Search results for "state space"
showing 10 items of 49 documents
Model-Based Transfer Entropy Analysis of Brain-Body Interactions with Penalized regression techniques
2020
The human body can be seen as a functional network depicting the dynamical interactions between different organ systems. This exchange of information is often evaluated with information-theoretic approaches which comprise the use of vector autoregressive (VAR) and state space (SS) models, normally identified with the Ordinary Least Squares (OLS). However, the number of time series to be included in the model is strictly related to the length of data recorded thus limiting the use of the classical approach. In this work, a new method based on penalized regressions, the so-called LASSO, was compared with OLS on physiological time-series extracted from 18 subjects during different stress condi…
Generalized-ensemble simulations and cluster algorithms
2010
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the partition function or thermal averages of interest. While this is true in terms of its simplicity and universal applicability, the resulting approach suffers from the presence of temporal correlations of successive samples naturally implied by the Markov chain underlying the importance-sampling simulation. In many situations, these autocorrelations are moderate and can be easily accounted for by an appropriately adapted analysis of simulation data. They turn out…
A Perturbative Approach to Continuous-Time Quantum Error Correction
2014
We present a novel discussion of the continuous-time quantum error correction introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame featur…
Reconstruction of Hamiltonians from given time evolutions
2010
In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state of the system. Our approach exploits the equivalence between an action of the group of evolution operators over the state space and an adjoint action of the unitary group over Hermitian matrices. The method is illustrated by two examples involving a pure and a mixed state.
State Space-Vector Model of Linear Induction Motors Including Iron Losses Part I: Theoretical Analysis
2018
This is the first part of a paper, divided into two parts, dealing with the definition of a space-vector dynamic model of the linear Induction motor (LIM) taking into consideration both the dynamic end-effects and the iron losses and its off-line identification. This first part specifically treats the theoretical formulation of this model, which has been expressed in a state form, so to be, in perspective, suitably adopted for developing novel non linear control techniques, non-linear observers as well as electrical losses minimization techniques (ELMTs). Besides the formulation of the dynamic model in space-vector state form, a steady-state analysis is proposed, highlighting the combined e…
State Space-Vector Model of Linear Induction Motors Including Iron Losses: Part II: Model Identification and Results
2018
This is the second part of a paper, divided into two parts, dealing with the definition of a space-vector dynamic model of the linear Induction motor (LIM) taking into consideration both the dynamic end-effects and the iron losses as well as the off-line identification of its parameters. The first part has treated the theoretical framework of the model. This second part is devoted to the description of an identification technique which has been suitably developed for the estimation of the parameters of the LIM dynamic model accounting for both the dynamic end-effects and iron losses, described in the first part of the paper. Such an identification technique is strictly related to the state …
Inversion of matrix pencils for generalized systems
1993
Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.
Multiscale Granger causality
2017
In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer a…
Estimating aggregated nutrient fluxes in four Finnish rivers via Gaussian state space models
2013
Reliable estimates of the nutrient fluxes carried by rivers from land-based sources to the sea are needed for efficient abatement of marine eutrophication. Although nutrient concentrations in rivers generally display large temporal variation, sampling and analysis for nutrients, unlike flow measurements, are rarely performed on a daily basis. The infrequent data calls for ways to reliably estimate the nutrient concentrations of the missing days. Here, we use the Gaussian state space models with daily water flow as a predictor variable to predict missing nutrient concentrations for four agriculturally impacted Finnish rivers. Via simulation of Gaussian state space models, we are able to esti…
Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model
2016
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…