The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected

1990 ◽  
Vol 332 (1627) ◽  
pp. 511-538 ◽  
Keyword(s):  
Exact Solution ◽  
Continuous Time ◽  
Asymptotic Form ◽  
Dead Time ◽  
Single Channel ◽  
Practical Applications ◽  
Exact Distributions ◽  
Discrete States ◽  
Sum Of Products ◽  
State Case

The openings and shuttings of individual ion channel molecules can be described by a Markov process with discrete states in continuous time. The predicted distributions of the durations of open times, shut times, bursts of openings, etc., are all described, in principle, by mixtures of exponential densities. In practice it is usually found that some of the open times, and/or shut times, are too short to be detected reliably. If a fixed dead-time r is assumed then it is possible to define, as an approximation to what is actually observed, an ‘ extended opening ’ or e-opening which starts with an opening of duration at least r followed by any number of openings and shuttings, all the shut times being shorter than r ; the e-opening ends when a shut time longer than r occurs. A similar definition is used for e-shut times. Several authors have derived approximations to the distribution of durations of e-openings and e-shuttings. In this paper the exact distributions are derived. They are defined piecewise over the intervals r to 2r, 2r to 3 r ,..., etc., the distribution in each interval being a sum of products of polynomials in t with exponential terms. The number of terms is finite, but increases as intervals get further from t = r. An asymptotic form for large t (for which the exact solution becomes difficult to compute) is given for the two state case. The exact solution is compared with several approximations, some of which are shown to be good enough for use in most practical applications.

Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events

1992 ◽  
Vol 337 (1282) ◽  
pp. 383-404 ◽  
Keyword(s):  
Continuous Time ◽  
Dead Time ◽  
Single Channel ◽  
Asymptotic Distributions ◽  
Accurate Approximation ◽  
Alternative Representation ◽  
Discrete States ◽  
Probability Densities ◽  
Model Independent ◽  
Two State Model

The openings and shuttings of individual ion channel molecules can be described by a Markov process with discrete states in continuous time. The predicted distributions of the durations of open times, shut times, bursts of openings, etc. are all described, in principle, by mixtures of exponential densities. In practice it is usually found that some of the open times, and the shut times, are too short to be detected reliably. If a fixed dead-time τ is assumed then it is possible to define, as an approximation to what is actually observed, an ‘extended opening’ or e-opening which starts with an opening of duration at least τ followed by any number of openings and shuttings, all the shut times being shorter than τ ; the e-opening ends when a shut time longer than τ occurs. A similar definition is used for e-shut times. The probability densities, f(t) , of these extended times have previously been obtained as expressions which become progressively more complicated, and numerically unstable to compute, as t→∞. In this paper we present, for the two-state model, an alternative representation as an infinite series of which a small number of terms gives a very accurate approximation of f(t) for large t . For the general model we present an asymptotic representation as a mixture of exponentials which is accurate for all except quite small values of t . Some simple model-independent corrections for missed events are discussed in relationship to the exact solutions.

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

scholarly journals Flight crew diagnostic using aviation simulator training data

2016 ◽  
Vol 9 (3) ◽  
pp. 118-137
Author(s):  
L.S. Kuravsky ◽  
P.A. Marmalyuk ◽  
G.A. Yuryev ◽  
O.B. Belyaeva ◽  
O.Yu. Prokopieva
Keyword(s):  
Continuous Time ◽  
Goodness Of Fit ◽  
Training Data ◽  
Simulator Training ◽  
Model Parameters ◽  
Flight Crew ◽  
Advantages And Disadvantages ◽  
Goodness Of Fit Tests ◽  
Flight Simulators ◽  
Discrete States

This paper describes a new concept of flight crew assessment based on flight simulators training result. It is based on representation of pilot gaze movement with the aid of continuous-time Markov processes with discrete states. Considered are both the procedure of model parameters identification provided with goodness-of-fit tests in use and the classifier-building technique, which makes it possible to estimate degree of correspondence between the observed gaze motion distribution under study and reference distributions identified for different diagnosed groups. The final assessing criterion is formed on the basis of integrated diagnostic parameters, which are determined by the parameters of the identified models. The article provides a description of the experiment, illustrations, and results of studies aimed at assessing the reliability of the developed models and criteria, as well as conclusions about the applicability of the approach, its advantages and disadvantages.

Markovian manpower models in continuous time

1977 ◽  
Vol 14 (02) ◽  
pp. 249-259 ◽  
Author(s):  
Alexander Mehlmann
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Asymptotic Form ◽  
New Approach ◽  
Limiting Behaviour

The problem of determining the asymptotic form of the stock vector n (t) in a continuous time Markovian manpower model is solved for asymptotically exponential recruitment functions {R(t)}. A new approach to the limiting behaviour of some manpower systems with given total sizes {N(t)} is then given by means of time-inhomogeneous Markov processes.

scholarly journals Discrete-Time First-Order Plus Dead-Time Model-Reference Trade-off PID Control Design

2019 ◽  
Vol 9 (16) ◽  
pp. 3220 ◽  
Author(s):  
Ryo Kurokawa ◽  
Takao Sato ◽  
Ramon Vilanova ◽  
Yasuo Konishi
Keyword(s):  
Discrete Time ◽  
Pid Control ◽  
Continuous Time ◽  
Dead Time ◽  
Design Method ◽  
Control Design ◽  
The Other ◽  
Time Model ◽  
Trade Off ◽  
First Order

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

A Single-Channel Printing Scaler for Photon Counting

1976 ◽  
Vol 30 (6) ◽  
pp. 614-620 ◽  
Author(s):  
G. J. Perreault ◽  
R. E. Cookingham ◽  
J. P. Spoonhower ◽  
A. Lewis
Keyword(s):  
Integrated Circuits ◽  
Dead Time ◽  
Single Channel ◽  
Photon Counting ◽  
Paper Tape ◽  
System A ◽  
On Line ◽  
Counting Mode ◽  
Edge Connector ◽  
Digital Counting

A device is described which counts pulses and generates serial code to punch a paper tape and produce formatted count listings on a Teletype. The digital counting mode employed by the printing scaler makes it ideal for photon counting or other event recording applications in spectroscopy. The count capacity is 5 digits (99 999 if decimal; 1 048 575 if hexadecimal). Provision is made to record initialization and overflow flags and two optional external flags. A data latch is included to allow simultaneous counting and printing for minimum dead time; the maximum print rate is 1 data point per sec on a 110 baud terminal. “Initialize” and “enable” signals must be supplied by external circuitry, such as a spectrometer timing and stepping control system. A “done” pulse is supplied by the printing scaler for use in external circuitry if desired. The circuit can also be used with other serial recording devices including an on-line computer; the baud rate is easily adjustable. This device contains 32 TTL SSI and MSI integrated circuits and a few associated discrete components. Our version was constructed on a single 36-position wire wrap breadboard with edge connector and housed in an inverted 8 by 12 by 3 in. chassis box with perforated cover. The required power can be obtained from an inexpensive 5 V, 1 A power supply.

A fast zero dead-time single channel analyzer for nuclear spectroscopy applications

1999 ◽  
Vol 46 (3) ◽  
pp. 417-419 ◽  
Author(s):  
L. Fabris ◽  
P.G. Allen ◽  
J.J. Bucher ◽  
N.M. Edelstein ◽  
D.A. Landis ◽  
...  
Keyword(s):  
Dead Time ◽  
Single Channel ◽  
Nuclear Spectroscopy ◽  
Single Channel Analyzer ◽  
Channel Analyzer

Effects of Temperature Rise on the Flow of a Viscous Liquid through a Concentric Annulus with an Inner Cylinder Rotating

1964 ◽  
Vol 6 (3) ◽  
pp. 258-263 ◽  
Author(s):  
L. A. Newbery
Keyword(s):  
Exact Solution ◽  
Viscous Liquid ◽  
Temperature Rise ◽  
Forced Flow ◽  
Fluid Temperature ◽  
Practical Applications ◽  
Concentric Annulus ◽  
Effects Of Temperature

An exact solution is presented for the forced flow of a viscous liquid through a concentric annulus in which the fluid temperature is increased and the viscosity decreased by rotation of the inner boundary. Such a solution has not previously appeared in the published literature. Some practical applications are mentioned.

The Effect of a Honeycomb Core on the Mechanical Properties of Composite Sandwich Plates

2005 ◽  
Vol 297-300 ◽  
pp. 2752-2757 ◽  
Author(s):  
Cheol Won Kong ◽  
Se Won Eun ◽  
Jae Sung Park ◽  
Ho Sung Lee ◽  
Young Soon Jang ◽  
...  
Keyword(s):  
Exact Solution ◽  
Compression Test ◽  
Sandwich Plate ◽  
Sandwich Beam ◽  
Honeycomb Core ◽  
Practical Applications ◽  
Composite Sandwich ◽  
Beam Shear ◽  
Aluminum Honeycomb ◽  
Honeycomb Cores

When comparing composite sandwich analysis with an exact solution, the results of finite element modeling with an ANSYS shell 91 element agreed well with the exact solution. The practical applications of the shell 91 element are demonstrated with a four-point bend test conducted on sandwich beam specimens. The specimens comprised carbon/epoxy fabric face sheets and a honeycomb core. Two kinds of honeycomb cores were used to fabricate the composite sandwich specimens: an aluminum one and a glass/phenolic one. The predictions with the shell 91 element were also agreed well with the experimental results. A variety of tests was conducted; namely, a long beam flexural test, a short beam shear test, a flatwise tensile test, a flatwise compression test and an edge compression test. The sandwich plate with the aluminum honeycomb core had a specific bending stiffness that was 1.7 to 2.0 times higher than that of the sandwich plate with the glass/ phenolic honeycomb core.

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