Open Access
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Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions , which we model as discrete contacts, and ties , which encode the strengths of relationships over time. To illustrate our tie-decay network formalism, we adapt the well-known PageRank centrality score to our tie-decay framework in a mathematically tractable and computationally efficient way. We apply this framework to a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.
5American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison
American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison
On the Consistency of the Lucas Pricing Formula
On the Consistency of the Lucas Pricing Formula
174On sliding mode observers via equivalent control approach
In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for a linear time invariant system both in continuous and discrete time. For the continuous case, the observer is designed using a recursive procedure; however, the observer is eventually expressed as a replica of the original system with an additional auxiliary input with a certain nested structure. A direct discrete time counterpart of the sliding mode realization of a reduced order asymptotic observer using the discrete time equivalent control is also developed. Simulation of a linearized truck-trailer during a manoeuvre illustrates the approach. Results show the effectiveness and the finite time convergence characteristics of the proposed discrete and continuous time sliding mode observers.
Read more14Optimal Hedging in Discrete and Continuous Time
Optimal Hedging in Discrete and Continuous Time
183Continuous approximation of collective system behaviour: A tutorial
Continuous approximation of collective system behaviour: A tutorial
10Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers
SummaryLinear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.
Read more22Hotelling revisits the lab: equilibration in continuous and discrete time
We investigate experimentally the impact of continuous time on a four-player Hotelling location game. The static pure strategy Nash equilibrium (NE) consists of firms paired-up at the first and third quartiles of the linear city. In a repeated simultaneous move (discrete time) treatment, we largely replicate previous findings in which subjects fail to converge to the NE. However, in asynchronous move (continuous time) treatments we see clear convergence towards the NE.
Read moreUse of the Step Invariant Transform to Design a 2nd Order Continuous Time Complex Sigma-Delta ADC
To reduce simulation times, continuous time (CT) sigma-delta modulators can be modeled as equivalent discrete time (DT) systems so that DT simulators can be used. This method reviews two popular methods of converting from CT to DT and applies them to a second order CT complex ADC. The ADC being designed is for use with a low IF receiver and achieves 80dB SNDR in simulation.
Read more32Automata over continuous time
Automata over continuous time
4Consensus in Asynchronous Multiagent Systems. I. Asynchronous Consensus Models
We present a survey of results on models of consensus in asynchronous multiagent systems with discrete and continuous time. We consider mathematical methods developed over recent years, which are used in the analysis of stability, stabilization, and consensus problems for linear multiagent systems with discrete time. These methods are based on the idea of using the notion of joint/generalized spectral radius of a set of matrices to analyze the rate of convergence of matrix products with factors drawn from certain sets of matrices with special properties.
Read more2Decentralized 2 degree of freedom loop shaping H<inf>∞</inf> controller for twin rotor aerodynamic system
In this paper, a decentralized controller is designed for cross coupled MIMO Twin rotor aerodynamic system (TRAS). The decentralized controller design is done by decoupling the MIMO system into two decoupled, a pitch and a yaw system. Then 2-DOF controller is designed using control technique in continuous and discrete time. The performance of these controllers are tested through extensive simulations in MatLAB and results are compared between discrete and continuous time systems.
Read more10Ch. 21. On the theory of discrete and continuous bilinear time series models
Ch. 21. On the theory of discrete and continuous bilinear time series models
7Formula omitted]-continuity, impatience and myopia for Choquet multi-period utilities
formula omitted]-continuity, impatience and myopia for Choquet multi-period utilities
1Stochastic decomposition in discrete-time queues with generalized vacations and applications
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive priority systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this decomposition property.
Read more6Small-Signal Modeling of SIMO DC-DC Converters and Comparative Continuous/Discrete-Time Results
Fundamental small-ripple approximation in a well- known averaging technique tends to limit the accuracy of continuous-time (CT) small-signal models of pulse-width- modulated (PWM) DC-DC converters up to 1/10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> of the switching frequency. This paper shows that their accuracy significantly degrades even at much lower frequencies for single-inductor- multiple-output (SIMO) DC-DC converters due to higher current ripple with multiple switch configurations. CT small-signal models are derived for a SIDO buck converter, and the transfer functions using circuit averaging and state-space averaging (SSA) techniques are found to be identical. Thereafter, exact discretetime (DT) large-signal models and accurate small-signal models are derived. Both CT and DT small-signal models are compared, and the accuracy of the latter is justified with the actual switch simulation using MATLAB. Frequency responses demonstrate significant inaccuracies using CT small-signal models for varying system parameters. The results will be useful for accurate modeling and stability analysis using DT modeling for SIMO DC- DC converters and also to understand the underlying dynamics.
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