercritical). The final fractions of crystal increase 10-fold from liquid (0.008) to gas-phase conditions (0.08--0.12), confirming that convective transport and phase state dominate over diffusion-limited mechanisms. Despite probabilistic nucleation, final crystal distributions are spatially rather uniform with no systematic inlet-outlet bias. These quantitative relationships between dimensionless parameters (Pe, Sh), kinetic constants (K, Ea) and phase-dependent displacement patterns provide critical benchmarks for validating pore-scale models and predicting near-wellbore permeability impairment in geological storage of saline and hypersaline CO2.

In this work, we propose a new spatio-directional neural encoding that is compact and efficient, and supports all-frequency signals in both space and direction. Current learnable encodings focus on Cartesian orthonormal spaces, which have been shown to be useful for representing high-frequency signals in the spatial domain. However, directly applying these encodings in the directional domain results in distortions, singularities, and discontinuities. As a result, most related works have used more traditional encodings for the directional domain, which lack the expressivity of learnable neural encodings. We address this by proposing a new angular encoding that generalizes the hash-grid approach from proach from Müller et al. [2022] to the directional domain by encoding directions using a hierarchical geodesic grid. Each vertex in the geodesic grid stores a learnable latent parameter, which is used to feed a neural network. Armed with this directional encoding, we propose a five-dimensional encoding for spatio-directional signals. We demonstrate that both encodings significantly outperform other hash-based alternatives. We apply our five-dimensional encoding in the context of neural path guiding, outperforming the state of the art by up to a factor of 2 in terms of variance reduction for the same number of samples.

Electrolyte solutions at high concentration are indispensable and yet poorly understood. In particular, the extent of speciation -- the formation of complexes composed of multiple species -- in concentrated ionic solutions is very challenging to obtain theoretically and experimentally, but can have a strong effect on solution properties. The literature is rife with contradictory estimates of speciation from experiments. We find that speciation affects transport properties, and is therefore, a prerequisite to accurately model concentrated solutions. We turn this to our advantage by showing that the viscosity can be used to determine the extent of complexation in concentrated aqueous solutions. Results of simulations as well as experimental measurements are presented. The atomistic Madrid-2019 force-field is extended to model FeCl$_2$. Solutions of FeCl$_2$ and MgCl$_2$ are compared and the observed difference in viscosity explained by more complexation in the former, a conclusion supported by recently reported X-ray absorption and neutron scattering experiments.

This work investigates the boundary stabilization of flows in star-shaped and tree-shaped networks of open channels governed by the Saint-Venant equations with a friction term. Due to the existence of the friction term, the steady-states are non-uniform. We show that any such network can be stabilized with only controls at the terminal nodes of the network, even when there are no controls at the nodes inside the network. The number of control is optimal. The main tool we use is the Lyapunov approach, and the main challenge is that the state-of-the-art Lyapunov functions developed for Saint-Venant equations with source terms cannot be used. In this work, we manage to construct a new efficient and explicit Lyapunov function and, in turn, we give explicit ranges of the control tuning parameters that depend only on the values of the given non-uniform steady-states at the ends of the branches. Moreover, this Lyapunov function also improves the existing conditions found in the last decade for a single channel modelled by Saint-Venant equations.

We develop a perturbative framework to calculate the mean-squared displacement (MSD) of active Brownian particles (ABPs) with a finite moment of inertia. Starting from the corresponding Fokker-Planck equation, we employ a Fourier transform for the spatial coordinates and Hermite polynomials as eigenfunctions for the angular velocity, which enables a systematic perturbative expansion of the MSD order by order. By resumming the resulting series in Laplace space and performing the inverse transform, we obtain an explicit expression for the MSD as a function of the moment of inertia. The analytical results are further validated by comparison with numerical simulations.

Shuffler-based differential privacy (shuffle-DP) is a privacy paradigm providing high utility by involving a shuffler to permute noisy report from users. Existing shuffle-DP protocols mainly focus on the design of shuffler-based categorical frequency oracle (SCFO) for frequency estimation on categorical data. However, numerical data is a more prevalent type and many real-world applications depend on the estimation of data distribution with ordinal nature. In this paper, we study the distribution estimation under pure shuffle model, which is a prevalent shuffle-DP framework without strong security assumptions. We initially attempt to transplant existing SCFOs and the naïve distribution recovery technique to this task, and demonstrate that these baseline protocols cannot simultaneously achieve outstanding performance in three metrics: 1) utility, 2) message complexity; and 3) robustness to data poisoning attacks. Therefore, we further propose a novel single-message \textit{adaptive shuffler-based piecewise} (ASP) protocol with high utility and robustness. In ASP, we first develop a randomizer by parameter optimization using our proposed tighter bound of mutual information. We also design an \textit{Expectation Maximization with Adaptive Smoothing} (EMAS) algorithm to accurately recover distribution with enhanced robustness. To quantify robustness, we propose a new evaluation framework to examine robustness under different attack targets, enabling us to comprehensively understand the protocol resilience under various adversarial scenarios. Extensive experiments demonstrate that ASP outperforms baseline protocols in all three metrics. Especially under small $ε$ values, ASP achieves an order of magnitude improvement in utility with minimal message complexity, and exhibits over threefold robustness compared to baseline methods.

Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $τ$ which, at large times, samples a microcanonical ensemble. In a previous work we showed that, for an interacting scalar theory in 1+1 dimensions, this framework captures genuine real time features that are inaccessible to Euclidean simulations. That original formulation suffers from two structural limitations, an ill defined non interacting limit and the lack of a direct correspondence between its correlation functions and those generated by the Feynman path integral. To solve these problems we introduced constrained symplectic quantization, a holomorphic reformulation in which fields and action are analytically continued and constraints are imposed on the intrinsic time Hamiltonian flow. The constraints select stable deterministic trajectories and they define convergent holomorphic integration cycles for the corresponding microcanonical measure. In the continuum limit we establish exact equivalence with the Feynman path integral at the level of the generating functional, thus providing a direct link between intrinsic time correlators and real time Green functions. In this contribution, we apply the method to the quantum harmonic oscillator on a real-time 1-dimensional lattice. Testing various observables, we find agreement between numerical and exact results for one- and two-point functions, and we reconstruct characteristic real-time features such as an oscillatory propagator, the discrete energy-gap spectrum, and the evolution of eigenstate probability densities. These tests provide numerical evidence that constrained symplectic quantization can sample real-time quantum observables and offers a practical route beyond Euclidean-time importance sampling.

Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily, weekly or yearly cycles. In this context, statistical inference is essential to distinguish genuine underlying effects from random variability. While tools like Analysis of Variance (ANOVA) provide such inference, they often lack interpretability and struggle with the complexities of multivariate data. To address these limitations, we propose a unified pipeline for the exploratory analysis of cyclostationary times series using ANOVA Simultaneous Component Analysis (ASCA). ASCA is an extension of ANOVA that is able to work in both univariate and multivariate cases. Combining inference with the visualization capabilities of Principal Component Analysis (PCA), ASCA provides powerful options for interpretability. ASCA's capabilities have been well-established in the analysis of experimental data, but they remain largely unexplored for observational data like time series. Our workflow introduces an algorithmic approach to modeling time-dependent data using ASCA, enabling control over multiple cyclostationary time scales while also accounting for the specific challenges of this type of data, such as autocorrelation. Furthermore, we observed that ASCA provides a better separation of variability across factors than ANOVA in unbalanced designs due to its multivariate nature. We demonstrate the efficacy of this methodology through two real-world case studies: water temperature trends in mountain lakes in Sierra Nevada, Spain, and airborne pollen trends over 30 years recorded in the city of Granada, Spain.

Black-hole uniqueness, i.e., the statement that all stationary vacuum black holes in the universe are described by the Kerr solution, is expected to break in theories beyond General Relativity. This breaking can take a particularly strong form, if several branches of black-hole solutions beyond the Kerr solution coexist. We find an example of a theory that exhibits such strong breaking. In this theory, a cubic coupling of a scalar field to the Gauss-Bonnet invariant triggers black-hole scalarization through a non-linear instability of the Kerr solution. At large spin, curvature-induced and spin-induced scalarization mechanisms compete at fixed sign of the coupling. This results in a rich phase structure of black-hole solutions and continuous as well as discontinuous transitions between the different branches of black holes.

We show that the $2$-component unlink in $S^4$ admits infinitely many isotopy classes of spanning $3$-disks that are Brunnian.

For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial fluctuations. We propose to describe this system by observables based on fluctuating fields. In terms of these "statistical observables" the probabilistic classical field theory becomes a quantum field theory. Non-commuting operators are associated to observables. The quantum rules follow from the laws for classical probabilities. We construct the functional integral for the quantum field theory, and discuss in detail the classical relativistic Klein-Gordon equation with interactions.

This thesis presents a comprehensive study of the renormalisation of chiral gauge theories in dimensional regularisation (DReg) at the multi-loop level. We employ the mathematically consistent Breitenlohner-Maison/`t~Hooft-Veltman (BMHV) scheme with non-anticommuting $γ_5$, whose modified algebraic relations induce a spurious violation of gauge and BRST invariance. A central focus is the systematic restoration of the broken symmetry, for which we provide a transparent and fully algorithmic procedure based on the quantum action principle. A major achievement of this work is the complete 4-loop renormalisation of an Abelian chiral gauge theory -- the highest-order application of the BMHV scheme to date. This calculation is made possible by an automated, high-performance computational framework incorporating several optimised algorithms. Our results demonstrate that a rigorous, self-consistent treatment of $γ_5$ is feasible even at very high loop orders. We further analyse dimensional ambiguities and evanescent details corresponding to different implementations of the regularisation, and identify practically efficient prescriptions for $D$-dimensional fermions and gauge interactions. Building on these insights, we present the complete 1-loop renormalisation of the full Standard Model (SM) in the BMHV scheme, providing a first step towards a fully self-consistent multi-loop renormalisation of the SM and establishing a solid foundation for future high-precision electroweak phenomenology.

We generalize a previously established ab initio approach-originally developed for hexagonal close-packed (hcp) metals-to accommodate solids with both internal and external degrees of freedom. This extension enables the thermodynamic and thermoelastic characterization of insulators, including those with non-vanishing piezoelectric and pyroelectric tensors. Utilizing Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) within the quasi-harmonic approximation, we derive the pressure and temperature dependence of these properties. Specifically, we investigate internal degrees of freedom using two distinct frameworks: the Zero Static Internal Stress Approximation (ZSISA) and Full Free Energy Minimization (FFEM). We then compare these approximations by computing internal and external thermal expansions, as well as temperature-dependent piezoelectric and pyroelectric tensors. Finally, we demonstrate the generalized formalism by calculating the thermodynamic properties of wurtzite ZnO across a broad range of pressures and temperatures.

We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is well-established and serves as a conceptual template: Post's lattice organizes fragments via Boolean clones and supports complexity classifications for standard reasoning tasks. For modal fragments, we then bring together two historically independent lines of investigation: a general framework where modal fragments are parameterized by a basis of "connectives" defined by arbitrary modal formulas (initially proposed and studied by logicians such as Kuznetsov and Ratsa in the 1970s), and the more tractable class of what we call simple modal fragments parameterized by Boolean functions plus selected modal operators, where Post-lattice methods enable systematic decidability and dichotomy results. Along the way, we collect and extend results on teachability and exact learnability from examples for both propositional fragments and simple modal fragments, and we conclude by identifying several open problems.

In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is possible by brute-force or standard Gröbner basis approaches. The method exploits the structured sparsity of the polynomial system to compute a univariate polynomial in the associated ideal through successive computations of resultants. A solution to the system can then be efficiently recovered from this univariate polynomial. Pseudocode is given for the proposed ResultantSolver algorithm, along with experiments and comparisons to rival methods. We also discuss further potential improvements, such as parallelizing parts of the computations.

We investigate the interference of Laughlin quasiparticles (QPs) in the fractional quantum Hall regime that are stochastically injected into a Fabry-Pérot interferometer. We find that the effective Aharonov-Bohm (AB) phase accumulated along the interferometer loop acquires an additional contribution of $\sin(2πλ)/2$ per QP present on it, where $πλ$ is the QP exchange phase. This contribution originates from time-domain braiding processes associated with injected QPs passing the interferometer quantum point contacts. In the limit of symmetric QP injection, the tunneling current noise exhibits AB oscillations as a function of the total injected current, providing access to the exchange phase $πλ$. In the regime of large total injection, we identify a universal Fano factor that displays power-law scaling and a characteristic phase shift reflecting real-space QP braiding along the interferometer edges. These results are relevant for accessing anyonic exchange statistics in mesoscopic interferometers.

We present an example of a linear partial differential equation whose Cauchy problem becomes well-posed when perturbed by noise. Specifically, we make clear how a suitable multiplicative Stratonovich perturbation of Brownian type renders a weakly hyperbolic operator with double involutive characteristics well-posed in the $C^{\infty}$-category, while its deterministic counterpart is only well-posed in the Gevrey $ s $ classes with $ 1 \leq s <2 $ .

We investigate the effects of dynamical dark energy (DDE) on the growth of cosmic structure using a two-fluid model. This framework allows the dark energy equation of state to smoothly cross the phantom divide, in agreement with recent DESI results. In this effective description, DDE supports propagating perturbations that behave like sound waves. These perturbations induce a scale dependence in the growth of matter fluctuations and in halo bias, which can be exploited to test the dynamical nature of dark energy at the level of its fluctuations. For cluster-sized halos, the amplitude of the scale-dependent halo bias is comparable to that produced by massless neutrinos in $Λ$CDM. Using a Fisher forecast for a multi-tracer analysis of the power spectrum (P) and bispectrum (B) of galaxy number counts, we find that bispectrum information is essential to detect the scale dependence induced by the DDE sound mode. For a survey of volume $V\sim 10\, h^{-3}{\rm Gpc}^3$ at redshift $z=0.5 - 1$, a two-tracer P+B analysis could detect this scale dependence if the sound speeds of the dark energy fluids are in the range $c_s^2\sim 10^{-2} - 10^{-4}$. Lower sound speeds cause halos to experience a gravitational drag force through the excitations of sound waves. This effect impacts measurements of the growth rate inferred from cluster-sized halos at the 10\% level if one of the fluids has a very low sound speed $c_s^2\sim 10^{-5}$. Larger sound speeds $c_s^2 > 10^{-2}$ could be probed with optimal weighting schemes that reduce shot noise and increase the effective bias.

Let $\mathcal{M}_1(λ)$ be the class of all meromorphic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}\}: |z|<1$ having a simple pole at $λ\in \overline{\mathbb{D}} \setminus \{0\}$ and satisfying the normalization $f'(0)=1$. Let $B(λ)$ and $L(λ)$ denote the Bloch and Landau constants, respectively, for this class. In this article, we first show that the Bloch constant $B(1)$ and the Landau constant $L(1)$ are infinite. Using these results and a conformal mapping technique, we establish that $B(p)$ and $L(p)$ are likewise infinite for any $p \in (0,1)$, thereby refuting a recent conjecture. Finally, we extend our study to the class of meromorphic functions having two simple poles and prove that their associated Bloch and Landau constants also remain infinite.

Galaxies grow very rapidly during the first Gyr of the Universe, mostly driven by high galaxy efficiencies, particularly relevant at $z>5$. This efficiency is related to high gas densities and/or compact gas distributions within these early galaxies. We want to understand the evolution of the size of galaxies at cosmic dawn, from $z=14$ to $z=5$ and its main drivers. We use the FirstLight database of 430 zoom-in cosmological simulations and radiative transfer calculations to generate synthetic images in seven JWST bands. We add observational effects, inspired by recent JWST deep extragalactic surveys. The size-mass relation is already in place at $z\simeq14$ and it shows a large diversity of galaxy sizes at a fixed mass. Extended (compact) galaxies tend to have higher (lower) specific star-formation rate (sSFR). The mass-dependent slope does not evolve significantly. This is driven by a complex interaction between stellar light and dust. Differential dust attenuation dims galaxy centers and it makes larger sizes, modifying the mass-size slope even in the rest-frame optical. At a fixed mass, galaxy size evolves very fast, as the normalization of the size-mass relation increases by 0.5 dex between $z\simeq14$ and $z\simeq6$, in 600 Myr. The SFR surface density increases with redshift, driven by higher sSFRs and smaller sizes at higher redshifts. Size evolution at a fixed stellar mass accelerates at cosmic dawn, driven by an increasing galaxy efficiency at $z\geq5$.

Understanding motivations of contributors for participating in community question and answer platforms is crucial for sustaining knowledge-sharing ecosystem, which is necessary to advance the discipline while also ensuring its longevity. This is particularly necessary in the age of LLMs, where data from such portals are used to train these models. Limited insights exist regarding how motivations of contributors vary across different national cultures. This research investigates Stack Overflow contributor motivations, analysing regional differences and relations to platform activity. We combined qualitative content analysis of Stack Overflow profiles with quantitative linguistic analysis of data from the United States, China, and Russia. Using deductive content analysis, we identified 17 motivational categories. We applied correlation analysis to identify associations between stated motivations and platform activities. Contributors are primarily motivated by advertising opportunities and altruistic problem solving desires. American contributors demonstrated stronger self promotional behaviours while Chinese contributors exhibited greater learning oriented engagement. Our correlation analysis showed that those with more detailed profiles tend to engage in advertising and social activities, while learning oriented users maintain minimal self presentation. Understanding these variations can inform strategies for enhancing cross cultural participation in software engineering.

Advanced photonic materials showing two-photon absorption (2PA) have been widely explored to develop three-dimensional imaging, micro and nanofabrication, all-optical switching, lithography on a nanoscale and many other enabling technologies. These all require nonlinear absorption chromophores with intrinsic 2PA cross-sections and long-term photo-and thermal stability. Here, we disclose the very first example of the dipolar carbenemetal-amide (CMA) material showing a enhanced 2PA cross-section up to 105 GM. Overall molecular design considerations such as extended $π$-conjugation (to increase polarizability), minimizing the singlet-triplet energy gap ($Δ$E ST ), and using heavy metal atoms are the first design principles to obtain bright one-and two-photon excited thermally activated delayed fluorescence (TADF) material, showing one of the highest radiative rate of 2.18$\bullet$10 6 s -1 across CMA materials. Bright red CMA 2P-TADF material shows excellent photostability (LT 50 = 3 h) to 20 mW femtosecond pulsed laser excitation at 1000 nm, encouraging further CMA exploration for future applications in advanced photonic technologies requiring third-order nonlinear optical properties.

The linearized double shuffle Lie algebra introduced by Brown reflects the depth-graded structure of multiple zeta values. In a previous paper, the first author introduced an extension of this Lie algebra that accommodates multiple q-zeta values and multiple Eisenstein series. Inspired by the stabilizer interpretation of the double shuffle Lie algebra given by Enriquez and Furusho, we provide in this paper a stabilizer interpretation of both Lie algebras and show that the stabilizers preserve the extension from the first linearized Lie algebra to the second one.

This paper studies patenting trends in artificial intelligence (AI) and robotics from 1980 to 2019. We introduce a novel distinction between traditional robotics and robotics embedding AI functionalities. Using patent data and a time-series econometric approach, we examine whether these domains share common long-run dynamics and how their trajectories differ across major innovation systems. Three main findings emerge. First, patenting activity in core AI, traditional robots, and AI-enhanced robots follows distinct trajectories, with AI-enhanced robotics accelerating sharply from the early 2010s. Second, structural breaks occur predominantly after 2010, indicating an acceleration in the technological dynamics associated with AI diffusion. Third, long-run relationships between AI and robotics vary systematically across countries: China exhibits strong integration between core AI and AI-enhanced robots, alongside a substantial contribution from universities and the public sector, whereas the United States displays a more market-oriented patenting structure and weaker integration between AI and robots. Europe, Japan, and South Korea show intermediate patterns.