scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

2020 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Vector Autoregressive ◽  
Conceptual Shift

Network analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector autoregressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous Time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

Amplitudes of Composition Fluctuations in the Simplest Chemical Reaction Equilibrium

2004 ◽  
Vol 218 (9) ◽  
pp. 1033-1040 ◽  
Author(s):  
M. Šolc ◽  
J. Hostomský
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Continuous Time ◽  
Time Scale ◽  
Numerical Study ◽  
Mean Amplitude ◽  
Time Interval ◽  
The Mean ◽  
Composition Fluctuations ◽  
Number Of Particles

AbstractWe present a numerical study of equilibrium composition fluctuations in a system where the reaction X1 ⇔ X2 having the equilibrium constant equal to 1 takes place. The total number of reacting particles is N. On a discrete time scale, the amplitude of a fluctuation having the lifetime 2r reaction events is defined as the difference between the number of particles X1 in the microstate most distant from the microstate N/2 visited at least once during the fluctuation lifetime, and the equilibrium number of particles X1, N/2. On the discrete time scale, the mean value of this amplitude, m̅(r̅), is calculated in the random walk approximation. On a continuous time scale, the average amplitude of fluctuations chosen randomly and regardless of their lifetime from an ensemble of fluctuations occurring within the time interval (0,z), z → ∞, tends with increasing N to ~1.243 N0.25. Introducing a fraction of fluctuation lifetime during which the composition of the system spends below the mean amplitude m̅(r̅), we obtain a value of the mean amplitude of equilibrium fluctuations on the continuous time scale equal to ~1.19√N. The results suggest that using the random walk value m̅(r̅) and taking into account a) the exponential density of fluctuations lifetimes and b) the fact that the time sequence of reaction events represents the Poisson process, we obtain values of fluctuations amplitudes which differ only slightly from those derived for the Ehrenfest model.

Evaluating the accuracy of biodiversity changes through geologic times: from simulation to solution

Paleobiology ◽  
2017 ◽  
Vol 43 (4) ◽  
pp. 667-692 ◽  
Author(s):  
Corentin Gibert ◽  
Gilles Escarguel
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Simple Algorithm ◽  
Time Discretization ◽  
Time Interval ◽  
Taxonomic Richness ◽  
Time Data ◽  
Worst Case ◽  
Data Set ◽  
Reconstructed Signal

AbstractEstimating biodiversity and its variations through geologic time is a notoriously difficult task, due to several taphonomic and methodological effects that make the reconstructed signal potentially distinct from the unknown, original one. Through a simulation approach, we examine the effect of a major, surprisingly still understudied, source of potential disturbance: the effect of time discretization through biochronological construction, which generates spurious coexistences of taxa within discrete time intervals (i.e., biozones), and thus potentially makes continuous- and discrete-time biodiversity curves very different. Focusing on the taxonomic-richness dimension of biodiversity (including estimates of origination and extinction rates), our approach relies on generation of random continuous-time richness curves, which are then time-discretized to estimate the noise generated by this manipulation. A broad spectrum of data-set parameters (including average taxon longevity and biozone duration, total number of taxa, and simulated time interval) is evaluated through sensitivity analysis. We show that the deteriorating effect of time discretization on the richness signal depends highly on such parameters, most particularly on average biozone duration and taxonomic longevity because of their direct relationship with the number of false coexistences generated by time discretization. With several worst-case but realistic parameter combinations (e.g., when relatively short-lived taxa are analyzed in a long-ranging biozone framework), the original and time-discretized richness curves can ultimately show a very weak to zero correlation, making these two time series independent. Based on these simulation results, we propose a simple algorithm allowing the back-transformation of a discrete-time taxonomic-richness data set, as customarily constructed by paleontologists, into a continuous-time data set. We show that the reconstructed richness curve obtained this way fits the original signal much more closely, even when the parameter combination of the original data set is particularly adverse to an effective time-discretized reconstruction.

Discrete-Time Equivalent of Continuous-Time Filtering Processes

1981 ◽  
Vol 103 (4) ◽  
pp. 417-419 ◽  
Author(s):  
Bernard Friedland
Keyword(s):  
Hamiltonian System ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Continuous Time ◽  
Finite Time ◽  
Transition Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Filtering Problem

The continuous-time Kalman filtering problem over a finite time interval can be made equivalent to a discrete-time filtering problem. The matrices in the latter are related to the submatrices of the transition matrix of a Hamiltonian system that corresponds to the continuous-time filtering problem.

scholarly journals Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

2009 ◽  
Vol 2009 ◽  
pp. 1-28 ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Sampling Period ◽  
Switched System ◽  
Time Interval ◽  
Stabilizing Controller ◽  
Switching Law ◽  
Discrete Dynamic System ◽  
Time Control

This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.

Uniform-in-time transition from discrete dynamics to continuous dynamics in the Cucker–Smale flocking

2018 ◽  
Vol 28 (09) ◽  
pp. 1699-1735 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Xiongtao Zhang
Keyword(s):  
Initial Data ◽  
Discrete Time ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Discrete Model ◽  
Stability Estimate ◽  
Functional Approach ◽  
Time Interval ◽  
Time Step ◽  
Time Model

We study a uniform-in-time convergence from the discrete-time (in short, discrete) Cucker–Smale (CS) model to the continuous-time CS model, which is valid for the whole time interval, as time-step tends to zero. Classical theory yields the convergence results which are valid only in any finite-time interval. Our uniform convergence estimate relies on two quantitative estimates “asymptotic flocking estimate” and “uniform[Formula: see text]-stability estimate with respect to initial data”. In the previous literature, most studies on the CS flocking have been devoted to the continuous-time model with general communication weights, whereas flocking estimates have been done for the discrete-time model with special network topologies such as the complete network with algebraically decaying communication weights and rooted leaderships. For the discrete CS model with a regular and algebraically decaying communication weight, asymptotic flocking estimate has been extensively studied in the previous literature. In contrast, for a general decaying communication weight, corresponding flocking dynamics has not been addressed in the literature due to the difficulty of extending the Lyapunov functional approach to the discrete model. In this paper, we present asymptotic flocking estimate for the discrete model using the Lyapunov functional approach. Moreover, we present a uniform [Formula: see text]-stability estimate of the solution for the discrete CS model with respect to initial data. We combine asymptotic flocking estimate and uniform stability to derive a uniform-in-time convergence from the discrete CS model to the continuous CS model, as time-step tends to zero.

Collision Detection of 3D Complex Objects

1994 ◽  
Author(s):  
Rong Mo ◽  
Horst Nowacki
Keyword(s):  
Discrete Time ◽  
Collision Detection ◽  
Continuous Time ◽  
Surface Modeling ◽  
Second Step ◽  
Time Interval ◽  
Parametric Surface ◽  
Complex Objects ◽  
Practical Applications ◽  
Detection Process

Abstract Collision detection of 3D complex objects is often needed for practical applications. In this paper, a new algorithm for testing collision is proposed. The algorithm combines the sweeping technique and a parametric surface modeling method. A collision detection process is carried out firstly in continuous time using sweeping, in order to determine a time interval for collision as early as possible. In the second step the collision detection is performed at discrete time in this time interval, so that exact collision positions and times are found.

scholarly journals Capacity Planning of Electric Car Charging Station Based on Discrete Time Observations and MAP(2)/G/c Queue

2018 ◽  
Author(s):  
Csaba Farkas ◽  
Miklós Telek
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Arrival Process ◽  
Time Interval ◽  
Correlation Parameter ◽  
Charging Station ◽  
Electric Car ◽  
Time Map ◽  
Discrete Time Observations ◽  
Charging Stations

The modeling of electric car charging stations is essential for determining the required number of chargers in order to ensure the required service quality. In this paper we propose a new estimation method for the stochastic modeling of electric car charging stations, based on Markov arrival process (MAP).The input of the proposed model is empirical data for the arrival and service process of electric cars, given as histograms: the number of arriving cars during a fixed time slot (5 minutes in our case) and the histogram of service times (in 5 minutes granularity). The fact that observations on the continuous time process of car charging are available in discrete time steps poses a modeling challenge, which was not considered before. We propose a procedure to fit the observed data with a continuous time MAP of order 2 such that three moments and a correlation parameter of the discrete time observations are matched with three moments and the correlation parameter of the continuous time MAP for the given time interval. We implemented the fitting procedure in MATLAB and verified the obtained model of car charging station against simulation. As the MAP model of the arrival processes is reasonably close to the observations, the obtained MAP/G/c queue allows a more accurate dimensioning of car charging station than the previously applied ones.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass
Sign in / Sign up

Export Citation Format

Share Document