We study the measure transition problem for bilateral Laplace transforms of meromorphic functions on vertical strips. Given a meromorphic function F admitting Laplace representations on two adjacent strips separated by a vertical line, we investigate how the corresponding determining measures are related. Our first result shows that in the absence of poles on the separatrix the determining measures coincide. We next derive explicit transition formulas for the case of finitely many poles and obtain sufficient conditions under which these formulas remain valid for infinitely many poles. Applications are given to the analytic continuation of the zeta function, periodic and almost periodic functions, and quotients of Gamma functions related to the confluent hypergeometric function. Finally, using generalized Cauchy integrals, we construct an entire function admitting distinct Laplace representations on the right and left half-planes, thereby producing a ghost transition. This provides a counterexample to uniqueness of solutions of the Cauchy problem for the heat equation.

For graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest integer $N$ such that every graph $Γ$ on $N$ vertices contains $G$ or its complement $\overlineΓ$ contains $H$ as a subgraph. In graph Ramsey theory, the star-cycle Ramsey number is well-studied throughout the years. Whereas the Ramsey number of $K_{2,n}$ versus cycle is challenging to determine due to increased structural complexity. In this article, we have obtained an exact value of the Ramsey number $R(K_{2,n}, C_{m})$ for even $m\in [n, 2n-4008]$ and $n\geq 4516$. In particular, we show that $$R(K_{1,n}, C_{m})= R(K_{2,n}, C_{m})$$ for all even $m\in [n, 2n-4008]$ and $n\geq 4516$. This leads to an interesting question: For fixed $t$, does there exist $n_0(t)\in \mathbb{N}$ such that $R(K_{1,n}, C_m)=R(K_{t,n}, C_m)$ for all $n \geq n_0(t)$ and for a given range of even $m$?

Energetic particles continuously process water ice across astrophysical and planetary environments, from interstellar clouds and comets to icy planetary surfaces. Interpreting the resulting observables requires a physically grounded description of the underlying interactions, both to identify radiation-driven signatures and to distinguish them from superimposed chemical, thermal, and microphysical effects. We present Geant4-IcyMoons, an extension of Geant4-DNA developed for irradiated water ice and, ultimately, for materials embedded within it. In this study, we model the elastic and inelastic interactions of electrons with amorphous and hexagonal ice. For the first time, this enables a transport-ready Monte Carlo simulation of electron irradiation in water ice, linking incident-particle environments to the evolution of icy surfaces. We apply this framework to Jupiter's moon Europa as a representative case of electron bombardment of an icy surface. We show that, on the trailing hemisphere, the stronger low-energy electron bombardment confines much of the deposited energy to the upper $\lesssim 0.1$ cm, whereas on the leading hemisphere, the more energetic incident population drives deposition patterns to depths of tens of centimeters. This may contribute to the observed lens-like enrichment of radiolysis products centered on the equator of the trailing hemisphere. This work lays the foundation for treatments of ion irradiation and radiation chemistry in water ice and embedded materials.

Optical circuits and light sources, such as lasers, undergo continuous miniaturization. In its extreme, nanolasers might be comprised of only a few molecules confined in plasmonic nanoresonators. Few-emitter lasers promise low energy requirements and fast responses in a footprint that can be inserted into any device or biological tissue. Utilizing the recently developed stacked hierarchy approach, informed from first principles, we demonstrate the impact of vibrational structure on lasing, using the example of few-molecule lasing in plasmonic cavities. Explicitly accounting for the entire vibrational manifold unveils resonances in the laser intensity that depend on the Stokes shift, drive strength, and the number of emitters. Our work identifies the limits of the omnipresent "incoherent drive"-approximation and paves the way for the understanding of nanolasers at the molecular scale.

The in-plane dielectric constant of nanoconfined water has attracted growing interest over the last years. Nevertheless, this magnitude is not well-defined at the nanoscale due to its dependence on the arbitrary choice of water width. We propose the in-plane 2D polarizability, $α_{\parallel}$, as an unambiguous characterization of the in-plane dielectric response under 2D confinement, in analogy to what has been recently done for the perpendicular response. Using classical molecular dynamics simulations, we compute $α_{\parallel}$ via two independent and consistent methods: based on fluctuation--dissipation theory, and from the induced dipole moment when water is placed in a capacitor. Our results provide the framework to quantify the in-plane dielectric response of polar liquids across simulations and experiments.

The STAR collaboration at RHIC and the ALICE collaboration at the LHC have reported dielectron spectra in the intermediate mass region, M = (1-3) GeV, which reveal a strikingly constant, energy-independent emission temperature $T_{IMR} \simeq 0.3~\textrm{GeV}$ over a broad range of collision energies, $\sqrt{s_{NN}} = 27 - 5020~\textrm{GeV}$. This unexpected ''thermostat'' behavior raises fundamental questions: why does the temperature remain constant despite increasing collision energy,and what mechanism governs this apparent universality?

We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time algorithm.

By viewing Einstein's field equations -- reduced to two dimensions -- as an integrable system, one can simultaneously obtain exact solutions to both the equations themselves and their associated Lax pair via a canonical Wiener-Hopf factorisation of a so-called monodromy matrix. In this article, we review this remarkable interplay between gravitational field equations, integrable systems, Riemann-Hilbert problems, and Wiener-Hopf factorisation theory, with particular emphasis on developments from the past decade enabled by advances in Wiener-Hopf factorisation techniques arising from the study of singular integral equations and Toeplitz operators. Through a variety of concrete examples, we illustrate how Wiener-Hopf factorisation yields explicit, exact solutions to the field equations of gravitational theories, and how its generalisation through a so-called $τ$-invariance property provides a new solution-generating method. Along the way, we aim to demonstrate the importance of an interdisciplinary approach -- grounded in General Relativity, Complex Analysis, and Operator Theory -- for the study of gravitational field equations.

In this work we derive a reduced one-fluid plasma model from the relativistic Vlasov--Boltzmann--Maxwell system using a moment hierarchy reduction combined with strong-guide-field anisotropic ordering. The unresolved higher-moment sector of the hierarchy is projected onto its dominant slow thermodynamic mode, producing a scalar regulator variable that represents a coarse-grained combination of charge imbalance, pressure anisotropy, and irreversible kinetic production channels. The resulting reduced state vector admits a GENERIC (General Equation for Non-Equilibrium Reversible--Irreversible Coupling) representation in which the reversible sector reproduces reduced electromagnetic field-line dynamics while the irreversible sector governs slow thermodynamic relaxation. Linearization yields a pair of electromagnetic eigenmodes together with an additional real thermodynamic eigenvalue. The fast modes recover the standard gyrotropic cold-plasma response, including familiar limits such as whistler dispersion, while the slow mode drives gradual drift of the effective electromagnetic spectrum and provides a reduced mechanism for variability in relativistic magnetized plasmas with slowly evolving macroscopic equilibrium. The previous 3-field model captured only the thermodynamic slow-mode sector, whereas the fully closed extended GENERIC model also contains the explicit reversible nonneutral charge degree of freedom, whose frozen-thermodynamic limit recovers the nonneutral whistler-Alfven equations as a strict subset. The model is formulated within the GENERIC framework, ensuring consistency with first-principles nonequilibrium thermodynamics.

We present an SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model. The theory is based on a fractionalization of the electron operators in fermionic chargons with a pseudospin degree of freedom, and charge neutral spinons capturing fluctuations of the spin orientation. The chargons are treated in a renormalized mean-field theory. We focus on regions of the phase diagram where they undergo stripe order. The spinons are described by a non-linear sigma model with pseudospin stiffnesses determined by the chargons. They prevent breaking of the physical SU(2) spin symmetry at any finite temperature, resulting in a charge ordered pseudogap phase with a reconstructed Fermi surface and a spin gap. The spectral function for single-particle excitations exhibits a collection of Fermi arcs and other structures. The arcs appear in various regions of the Brillouin zone, but never exclusively around the Brillouin zone diagonals.

Spectral functions encode key many-body information but are costly to compute with high fidelity. Machine-learning surrogates have emerged as a powerful alternative, yet many approaches require large training datasets. We develop a data-efficient surrogate for spectral functions using the $t$-$t'$-$t''$-$J$ model, which describes the motion of a hole in a quantum antiferromagnet. Using $\sim$ 10$^5$ self-consistent Born approximation-based spectra from Lee, Carbone and Yin (Phys. Rev. B 107, 205132 (2023)), we train a deep-kernel Gaussian process surrogate model with sparse variational inference (DKL-SVGP) using only 10% of the available training spectra. We benchmark against feed-forward neural networks (FFNN) trained on the same reduced subset and on the full dataset. The proposed DKL-SVGP model consistently outperforms the reduced-data FFNN and, despite using only 10% of the training spectra, achieves spectrum-wise errors within the same order-of-magnitude as the full-data FFNN baseline. Worst-tail diagnostics show improved fidelity on difficult spectra, while peak-level analysis indicates that DKL-SVGP recovers dominant peak heights with comparable accuracy and improves peak-location agreement under a matched-peak evaluation that mitigates rare peak-swapping cases. Overall, these results highlight GP-based surrogates as a competitive and data-efficient approach for spectral-function prediction in scarce-data regimes.

This paper is concerned with Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra--Heston model. Due to the non-Markovianity and non-semimartingality of the underlying processes, the classical stochastic control approach cannot be directly applied in this setting. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). Our approach is inspired by the martingale optimality principle combined with a suitable verification argument. The resulting optimal strategies for Merton's problems are derived in semi-closed form depending on the solutions to time-dependent multivariate Riccati-Volterra equations, while the optimal value is expressed using the solution to this original Riccati BSDE. Numerical results on a two dimensional fake stationary rough Heston model illustrate the impact of stationary rough volatilities on the optimal Merton strategies.

We study Krylov (spread) complexity in strongly coupled six-dimensional ${\cal N}=(1,0)$ superconformal field theories with holographic duals in massive type IIA supergravity. Extending recent holographic proposals relating Krylov complexity growth to the proper momentum of an infalling particle, we analyse the dynamics of massive geodesic probes in these geometries. In our setup, the bulk particle is allowed to move along three directions: the radial AdS coordinate, the internal $S^2$ associated with the $SU(2)_R$ symmetry, and the coordinate parametrising the quiver. In the dual field theory these motions encode, respectively, operator growth, the presence of R-symmetry charges, and spreading across different nodes of the quiver. We analyse the geodesic motion both analytically and numerically for representative quiver configurations. The motion along the quiver direction is typically damped and localised at early times, while the late-time behaviour is dominated by the radial AdS motion. As a consequence, the generalised proper momentum grows linearly at late times, consistent with expectations for Krylov complexity in conformal theories. The inclusion of angular momentum ($SU(2)_R$ charge) introduces additional constraints on the allowed motion and modifies the early-time dynamics while leaving the asymptotic behaviour unchanged. These results provide a first exploration of Krylov complexity in higher-dimensional holographic conformal theories and reveal how operator growth can probe both internal symmetries and quiver structure in strongly coupled conformal field theories.

Understanding phase stability and phase transformations is central to predicting material behavior under varying thermodynamic conditions. One of the earliest and most influential applications of density functional theory in materials science has been the prediction of pressure-induced phase transitions at 0 K. Extending these calculations to finite temperatures, however, requires accounting for thermal, quantum, and anharmonic contributions to the free energy, often at significant computational cost. In this work, we present a general and efficient framework for calculating low-temperature phase boundaries by combining the Clausius-Clapeyron equation with the quasi-harmonic approximation. This methodology requires a minimal number of calculations, while naturally incorporating internal degrees of freedom as well as quantum and low-order anharmonic effects. We illustrate the accuracy and efficiency of the approach by constructing the phase diagram of silica in the pressure range from -2 to 12 GPa and temperatures up to 1750 K. To this end, we employ a machine-learned interatomic potential trained on density functional theory reference data, enabling well-converged free energy estimates via efficient thermodynamic sampling and a rigorous comparison between the proposed framework and free energy integration.

Let $X_1,\dots,X_n$ be independent normal random variables with $X_i\sim N(μ_i,σ_i^2)$, and set $Z=\prod_{i=1}^n X_i$. We derive asymptotic approximations for the right tail probability $\mathbb{P}(Z>x)$ as $x\to\infty$. When at least one mean is nonzero, the asymptotic formula remains explicit and involves a finite multiplicative factor arising from admissible sign patterns (reflecting the different ways the product can be positive); it includes an explicit first relative correction term of order $x^{-1/n}$, with remaining relative error $O(x^{-2/n})$. The proof uses a boundary saddle-point/Laplace method: first a multidimensional Laplace approximation near the boundary saddle, then a one-dimensional endpoint Laplace approximation.

Agentic AI systems combine LLM-based reasoning, orchestration, tool invocation, and interaction with external environments. These systems introduce faults that are difficult to characterize using existing taxonomies. To address this gap, we present an empirical study of faults in agentic AI systems. We collected 13,602 issues and pull requests from 40 repositories and, using stratified sampling, selected 385 faults for analysis. Through grounded theory, we derived taxonomies of fault types, symptoms, and root causes. We then used Apriori-based association rule mining to identify relationships among faults, symptoms, and root causes, and validated the taxonomy through a developer study with 145 practitioners. Our analysis produced a taxonomy of 34 fault types, organized into four architectural dimensions. These faults manifested as failures in structured-output interpretation, tool calls, runtime execution, and exception handling, with root causes including data schema mismatches, dependency drift, state management complexity, and model interface instability. Furthermore, association rules showed recurring cross-component propagation, linking structured data, dependency, and state management faults to their symptoms and root causes. Practitioners considered the taxonomy representative of agentic AI failures and suggested refinements related to multi-agent coordination and observability. These findings provide an empirical basis for diagnosing faults and improving reliability in agentic AI systems.

Amplitude estimation, in its original form, is formulated as phase estimation upon the Grover iterate. Subsequent improvements to the algorithm have eliminated the need for phase estimation and introduced low-depth variants that trade speedups for lower circuit depth. We make the key observation that amplitude estimation is equivalent to estimating the energy gap of an effective Hamiltonian, whereby discrete-time evolution is generated by amplitude amplification. This enables us to develop an amplitude estimation algorithm for both Heisenberg-limited and low-depth circuit regimes, inspired by statistical phase estimation techniques developed for early fault-tolerant ground-state energy estimation. In the Heisenberg-limited regime, our approach achieves performance comparable to state-of-the-art methods while using simplified classical post-processing. In the low-depth regime, it obtains optimal query--depth tradeoffs up to polylogarithmic factors, with provable guarantees and improved empirical performance over prior approaches. The resulting protocol is ancilla-free and requires only standard Grover reflections. Due to its flexibility, generality, and robustness, we expect our approach to be a key enabler for a broad range of early fault-tolerant applications.

The two-dimensional O(3) nonlinear sigma model is a well known toy model for studying non-perturbative phenomena in quantum field theory. A central challenge is the renormalization of the energy-momentum tensor, which is complicated by the nonlinear realization of the $O(3)$ symmetry leading to non-trivial operator mixing patterns, and by large discretization artifacts affecting the determination of renormalization constants. We present results for the renormalization constants in the non-singlet sector, employing a modified lattice action with shifted boundary conditions and defining the renormalized coupling through the gradient flow. With this we obtain a precise determination of the renormalization constants $z_T$ and $Z_T$

We analyse the coherent-state (CS) transformation in quantum electrodynamics coupled cluster (QED-CC) theory from the perspective of its non-vanishing commutator with the polaritonic cluster operator. Specifically, we show that a QED Hartree-Fock (QED-HF) reference state parametrized by the CS transformation leads to a QED-CC Lagrangian formally determined by CS-representations of polaritonic Hamiltonian, polaritonic cluster and polaritonic deexcitation operators. Moreover, the herein proposed approach differs from the original formulation of QED-CC theory in the definition of the photon state basis and exploits photon-added coherent states in contrast to previously considered displaced number states. We find a renormalization of both QED-CC correlation energy and QED-CC ground state induced by the CS transformation, which depends on the mean-field expectation value of the molecular dipole operator and therefore breaks origin invariance for charged systems. Electronic contributions to correlation energy and QED-CC ground state are renormalized by CS-transformed mixed excitation and deexcitation operators. In contrast, the CS-transformed single-photon excitation affects only the QED-CC ground state but not directly the correlation energy. The renormalized QED-CC ansatz becomes similar to the original QED-CC formulation for large cavity frequencies leading to small renormalization corrections. A divergent correlation energy for molecules with a non-vanishing molecular dipole moment is found in the low-frequency limit, which we discuss with respect to multi-photon excitations in the polaritonic cluster operator and the relevance of the cavity-Born-Oppenheimer framework.

In a decentralized balancing model, Balance Responsible Parties (BRPs) are encouraged by the Transmission System Operator (TSO) to deviate from their schedule to help the system restore balance, also referred to as implicit balancing. This could reduce balancing costs for the grid operator and lower the entry barrier for flexible assets compared to explicit balancing services. However, these implicit reactions may overshoot when their total capacity is high, potentially requiring more explicit activations. This study analyses the effect of increased participation in the decentralized balancing model in Belgium. To this end, we develop a market simulator that produces price signals on minute-level and simulate the implicit reactions for battery assets with different risk profiles. Besides the current price formula, we also study two potential candidates for the near-term presented by the TSO. A simulation study is conducted using Belgian market data for the year 2023. The findings indicate that, while having a significant positive effect on the balancing costs at first, the risk of overshoots can outweigh the potential benefits when the total capacity of the implicit reactions becomes too large. Furthermore, even when the balancing costs start to increase for the TSO, BRPs were still found to benefit from implicit balancing.

We investigate quantum and classical signatures of a Schwarzschild black hole embedded in a Hernquist dark matter halo. Starting from the exact spherically symmetric solution describing this composite system, we analyze particle production for both bosonic and fermionic fields using semiclassical techniques. Hawking radiation is derived through Bogoliubov transformations and independently via the tunneling method with energy conservation, allowing us to identify the effective temperature, emission spectrum, and the role of dark matter parameters in suppressing particle creation. The evaporation process is examined in the high-frequency regime, leading to modified evaporation times and emission rates relative to the vacuum Schwarzschild case. We further study absorption and scattering of massless scalar waves employing a partial-wave analysis, computing phase shifts, partial and total cross sections, and assessing the impact of the Hernquist scale radius and density on these observables. Finally, null and timelike geodesics are explored to characterize light propagation and particle motion in the presence of the dark matter halo.

Deceptive reviews, refer to fabricated feedback designed to artificially manipulate the perceived quality of products. Within modern e-commerce ecosystems, these reviews remain a critical governance challenge. Despite advances in review-level and graph-based detection methods, two pivotal limitations remain: inadequate generalization and lack of interpretability. To address these challenges, we propose JARVIS, a framework providing Judgment via Augmented Retrieval and eVIdence graph Structures. Starting from the review to be evaluated, it retrieves semantically similar evidence via hybrid dense-sparse multimodal retrieval, expands relational signals through shared entities, and constructs a heterogeneous evidence graph. Large language model then performs evidence-grounded adjudication to produce interpretable risk assessments. Offline experiments demonstrate that JARVIS enhances performance on our constructed review dataset, achieving a precision increase from 0.953 to 0.988 and a recall boost from 0.830 to 0.901. In the production environment, our framework achieves a 27% increase in the recall volume and reduces manual inspection time by 75%. Furthermore, the adoption rate of the model-generated analysis reaches 96.4%.

Equilibrium statistical ensembles commute with the Hamiltonian and thus carry no coherence in the energy eigenbasis. We develop a framework in which energy fluctuations can retain genuinely quantum-coherent contributions. We foliate state space into ``minimum-variance leaves,'' defined by minimizing the average energy variance over all pure-state decompositions, with the minimum set by the quantum Fisher information. On each leaf we construct the least-biased state compatible with normalization and mean energy, defining a leaf-canonical ensemble. The Gibbs ensemble is recovered on the distinguished commuting leaf, while generic states are organized by their leaf label. This structure provides a natural setting to extend eigenstate thermalization beyond equilibrium via a ``leaf typicality'' hypothesis. According to that hypothesis, local observables depend only on the leaf and energy and are reproduced by a representative pure state drawn from the optimal ensemble, whose minimized energy spread reduces the complexity of time evolution.

The rapid adoption of AI-powered coding assistants is transforming software development practices, yet systematic comparisons of their effectiveness across different task types and over time remain limited. This paper presents an empirical study comparing five popular agents (OpenAI Codex, GitHub Copilot, Devin, Cursor, and Claude Code), analyzing 7,156 pull requests (PRs) from the AIDev dataset. Temporal trend analysis reveals heterogeneous evolution patterns: Devin exhibits the only consistent positive trend in acceptance rate (+0.77% per week over 32 weeks), whereas other agents remain largely stable. Our analysis suggests that the PR task type is a dominant factor influencing acceptance rates: documentation tasks achieve 82.1% acceptance compared to 66.1% for new features - a 16 percentage point gap that exceeds typical inter-agent variance for most tasks. OpenAI Codex achieves consistently high acceptance rates across all nine task categories (59.6%-88.6%), with stratified Chi-square tests confirming statistically significant advantages over other agents in several task categories. However, no single agent performs best across all task types: Claude Code leads in documentation (92.3%) and features (72.6%), while Cursor excels in fix tasks (80.4%).

Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin estimator is the unique estimator which both respects the symmetries of the problem and has non-trivial rate. We resolve the open problem of constructing principled prediction intervals for it. For intermediate $m$ we propose a new estimator which has a vastly improved worst case MSE compared to competing methods and we expect that our method can be applied to other species sampling problems. For large $m$ we follow previous authors in assuming a power law tail and show that a simple estimator achieves the same rate and better empirical performance than a recent sophisticated method. Moreover, we give pre-asymptotic guarantees. We extend the rate guarantees to incidence data, without further independence assumptions, provided that the sets are of bounded size. In the process we use Stein's method to obtain concentration inequalities for some natural functionals of sequences of i.i.d. discrete-set-valued random variables which are of independent interest.

Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified microscopic, mechanistic framework for deriving effective metapopulation and metacommunity models from individual-based ecological dynamics on arbitrary dispersal networks. The resulting coarse-grained description features an effective dispersal kernel that encodes both microscopic dynamical parameters and network topology. Based on this framework, we demonstrate exact analytical results for species persistence in both homogeneous and heterogeneous landscapes, including a generalization of the classical concept of metapopulation capacity to non-uniform local extinction rates. Incorporating stochasticity arising from finite carrying capacities, we obtain a reduced one-dimensional description that reveals universal finite-size scaling laws for extinction times and fluctuations. Extending the approach to multiple competing species, we prove that in homogeneous environments monodominance can be avoided only in a fine-tuned, marginally stable coexistence state, and that the classic metapopulation capacity gives only a necessary but not sufficient condition for persistence. We demonstrate that heterogeneous habitats can support stable coexistence, but only above a critical level of heterogeneity. Finally, we outline how additional ecological processes can be systematically incorporated within the same formalism. Together, these results provide analytical benchmarks and a general route for constructing spatially explicit ecological theories based on an interpretable underlying mechanistic foundation.

Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS), owing to the additional thermodynamic resources inherently present in the squeezed state. We introduce a formal extension of the principle to such unitarily transformed thermal states. By defining an effective Hamiltonian, we rigorously establish a generalized Landauer inequality, which naturally reduces to the standard case for an ordinary thermal reservoir as a special instance. The framework further yields a consistent definition of entropy production and a proof of its non-negativity. We illustrate its utility by studying an arbitrarily moving Unruh-DeWitt detector coupled to a quantum field initially prepared in the STS. Using perturbation theory, we compute the entropy production explicitly, confirming its positivity. As a result of the symmetry breaking induced by the unitary transformation, it depends on both the proper time interval and the absolute spacetime position. Our work resolves the apparent violation of Landauer's principle with STSs. It also provides a robust tool for analyzing quantum thermodynamics in non-equilibrium and relativistic settings, with potential implications for quantum thermal machines and information protocols.

Wilson loops are essential objects in QCD and have been pivotal in scale setting and demonstrating confinement. Various generalizations are crucial for computations needed in effective field theories. In lattice gauge theory, Wilson loop calculations face challenges, including excited-state contamination at short times and the signal-to-noise ratio issue at longer times. To address these problems, we develop a new method by using neural networks to parametrize interpolators for the static quark-antiquark pair. We construct gauge-equivariant layers for the network and train it to find the ground state of the system. The trained network itself is then treated as our new observable for the inference. Our results demonstrate a significant improvement in the signal compared to traditional Wilson loops, performing as well as Coulomb-gauge Wilson-line correlators while maintaining gauge invariance. Additionally, we present an example where the optimized ground state is used to measure the static force directly, as well as another example combining this method with the multilevel algorithm. Finally, we extend the formalism to find excited-state interpolators for static quark-antiquark systems. To our knowledge, this work is the first study of neural networks with a physically motivated loss function for Wilson loops.

Contradictory experimental reports on the relationship between efficiency and stimulation frequency have hindered mechanistic understanding in converting neural activity into mechanical work during muscle contraction. To resolve this issue, we develop a biophysical model integrating calcium-mediated excitation with a detailed cross-bridge cycle to enable single-fiber simulations. Our model predictions indicate that the emergent shortening velocity is the primary determinant of cross-bridge efficiency: efficiency peaks at an optimal velocity and declines at higher or lower velocities, while frequency appears to exert secondary influence. Critically, the velocity yielding peak efficiency remains almost consistent across frequencies, with a slight upward shift at higher frequencies in most of our parametric studies. Interestingly, elevated inorganic phosphate ([Pi]) appears to amplify the efficiency disparity between high- and low-frequency regimes in our analysis. Our work suggests that stimulation frequency modulates efficiency predominantly through its regulation of shortening velocity, which primarily governs the kinetics of the myosin power stroke. This work may help clarify neural control of muscle energetics, and provide a quantitative foundation for studying muscle function in physiological and pathological contexts.

The process-independence of the color dipole amplitude is a cornerstone of high-energy Quantum Chromodynamics (QCD). However, standard phenomenological approaches typically rely on rigid parametric ansatzes and often require ad-hoc geometric adjustments to reconcile inclusive and diffractive measurements. To resolve this tension, we introduce Physics-Informed Neural Networks (PINNs) employing a ``Teacher--Student'' strategy. The physics-based momentum-space Balitsky-Kovchegov evolution dynamics act as the ``Teacher,'' constraining the solution manifold, while the network ``Student'' is refined against inclusive HERA $F_2$ data. This approach extracts a model-independent dipole amplitude without assuming initial states. Strikingly, we demonstrate that this amplitude -- without parameter retuning or geometric rescaling -- successfully predicts the absolute normalization and kinematic dependence of exclusive $J/ψ$ photoproduction cross-sections. This parameter-free prediction of the saturation dynamics provides promising evidence for the process-independence of the gluon saturation scale and establishes PINNs as a transformative paradigm for uncovering non-perturbative QCD structures.