We prove that the laws of the BPHZ random models satisfy some transportation cost inequalities in the full subcritical regime if there is no 'variance blowup' and the law of the noise is translation invariant and satisfies some transportation cost inequality. We emphasize two consequences of this result or its proof: The automatic integrability properties of the invariant probability measures of a number of singular stochastic partial differential equations, including the $Φ^4_{4-δ}$ measures over the $4$-dimensional torus, for all $0 < δ< 4$, and a general large deviation principle satisfied by the BPHZ models.

This paper investigates the conditions under which a given circular (synchronizing) DFA is \emph{simple} (sometimes referred to as \emph{primitive}) and when it is \emph{irreducible}. Our notion of irreducibility slightly differs from the classical one, since we are considering our monoid representations to be over $\mathbb{C}$ instead of $\mathbb{Q}$; nevertheless, several well-known results remain valid-for instance, the fact that every irreducible automaton is necessarily simple. We provide a complete characterization of simplicity in the circular case by means of the \emph{weak contracting property}. Furthermore, we establish necessary and sufficient conditions for a circular \emph{contracting automaton} (a stronger condition than the weakly contracting one) to be irreducible, and we present examples illustrating our results.

We explain why on certain five-manifolds, topological 5d $\mathcal{N} = 2$ gauge theory of Haydys-Witten twist with gauge group $G$, is dual to that of Geyer-Mülsch twist with gauge group $^LG$, where $G$ is a real, compact Lie group with Langlands dual $^LG$. In turn, via their 2d and 3d gauged A/B-twisted Landau-Ginzburg model interpretations, we can show that (i) a Fukaya-Seidel-type $A_\infty$-1-category of an HW$_4$-instanton Floer homology of three-manifolds and (ii) a Fueter-type $A_\infty$-2-category of an HW$_3$-instanton Floer homology of two-manifolds, are dual to (i) an Orlov-type $A_\infty$-1-category of a novel holomorphic $^LG_{\mathbb{H}}$-flat Floer homology of three-manifolds and (ii) a Rozansky-Witten-type $A_\infty$-2-category of a novel holomorphic $^LG_{\mathbb{O}}$-flat Floer homology of two-manifolds, respectively. We also derive their Atiyah-Floer-type correspondences to symplectic categories. Our work, which demonstrates a mirror symmetry and Langlands duality of (higher) $A_\infty$-categories of Floer homologies, therefore furnishes purely physical proofs and gauge-theoretic generalizations of the mathematical conjectures by Bousseau [1] and Doan-Rezchikov [2], and more.

We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding into a larger Hilbert space. In this framework, error models are classified according to the isotypic decomposition of the conjugation action on the operator algebra. Our main result, the \emph{Schur bootstrap}, shows that if an intrinsic code satisfies the Knill--Laflamme conditions on a given symmetry sector, then the same error-protection relations hold for every extrinsic realization obtained from a group-equivariant isometric embedding into a larger Hilbert space. Thus a single intrinsic verification certifies the corresponding symmetry-resolved error-correction conditions across an entire family of physical realizations. We further introduce an intrinsic notion of distance, called depth, defined via adjoint order. For standard multi-qudit systems this coincides with conventional code distance, while for more general representations it refines the usual weight-based notion. We also prove an intrinsic Eastin--Knill theorem: any intrinsic code of depth at least two has a discrete logical symmetry group, with the obstruction to continuous covariant gates arising from the representation-theoretic structure of the adjoint action. We illustrate the framework with several examples, including a minimal $\mathrm{SU}(2)$ construction that unifies permutation-invariant qubit codes and bosonic codes, and higher-dimensional constructions exhibiting transversal Clifford symmetries and realizations beyond qubit systems.

This study examines the quantitative relationship between linguistic regularities and computational search complexity through a hybrid classical-quantum framework applied to Renaissance Italian texts. Using four representative works from the fifteenth and sixteenth centuries-Il Principe (Machiavelli), Il Cortegiano (Castiglione), I Ricordi (Guicciardini), and Orlando Furioso (Ariosto)-we construct character-based n-gram models under both a historically grounded 25-letter orthography and the full modern Italian alphabet. These models provide corpus-derived probabilistic baselines for evaluating substitution-cipher search processes. Combining classical hill climbing and simulated annealing with Grover-style quantum-inspired estimates and a QUBO annealing formulation, we quantify how the probability that a key produces a linguistically plausible decryption (pgood) relates to expected computational effort. Across cipher lengths from 200 to 1000 characters, empirical results confirm the predicted dependence of Grover oracle calls on 1/sqrt(pgood) and show that longer texts yield sharper score distributions and smaller feasible key regions. Overall, the findings establish a link between linguistic redundancy and search-space contraction, providing an empirical framework for comparing classical, quantum-inspired, and idealized quantum search dynamics under unified corpus-driven constraints.

The potential of solid-state quantum emitters for applications critically depends on several key figures of merit. One of the most important is the quantum coherence of the emitted single photons, which can be compromised by fast dephasing and spectral diffusion. In hexagonal boron nitride (hBN), blue-emitting color centers (or B centers) are seen as favorable in this regard, in the light of prior studies mainly based on resonant excitation. Yet, their coherence properties in the more accessible regime of non-resonant excitation (or photoluminescence) has not been extensively characterized. Here, we investigate the coherence and spectral diffusion of the photoluminescence from a B center in the continuous wave regime using photon correlation Fourier spectroscopy. We determine that the emission lineshape consists in a homogeneous contribution, whose linewidth increases with the laser power, and which is broadened by spectral diffusion at a timescale of 10 to 100 microseconds. At low power and short time, the emission line is only a factor ~2 above the Fourier limit, while at long times, the inhomogeneous linewidth increases up to more than a gigahertz. Our work deepens the understanding of decoherence processes of this preeminent family of quantum emitters in hBN.

In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics. Our contribution extends some recently proved similar results for stochastic processes to the case of continuous random fields. As a by-product, we introduce some new results on multiple Riemann-Stieltjes integrals.

This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach.

We present a full-sky, covariance-weighted analysis of redshift-frame transformations in the Pantheon+ Type Ia supernova sample to assess their impact on local measurements of the Hubble constant. Using 1,543 supernovae with heliocentric and CMB-frame redshifts, we study the residual field delta z = zCMB - zHEL, which traces the Solar System's kinematic correction. We recover the expected monopole <delta z> = (-3.8 +/- 0.1) x 10^-4 and a dipole amplitude A = (1.5 +/- 0.1) x 10^-3 aligned within 1 degree of the CMB dipole, confirming internal consistency. Propagating these residuals through the full Pantheon+ covariance matrix yields a negligible shift in H0, at the <= 2% level of the current tension, placing a quantitative upper bound on redshift-frame systematics.

Among the variety of quantum emitters in hexagonal boron nitride (hBN), blue-emitting color centers, or B centers, have gathered a particular interest owing to their excellent quantum optical properties. Moreover, the fact that they can be locally activated by an electron beam makes them suitable for top-down integration in photonic devices. However, in the absence of a real-time monitoring technique sensitive to individual emitters, the activation process is stochastic in the number of emitters, and its mechanism is under debate. Here, we implement an in-situ cathodoluminescence monitoring setup capable of detecting individual quantum emitters in the blue and ultraviolet (UV) range. We demonstrate that the activation of individual B centers is spatially and temporally correlated with the deactivation of individual UV centers emitting at 4.1 eV, which are ubiquitous in hBN. We then make use of the ability to detect individual B center activation events to demonstrate the controlled creation of an array with only one emitter per irradiation site. Additionally, we demonstrate a symmetric technique for heralded selective deactivation of individual emitters. Our results provide insights into the microscopic structure and activation mechanism of B centers, as well as versatile techniques for their deterministic integration.

The strong coupling regime of four-dimensional N=2 supersymmetric vacua of the heterotic string is analyzed from a dual domain wall perspective. Using modular invariance, we compute a closed form for the non-perturbative corrections to the supersymmetric domain wall equations, which enables a quantitative study of gravitational strong coupling regimes. A strong coupling singularity for the hidden Horava-Witten 9-brane is resolved, and the domain wall interpolates between the visible 9-brane and a supersymmetric Anti-de Sitter vacuum, thereby realizing a variant of the Randall-Sundrum model.

The scale of the seesaw mechanism is typically much larger than the electroweak scale. This hierarchy can be naturally explained by $U(1)_{B-L}$ symmetry, which after spontaneous symmetry breaking, simultaneously generates Majorana masses for neutrinos and produces a network of cosmic strings. Such strings generate a gravitational wave (GW) spectrum which is expected to be almost uniform in frequency unless there is a departure from the usual early radiation domination. We explore this possibility in Type I, II and III seesaw frameworks, finding that only for Type-I, long-lived right-handed neutrinos (RHN) may provide a period of early matter domination for parts of the parameter space, even if they are thermally produced. Such a period leaves distinctive imprints in the GW spectrum in the form of characteristic breaks and a knee feature, arising due to the end and start of the periods of RHN domination. These features, if detected, directly determine the mass $M$, and effective neutrino mass $\tilde m$ of the dominating RHN. We find that GW detectors like LISA and ET could probe RHN masses in the range $M\in[0.1,10^{9}]$ GeV and effective neutrino masses in the $\tilde m\in[10^{-10},10^{-8}]$ eV range. We investigate the phenomenological implications of long-lived right-handed neutrinos for both local and global $U(1)_{B-L}$ strings, focusing on dark matter production and leptogenesis. We map the viable and detectable parameter space for successful baryogenesis and asymmetric dark matter production from right-handed neutrino decays. We derive analytical and semi-analytical relations correlating the characteristic gravitational-wave frequencies to the neutrino parameters $\tilde m$ and $M$, as well as to the relic abundances of dark matter and baryons.

We review recent progress concerning the analysis of Lagrangians on immersions into $\mathbb{R}^d$ depending on the first and second fundamental forms and their covariant derivatives.

Effective field theories featuring light scalar fields play a pivotal role in addressing fundamental questions in (astro)particle physics and cosmology. However, such theories often confront hierarchy problems in the absence of a symmetry. Self-completion via classicalization offers a non-Wilsonian approach to ultraviolet (UV) completion, wherein new scalar self-interactions involving derivatives give rise to Vainshtein-like screening around energy-momentum sources. Rather than introducing new UV degrees of freedom to restore unitarity at high energies, these theories reshuffle their infrared (IR) degrees of freedom by generating extended semi-classical objects -- referred to as classicalons -- which decay into a multitude of soft particles. This mechanism incorporates non-localizable fields, thereby realizing a form of UV/IR mixing that is analogous to the dynamics of black holes in gravitational theories. In this article, having reviewed the fundamental principles of classicalization with a simple k-essence model, we then argue the necessity of maintaining a little hierarchy between the scalar mass and the scale of the first new resonances, thereby illustrating the impact of UV/IR mixing on hierarchy problems. Additionally, we investigate the effects of a scalar potential and couplings to fermions on the Vainshtein screening mechanism. We discuss that a chameleon-like screening mechanism must accompany the Vainshtein screening to preserve the integrity of classicalon solutions.

The dependence of transformation pattern in superelastic NiTi tubes on tube outer diameter D and wall-thickness t is investigated through quasi-static uniaxial tension and large-rotation bending experiments. The evolution of outer-surface strain fields is synchronized with global stress-strain and moment-curvature responses using a multi-magnification, high-resolution stereo digital image correlation system at 0.5-2x magnifications. The transformation patterns exhibit systematic size-dependent behaviors. Under tension and for a specific D, as the diameter-to-thickness ratio D/t decreases, a decreasing number of fat/diffuse helical bands emerge, in contrast to sharp/slim bands in thin tubes. Consequently, the austenite-martensite front morphology transitions from finely-fingered to coarsely-fingered with decreasing D/t. Below a characteristic D/t, front morphology no longer exhibits patterning and phase transformation proceeds via propagation of a finger-less front. Moreover, the transformation pattern exhibits an interrelation between D and D/t, where a front possessing diffuse fingers is observed in a thin but small tube. Under bending, both the global moment-curvature response and transformation pattern exhibit D- and D/t-dependence. While wedge-like martensite domains consistently form across all tube sizes, their growth is noticeably limited in smaller and thicker tubes due to geometrical constraints. A gradient-enhanced model of superelasticity is employed to analyze the distinct transformation patterns observed in tubes of various dimensions. The size-dependent behavior is explained based on the competition between bulk and interfacial energies, and the energetic cost of accommodating martensite fingers. By leveraging an axisymmetric tube configuration as a reference energy state, the extra energy associated with the formation of fingers is quantified.

Reliable downlink communication in satellite-to-underground networks remains challenging due to severe signal attenuation caused by underground soil and refraction in the air-soil interface. To address this, we propose a novel cooperative rate-splitting (CRS)-aided transmission framework, where an aboveground relay decodes and forwards the common stream to underground devices (UDs). Based on this framework, we formulate a max-min fairness optimization problem that jointly optimizes power allocation, message splitting, and time slot scheduling to maximize the minimum achievable rate across UDs. To solve this high-dimensional non-convex problem under uncertain channels, we develop a deep reinforcement learning solution framework based on the proximal policy optimization (PPO) algorithm that integrates distribution-aware action modeling and a multi-branch actor network. Simulation results under a realistic underground pipeline monitoring scenario demonstrate that the proposed approach achieves average max-min rate gains exceeding $167\%$ over conventional benchmark strategies across various numbers of UDs and underground conditions.

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

Rare decays of the Z boson provide a sensitive probe for physics beyond the Standard Model (SM). This study investigates the $e^{+}e^{-} \to Z \to ν\barνγ$ process within the context of the Tera-Z programmes at future colliders such as the FCC-ee and CEPC. The SM predicts a one-loop branching ratio of $7.16 \times 10^{-10}$ for $Z \to ν\barνγ$, a value four times smaller than the current experimental limit from the LEP. To explore this window for new physics, we parameterize anomalous $Zν\barνγ$ interactions using an Effective Field Theory framework, considering both dimension-6 and dimension-8 operators. A detailed simulation is performed by generating signal and background events with MadGraph, modeling particle showers with Pythia, and simulating detector effects with Delphes. The analysis employs key kinematic variables-including the photon energy ($E_γ$), missing transverse energy ($\not{E}_T$), and the missing transverse energy significance ($S_{\not{E}_T}$) to isolate the signal. The results yield upper limits on the anomalous couplings, from which we infer branching ratios for $Z \to ν\barνγ$ on the order of $10^{-9}$. This represents a significant improvement of several orders of magnitude over the LEP sensitivity. Consequently, this study demonstrates the unique potential of the Tera-Z runs not only to test the SM loop-level predictions with unprecedented precision but also to tightly constrain or reveal new anomalous interactions.

We investigate the diffusion of an intruder in a granular gas, with both components modeled as smooth hard spheres, both immersed in a low viscosity carrier fluid to form a particle-laden suspension. In this system, dissipative particle collisions coexist with the action of a solvent. The latter is modeled via a viscous drag force and a stochastic Langevin-like force proportional to the background fluid temperature. Building on previous kinetic theory and random-walk results of the tracer diffusion coefficient [R. Gómez González, E. Abad, S. Bravo Yuste, and V. Garzó, Phys. Rev. E \textbf{108}, 024903 (2023)], where random-walk predictions were compared with Chapman--Enskog results up to the second Sonine approximation, we assess the robustness of the Enskog framework by incorporating molecular dynamics (MD) simulations, using direct simulation Monte Carlo (DSMC) results as an intermediate reference. In particular, we focus on the intruder velocity autocorrelation function, considering intruders different masses (from 0.01 to 100 times the mass of the granular particles), and analyse the behavior of the intruder temperature and diffusion coefficient. Our results clarify the influence of the friction parameter and the conditions under which Enskog kinetic theory reliably describes intruder diffusion in granular suspensions.

We develop the theory of $L^2$-torsion of an automorphism of a group and compute it for every automorphism of a group which is hyperbolic and one-ended relative to a finite collection of virtually polycyclic groups. We also prove a combination formula for the $L^2$-torsion of a group in terms of the $L^2$-torsion of its stabilisers of a sufficiently nice action on a contractible space. We apply it to compute the $L^2$-torsion of a selection of CAT(0) lattices, of many relatively hyperbolic groups and their automorphisms, of higher dimensional graph manifolds, and of handlebody groups.

Lattice simulations and theoretical analyses consistently identify center vortices and monopoles as key nonperturbative configurations in Yang-Mills theory. In the continuum, the effective representation of mixed oriented and nonoriented center vortices showed that these degrees of freedom generate a confining flux tube with $N$-ality. Independently, studies of correlation functions reveal an infrared behavior characterized by massivelike scales. In this Letter, field correlators are computed for the first time in a theoretical framework based on center vortices. Using an Abelian-projected vacuum wave functional peaked on the mixed ensemble, we show the emergence of a massivelike gauge-invariant field strength correlator. For this behavior, the nonoriented component in the center-vortex condensate turns out to be essential, as is also the case for producing the correct properties of confining flux tubes.

Trajectory design in cislunar space under a High-Fidelity Ephemeris Model (HFEM) is pursued through a nonlinear optimization perspective anchored on the transition of solutions from lower fidelity models, namely the Circular Restricted Three-Body Problem (CR3BP). The optimization problem is posed in the likeness of a multiple-shooting approach, aiming for segment-to-segment continuity while tracking proximity to the original CR3BP structures. The analysis of various formulations leads to the selection of an unconstrained least-squares problem for further investigation. The nonlinear optimization problem is convexified and the use of the Levenberg-Marquardt algorithm, as an alternative to the minimum-norm update equation found in most literature, is investigated for its control over the update step and inherent robustness. Additional techniques, such as adaptive weighting, are employed to further consolidate the behavior of the proposed algorithm in challenging scenarios. Numerical trials evaluate the adequacy of the methodology presented and compare it to the minimum-norm baseline over various application cases, including the generation of quasi-periodic trajectories and orbital transfers between them. The proposed technique is found to be a suitable alternative to the minimum-norm scheme, generally retaining better proximity to the original CR3BP trajectories and providing benefits in numerical robustness and stability. Moreover, the ease of including proximity objectives in a relaxed manner is shown to facilitate control over the shape of the final converged solution.

Recent experiment on Fe-doped CoSn has uncovered a series of correlated phases upon hole doping of the kagome flat bands. Among the phases observed, a nematic phase with a six- to two-fold rotation symmetry breaking is found to prevail over a wide doping and temperature range. Motivated by these observations, we investigate the interaction-driven phases realized in a kagome model with partially filled, weakly dispersing flat bands. Density-density interactions up to second-nearest neighbors are considered. We identify a close competition between ferromagnetic and nematic phases in our self-consistent Hartree-Fock calculations: while on-site interaction favors ferromagnetism, the sizable inter-sublattice interactions stabilize nematicity over a wide doping window. Competition from translational-symmetry-breaking phases is also considered. Overall, our results show that nematicity is a generic outcome of partially filled kagome flat bands and establish a minimal framework for understanding correlated flat-band phases.

Polarized synchrotron emission from ultra-relativistic electrons spiraling the Galactic magnetic field has become one of the most relevant emissions in the Interstellar medium these last years due to the improvement in the quality of low-frequency observations. One of the recent experiments designed to explore this emission is the QUIJOTE experiment. We aim to study the spatial variations of the synchrotron emission in the QUIJOTE MFI data, by dividing the sky into physically separated regions. For such task, we firstly use a novel component separation method based on artificial neural networks to clean the synchrotron maps. After training the network with simulations, we fit both $EE$ and $BB$ spectra by assuming a power-law model. Then, we give estimations for the index $α_{S}$, the amplitude, and the ratio between $B$ and $E$ amplitudes. When analyzing the real data, we found a clear spatial variation of the synchrotron properties along the sky at 11 GHz, obtaining a steeper index in the Galactic plane of $α_{S}^{EE} = -3.1 \pm 0.3$ and $α_{S}^{BB} = -3.1 \pm 0.4$ and a flatter one at high Galactic latitudes of $α_{S}^{EE} = -3.05 \pm 0.2$ and $α_{S}^{B} = -2.98 \pm 0.27$. We found average values at all sky of $α_{S}^{EE} = -3.04 \pm 0.21$ and $α_{S}^{BB} = -3.00 \pm 0.34$. Furthermore, after obtaining an average value of $A_{S}^{EE} = 3.31 \pm 0.17$ $μK^{2}$ and $A_{S}^{BB} = 0.93 \pm 0.04$ $μK^{2}$, we estimate a ratio between $B$ and $E$ amplitudes of $A_{S}^{BB}/A_{S}^{EE} = 0.28 \pm 0.08$. Based on the results we conclude that, although neural networks seem to be valuable methods to apply on real ISM observations, combined analyses with Planck, WMAP and/or CBASS data are mandatory to reduce the contamination from QUIJOTE maps and then improve the accuracy of the estimations.

Treatment planning in radiotherapy is inherently a multi-criteria optimization (MCO) problem. Traditionally, the treatment's robustness is not formulated as a part of this decision making problem, but dealt with separately through margins or robust optimization. This work facilitates integration of robustness into multi-criteria optimization using a recently proposed efficient scenario-free (s-f) robust optimization approach: The s-f approach relies on the fast evaluation of the expected dose distribution and mean variance during optimization. This is achieved by precomputation of probabilistic quantities, which can then be used for repeated solving of subproblems in the two explored MCO approaches: Lexicographic Ordering (LO) and Pareto Front (PF) approximation. Different prioritization strategies within the LO approach are used to assess the impact of variance reduction while a 3-objective PF approximation, including a variance reduction objective, is generated to visualize and analyze trade-offs between the competing objectives. The robust optimization is performed including 100 scenarios modeling setup and range errors, as well as organ motion, on 3D- and 4DCT lung cancer patient datasets. Robustness analysis is performed to assess and explore the efficacy of all optimization strategies. The s-f approach enabled robust optimization in MCO with computational times comparable to nominal MCO. Both MCO strategies highlighted the interplay between dosimetric and variance reduction objectives. The LO approach showed how prioritization affects plan quality and robustness, while the PF analysis revealed a clear trade-off between robustness and organ-at-risk sparing. The reported analysis highlighted the conflicting trade-off nature of plan robustness and dosimetric quality, demonstrating how robust MCO supports a more informed and flexible decision-making process in treatment planning.

Thermal phonons are a major source of decoherence in quantum mechanical systems. Operating in the quantum ground state is therefore often an experimental prerequisite. Additionally to passive cooling in a cryogenic environment, active laser cooling enables the reduction of phonons at specific acoustic frequencies. Brillouin cooling has been used to show efficient reduction of the thermal phonon population in waveguides at GHz frequencies down to 74 K. In this letter, we demonstrate cooling of a 7.608 GHz acoustic mode by combining Brillouin active cooling with precooling from 77 K using liquid nitrogen. We show a 69 % reduction in the phonon population, resulting in a final temperature of 24.3 K, 50 K lower than previously reported.

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of validity for the classification of bifurcation diagrams in two classes of continuous-time networked dynamical systems, analogous in structure to the Hopfield and the Firing Rate dynamic neural network models. Our approach leverages recent advances in computing the bounds for the validity of Lyapunov-Schmidt reduction, a reduction method widely employed in nonlinear systems analysis. Using these bounds we rigorously characterize neighbourhoods around bifurcation points where predictions from reduced-order bifurcation equations remain reliable. We further demonstrate how these bounds can be applied to an illustrative family of nonlinear opinion dynamics on k-regular graphs, which emerges as a special case of the general framework. These results provide new analytical tools for quantifying the robustness of bifurcation phenomena in dynamics over networked systems and highlight the interplay between network structure and nonlinear dynamical behaviour.

In this chapter we introduce the $θ$-dependence and the topological properties of QCD, features of the strongly interacting sector which give rise to the strong CP problem in the more general context of the Standard Model of particle physics. We discuss the analytical approaches that can be used to obtain qualitative, or in some cases quantitative, information on the $θ$-dependence of QCD and QCD-like models, discussing their range of validity and comparing their predictions with the numerical results obtained by means of lattice simulations.

We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.

We analyze noise in a quantum-enhanced fiber optic gyroscope (FOG), focusing on one of the leading sources of phase uncertainty - uncorrelated photon saturation. Taking a squeezed state input as a source for N00N states, we compute the uncorrelated false coincidence counts at the optimal phase bias, and determine an upper limit to the squeezed amplitude $ξ$ which allows for sub-shot noise precision. As examples, we apply parameters of present-day quantum FOG experiments, and determine the maximum possible precision enhancement based on their respective $ξ$ and optimal phase bias points. Aiming to future FOG setups with higher N00N state fluxes, our result highlights the need to transition to multimode states to bypass the $ξ$ limitation, such as photon pairs generated by the dynamical Casimir effect.