scholarly journals Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 45359-45371 ◽  
Author(s):  
Qiuhong Xiang ◽  
Weibing Li ◽  
Bolin Liao ◽  
Zhiguan Huang
Keyword(s):  
Discrete Time ◽  
Computing Time ◽  
Lyapunov Equation ◽  
Time Dependent ◽  
Neural Dynamics

scholarly journals Elliptic Solutions of Dynamical Lucas Sequences

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 183
Author(s):  
Michael J. Schlosser ◽  
Meesue Yoo
Keyword(s):  
Discrete Time ◽  
Time Dependent ◽  
Fibonacci Polynomials ◽  
Lucas Sequences ◽  
Elliptic Solutions

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.

scholarly journals Time-dependent performance analysis of a discrete-time priority queue

2008 ◽  
Vol 65 (9) ◽  
pp. 641-652 ◽  
Author(s):  
Joris Walraevens ◽  
Dieter Fiems ◽  
Herwig Bruneel
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
Priority Queue ◽  
Time Dependent

Elastic Interfaces for Visual Data Browsing

2006 ◽  
pp. 187-195
Author(s):  
Wolfgang Hürst
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Target Position ◽  
Rubber Band ◽  
Time Dependent ◽  
Elastic Behavior ◽  
Independent Data ◽  
Visual Data ◽  
Elastic Interfaces ◽  
Data Browsing

In this article, we discuss the concept of elastic interfaces, which was originally introduced by Masui, Kashiwagi, and Borden (1995) a decade ago for the manipulation of discrete, time-independent data. It gained recent attraction again by our own work in which we adapted and extended it in order to use it in a couple of other applications, most importantly in the context of continuous, time-dependent documents (Hürst & Götz, 2004; Hürst, Götz, & Lauer, 2004). The basic idea of an elastic interface is illustrated in Figure 1. Normally, objects are moved by dragging them directly to the target position (direct positioning). With elastic interfaces, the object follows the cursor or mouse pointer on its way to the target position with a speed s that is a function of the distance d between the cursor and the object. They are called elastic because the behavior can be explained by the rubber-band metaphor, in which the connection between the cursor and the object is seen as a rubber band: The more the band is stretched, the stronger the force between the object and the cursor gets, which makes the object move faster. Once the object and cursor come closer to each other, the pressure on the rubber band decreases, thus slowing down the object’s movement. In the next section we describe when and why elastic interfaces are commonly used and review related approaches. Afterward, we illustrate different scenarios and applications in which elastic interfaces have been used successfully for visual data browsing, that is, for skimming and navigating through visual data. First, we review the work done by Masui (1998) and Masui et al. (1995) in the context of discrete, time-independent data. Then we describe our own work, which applies the concept of elastic interfaces to continuous, time-dependent media streams. In addition, we discuss specific aspects considering the integration of such an elastic behavior into common GUIs (graphical user interfaces) and introduce a new interface design that is especially useful in context with multimedia-document skimming.

Imputing missing time-dependent covariate values for the discrete time Cox model

2019 ◽  
Vol 29 (8) ◽  
pp. 2074-2086
Author(s):  
Havi Murad ◽  
Rachel Dankner ◽  
Alla Berlin ◽  
Liraz Olmer ◽  
Laurence S Freedman
Keyword(s):  
Discrete Time ◽  
Missing Values ◽  
Cox Regression ◽  
Cox Model ◽  
Missing At Random ◽  
Time Dependent ◽  
Outcome Variable ◽  
Sequential Approach ◽  
Random Patterns ◽  
Event Times

We describe a procedure for imputing missing values of time-dependent covariates in a discrete time Cox model using the chained equations method. The procedure multiply imputes the missing values for each time-period in a time-sequential manner, using covariates from the current and previous time-periods as well as the survival outcome. The form of the outcome variable used in the imputation model depends on the functional form of the time-dependent covariate(s) and differs from the case of Cox regression with only baseline covariates. This time-sequential approach provides an approximation to a fully conditional approach. We illustrate the procedure with data on diabetics, evaluating the association of their glucose control with the risk of selected cancers. Using simulations we show that the suggested estimator performed well (in terms of bias and coverage) for completely missing at random, missing at random and moderate non-missing-at-random patterns. However, for very strong non-missing-at-random patterns, the estimator was seriously biased and the coverage was too low. The procedure can be implemented using multiple imputation with the Fully conditional Specification (FCS) method (MI procedure in SAS with FCS statement or similar packages in other software, e.g. MICE in R). For use with event times on a continuous scale, the events would need to be grouped into time-intervals.

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