A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degreeof-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework

Differential Expression of MicroRNAs in Adipose Tissue after Long-Term High-Fat Diet-Induced Obesity in Mice

Obesity is a major health concern worldwide which is associated with increased risk of chronic diseases such as metabolic syndrome, cardiovascular disease and cancer. The elucidation of the molecular mechanisms involved in adipogenesis and obesogenesis is of essential importance as it could lead to the identification of novel biomarkers and therapeutic targets for the development of anti-obesity drugs. MicroRNAs (miRNAs) have been shown to play regulatory roles in several biological processes. They have become a growing research field and consist of promising pharmaceutical targets in various fields such as cancer, metabolism, etc. The present study investigated the possible implication of miRNAs in adipose tissue during the development of obesity using as a model the C57BLJ6 mice fed a high-fat diet

On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation

The very strict positive real lemma is further developed for nonminimal 1-D continuous-time systems and is used to study the 2-D continuous-time Lyapunov equation. Based on it, an extended condition for the bivariate characteristic polynomial of a matrix to be very strict Hurwitz is proposed for general 2-D analog systems with characteristic polynomials involving 1-D factor polynomials. It is also shown that in such a case the bivariate polynomial can be decomposed into a 2-D bivariate polynomial with the corresponding matrix satisfying certain controllability and observability conditions and into up to two 1-D polynomials. Further, two algorithms for computing the positive definite solutions to the 2-D Lyapunov equation are presented.link_to_subscribed_fulltex

Stability and the Lyapunov equation for n-dimensional digital systems

The discrete-time bounded-real lemma is further developed for nonminimal digital systems. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for n-dimensional (n-D) digital systems are proposed. These new conditions are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (o ≤ k ≤ n) subsystem and m (1 ≤ m ≤ n) 1-D subsystems. This could significantly simplify the complexity of solving the n-D Lyapunov equation for such cases.link_to_subscribed_fulltex

Coefficient sensitivity and structure optimization of multidimensional state-space digital filters

In this brief, a new coefficient sensitivity measure for multidimensional (n-D) digital systems in state-space representation is proposed. This is motivated by the fact that coefficients equal to 0 or ±1 can be implemented exactly using finite wordlength, and thus have no contribution to coefficient quantization errors. The relationship between commonly used sensitivity measures for 2-D and n-D systems and the new one proposed in this brief is discussed. It is shown that in evaluating the accuracy between a finite wordlength implementation of a transfer function and the ideal one, the proposed sensitivity measure is more useful than the commonly used ones. Furthermore, the proposed measure confirms that realizations with Schur and/or Hessenberg structures can be used to obtain more accurate finite wordlength implementations of transfer functions than the ones obtained using fully parametrized minimum sensitivity structures. © 1998 IEEE.link_to_subscribed_fulltex

Stability and the lyapunov equation for n-dimensional digital systems

The discrete-time bounded-real lemma for nonminimal discrete systems is presented. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for ra-dimensional (n-D) digital systems are proposed. These new conditions can be applied to n-D digital systems with n-D characteristic polynomials involving factor polynomials of any dimension, 1-D to n-D. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of an n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (0 < k < n) subsystem and m (1 < m < n) 1-D subsystems. This could significantly simplify the complexity of solving the n-D Lyapunov equation for such cases. ©1997 ieee.link_to_subscribed_fulltex