We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.
We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods. The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.
Oxidative stress appears to possess a central role in CIN pathophysiology. Resveratrol (Res) and lycopene (Lyc) are strong natural antioxidants evaluated in a limited number of CIN animal studies in vivo. The aim of the study was to evaluate the potential renoprotective effects of Res/Lyc in a CIN rabbit model. Twenty-four adult male New Zealand white rabbits were equally assigned into four groups: control (saline), CIN (intravenous iopromide; 7.5 g iodine/kg), Res + CIN (per os Res; 5 mg/kg), and Lyc + CIN (per os Lyc; 4 mg/kg). Serum Cr (sCr); symmetric/asymmetric dimethylarginine (SDMA/ADMA); oxidative stress biomarkers: malondialdehyde; total antioxidant capacity; catalase; glutathione) were evaluated in blood samples at three time points: right after (0 h); 24 h; 48 h after iopromide/saline administration. CD20+/CD3+ lymphocytes were determined (48 h). All animals were sacrificed at 48 h and both kidneys collected. Oxidative stress biomarkers were measured in renal tissue. sCr and SDMA/ADMA levels increased significantly in CIN compared to all groups. Oxidative stress secondary to CIN in blood/kidneys was suppressed by Res/Lyc. B and T lymphocytes decreased significantly in CIN compared to all groups. The present study provides emerging evidence that Res/Lyc ameliorate CIN by modulating oxidant/antioxidant balance in blood/renal tissue and by inhibiting vasoconstriction/blood cytotoxicity.
We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from nonanalytic potentials. In particular, we study the dynamics of a model governed by a “graphene-type” force law and one inspired by Hollomon’s law describing “work-hardening” effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of nonanalytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi–Pasta–Ulam–Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles [Formula: see text] and the total energy [Formula: see text] are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large [Formula: see text], it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.
We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as $t\rightarrow \infty$. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop's model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid [2], which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.
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