Regions Of Space Research Articles

EEG classification with limited data: A deep clustering approach

In this paper, we propose a novel training strategy designed to prevent deep neural networks from overfitting when trained on a very limited number of samples. This approach enables the use of very deep networks in applications like EEG classification, where data collection is challenging, leading to significant overfitting issues. To address this issue, we introduce a classification network that leverages a deep clustering operation in its latent space. The network utilizes a set of dictionary elements as auxiliary inputs and learns to guide each input sample toward one of the clusters, each derived from a dictionary element. This process facilitates the grouping of samples from the same class within the same region of the latent space, thereby reducing the risk of complex class boundaries and overfitting. Additionally, we introduce two probabilistic models within our clustering approach to mitigate outlier issues and address augmentation challenges commonly encountered with EEG signals. Experimental evaluations on two widely recognized databases, EEG-ImageNet and BCIIV2a, demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches, achieving 97.9% accuracy on EEG-ImageNet and 84.1% accuracy on BCIIV2a.

Smooth reheating and dark matter via non-Abelian gauge theory

We demonstrate how a dark sector can provide a crucial link between a vacuum-dominated early universe and the later radiation-dominated epoch. As an example, we consider a feeble axion-like coupling of dark non-Abelian gauge fields with a single inflaton. In this scenario, a dark heat bath emerges at the end of inflation. As the dark sector cools down, its gauge fields confine into composite glueball states. The reheating of the visible sector is realized through portal interactions. After confinement, discrete symmetries protect part of the glueball states that form relic dark matter, while the others keep decaying into Standard Model degrees of freedom. The dark relic abundance depends mostly on the departure from equilibrium dynamics after the phase transition, constraining the confinement scale of the dark sector. Moreover, indirect detection and Big-Bang nucleosynthesis set bounds on the scale of portal interactions. We show that in a narrow but non-vanishing region of the parameter space, the correct dark matter abundance and sufficient reheating temperature are simultaneously reached.

Quantum Topological Atomic Properties of 44K molecules

We present a data set of quantum topological properties of atoms of 44K randomly selected molecules from the GDB-9 data set. These atomic properties were obtained as defined by the quantum theory of atoms in molecules (QTAIM) within an atomic basin, a region of real space bounded by zero-flux surfaces in the electron density gradient vector field. The wave function files were generated through DFT static calculations (B3LYP/6-31G), and the atomic properties were calculated using QTAIM. The calculated atomic properties include the energy of the atomic basin, the electronic population, the magnitude of the total dipole moment, and the magnitude of the total quadrupole moment. The atomic properties allow one to understand the chemical structure, reactivity, and molecular recognition. They can be incorporated into force fields for molecular dynamics or for predicting reactive sites. We believe that this data set could facilitate new studies in chemical informatics, machine learning applied to chemistry, and computational molecular design.

Structural stability hypothesis of dual unitary quantum chaos

Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits—a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focusing on the , i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions. Published by the American Physical Society 2024

Robust H-Infinity Speed Controller based Optimization Technique for Doubly Salient Singly Excited Motor Drive

This research presents a novel robust controller for Doubly Salient Singly Excited motor (DSSEM) speed controlling. This algorithm aims to minimize the influence of disturbances that affect motor function and offer the best duty cycles possible to accomplish tracking performance. The H-infinity () tracking control approach can optimally solve the tracking game algebraic Riccati equation online by using reinforcement learning. This method enhances the Doubly Salient Singly Excited Motor (DSSEM) system model with the reference current model to produce a quadratic value function. The quadratic value function facilitates the implementation of a linear quadratic tracker, similar to control. By partitioning and organizing the nonlinear domain of the DSSEM into a table of nodes, the system can manage complex nonlinearities efficiently. Each node in the table represents a specific region of the control space, allowing for precise and robust tracking of desired reference signals. This structure ensures that the DSSEM achieves optimal performance and stability, adapting dynamically to operational changes. Furthermore, the tracking control is outfitted with a linear interpolation method to facilitate a seamless transition between matrices in the table. Finally, this paper presents simulation results to validate the proposed control algorithm.

Simulating heavy neutral leptons with general couplings at collider and fixed target experiments

Heavy neutral leptons (HNLs) are motivated by attempts to explain neutrino masses and dark matter. If their masses are in the MeV to several GeV range, HNLs are light enough to be copiously produced at collider and accelerator facilities, but also heavy enough to decay to visible particles on length scales that can be observed in particle detectors. Previous studies evaluating the sensitivities of experiments have often focused on simple but not particularly well-motivated models in which the HNL mixes with only one active neutrino flavor. In this work, we accurately simulate models for HNL masses between 100 MeV and 10 GeV and arbitrary couplings to e, μ, and τ leptons. We include over 150 HNL production channels and over 100 HNL decay modes, including all of the processes that can be dominant in some region of the general parameter space. The result is , a user-friendly, fast, and flexible library to compute the properties of HNL models. As examples, we implement to extend the package to evaluate the prospects for HNL discovery at forward LHC experiments. We present sensitivity reaches for FASER and FASER2 in five benchmark scenarios with coupling ratios |Ue|2∶|Uμ|2∶|Uτ|2=1∶0∶0, 0∶1∶0, 0∶0∶1, 0∶1∶1, and 1∶1∶1, where the latter two have not been studied previously. Comparing these to current constraints, we identify regions of parameter space with significant discovery prospects. Published by the American Physical Society 2024

Structure-Based Drug Design with a Deep Hierarchical Generative Model.

Recently, the remarkable growth of available crystal structure data and libraries of commercially available or readily synthesizable molecules have unlocked previously inaccessible regions of chemical space for drug development. Paired with improvements in virtual ligand screening methods, these expanded libraries are having a notable impact on early drug design efforts. Yet screening-based methods still face scalability limits, due to computational constraints and the sheer scale of drug-like space. Machine learning approaches are overcoming these limitations by learning the fundamental intra- and intermolecular relationships in drug-target systems from existing data. Here, we introduce DrugHIVE, a deep hierarchical variational autoencoder that outperforms state-of-the-art autoregressive and diffusion-based methods in both speed and performance on common generative benchmarks. DrugHIVE's hierarchical design enables improved control over molecular generation. Its capabilities include dramatically increasing virtual screening efficiency and accelerating a wide range of common drug design tasks, including de novo generation, molecular optimization, scaffold hopping, linker design, and high-throughput pattern replacement. Our highly scalable method can even be applied to receptors with high-confidence AlphaFold-predicted structures, extending the ability to generate high-quality drug-like molecules to a majority of the unsolved human proteome.

Exhaustive local chemical space exploration using a transformer model

How many near-neighbors does a molecule have? This fundamental question in chemistry is crucial for molecular optimization problems under the similarity principle assumption. Generative models can sample molecules from a vast chemical space but lack explicit knowledge about molecular similarity. Therefore, these models need guidance from reinforcement learning to sample a relevant similar chemical space. However, they still miss a mechanism to measure the coverage of a specific region of the chemical space. To overcome these limitations, a source-target molecular transformer model, regularized via a similarity kernel function, is proposed. Trained on a largest dataset of ≥200 billion molecular pairs, the model enforces a direct relationship between generating a target molecule and its similarity to a source molecule. Results indicate that the regularization term significantly improves the correlation between generation probability and molecular similarity, enabling exhaustive exploration of molecule near-neighborhoods.

Comparison of Optimization Methods for the Attitude Control of Satellites

The definition of multiple operational modes in a satellite is of vital importance for the adaptation of the satellite to the operational demands of the mission and environmental conditions. In this work, three optimization methods were implemented for the initial calibration of an attitude controller based on fuzzy logic with the purpose of performing an initial exploration of optimal regions of the design space: a multi-objective genetic algorithm (GAMULTIOBJ), a particle swarm optimization (PSO), and a multi-objective particle swarm optimization (MOPSO). The performance of the optimizers was compared in terms of energy cost, accuracy, computational cost, and convergence capabilities of each algorithm. The results show that the PSO algorithm demonstrated superior computational efficiency compared to the others. Concerning the exploration of optimum regions, all algorithms exhibited similar exploratory capabilities. PSO’s low computational cost allowed for thorough scanning of specific interest regions, making it ideal for detailed exploration, whereas MOPSO and GAMULTIOBJ provided more balanced performance with constrained Pareto front elements.

Hubble tension and cosmological imprints of U(1)X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_X$$\\end{document} gauge symmetry: U(1)B3-3Li\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_{B_3-3 L_i}$$\\end{document} as a case study

The current upper limit on Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}$$\\end{document} at the time of CMB by Planck 2018 can place stringent constraints in the parameter space of BSM paradigms where their additional interactions may affect neutrino decoupling. Motivated by this fact in this paper we explore the consequences of light gauge boson (Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document}) emerging from local U(1)X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_X$$\\end{document} symmetry in Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}$$\\end{document} at the time of CMB. First, we analyze the generic U(1)X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_X$$\\end{document} models with arbitrary charge assignments for the SM fermions and show that, in the context of Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}$$\\end{document} the generic U(1)X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_X$$\\end{document} gauged models can be broadly classified into two categories, depending on the charge assignments of first generation leptons. We then perform a detailed analysis with two specific U(1)X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_X$$\\end{document} models: U(1)B3-3Le\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_{B_3-3L_e}$$\\end{document} and U(1)B3-3Lμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U(1)_{B_3-3L_\\mu }$$\\end{document} and explore the contribution in Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}$$\\end{document} due to the presence of Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document} realized in those models. For comparison, we also showcase the constraints from low energy experiments like: Borexino, Xenon 1T, neutrino trident, etc. We show that in a specific parameter space, particularly in the low mass region of Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document}, the bound from Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}$$\\end{document} (Planck 2018) is more stringent than the experimental constraints. Additionally, a part of the regions of the same parameter space may also relax the H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} tension.

Snapback Repellers, Computational Chaos and Extreme Multistability in Discrete-Time Memristor Murali–Lakshmanan–Chua Circuit

Discretization schemes such as Euler method and Runge–Kutta techniques are extensively used to find approximate solutions of Continuous-Time (CT) dynamical system. While the approximation is good for small discretization step sizes, as pointed out by Lorenz, when the step size increases, computational chaos and computational instability are frequently observed, the former phenomenon being a precursor to the latter. By computational instability, it is meant that there is a blow up of trajectories for the Discrete-Time (DT) system. Computational chaos instead means that for certain step sizes, the DT system displays chaos while the CT counterpart is not chaotic. This paper studies the dynamics of a class of second-order maps obtained via the discretization of a Memristor Murali–Lakshmanan–Chua Circuit (MMLCC). The discretization, which is based on the DT Flux–Charge Analysis Method (FCAM), guarantees that the first integrals of a CT-MMLCC are preserved exactly for the DT system. Hence the dynamics of DT-MMLCC evolves on invariant manifolds and it is characterized by the coexistence of infinitely many different attractors (extreme multistability). The paper uses analytic techniques introduced by Marotto, based on the concept of snapback repellers and transverse homoclinic orbits, to study the chaotic behaviors of the maps. Regions of the parameter space are singled out where there exist snapback repellers for DT-MMLCC, thus implying that the maps display chaos in the Marotto and in the Li–Yorke sense. Since the corresponding CT-MMLCC does not display chaos, the observed chaos of DT-MMLCC is genuinely a consequence of the discretization scheme used in the paper, i.e. it can be actually considered as computational chaos. It is also verified that computational chaos is a precursor to computational instability of the DT-MMLCC maps. Finally, the paper analyzes the effect on chaos obtained by changing the invariant manifold where the dynamics evolves.

Tomonaga-Luttinger liquid and quantum criticality in spin- antiferromagnetic Heisenberg chain C 14 H 18 CuN 4 O 10 via Wilson ratio.

The ground state of a one-dimensional spin- uniform antiferromagnetic Heisenberg chain (AfHc) is a Tomonaga-Luttinger liquid which is quantum-critical with respect to applied magnetic fields up to a saturation field beyond which it transforms to a fully polarized state. Wilson ratio has been predicted to be a good indicator for demarcating these phases [Phys. Rev. B 96, 220401 (2017)]. From detailed temperature and magnetic field-dependent magnetization, magnetic susceptibility and specific heat measurements in a metalorganic complex and comparisons with field theory and quantum transfer matrix method calculations, the complex was found to be a very good realization of a spin- AfHc. Wilson ratio obtained from experimentally obtained magnetic susceptibility and magnetic contribution of specific heat values was used to map the magnetic phase diagram of the uniform spin- AfHc over large regions of phase space demarcating Tomonaga-Luttinger liquid, saturation field quantum critical, and fully polarized states. Luttinger parameter and spinon velocity were found to match very well with the values predicted from conformal field theory.

Extension of the SpK atomic physics code to generate global equation of state data

Global microphysics models are required for the modelling of high-energy-density physics (HEDP) experiments, the improvement of which are critical to the path to inertial fusion energy. This work presents further developments to the atomic and microphysics code, SpK, part of the numerical modelling suite of Imperial College London and First Light Fusion. We extend the capabilities of SpK to allow the calculation of the equation of state (EoS). The detailed configuration accounting calculations are interpolated into finite-temperature Thomas–Fermi calculations at high coupling to form the electronic component of the model. The Cowan model provides the ionic contribution, modified to approximate the physics of diatomic molecular dissociation. By utilising bonding corrections and performing a Maxwell construction, SpK captures the EoS from states ranging from the zero-pressure solid, through the liquid–vapour coexistence region and into plasma states. This global approach offers the benefit of capturing electronic shell structure over large regions of parameter space, building highly-resolved tables in minutes on a simple desktop. We present shock Hugoniot and off-Hugoniot calculations for a number of materials, comparing SpK to other models and experimental data. We also apply EoS and opacity data generated by SpK in integrated simulations of indirectly-driven capsule implosions, highlighting physical sensitivities to the choice of EoS models.

Stability of fronts in the diffusive Rosenzweig–MacArthur model

AbstractWe consider a diffusive Rosenzweig–MacArthur predator–prey model in the situation when the prey diffuses at a rate much smaller than that of the predator. In a certain parameter regime, the existence of fronts in the system is known: the underlying dynamical system in a singular limit is reduced to a scalar Fisher–KPP (Kolmogorov–Petrovski–Piskunov) equation and the fronts supported by the full system are small perturbations of the Fisher–KPP fronts. The existence proof is based on the application of the Geometric Singular Perturbation Theory with respect to two small parameters. This paper is focused on the stability of the fronts. We show that, for some parameter regime, the fronts are spectrally and asymptotically stable using energy estimates, exponential dichotomies, the Evans function calculation, and a technique that involves constructing unstable augmented bundles. The energy estimates provide bounds on the unstable spectrum which depend on the small parameters of the system; the bounds are inversely proportional to these parameters. We further improve these estimates by showing that the eigenvalue problem is a small perturbation of some limiting (as the modulus of the eigenvalue parameter goes to infinity) system and that the limiting system has exponential dichotomies. Persistence of the exponential dichotomies then leads to bounds uniform in the small parameters. The main novelty of this approach is related to the fact that the limit of the eigenvalue problem is not autonomous. We then use the concept of the unstable augmented bundles and by treating these as multiscale topological structures with respect to the same two small parameters consequently as in the existence proof, we show that the stability of the fronts is also governed by the scalar Fisher–KPP equation. Furthermore, we perform numerical computations of the Evans function to explicitly identify regions in the parameter space where the fronts are spectrally stable.

Neglected Tropical Diseases: A Chemoinformatics Approach for the Use of Biodiversity in Anti-Trypanosomatid Drug Discovery.

The development of new treatments for neglected tropical diseases (NTDs) remains a major challenge in the 21st century. In most cases, the available drugs are obsolete and have limitations in terms of efficacy and safety. The situation becomes even more complex when considering the low number of new chemical entities (NCEs) currently in use in advanced clinical trials for most of these diseases. Natural products (NPs) are valuable sources of hits and lead compounds with privileged scaffolds for the discovery of new bioactive molecules. Considering the relevance of biodiversity for drug discovery, a chemoinformatics analysis was conducted on a compound dataset of NPs with anti-trypanosomatid activity reported in 497 research articles from 2019 to 2024. Structures corresponding to different metabolic classes were identified, including terpenoids, benzoic acids, benzenoids, steroids, alkaloids, phenylpropanoids, peptides, flavonoids, polyketides, lignans, cytochalasins, and naphthoquinones. This unique collection of NPs occupies regions of the chemical space with drug-like properties that are relevant to anti-trypanosomatid drug discovery. The gathered information greatly enhanced our understanding of biologically relevant chemical classes, structural features, and physicochemical properties. These results can be useful in guiding future medicinal chemistry efforts for the development of NP-inspired NCEs to treat NTDs caused by trypanosomatid parasites.

Improving derivative-free optimization algorithms through an adaptive sampling procedure

Black-box optimization plays a pivotal role in addressing complex real-world problems where the underlying mathematical model is unknown or expensive to evaluate. In this context, this work presents a method to enhance the performance of derivative-free optimization algorithms by integrating an adaptive sampling process. The proposed methodology aims to overcome the limitations of traditional methods by intelligently guiding the search towards promising regions of the search space. To achieve this, we utilize machine learning models, which effectively substitute first principles models. Furthermore, we employ the error maximization approach to steer the exploration towards areas where the surrogate model deviates significantly from the true model. Moreover, we involve a heuristic method, an adaptive sampling procedure, that repeats calls to a widely-used derivative-free optimization algorithm, SNOBFIT, allowing for the creation of new and improved surrogate models. To evaluate the efficiency of the proposed method, we conduct a comparative analysis across a benchmark set of 776 continuous problems. Our findings indicate that our approach successfully solved 93% of the problems. Notably, for larger problems, our method outperformed the standard SNOBFIT algorithm by achieving a 19% increase in problem-solving rate, and when, we introduced an additional termination criterion to enhance computational efficiency, the proposed method achieved a 31% time reduction compared to SNOBFIT.

AI-based derivation of atrial fibrillation phenotypes in the general and critical care populations

Atrial fibrillation (AF) is the most common heart arrhythmia worldwide and is linked to a higher risk of mortality and morbidity. To predict AF and AF-related complications, clinical risk scores are commonly employed, but their predictive accuracy is generally limited, given the inherent complexity and heterogeneity of patients with AF. By classifying different presentations of AF into coherent and manageable clinical phenotypes, the development of tailored prevention and treatment strategies can be facilitated. In this study, we propose an artificial intelligence (AI)-based methodology to derive meaningful clinical phenotypes of AF in the general and critical care populations. Our approach employs generative topographic mapping, a probabilistic machine learning method, to identify micro-clusters of patients with similar characteristics. It then identifies macro-cluster regions (clinical phenotypes) in the latent space using Ward's minimum variance method. We applied it to two large cohort databases (UK-Biobank and MIMIC-IV) representing general and critical care populations. The proposed methodology showed its ability to derive meaningful clinical phenotypes of AF. Because of its probabilistic foundations, it can enhance the robustness of patient stratification. It also produced interpretable visualisation of complex high-dimensional data, enhancing understanding of the derived phenotypes and their key characteristics. Using our methodology, we identified and characterised clinical phenotypes of AF across diverse patient populations. Our methodology is robust to noise, can uncover hidden patterns and subgroups, and can elucidate more specific patient profiles, contributing to more robust patient stratification, which could facilitate the tailoring of prevention and treatment programs specific to each phenotype. It can also be applied to other datasets to derive clinically meaningful phenotypes of other conditions. This study was funded by the DECIPHER project (LJMU QR-PSF) and the EU project TARGET (10113624).

Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds

The goal of this paper is to study the number of sliding limit cycles of regularized piecewise linear visible–invisible twofolds using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most 1 zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most 2 limit cycles. Moreover, we detect regions in the parameter space with 2 limit cycles.

The Riemann Hilbert dressing method and wave breaking for two (2 + 1)-dimensional integrable equations

Abstract In this article, we present a method for generating (2 + 1)-dimensional integrable equations, resulting in the generalized Pavlov equation and dispersionless Kadomtsev–Petviashvili (dKP) equation, which can further be reduced to the standard Pavlov equation and dKP equation. Inspired by the inverse spectral transform presented in existing literature, we introduce the Riemann–Hilbert (RH) dressing method to construct the formal solutions of the Cauchy problems for the generalized Pavlov equation and dKP equation, providing a spectral representation of the solutions. Subsequently, we also extensively investigate the longtime behavior of solutions to these two equations in specific space regions. In particular, for the generalized dKP equation, we conduct a dedicated study on its implicit solutions expressed by arbitrary differential function through linearizing their RH problems. In the final section, we elaborate in detail on the analytic aspects of the wave breaking of a localized two-dimensional wave evolving according to the Hopf equation. With the assistance of a transformation, the longtime breaking of solutions to the generalized dKP equation can then be further characterized.

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.