Inference in extreme value theory relies on a limited number of extreme observations, making estimation challenging. To address this limitation, we propose a non-parametric simulation scheme, the multivariate extreme events spectral bootstrap simulation procedure, relying on the spectral representation of multivariate generalized Pareto-distributed random vectors. Unlike standard bootstrap methods, our approach preserves the joint tail behaviour of the data and generates additional synthetic extreme data, thereby improving the reliability of inference. We demonstrate the effectiveness of our procedure on the estimation of tail risk metrics, under both simulated and real data. The results highlight the potential of this method for enhancing risk assessment in high-dimensional extreme scenarios.

We present an infinite set of non-local integrals of motion for deformed $W$-algebras of types $A_l, D_l$, and $E_{6,7,8}$. They can be regarded as a two-parameter deformation of trace of the monodromy matrix of the $g$-KdV theory. Commutativity of the non-local integrals of motion is shown in the case of $A_l$ and $D_l$ by a direct calculation. In the case of $E_{6,7,8}$ it is a conjecture.

We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise dispersive decay estimates for the linearized equation. In the incompressible limit, this improves current bounds for the incompressible Euler-Coriolis system as well.

We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using two families of entropic measures, namely the square root of the Jensen-Shannon divergence, which in turn defines a faithful distance of quantum states, and the square root of the quantum Jeffreys divergence. The results apply to both closed and open quantum systems, and are evaluated in terms of the Schatten speed of the evolved state, as well as cost functions that depend on the smallest and largest eigenvalues of both initial and instantaneous states of the quantum system. To illustrate our findings, we focus on the unitary and nonunitary dynamics of mixed single-qubit states. In the first case, we obtain speed limits $\textit{à la}$ Mandelstam-Tamm that are inversely proportional to the variance of the Hamiltonian driving the evolution. In the second case, we set the nonunitary dynamics to be described by the noisy operations: depolarizing channel, phase damping channel, and generalized amplitude damping channel. We provide analytical results for the two entropic measures, present numerical simulations to support our results on the speed limits, comment on the tightness of the bounds, and provide a comparison with previous QSLs. Our results may find applications in the study of quantum thermodynamics, entropic uncertainty relations, and also complexity of many-body systems.

Two-dimensional (2D) magnets host a wide range of exotic magnetic textures, whose low-energy excitations and finite-temperature properties are typically described by effective spin models based on Heisenberg-like Hamiltonians. A key challenge in this framework is the reliable determination, from ab initio calculations, of exchange parameters and their anisotropic components, crucial for stabilising long-range order. Among the different strategies proposed for this task, the energy-mapping method -- based on total-energy calculations within Density Functional Theory (DFT) -- is the most widely adopted, but it typically requires laborious, multi-step procedures. To overcome this limitation, we introduce AMaRaNTA (Automating Magnetic paRAmeters iN a Tensorial Approach), a computational package that systematically automates the energy-mapping method, specifically through its ``four-state'' formulation, to extract exchange and anisotropy parameters in 2D magnets. In its current implementation, AMaRaNTA returns the nearest-neighbour exchange tensor, complemented by scalar parameters for second- and third-nearest-neighbour exchange interactions as well as single-ion anisotropy. Together, these provide a minimal yet sufficient set of parameters to capture magnetic frustration and anisotropies, essential for stabilising several observed magnetic states in 2D materials. Applied to a representative subset of the Materials Cloud 2D Structure database, AMaRaNTA demonstrates robust, automated and reproducible screening of magnetic interactions, with clear potential for high-throughput simulations.

This paper describes the cryogenic and purification systems of the ICARUS T600 detector in its present implementation at the Fermi National Laboratory, Illinois, USA. The ICARUS T600 detector is made of four large Time Projection Chambers, installed in two separate containers of about 275 m3 each. The detector uses liquid argon both as target and as active media. For the correct operation of the detector, the liquid argon must be kept in very stable thermal conditions and the contamination of electronegative impurities must be consistently kept at the level of small fractions of parts per billion. The detector was previously operated in Italy, at the INFN Gran Sasso Underground laboratory, in a 3 year duration run on the CERN to LNGS Long Baseline Neutrino Beam. For its operation on the Booster and NuMI neutrino beams, at Fermilab, for the search of sterile neutrinos and measurements of neutrino-argon cross sections, the detector was moved from Gran Sasso to CERN for the upgrades required for operation at shallow depth with high intensity neutrino beams. The liquid argon containers, the thermal insulation and all the cryogenic equipment, have been completely re-designed and rebuild, following the schemes of the previous installation in Gran Sasso. The detector and all the equipment have been transported to Fermilab, where they have been installed, tested and recently put into operation. The work described in this paper has been conducted as a joint responsibility of CERN and Fermilab with the supervision provided by the Icarus Collaboration. Design, installation, testing, commissioning and operation is the result of a common effort of CERN, Fermilab and INFN Groups.

For any symmetrizable generalized Cartan matrix $A$, we introduce an algebra $\widehat{\mathcal{DY}}(A)$, which is essentially the centrally extended double Yangian when $A$ is of finite type, and we give a new field (current) presentation of $\widehat{\mathcal{DY}}(A)$. Among the main results, for any $\ell\in \mathbb C$ we construct a universal vacuum $\widehat{\mathcal{DY}}(A)$-module $\mathcal{V}_A(\ell)$ of level $\ell$, prove that there exists a natural $\hbar$-adic weak quantum vertex algebra structure on $\mathcal{V}_A(\ell)$, and give an isomorphism between the category of restricted $\widehat{\mathcal{DY}}(A)$-modules of level $\ell$ and the category of $\mathcal{V}_A(\ell)$-modules.

The digital transformation of religious practice has reshaped how billions of people engage with spiritual content, with video-sharing platforms becoming central to contemporary religious communication. Yet HCI research lacks systematic understanding of how narrative and visual elements create meaningful spiritual experiences and foster viewer engagement. We present a mixed-methods study of religious videos on YouTube across major religions, developing taxonomies of narrative frameworks, visual elements, and viewer interaction. Using LLM-assisted analysis, we studied relationships between content characteristics and viewer responses. Religious videos predominantly adopt lecture-style formats with authority-based persuasion strategies, using salvation narratives for guidance. All prefer bright lighting, with Buddhism favoring warm tones and prominent symbols, Judaism preferring indoor settings, and Hinduism emphasizing sacred objects. We identified differentiated patterns of emotional sharing among religious viewers while revealing significant correlations between content characteristics and engagement, particularly regarding AI-generated content. We provide evidence-based guidance for creating inclusive and engaging spiritual media.

In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as \emph{order by quantum disorder} (ObQD). For frustrated spin-$\frac{1}{2}$ models, unbiased numerical methods able to expose ObQD are necessary. We show that ObQD can be identified from exact diagonalization (ED) calculations through an analysis akin to the Anderson tower of states associated with spontaneous symmetry breaking. By defining an effective quantum rotor model, we describe the competition between ObQD-induced localization of the rotor and its tunneling between symmetry-related ground states, identifying the crossover lengthscale from the finite-size regime where the rotor is delocalized, to the infinite system-size limit where it becomes localized. This rotor model relates the characteristic splittings in the ED energy spectrum to the ObQD selection energy scale, providing an estimate that can be compared to spin wave calculations. We demonstrate the general applicability of this approach in one-, two- and three-dimensional frustrated spin models that exhibit ObQD.

We survey the main results in Jeremy Rickard's seminal papers `Morita theory for derived categories' and `Derived equivalences and derived functors'. These papers catalysed the later development of the Morita theory of (enhanced) compactly generated triangulated categories by Keller in the algebraic setting and by Schwede and Shipley in the topological setting. We also discuss the role of Rickard's notion of splendid equivalence in the context of Broué's abelian defect group conjecture, and indicate an alternative proof of parts of Rickard's Derived Morita Theorem that leverages the notion of completion of a triangulated category.

The boson peak is a characteristic anomaly of amorphous solids broadly defined as a low-energy excess in the density of states and heat capacity compared to the textbook predictions of Debye theory. The origin of this anomaly has long been the subject of ongoing debate and remains a topic of active controversy. We propose that the boson peak may have a defining dynamical feature: the accumulation of vibrational spectral weight within a narrow frequency window that is only weakly dependent on wavevector. In this perspective, the boson peak reflects a flat or weakly dispersive band in the dynamical structure factor rather than a propagating excitation. We revisit both experimental and simulation data from the literature through this lens and conduct further simulations in 2D and 3D amorphous systems. Taken together, these analyses provide compelling converging evidence for this interpretation and sharply constrain the space of viable theoretical descriptions of the boson peak.

Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: simulating large multi-mode generators is computationally demanding, and benchmarks such as the \emph{stellar rank} do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the \emph{non-Gaussian control parameters} $(s_0,δ_0)$, a continuous and operational measure that goes beyond stellar rank. Leveraging these parameters, we develop a universal optimization method that reduces photon-number requirements and greatly enhances success probabilities while preserving state quality. Applied to the Gottesman--Kitaev--Preskill (GKP) state generation, for example, our method cuts the required photon detections by a factor of three and raises the preparation probability by nearly $10^8$. Demonstrations across cat states, cubic phase states, GKP states, and even random states confirm broad gains in experimental feasibility. Our results provide a unifying principle for resource-efficient non-Gaussian state generation, charting a practical route toward scalable optical quantum technologies and fault-tolerant quantum computation.

The quantum Pontus-Mpemba effect (QPME) is a counterintuitive phenomenon wherein a quantum system relaxes more rapidly through a two-step evolution protocol than through direct evolution under a symmetric Hamiltonian alone. In this protocol, the system first evolves under a symmetry-breaking Hamiltonian and then switches to a symmetric one. We demonstrate that QPME occurs under both real-time and imaginary-time dynamics with respect to $U(1)$-symmetry. Using tilted ferromagnetic initial states, we demonstrate that a transient asymmetric evolution significantly accelerates thermalization or convergence to the ground state for both real-time and imaginary-time evolutions, respectively. The effect is pronounced for small tilt angles, while larger tilts or antiferromagnetic initial states suppress it. Numerical evidence across different system sizes confirms the robustness of QPME, demonstrating its stability in the thermodynamic limit. This work extends the framework of nonequilibrium quantum phenomena to incorporate active state preparation, with direct implications for the implementation of quantum simulation.

For a finite subset $A$ of a group $G$, we define the right quotient set and the left quotient set of $A$, respectively, as $AA^{-1} := \{a_1a_2^{-1}:a_1,a_2\in A\}$, $A^{-1}A := \{a_1^{-1}a_2:a_1,a_2\in A\}$. While the right and left quotient sets are equal if $G$ is abelian, subtleties arise when $G$ is a nonabelian group, where the cardinality difference $|AA^{-1}| - |A^{-1}A|$ may be take on arbitrarily large values. Using the results of Martin and O'Bryant on the cardinality differences of sum sets and difference sets in $\mathbb{Z}$, we prove in the infinite dihedral group, $D_\infty \cong \mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}$, every integer difference is achievable. Further, we prove that in $F_2$, the free group on $2$ generators, an integer difference is achievable if and only if that integer is even, and we explicitly construct subsets of $F_2$ that achieve every even integer. We further determine the minimum cardinality of $A \subset G$ so that the difference between the cardinalities of the left and right quotient sets is nonzero, depending on the existence of order $2$ elements in $G$. To prove these results, we construct difference graphs $D_A$ and $D_{A^{-1}}$ which encode equality, respectively, in the right and left quotient sets. We observe a bijection from edges in $D_A$ to edges in $D_{A^{-1}}$ and count connected components in order to obtain our results on cardinality differences $|AA^{-1}| - |A^{-1}A|$.

In this paper, we present the first explicit examples of low-conductance permutations. The notion of conductance of permutations was introduced by Dodis et al. in "Indifferentiability of Confusion-Diffusion Networks", where the search for low-conductance permutations was first initiated and motivated. As part of our contribution, we not only provide these examples, but also offer a general characterization of the problem: we show that low-conductance permutations are equivalent to permutations possessing the information-theoretic properties of Multi-Source-Somewhere-Condensers, a specific variant of somewhere condensers.

Rudyak's conjecture states that for any degree one map $f:M\to N$ between oriented closed manifolds there is the inequality $\cat (M)\ge \cat(N)$ for the Lusternik-Shnirelmann category. We prove the Rudyak's conjecture for $ n$-dimensional simply connected spin manifolds for $n\le 8$.

An amplitude analysis of the $B^+\to(π^+π^-)(K^0_{\mathrm{S}}π^+)$ decay is performed in the mass regions $0.30 < m_{π^+π^-} < 1.10\,\mathrm{GeV}/c^2$ and $0.75 < m_{K^0_{\mathrm{S}}π^+} < 1.20\,\mathrm{GeV}/c^2$, using $pp$ collision data recorded with the LHCb detector corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$. The polarization fractions and $CP$ asymmetries for $B^+\toρ(770)^0K^*(892)^+$ decays are measured. Violation of the $CP$ symmetry in the decay $B^+\toρ(770)^0K^*(892)^+$ is observed for the first time, with a significance exceeding nine standard deviations. The $CP$ asymmetry is measured to be ${\cal A}_{CP} = 0.507 \pm 0.062\ \text{(stat)} \pm 0.024\ \text{(syst)}$ and the $CP$-averaged longitudinal polarization fraction of $f_L = 0.720 \pm 0.028\ \text{(stat)} \pm 0.009\ \text{(syst)}$. The measurements help to shed light on the polarization puzzle of $B$ mesons decaying to two vector mesons.

Magnetic skyrmions are chiral spin structures with non-trivial topology that comprise two-dimensional quasi-particles and are promising information carriers for data storage and processing devices. Skyrmion lattices in magnetic thin films exhibit Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) phase transitions and have garnered significant interest for studying emergent 2D phase behavior. In experimental skyrmion lattices, the main factor limiting the quasi-long-range order in thin films has been the non-flat energy landscape - often referred to as pinning effects. We demonstrate direct control of the skyrmion lattice order by effectively tuning the energy landscape employing magnetic field oscillations. By quantifying lattice order and dynamics, we explore how domain boundaries form and evolve due to pinning effects in Kerr microscopy experiments and in Brownian dynamics simulations, offering a pathway to control and study emergent skyrmion lattice properties and 2D phase behavior.

For a non-empty locally compact Hausdorff space $X$ and a Dedekind complete normal vector lattice $E$, we show that the vector lattice of norm to order bounded operators from ${\text C}_{\text c}(X)$ or ${\text C}_0(X)$ into $E$ is isomorphic to the vector lattice of $E$-valued regular Borel measures on $X$. When $E$ is an order continuous Banach lattice, the isomorphism is an isometric isomorphism between Banach lattices. When $X$ is compact, every regular operator from $\mathrm{C}(X)$ into $E$ is norm to order bounded. For some spaces $E$, such as KB-spaces or the regular operators on a KB-space, every regular operator from ${\mathrm C}_0(X)$ into $E$ is norm to order bounded. Additional results are obtained for the whole space of regular operators from ${\text C}_{\text c}(X)$ into an order continuous Banach lattice. As a preparation, vector lattices and Banach lattices, resp. cones, of measures with values in a Dedekind complete vector lattice $E$, resp. in the extended positive cone of $E$, are investigated, as well as vector and Banach lattices of norm to order bounded operators. When $E$ is the real numbers, our results specialise to the well-known Riesz representation theorems for the order and norm duals of ${\text C}_{\text c}(X)$ and ${\text C}_0(X)$.

Snap-through occurs in elastic structures when a stable equilibrium configuration becomes unstable, resulting in rapid motion towards a new and distinct stable state. While static analyses of snap-through are well documented, the dynamics of snap-through remain under-explored, particularly in structures with natural curvature. Using a combination of finite element simulations and multiple-scales analysis, we show that the snap-through dynamics of an arch under a central point load are controlled by its slenderness and imperfections embedded in the system. As the slenderness increases, the snap-through dynamics slow down, and the mode of snap-through changes from limit-point buckling to bifurcation buckling. When bifurcation buckling occurs, snap-through is preceded by an extended period of oscillatory behaviour. The duration of these pre-snap-through oscillations, and hence the snap-through time, is entirely controlled by imperfections in the system. Increasing the strength of imperfections dramatically reduces the snap-through time. Analytical expressions for the snap-through times are presented for limit point and bifurcation buckling. Our work suggests that natural curvature and deliberately introduced imperfections can be used to tune the snap-through dynamics of new functional materials.

Automatic differentiation (AD) enables powerful metasurface inverse design but requires extensive theoretical and programming expertise. We present a Model Context Protocol (MCP) assisted framework that allows researchers to conduct inverse design with differentiable solvers through large language models (LLMs). Since LLMs inherently lack knowledge of specialized solvers, our proposed solution provides dynamic access to verified code templates and comprehensive documentation through dedicated servers. The LLM autonomously accesses these resources to generate complete inverse design codes without prescribed coordination rules. Evaluation on the Huygens meta-atom design task with the differentiable TorchRDIT solver shows that while both natural language and structured prompting strategies achieve high success rates, structured prompting significantly outperforms in design quality, workflow efficiency, computational cost, and error reduction. The minimalist server design, using only 5 APIs, demonstrates how MCP makes sophisticated computational tools accessible to researchers without programming expertise, offering a generalizable integration solution for other scientific tasks.

Topological band theory has expanded into various domains in applied physics, offering significant potential for future technologies. Recent developments indicate that unique bulk band topology perceived for electrons can be realized in a system of light-matter quasiparticles with reduced crystal symmetry by utilizing tunable light-matter interaction. In this work we realize topologically non-trivial energy band dispersion of exciton-polaritons confined in two-dimensional anisotropic materials inside an optical microcavity, and show the emergence of exceptional points (EPs) due to non-Hermitian topology arising from excitonic dipole oscillators with finite quasiparticle lifetime. Fourier-plane imaging reveals two pairs of EPs connected by bulk Fermi arcs for each of the transverse electric and magnetic polarized modes. An anisotropic Lorentz oscillator model captures the exact band dispersion observed in our experiment in two-dimensional momentum space. Our findings establish anisotropic two-dimensional materials as a platform for exploring non-Hermitian topological physics, with implications for polarization-controlled optical technologies.

Large language models (LLMs) can now generate physics practice problems in real time, yet the educational value of these items hinges on rapid, reliable post-generation vetting. In this exploratory study, we investigated which automated checks are both technically feasible and pedagogically meaningful when exercises are produced on demand within a chatbot interface. A cohort of 34 introductory-physics students generated and attempted 543 practice problems during exam preparation. Each item was labeled by an expert on a wide range of quality attributes and presented to the learners in pairs to record their preference. We then (i) benchmarked three commodity LLMs as ``judges'' against the expert labels, (ii) quantified which attributes predict student choice via random-forest models, and (iii) triangulated these results with free-form exit surveys. Only a small subset of the original metric items proved necessary to reliably address student preferences either directly or by proxy. The study demonstrates that scalable formative assessment does not require exhaustive scoring: a carefully curated core of structural and learner-visible checks is sufficient to ensure both technical soundness and user appeal. The findings provide a practical blueprint for deploying real-time, AI-generated practice in physics and other quantitative disciplines.

In this paper, we describe the non-commutative formal geometry underlying a certain class of discrete integrable systems. Our main example is a non-commutative analog, labeled $q$-P$(A_3)$, of the sixth $q$-Painlevé equation. The system $q$-P$(A_3)$ is constructed by postulating an extended birational representation of the extended affine Weyl group $\widetilde{W}$ of type $D_5^{(1)}$ and by selecting the same translation element in $\widetilde{W}$ as in the commutative case. Starting from this non-commutative discrete system, we develop a non-commutative version of Sakai$'$s surface theory, which allows us to derive the same birational representation that we initially postulated. Moreover, we recover the well-known cascade of multiplicative discrete Painlevé equations rooted in $q$-P$(A_3)$ and establish a connection between $q$-P$(A_3)$ and the non-commutative $d$-Painlevé systems introduced in I. Bobrova. Affine Weyl groups and non-Abelian discrete systems: an application to the $d$-Painlevé equations.

Recent studies have drawn growing attention on non-relativistic odd-parity magnetism in the wake of altermagnets. Nevertheless, odd-parity spin splitting is often believed to appear in non-collinear magnetic configurations. Here, using symmetry arguments and effective model analysis, we show that Floquet engineering offers a universal strategy for achieving odd-parity magnetism in two-dimensional (2D) collinear antiferromagnets under irradiation of periodic driving light fields such as circularly polarized light, elliptically polarized light, and bicircular light. A comprehensive classification of potential candidates for collinear monolayer or bilayer antiferromagnets is established. Strikingly, the light-induced odd-parity spin splitting can be flexibly controlled by adjusting the crystalline symmetry or the polarization state of incident light, enabling the reversal or conversion of spin-splitting. By combining first-principles calculations and Floquet theorem, we present illustrative examples of 2D collinear antiferromagnetic (AFM) materials to verify the light-induced odd-parity magnetism. Our work not only offers a powerful approach for uniquely achieving odd-parity spin-splitting with high tunability, but also expands the potential of Floquet engineering in designing unconventional compensated magnetism.

Conventional spectrometer and polarimeter systems rely on bulky optics, fundamentally limiting compact integration and hindering multi-dimensional optical sensing capabilities. Here, we propose a spectropolarimeter enabled by metasurface-based diffractive optical networks that simultaneously performs spectrometric and polarimetric measurements in a compact device. By leveraging the wavelength- and polarization-dependent phase modulation of metasurfaces, our system encodes the spectral and polarization information of incident light into spatially resolved intensity distributions, which are subsequently decoded by a trained deep neural network, enabling simultaneous high-accuracy reconstruction of both spectral compositions and Stokes parameters through a single-shot measurement. Experiments validate the proposed network's accurate reconstruction of the spectral and polarization information across a broad wavelength range, and further confirm its imaging capability. Notably, we demonstrate a chip-integrated sensor prototype combing both measurement functionalities into a commercial CMOS image sensor. This integrated platform provides a compact solution for on-chip multi-dimensional optical sensing, holding significant potential for versatile sensing, biomedical diagnosis, and industrial metrology.

We present a novel Bayesian spatial disaggregation model for count data, providing fast and flexible inference at high resolution. First, it incorporates non-linear covariate effects using penalized splines, a flexible approach that is not typically included in existing spatial disaggregation methods. Additionally, it employs a spline-based low-rank kriging approximation for modeling spatial dependencies. The use of Laplace approximation provides computational advantages over traditional Markov Chain Monte Carlo (MCMC) approaches, facilitating scalability to large datasets. We explore two estimation strategies: one using the exact likelihood and another leveraging a spatially discrete approximation for enhanced computational efficiency. Simulation studies demonstrate that both methods perform well, with the approximate method offering significant computational gains. We illustrate the applicability of our model by disaggregating disease rates in the United Kingdom and Belgium, showcasing its potential for generating high-resolution risk maps. By combining flexibility in covariate modeling, computational efficiency and ease of implementation, our approach offers a practical and effective framework for spatial disaggregation.

Cognitive effort, defined as the relationship between cognitive load and task performance, provides insight into how individuals allocate mental resources during demanding tasks. This construct is particularly important in high-stakes public health and clinical training, where excessive cognitive load is associated with medical errors and burnout. This study investigates whether cognitive effort varies across task segments and whether it can be estimated at the individual level using brain signal data and machine learning. Functional near-infrared spectroscopy (fNIRS) data were collected from 16 participants performing a structured digital cognitive task consisting of four sequential segments separated by short and long rest intervals. Cognitive effort was operationalized using relative neural efficiency and relative neural involvement, integrating prefrontal hemodynamic activity with task performance. The analysis followed a two-stage approach. First, segment-level group analysis tested whether cognitive effort differed across task segments, assessing whether the task structure induced meaningful variation in cognitive demand. Second, participant-independent machine learning models were used to predict task performance from brain signal features. These predicted scores were then combined with neural measures to estimate individual-level cognitive effort. Results showed significant differences in cognitive effort across the four task segments, indicating that variations in task structure influence collective cognitive efficiency. In addition, machine learning models successfully predicted performance from fNIRS data. Cognitive effort derived from predicted scores closely matched that based on actual performance, suggesting that the proposed metric primarily reflects brain signal patterns.

We discuss physics-informed renormalisation group flows (PIRGs) for general operators. We show that operator PIRGs provide a comprehensive access to all correlation functions of the quantum field theory under investigation. The operator PIRGs can be seen as a completion of the PIRG-approach, whose qualitative computational simplification and structural insights are now fully accessible for general applications. The potential of this setup is assessed within a simple analytic example of the zero-dimensional $ϕ^4$-theory for which the generating functions of the fundamental field are computed within a vertex expansion, using the one- to ten-point functions.

Physics perfectly describes neuronal operation, provided that we take into account that biology uses slow, positively charged ions rather than electrons as charge carriers and remove untested ad hoc hypotheses that contradict science's first principles. We also incorporate recent experimental discoveries into the outdated classic theoretical description. Lipid mechanisms are really very important for cellular biology, but they are certainly not suitable for describing the phenomena we discuss. We introduce the correct physical model, significantly enhancing the classic \gls{HH} model; furthermore, the fundamentally bio-electrically triggered operation leads to changes in the electrical, mechanical, and thermodynamic properties of living matter. We derive the resting potential from first principles of science, showing that it is unrelated to an ad hoc linear combination of mobilities or reversal potentials, as the \gls{GHK} equation claims. Furthermore, we derive an "equivalent thermodynamic electric field" that enables discussion of, among others, the operation of ion channels, their ion selectivity, and voltage sensing. We demonstrate that a simple electrical-thermodynamic control circuit regulates neuronal operation, setting and maintaining a stable resting potential and handling an unstable transient process known as the \gls{AP}. Its setpoint entirely defines the resting potential, explaining its robustness during growth and evolution. Our cross-disciplinary approach naturally fuses the electrical and mechanical/thermodynamic description of neuronal operation, resolves the decades-old mystery of "heat absorption" and "leakage current" (with their far-reaching consequences), and derives the thermodynamic description of neural computing. We defy that science cannot describe life.