Remote Analysis of Respiratory Sounds in Patients With COVID-19: Development of Fast Fourier Transform-Based Computer-Assisted Diagnostic Methods.

BACKGROUND: Respiratory sounds have been recognized as a possible indicator of behavior and health. Computer analysis of these sounds can indicate characteristic sound changes caused by COVID-19 and can be used for diagnostics of this illness. OBJECTIVE: The aim of the study is to develop 2 fast, remote computer-assisted diagnostic methods for specific acoustic phenomena associated with COVID-19 based on analysis of respiratory sounds. METHODS: Fast Fourier transform (FFT) was applied for computer analysis of respiratory sound recordings produced by hospital doctors near the mouths of 14 patients with COVID-19 (aged 18-80 years) and 17 healthy volunteers (aged 5-48 years). Recordings for 30 patients and 26 healthy persons (aged 11-67 years, 34, 60%, women), who agreed to be tested at home, were made by the individuals themselves using a mobile telephone; the records were passed for analysis using WhatsApp. For hospitalized patients, the illness was diagnosed using a set of medical methods; for outpatients, polymerase chain reaction (PCR) was used. The sampling rate of the recordings was from 44 to 96 kHz. Unlike usual computer-assisted diagnostic methods for illnesses based on respiratory sound analysis, we proposed to test the high-frequency part of the FFT spectrum (2000-6000 Hz). RESULTS: Comparing the FFT spectra of the respiratory sounds of patients and volunteers, we developed 2 computer-assisted methods of COVID-19 diagnostics and determined numerical healthy-ill criteria. These criteria were independent of gender and age of the tested person. CONCLUSIONS: The 2 proposed computer-assisted diagnostic methods, based on the analysis of the respiratory sound FFT spectra of patients and volunteers, allow one to automatically diagnose specific acoustic phenomena associated with COVID-19 with sufficiently high diagnostic values. These methods can be applied to develop noninvasive screening self-testing kits for COVID-19.

Effective tight-binding models for excitons in branched conjugated molecules.

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices to be described in terms of a small number of lattice parameters which can be obtained from quantum-chemical computations using the exciton scattering approach as a tool. We illustrate the tight-binding model approach using the time-dependent Hartree-Fock computations in phenylacetylene oligomers. The on-site energies and hopping constants have been identified from the exciton dispersion and scattering matrices. In particular, resonant, as well as bound states, are reproduced for a symmetric quadruple branching center. The capability of the tight-binding model approach to describe the exciton-phonon coupling and energetic disorder in large branched conjugated molecules is briefly discussed.

Exciton scattering on symmetric branching centers in conjugated molecules.

The capability of the exciton scattering approach, an efficient methodology for excited states in branched conjugated molecules, is extended to include symmetric triple and quadruple joints that connect linear segments on the basis of the phenylacetylene backbone. The obtained scattering matrices that characterize these vertices are used in application of our approach to several test structures, where we find excellent agreement with the transition energies computed by the reference quantum chemistry. We introduce topological charges, associated with the scattering matrices, which help to formulate useful relations between the number of excitations in the exciton band and the number of repeat units. The obtained features of the scattering phases are analyzed in terms of the observed excited state electronic structure.

Exciton scattering approach for branched conjugated molecules and complexes. IV. Transition dipoles and optical spectra.

The electronic excitation energies and transition dipole moments are the essential ingredients to compute an optical spectrum of any molecular system. Here we extend the exciton scattering (ES) approach, originally developed for computing excitation energies in branched conjugated molecules, to the calculation of the transition dipole moments. The ES parameters that characterize contributions of molecular building blocks to the total transition dipole can be extracted from the quantum-chemical calculations of the excited states in simple molecular fragments. Using these extracted parameters, one can then effortlessly calculate the oscillator strengths and optical spectra of various large molecular structures. We illustrate application of this extended ES approach using an example of phenylacetylene-based molecules. Absorption spectra predicted by the ES approach show close agreement with the results of the reference quantum-chemical calculations.

Transition times in the low-noise limit of stochastic dynamics.

We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding the most probable trajectory. We demonstrate that finding the transition time distribution reduces to a one-dimensional problem. The resulting transition time distribution has a universal and compact form. We suggest that transition barriers can be estimated from a single-temperature experiment if both the life times and the transition times are measured.

Exciton scattering approach for branched conjugated molecules and complexes. I. Formalism.

We develop a formalism for the exciton scattering (ES) approach to calculation of the excited state electronic structure of branched conjugated polymers with insignificant numerical expense. The ES approach attributes electronic excitations in quasi-one-dimensional molecules to standing waves formed by the scattering of quantum quasiparticles. We derive the phenomenology from the microscopic description in terms of many-electron excitations. The presented model can be used to compute both excited state frequencies and transition dipoles in large molecules after the ES ingredients are extracted from smaller molecular fragments.

Exciton scattering approach for branched conjugated molecules and complexes. II. Extraction of the exciton scattering parameters from quantum-chemical calculations.

We obtain the parameters of the exciton scattering (ES) model from the quantum-chemical calculations of the electronic excitations in simple phenylacetylene-based molecules. We determine the exciton dispersion and the frequency-dependent scattering matrices which describe scattering properties of the molecular ends as well as of meta- and orthoconjugated links. The extracted functions are smooth, which confirms the validity of the ES picture. We find a good agreement between the ES and quantum-chemical results for the excitation energies in simple test molecules.

Exciton scattering approach for branched conjugated molecules and complexes. III. Applications.

The exciton scattering (ES) approach is an efficient tool to calculate the excited states electronic structure in large branched polymeric molecules. Using the previously extracted parameters, we apply the ES approach to a number of phenylacetylene-based test molecules. Comparison of ES predictions with direct quantum chemistry results for the excitation energies shows an agreement within several meV. The ES framework provides powerful insights into photophysics of macromolecules by revealing the connections between the molecular structure and the properties of the collective electronic states, including spatial localization of excitations controlled by the energy.

Classical nonlinear response of a chaotic system. I. Collective resonances.

We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.

Classical nonlinear response of a chaotic system. II. Langevin dynamics and spectral decomposition.

The spectrum of a strongly chaotic system consists of discrete complex Ruelle-Pollicott (RP) resonances. We interpret the RP resonances as eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal diffusion term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long-time asymptotic expansion in the deterministic case.

Collective oscillations in the classical nonlinear response of a chaotic system.

We establish a general semiquantitative phase-space picture of the classical nonlinear response in a strongly chaotic system. As opposed to the case of stable dynamics, the response functions decay exponentially at long times. Damped oscillations in response functions are attributed to collective resonances which do not correspond to any periodic classical motions. We calculate analytically the second-order response in a simple chaotic system and demonstrate the relevance of the concept for the interpretation of spectroscopic data.

Multiscale modeling of electronic excitations in branched conjugated molecules using an exciton scattering approach.

The exciton scattering (ES) approach attributes excited electronic states in quasi-1D branched polymer molecules to standing waves of quantum quasiparticles (excitons) scattered at the molecular vertices. We extract their dispersion and frequency-dependent scattering matrices at termini, ortho, and meta joints for pi-conjugated phenylacetylene-based molecules from atomistic time-dependent density-functional theory (TD DFT) calculations. This allows electronic spectra for any structure of arbitrary size within the considered molecular family to be obtained with negligible numerical effort. The agreement is within 10-20 meV for all test cases, when comparing the ES results with the reference TD DFT calculations.

Coulomb blockade and transport in a chain of one-dimensional quantum dots.

A long one-dimensional wire with a finite density of strong random impurities is modeled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by breaks: randomly occurring clusters of quantum dots with a special length distribution pattern that inhibit the transport. Because of the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.