Learning Governing Equations of Unobserved States in Dynamical Systems

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system equations are set to be governed by a neural network, have become a popular tool for this challenge in recent years. However, less emphasis has been placed on systems that are only partially-observed. In this work, we employ a hybrid neural ODE structure, where the system equations are governed by a combination of a neural network and domain-specific knowledge, together with symbolic regression (SR), to learn governing equations of partially-observed dynamical systems. We test this approach on two case studies: A 3-dimensional model of the Lotka-Volterra system and a 5-dimensional model of the Lorenz system. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems, with robustness to measurement noise

First observation of strong OZI rule violation in πN\pi N interactions

The data of the CERN WA56 experiment that triggered the fast proton produced in the $\pi^{+}p$ and $\pi^{-}p$ interactions at beam momenta 20 GeV/c and 12 GeV/c, respectively, are used to analyse the final states $p_{f} \phi (\omega)\pi^{\pm}$. A large excess (up to two orders of magnitude) of the $\phi/\omega$ cross sections ratio over the OZI prediction is observed

Radiation from a charge circulating inside a waveguide with dielectric filling

The emitted power of the radiation from a charged particle moving uniformly on a circle inside a cylindrical waveguide is considered. The expressions for the energy flux of the radiation passing through the waveguide cross-section are derived for both TE and TM waves. The results of the numerical evaluation are presented for the number of emitted quanta depending on the waveguide radius, the radius of the charge rotation orbit and dielectric permittivity of the filling medium. These results are compared with the corresponding quantities for the synchrotron radiation in a homogeneous medium.Comment: 10 pages, Latex, four EPS figure

A hybrid neural ordinary differential equation model of the cardiovascular system

Peer reviewe

Observation of Resonant Diffusive Radiation in Random Multilayered Systems

Diffusive Radiation is a new type of radiation predicted to occur in randomly inhomogeneous media due to the multiple scattering of pseudophotons. This theoretical effect is now observed experimentally. The radiation is generated by the passage of electrons of energy 200KeV-2.2MeV through a random stack of films in the visible light region. The radiation intensity increases resonantly provided the Cherenkov condition is satisfied for the average dielectric constant of the medium. The observed angular dependence and electron resonance energy are in agreement with the theoretical predictions. These observations open a road to application of diffusive radiation in particle detection, astrophysics, soft X-ray generation and etc.. `Comment: 4pages, 4figure

The Phonon Drag Effect in Single-Walled Carbon Nanotubes

A variational solution of the coupled electron-phonon Boltzmann equations is used to calculate the phonon drag contribution to the thermopower in a 1-D system. A simple formula is derived for the temperature dependence of the phonon drag in metallic, single-walled carbon nanotubes. Scattering between different electronic bands yields nonzero values for the phonon drag as the Fermi level varies.Comment: 8 pages, 4 figure

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Peer reviewe

Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

We introduce a family of equations of state (EoS)for hybrid neutron star (NS) matter that is obtained by atwo-zone parabolic interpolation between a soft hadronicEoS at low densities and a set of stiff quark matter EoSat high densities within a finite region of chemical potentialsμH < μ < μQ. Fixing the hadronic EoS as the APRone and choosing the color-superconducting, nonlocal NJLmodel with two free parameters for the quark phase, we performBayesian analyses with this two-parameter family ofhybrid EoS. Using three different sets of observational constraintsthat include the mass of PSR J0740+6620, the tidaldeformability for GW170817, and the mass-radius relationfor PSR J0030+0451 from NICER as obligatory (set 1), whileset 2 uses the possible upper limit on themaximummass fromGW170817 as an additional constraint and set 3 instead ofthe possibility that the lighter object in the asymmetric binarymerger GW190814 is a neutron star. We confirm that in anycase, the quark matter phase has to be color superconductingwith the dimensionless diquark coupling approximately fulfillingthe Fierz relation ηD = 0.75 and the most probablesolutions exhibiting a proportionality between ηD and ηV , thecoupling of the repulsive vector interaction that is requiredfor a sufficiently largemaximummass.We used theBayesiananalysis to investigate with the method of fictitious measureaments the consequences of anticipating different radii for themassive 2 M PSR J0740+6220 for the most likely equationof state. With the actual outcome of the NICER radius measurementon PSR J0740+6220 we could conclude that for themost likely hybrid star EoS would not support a maximummass as large as 2.5 M so that the event GW190814 was abinary black hole merger.Fil: Ayriyan, Alexander. Laboratory of Information Technologies; Rusia. A. Alikhanyan National Laboratory; Armenia. Dubna State University; RusiaFil: Blaschke, David. University of Wroclaw; Polonia. Bogoliubov Laboratory for Theoretical Physics; Rusia. National Research Nuclear University; RusiaFil: Grunfeld, Ana Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Alvarez Castillo, D. E.. Bogoliubov Laboratory for Theoretical Physics; Rusia. Henryk Niewodniczanski Institute of Nuclear Physics; PoloniaFil: Grigorian, H.. A. Alikhanyan National Laboratory; Armenia. Yerevan State University; Armenia. Laboratory of Information Technologies; RusiaFil: Abgaryan, V.. Laboratory of Information Technologies; Rusia. A. Alikhanyan National Laboratory; Armenia. Peoples’ Friendship University of Russia; Rusi