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Parkinson's disease (PD) is a neurological disorder requiring early and accurate diagnosis for effective management. Machine learning (ML) has emerged as a powerful tool to enhance PD classification and diagnostic accuracy, particularly by leveraging wearable sensor data. This survey comprehensively reviews current ML methodologies used in classifying Parkinsonian tremors, evaluating various tremor data acquisition methodologies, signal preprocessing techniques, and feature selection methods across time and frequency domains, highlighting practical approaches for tremor classification. The survey explores ML models utilized in existing studies, ranging from traditional methods such as Support Vector Machines (SVM) and Random Forests to advanced deep learning architectures like Convolutional Neural Networks (CNN) and Long Short-Term Memory networks (LSTM). We assess the efficacy of these models in classifying tremor patterns associated with PD, considering their strengths and limitations. Furthermore, we discuss challenges and discrepancies in current research and broader challenges in applying ML to PD diagnosis using wearable sensor data. We also outline future research directions to advance ML applications in PD diagnostics, providing insights for researchers and practitioners., Comment: 28 pages, 9 figures, 3 tables, Journal Artificial Intelligence In Medicine

The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schr\"odinger equation (GNLSE). We use the variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystal, finding that the VA equations involve the dilogarithm special function. The VA predicts that solitons and breathers exist, and the Vakhitov-Kolokolov criterion predicts that the solitons are stable solutions. Direct simulations of the underlying GNLSE corroborates the existence of such stable modes. The numerical solutions produce both regular breathers and ones featuring beats (long-period modulations of fast oscillations). In the latter case, the Fourier transform of amplitude oscillations reveals a nearly discrete spectrum characterizing the beats dynamics. Numerical solutions of another type demonstrate spontaneous splitting of the input pulse in two or several secondary ones., Comment: 34 pages, 28 figures, 56 references. To be published in a special issue of journal AXIOMS on the topic "Nonlinear Schroedinger equations"

In this article, we factor the composite $4n^2 +1$ using Fermat's factorization method. Consequently, we characterized all proper factors of composite $4n^2 +1$ in terms of its form. Furthermore, the composite Fermat's number is considered in this study., Comment: 8 pages, article

The Oscura experiment will lead the search for low-mass dark matter particles using a very large array of novel silicon Charge Coupled Devices (CCDs) with a threshold of two electrons and with a total exposure of 30 kg-yr. The R&D effort, which began in FY20, is currently entering the design phase with the goal of being ready to start construction in late 2024. Oscura will have unprecedented sensitivity to sub-GeV dark matter particles that interact with electrons, probing dark matter-electron scattering for masses down to 500 keV and dark matter being absorbed by electrons for masses down to 1 eV. The Oscura R&D effort has made some significant progress on the main technical challenges of the experiment, of which the most significant are engaging new foundries for the fabrication of the CCD sensors, developing a cold readout solution, and understanding the experimental backgrounds.

The nowadays notable development of all the modern technology, fundamental for the progress and well being of world society, imposes a great deal of stress in the realm of basic Physics, more precisely on Thermo-Mechanical Statistics. In electronics and optoelectronics we face situations involving physical-chemical systems far-removed-from equilibrium, where ultrafast (in pico- and femto-second scale) and non-linear processes are present. Here we describe in an extended overview the question of ultrafast relaxation processes in the excited plasma in semiconductors., Comment: arXiv admin note: text overlap with arXiv:1210.8108

A theoretical investigation of the excess energy dissipation of highly excited photoinjected electrons in both wurtzite and zincblende GaN is presented. The calculations are performed by solving numerically coupled quantum transport equations for the carriers and the acoustic, transversal and longitudinal optical phonon in order to derive the evolution of their nonequilibrium temperatures, dubbed quasi-temperatures. It is shown that the electron energy dissipation is always faster in the wurtzite structure than in zincblende, both occurring in a subpicosecond time scale (< 0.2 ps)., Comment: arXiv admin note: substantial text overlap with arXiv:2110.00854

A study of the mobility of n-doped wurtzite III-Nitrides is reported. We have determined the nonequilibrium thermodynamic state of the III-Nitrides systems, driven far away from equilibrium by a strong electric field, in the steady state, which follows after a very fast transient. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength is derived, which decreases with the strength of electric field. We analyzed the contributions to the mobility arising out of the different channels of electron scattering, namely, the polar optic, deformation, piezoelectric, interactions with the phonons, and with impurities. The case of n-InN, n-GaN, and n-AlN have been analyzed: as expected the main contribution comes from the polar-optic interactions in these strongly polar semiconductors. The other interactions are in decreasing order, the deformation acoustic, the piezoelectric, and the one due to impurities., Comment: arXiv admin note: substantial text overlap with arXiv:2110.00847

Semiconducting Transition Metal Dichalcogenides (TMDs) have significant nonlinear optical effects. In this work we have used second-harmonic generation (SHG) and the four-wave mixing (FWM) spectroscopy in resonance with the excitons in MoS2, MoSe2, and WS2 monolayers to characterize the nonlinear optical properties of these materials. We show that trions and excitons are responsible for enhancing the nonlinear optical response, and determine the exciton and trion energies by comparing with the photoluminescence spectra. Moreover, we extract the second and third order optical sheet susceptibility near exciton energies and compare with values found in the literature. We also demonstrate the ability to generate different nonlinear effects in a wide spectral range in the visible region for monolayer MoS2, opening the possibility of using two-dimensional materials for nonlinear optoelectronic and photonic applications., Comment: 8 pages, 4 figures

In addition to the ongoing development, pre-salt carbonate reservoir characterization remains a challenge, primarily due to inherent geological particularities. These challenges stimulate the use of well-established technologies, such as artificial intelligence algorithms, for image classification tasks. Therefore, this work intends to present an application of deep learning techniques to identify patterns in Brazilian pre-salt carbonate rock microtomographic images, thus making possible lithological classification. Four convolutional neural network models were proposed. The first model includes three convolutional layers followed by fully connected layers and is used as a base model for the following proposals. In the next two models, we replace the max pooling layer with a spatial pyramid pooling and a global average pooling layer. The last model uses a combination of spatial pyramid pooling followed by global average pooling in place of the last pooling layer. All models are compared using original images, when possible, as well as resized images. The dataset consists of 6,000 images from three different classes. The model performances were evaluated by each image individually, as well as by the most frequently predicted class for each sample. According to accuracy, Model 2 trained on resized images achieved the best results, reaching an average of 75.54% for the first evaluation approach and an average of 81.33% for the second. We developed a workflow to automate and accelerate the lithology classification of Brazilian pre-salt carbonate samples by categorizing microtomographic images using deep learning algorithms in a non-destructive way., Comment: 13 pages, 8 figures

In this work we introduce a well-posed mathematical model for the processes involved in the artificial circulation of water, in order to avoid eutrophication phenomena, for instance, in a lake. This novel and general formulation is based on the modified Navier-Stokes equations following the Smagorinsky model of turbulence, and presenting a suitable nonhomogeneous Dirichlet boundary condition. For the analytical study of the problem, we prove several theoretical results related to existence, uniqueness and smoothness for the solution of this recirculation model.

In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approach.

This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer equation with the modified Navier-Stokes system following a Smagorinsky turbulence model, completed with a suitable set of mixed, nonhomogeneous boundary conditions of diffusive, convective and radiative type. We prove several theoretical results related to existence of solution, and propose a full algorithm for its computation, illustrated with some realistic numerical examples.

A non-equilibrium statistical-thermodynamic approach to the study of a Fr\"ohlich-Bose-Einstein condensation of magnons under radio-frequency radiation pumping is presented. Such a system displays a complex behavior consisting in steady-state conditions to the emergence of a synergetic dissipative structure resembling the Bose-Einstein condensation of systems in equilibium. A kind of "two fluid model" arises: the "normal" non-equilibrium structure and Fr\"ohlich condensate or "non-equilibrium" one, which is shown to be an attractor to the system. We analyze some aspects of the irreversible thermodynamics of this dissipative complex system, namely, its informational entropy, expressions for the fluctuations in non-equilibrium conditions, the associated Maxwell relations and the formulation of a generalized $\mathscr{H}$-theorem. We also study the informational entropy production of the system, an order parameter is introduced and Glansdorff-Prigogine criteria for evolution and (in)stability are verified., Comment: arXiv admin note: text overlap with arXiv:1302.1765

We define a hierarchy of special classes of constrained Willmore surfaces by means of the existence of a polynomial conserved quantity of some type, filtered by an integer. Type 1 with parallel top term characterises parallel mean curvature surfaces and, in codimension 1, type 1 characterises constant mean curvature surfaces. We show that this hierarchy is preserved under both spectral deformation and Baecklund transformation, for special choices of parameters, defining, in particular, transformations of constant mean curvature surfaces into new ones, with preservation of the mean curvature, in the latter case., Comment: v2: Abstract, Introduction and necessary background reformulated v3: minor corrections implemented

The Gemini Multi-conjugate adaptive optics System (GeMS) at the Gemini South telescope in Cerro Pach{\'o}n is the first sodium-based multi-Laser Guide Star (LGS) adaptive optics system. It uses five LGSs and two deformable mirrors to measure and compensate for atmospheric distortions. The GeMS project started in 1999, and saw first light in 2011. It is now in regular operation, producing images close to the diffraction limit in the near infrared, with uniform quality over a field of view of two square arcminutes. The present paper (I) is the first one in a two-paper review of GeMS. It describes the system, explains why and how it was built, discusses the design choices and trade-offs, and presents the main issues encountered during the course of the project. Finally, we briefly present the results of the system first light., Comment: 17 pages, 7 figures, Accepted for publication in MNRAS

We use the dressing method to construct transformations of constrained Willmore surfaces in arbitrary codimension. An adaptation of the Terng--Uhlenbeck theory of dressing by simple factors to this context leads us to define B\"acklund transforms of these surfaces for which we prove Bianchi permutability. Specialising to codimension 2, we generalise the Darboux transforms of Willmore surfaces via Riccati equations, due to Burstall-Ferus-Leschke-Pedit-Pinkall, to the constrained Willmore case and show that they amount to our B\"acklund transforms with real spectral parameter., Comment: 31 A4 pages. v2: metadata adjusted. v3: references added; minor clarifications made

A Response Function Theory and Scattering Theory applicable to the study of physical properties of systems driven arbitrarily away from equilibrium, specialized for dealing with ultrafast processes and in conditions of space resolution (including nanometric scale), are presented. The derivation is done in the framework of a Gibbs-style Nonequilibrium Statistical Ensemble Formalism. It is shown the connection of the observable properties with time and space-dependent correlation functions out of equilibrium. A generalized fluctuation-dissipation theorem, which relates these correlation functions with generalized susceptibilities is derived. It is also presented the method, useful for calculations, of nonequilibrium-thermodynamic Green functions. A couple of illustration with application of the formalism, consisting of the study of optical responses in ultrafast laser spectroscopy and Raman Scattering of electrons in III-N semiconductors (of "blue diodes") driven away from equilibrium by action of electric fields of moderate to high intensities, are described., Comment: 60 pages, 9 figures

This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric connections; Baecklund transformations, by applying a dressing action; and, in 4-space, Darboux transformations, based on the solution of a Riccati equation. We establish a permutability between spectral deformation and Baecklund transformation and prove that non-trivial Darboux transformation of constrained Willmore surfaces in 4-space can be obtained as a particular case of Baecklund transformation. All these transformations corresponding to the zero multiplier preserve the class of Willmore surfaces. We verify that, for special choices of parameters, both spectral deformation and Baecklund transformation preserve the class of constrained Willmore surfaces admitting a conserved quantity, and, in particular, the class of CMC surfaces in 3-dimensional space-form., Comment: Based on the author's PhD Thesis, submitted to the University of Bath, UK on September 2008; 225 pages; 2 figures. v2: January 2010 errata to the printed version attached to v1

When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard approach to the well established, physically and logically sound, Boltzmann-Gibbs statistics. To circumvent such difficulties, in order to make predictions on properties of the system and looking for an understanding of the physics involved (for example in analyzing the technological characteristics of fractal-structured devices) can be introduced large families of auxiliary statistics. We present here a systematization of these different styles in what can be termed as Unconventional Statistical Mechanics, accompanied of an analysis of the construction and a clarification of its scope and interpretation. As illustrations are derived heterotypical Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann distributions, and several applications including studies of experimental works are briefly described., Comment: 33 pages, 4 figures

Construction of a nonlinear higher-order thermo-hydrodynamics, including correlations, in the framework of a Generalized Nonequilibrium Statistical Grand-Canonical Ensemble is presented. In that way it is provided a particular formalism for the coupling and simultaneous treatment of the kinetics and hydrodynamic levels of description. It is based on a complete thermostatistical approach in terms of the densities of energy and of matter and their fluxes of all orders, as well as on their direct and cross correlations, covering systems arbitrarily driven-away-from equilibrium. The set of coupled nonlinear integro-differential hydrodynamic equations is derived. Illustrations of the application of the theory are described in the follow up article., Comment: 26 pages

The construction of a generalized (higher-order) nonlinear thermo-hydrodynamics, based on a nonequilibrium ensemble formalism has been presented in the preceding article. The working of such theory is illustrated in the present one. We consider here the case of two ideal classical fluids in interaction between them, and the nonlinear equations of evolution for the density (a hyperbolic one) and for the velocity field describing motion under flow are derived. Also, now at the quantum level, it is described the nonlinear transport in the fluid of electrons in doped polar semiconductors, and comparison with Monte Carlo calculations and with experimental data is done, obtaining very good agreement., Comment: 24 pages, 4 figures

Competing styles in Statistical Mechanics have been introduced to investigate physico-chemical systems displaying complex structures, when one faces difficulties to handle the standard formalism in the well established Boltzmann-Gibbs statistics. After a brief description of the question, we consider the particular case of Renyi statistics whose use is illustrated in a study of the question of the ''anomalous'' (non-Fickian) diffusion that it is involved in experiments of cyclic voltammetry in electro-physical chemistry. In them one is dealing with the fractal-like structure of the thin film morphology present in eletrodes in microbatteries which leads to fractional-power laws for describing voltammetry measurements and in the determination of the interphase width derived using atomic force microscopy. The fractional-powers associated to these quantities are related to each other and to the statistical fractal dimension, and can be expressed in terms of a power index, on which depends Renyi's statistical mechanics. It is clarified the important fact that this index, which is limited to a given interval, provides a measure of the microroughness of the electrode surface, and is related to the dynamics involved, the non-equilibrium thermodynamic state of the system, and to the experimental protocol. \\, Comment: 25 pages, 3 figures

Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies associated to Information Theory, which are in fact generating functionals for the derivation of probability distributions and not thermodynamic functions of state. The role of them in the construction of the so-called Unconventional Statistical Mechanics, and the meaning and use of the latter, is discussed. Particular attention is given to the situation involving far-from-equilibrium systems., Comment: 50 pages, 1 figure

In the present follow-up article of a previous one [1] we illustrate the use of the Unconventional Statistical Mechanics described and discussed in the latter. This is done via the analysis, resorting to Renyi approach, of experimental results in the case of so-called "anomalous" luminescence in nanometric quantum wells in semiconductor heterostructures, and the so-called "anomalous" cyclic voltammetry in fractal-like electrodes in microbatteries. Also a purely theoretical analysis is done in the cases of an ideal gas and of radiation comparing the conventional and unconventional approaches. In all of these situations it is discussed which is the failure to satisfy the Criteria of Efficiency and/or Sufficiency thus requiring to resort to the unconventional approach, and what determines the value of the infoentropic index in each case, and its dependence on the system characteristics. Moreover, on the basis of the results we obtain, it is conjectured that the infoentropic index may satisfy what we call a law defining a "path to sufficiency". PACS: 05.70.Ln; 82.20.Mj; 82.20.Db Keywords: Renyi Statistics; Escort Probability; Fractal Structured Systems; Power Law Properties., Comment: 56 pages, 1 table, 2 figures

Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her capacity for satisfying the Criteria of Efficiency and/or Sufficiency in statistics [Fisher, 1922], that is, a failure in the characterization (presence of fractality, scaling, etc.) of the system related to some aspect relevant to the given physical situation. To patch this limitation on the part of the observer, in order to make predictions on the values of observables and response functions, are introduced unconventional approaches. We present a detailed description of their construction and a clarification of its scope and interpretation. Also, resorting to the use of the particular case of Renyi's unconventional statistics is built a nonequilibrium ensemble formalism. The unconventional distribution functions of fermions and bosons are obtained, and in a follow-up article [cond-mat/0306247] we describe applications to the study of experimental results in semiconductor physics and in electro-chemistry involving nanometric scales and fractal-like structures, and some additional theoretical analysis is added. PACS: 05.70.Ln, 82.20.Mj, 82.20.Db Keywords: Nonequilibrium Ensemble Formalism; Generalized Informational Entropies; Generalized Statistics; Nonextensive Statistics; Renyi Statistics; Escort Probability., Comment: 33 pages, 1 figure