In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the Loligo squid exemplifies such models. Although qualitatively correct, the H-H model does not describe every type of excitable membrane accurately, since it considers only two ions (sodium and potassium), each with only one type of voltage-sensitive channel. However, other ions such as calcium may be important and there is a great diversity of channels for all ions. As an example, the cardiac action potential illustrates how differently shaped action potentials can be generated on membranes with voltage-sensitive calcium channels and different types of sodium/potassium channels. The second type of mathematical model is a simplification of the first type; the goal is not to reproduce the experimental data, but to understand qualitatively the role of action potentials in neural circuits. For such a purpose, detailed physiological models may be unnecessarily complicated and may obscure the "forest for the trees". The FitzHugh–Nagumo model is typical of this class, which is often studied for its entrainment behavior. Entrainment is commonly observed in nature, for example in the synchronized lighting of fireflies, which is coordinated by a burst of action potentials; entrainment can also be observed in individual neurons. Both types of models may be used to understand the behavior of small biological neural networks, such as the central pattern generators responsible for some automatic reflex actions. Such networks can generate a complex temporal pattern of action potentials that is used to coordinate muscular contractions, such as those involved in breathing or fast swimming to escape a predator. (Wikipedia).
B27 Introduction to linear models
Now that we finally now some techniques to solve simple differential equations, let's apply them to some real-world problems.
From playlist Differential Equations
Introduction to Population Models and Logistic Equation (Differential Equations 31)
https://www.patreon.com/ProfessorLeonard How differential equations can be applied to population models. We also explore the Logistic Equation, Population Explosion, and Population Extinction from a mathematical perspective involving limits.
From playlist Differential Equations
From playlist STAT 501
Ex: Write a Recursive and Explicit Equation to Model Linear Growth
This video provides an basic example of how to determine a recursive and explicit equation to model linear growth given P_0 and P_1. http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
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From playlist ICTP-ICTS Winter School on Quantitative Systems Biology (ONLINE)
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My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
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PROGRAM ICTP-ICTS WINTER SCHOOL ON QUANTITATIVE SYSTEMS BIOLOGY (ONLINE) ORGANIZERS: Vijaykumar Krishnamurthy (ICTS-TIFR, India), Venkatesh N. Murthy (Harvard University, USA), Sharad Ramanathan (Harvard University, USA), Sanjay Sane (NCBS-TIFR, India) and Vatsala Thirumalai (NCBS-TIFR,
From playlist ICTP-ICTS Winter School on Quantitative Systems Biology (ONLINE)
Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.
From playlist Learning medical statistics with python and Jupyter notebooks
Qualitative And Quantitative Risk Analysis Explained | Risk Analysis Techniques | Simplilearn
In this video on Qualitative and Quantitative Risk Analysis, we'll go into detail about how each of them work, how it's performed and the tools and techniques required to document it. 🔥Explore Our Free Courses With Completion Certificate by SkillUp: https://www.simplilearn.com/skillup-free
From playlist PMI-RMP® Training Videos [2022 Updated]
C67 The physics of simple harmonic motion
See how the graphs of simple harmonic motion changes with changes in mass, the spring constant and the values correlating to the initial conditions (amplitude)
From playlist Differential Equations
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PROGRAM ICTP-ICTS WINTER SCHOOL ON QUANTITATIVE SYSTEMS BIOLOGY (ONLINE) ORGANIZERS: Vijaykumar Krishnamurthy (ICTS-TIFR, India), Venkatesh N. Murthy (Harvard University, USA), Sharad Ramanathan (Harvard University, USA), Sanjay Sane (NCBS-TIFR, India) and Vatsala Thirumalai (NCBS-TIFR,
From playlist ICTP-ICTS Winter School on Quantitative Systems Biology (ONLINE)
peter hollenbeck (2) - Mitochondrial Transport, Metabolism and ROS Production in Disease Models
PROGRAM:Axonal Transport and Neurodgenerative Disorders DATES:Sunday 13 Jan, 2013 - Saturday 26 Jan, 2013 VENUE:IIT Bombay and The Club Mahabaleshwar DESCRIPTION: Neurodegeneration, a broad symptom which arises out of several different dysfunctions, is prevalent in aging populations, and
From playlist Axonal Transport and Neurodgenerative Disorders
Digging into Data: Linear and Regularized Regression
Making predictions about real-valued data.
From playlist Digging into Data
Least squares method for simple linear regression
In this video I show you how to derive the equations for the coefficients of the simple linear regression line. The least squares method for the simple linear regression line, requires the calculation of the intercept and the slope, commonly written as beta-sub-zero and beta-sub-one. Deriv
From playlist Machine learning
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This video on Quantitative Risk Analysis will help you understand how to perform Quantitative RIsk Analysis, List the tools and Techniques required for the analysis.This Video will also help you in EMV analysis and Probability Distribution. #QuantitativeRiskAnalysis #WhatIsQuantitativeRis
From playlist PMI-RMP® Training Videos [2022 Updated]
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This video on Quantitative Risk Analysis will help you understand how to perform Quantitative RIsk Analysis, List the tools and Techniques required for the analysis. This Video will also help you in EMV analysis and Probability Distribution. 🔥Free Project Management Course: https://www.sim
From playlist PMI-RMP® Training Videos [2022 Updated]
Studying thermal QCD matter on the lattice (LQCD1 - Lecture 4) by Peter Petreczky
PROGRAM THE MYRIAD COLORFUL WAYS OF UNDERSTANDING EXTREME QCD MATTER ORGANIZERS: Ayan Mukhopadhyay, Sayantan Sharma and Ravindran V DATE: 01 April 2019 to 17 April 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Strongly interacting phases of QCD matter at extreme temperature and
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Nicolas Dirr: "Scaling Limits and Stochastic Homogenization"
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This seminar series looks at four important linear models (linear regression, analysis of variance, analysis of covariance, and logistic regression). A video that explains all four model types is at https://www.youtube.com/watch?v=SV9AxXFWZnM&t=12s This video is on linear regression usin
From playlist Statistics
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Indian Statistical Physics Community Meeting 2016 URL: https://www.icts.res.in/discussion_meeting/details/31/ DATES Friday 12 Feb, 2016 - Sunday 14 Feb, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community wh
From playlist Indian Statistical Physics Community Meeting 2016