scholarly journals Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

2018 ◽  
Vol 6 (1) ◽  
pp. 41-64 ◽  
Author(s):  
Aslak Tveito ◽  
Mary M. Maleckar ◽  
Glenn T. Lines
Keyword(s):  
Differential Equations ◽  
Markov Model ◽  
Stochastic Models ◽  
Markov Models ◽  
Single Channel ◽  
Probability Density Functions ◽  
Density Functions ◽  
Mathematical Framework ◽  
Wild Type ◽  
Channel Dynamics

AbstractSingle channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.

Stochastic formulations of the parametrix method

2018 ◽  
Vol 22 ◽  
pp. 178-209
Author(s):  
Arturo Kohatsu-Higa ◽  
Gô Yûki
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Lower Bounds ◽  
Probability Density Functions ◽  
Upper And Lower Bounds ◽  
Density Functions ◽  
Holder Continuity ◽  
Gaussian Type

In this manuscript, we consider stochastic expressions of the parametrix method for solutions of d-dimensional stochastic differential equations (SDEs) with drift coefficients which belong to Lp(Rd), p > d. We prove the existence and Hölder continuity of probability density functions for distributions of solutions at fixed points and obtain an explicit expansion via (stochastic) parametrix methods. We also obtain Gaussian type upper and lower bounds for these probability density functions.

Fuzzy Observable Markov Models for Pattern Recognition

2007 ◽  
Vol 11 (6) ◽  
pp. 662-667
Author(s):  
Dat Tran ◽  
◽  
Wanli Ma ◽  
Dharmendra Sharma
Keyword(s):  
Pattern Recognition ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Vector Quantization ◽  
Markov Models ◽  
Hidden Markov ◽  
Gaussian Mixture ◽  
Written Language ◽  
Mathematical Framework ◽  
Fuzzy Observable

This paper presents a mathematical framework for fuzzy discrete and continuous observable Markov models (OMMs) and their applications to written language, spam email and typist recognition. Experimental results show that the proposed OMMs are more effective than models such as vector quantization, Gaussian mixture model and hidden Markov model.

scholarly journals Identification of Structures for Ion Channel Kinetic Models

2021 ◽  
Author(s):  
Kathryn E. Mangold ◽  
Wei Wang ◽  
Eric K. Johnson ◽  
Druv Bhagavan ◽  
Jonathan D. Moreno ◽  
...  
Keyword(s):  
Markov Model ◽  
Ion Channel ◽  
Markov Models ◽  
Left Ventricular ◽  
Channel Dynamics ◽  
Voltage Gated ◽  
Minimum Number ◽  
Voltage Gated Ion Channels ◽  
Channel Currents ◽  
Channel Kinetic

AbstractMarkov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium and human left ventricular fast transient outward potassium currents. In addition to optional biophysically inspired restrictions on the number of connections from a state and elimination of long-range connections, this study further suggests successful models have more than minimum number of connections for set number of states. When working with topologies with more than the minimum number of connections, the topologies with three and four connections to the open state tend to serve well as Markov models of ion channel dynamics.Significance StatementHere, we present a computational routine to thoroughly search for Markov model topologies for simulating whole-cell currents given an experimental dataset. We test this method on two distinct types of voltage-gated ion channels that function in the generation of cardiac action potentials. Particularly successful models have more than one connection between an open state and the rest of the model, and large models may benefit from having even more connections between the open state and the rest of the other states.

scholarly journals Conversion of Body Conducted Unvoiced Speech(Murmur) to Normal Speech Using Hidden Markov Model (HMM)

2018 ◽  
Vol 7 (2.32) ◽  
pp. 400
Author(s):  
T RajeshKumar ◽  
M Srinagamani ◽  
M Sai ram chandu ◽  
S Mounika
Keyword(s):  
Big Data ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Statistical Learning ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Data Signal ◽  
Normal Speech

The main purpose of this paper is Conversion of  non- audible murmured voice into the normal speech using Hidden Markov Model(HMM).This non audible murmur voice NAM is a one type of murmured voice which can be delivered by a NAM microphone which is attached behind the speaker’s ear. The Hidden Markov Models(HMMs) are stochastic models of statistical learning .These are very useful in speech recognition .The point of the paper is to collect as much as data from the device and convert it into audible and clear data signal that can be used for further sensory based applications. Hence, having an insight of how to convert the NAM to speech and then to whisper has a lot of benefits while keeping in mind the disadvantages of such conversion. Since, NAM is minute details of a communication between one’s own self it is highly recommended to the data in as much as discrete format as necessary since a speech signal can have various frequencies over a portion of the signal, big data approach is recommended. 

scholarly journals Numerical modeling of boundary value problems for differential equations with random coefficients

2021 ◽  
Vol 2099 (1) ◽  
pp. 012065
Author(s):  
B S Dobronets ◽  
O A Popova ◽  
A M Merko
Keyword(s):  
Numerical Modeling ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Random Fields ◽  
Boundary Value ◽  
Probability Density Functions ◽  
Random Coefficients ◽  
Independent Random Variables ◽  
Density Functions ◽  
Elliptic Type

Abstract This paper deals with the numerical modeling of differential equations with coefficients in the form of random fields. Using the Karhunen-Lo´eve expansion, we approximate these coefficients as a sum of independent random variables and real functions. This allows us to use the computational probabilistic analysis. In particular, we apply the technique of probabilistic extensions to construct the probability density functions of the processes under study. As a result, we present a comparison of our approach with Monte Carlo method in terms of the number of operations and demonstrate the results of numerical experiments for boundary value problems for differential equations of the elliptic type.

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