Methodological Development for Time-Dependent AHP Using Probability Distribution

2021 ◽  
pp. 467-476
Author(s):  
Arpan Garg ◽  
Talari Ganesh
Keyword(s):  
Probability Distribution ◽  
Time Dependent ◽  
Methodological Development

scholarly journals Analysis of correlated data with feedback for time-dependent covariates in psychiatry research

2020 ◽  
Vol 33 (5) ◽  
pp. e100263
Author(s):  
Elsa Vazquez Arreola ◽  
Jeffrey R Wilson ◽  
Ding-Geng Chen
Keyword(s):  
Data Collection ◽  
Repeated Measures ◽  
Correlated Data ◽  
Time Dependent ◽  
Methodological Development ◽  
Marginal Models ◽  
Feedback Effects ◽  
The Hierarchical Structure ◽  
The Subject ◽  
Time Dependent Covariates

In studies on psychiatry and neurodegenerative diseases, it is common to have data that are correlated due to the hierarchical structure in data collection or to repeated measures on the subject longitudinally. However, the feedback effect created due to time-dependent covariates in these studies is often overlooked and seldom modelled. This article reviews the methodological development of feedback effects with marginal models for longitudinal data and discusses their implementation.

Probability Distribution of the Residence Times in Periodically Fluctuating Metastable Systems

1998 ◽  
Vol 08 (04) ◽  
pp. 783-790 ◽  
Author(s):  
Rosario N. Mantegna ◽  
Bernardo Spagnolo
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Numerical Simulations ◽  
Gaussian Function ◽  
Model System ◽  
Time Dependent ◽  
Residence Times ◽  
Dependent Potential ◽  
Metastable Systems ◽  
Enhanced Stability

We investigate experimentally and numerically the probability distribution of the residence times in periodically fluctuating metastable systems. The experiments are performed in a physical metastable system which is the series of a biasing resistor with a tunnel diode in parallel to a capacitor. The numerical simulations are performed in an overdamped model system with a time-dependent potential. We investigate both the cases where the system is deterministically overall-stable and overall-unstable. In the overall-unstable regime, the experimental and the numerically investigated systems show noise enhanced stability in the presence of a finite amount of noise. The determined P(T) is multi-peaked with an exponentially decaying envelop. We note that the shape of the nth peak in the P(T) is roughly fitted by a Gaussian function with standard deviation independent of n.

scholarly journals Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Marcelo A. Pires ◽  
Giuseppe Di Molfetta ◽  
Sílvio M. Duarte Queirós
Keyword(s):  
Probability Distribution ◽  
Uniform Distribution ◽  
Quantum Walk ◽  
Step Length ◽  
Quantum Walks ◽  
Time Dependent ◽  
Asymptotic Approach ◽  
Diffusive Regime ◽  
Dynamical Regimes ◽  
Functional Forms

AbstractWe extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the variance grows cubicly with time, σ2 ∝ t3, and a Gaussian for the position of the walker. We investigate this proposal both locally and globally with the results showing that the time-dependent interplay between interference, memory and long-range hopping leads to multiple transitions between dynamical regimes, namely ballistic → diffusive → superdiffusive → ballistic → hyperballistic for non-hermitian coin whereas the first diffusive regime is quelled for implementations using the Hadamard coin. In addition, we observe a robust asymptotic approach to maximal coin-space entanglement.

Finite dams with inputs forming a Markov chain

1970 ◽  
Vol 7 (02) ◽  
pp. 291-303 ◽  
Author(s):  
M.S. Ali Khan
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Generating Functions ◽  
State Transition ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Time Dependent ◽  
Probability Generating Functions ◽  
State Transition Probability ◽  
Finite Dam

This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.

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