Mathematical modeling | Nonlinear systems
The quadratic integrate and fire (QIF) model is a biological neuron model and a type of integrate-and-fire neuron which describes action potentials in neurons. In contrast to physiologically accurate but computationally expensive neuron models like the Hodgkin–Huxley model, the QIF model seeks only to produce action potential-like patterns and ignores subtleties like gating variables, which play an important role in generating action potentials in a real neuron. However, the QIF model is incredibly easy to implement and compute, and relatively straightforward to study and understand, thus has found ubiquitous use in computational neuroscience. A quadratic integrate and fire neuron is defined by the autonomous differential equation, where is a real positive constant. Note that a solution to this differential equation is the tangent function, which blows up in finite time. Thus a "spike" is said to have occurred when the solution reaches positive infinity, and the solution is reset to negative infinity. When implementing this model in computers, a threshold crossing value and a reset value is assigned, so that when the solution rises above the threshold, , the solution is immediately reset to * v * t * e (Wikipedia).
Solving a quadratic by completing the square
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha
From playlist Solve a Quadratic by Completing the Square | Fractions
Solving a quadratic by completing the square
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha
From playlist Solve a Quadratic by Completing the Square | Fractions
Solving a quadratic by completing the square
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha
From playlist Solve a Quadratic by Completing the Square | Fractions
Solving an equation by completing the square
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha
From playlist Solve a Quadratic by Completing the Square | Fractions
Learn how solve a quadratic by completing the square with fractions
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha
From playlist Solve a Quadratic by Completing the Square | Fractions
Stark-Heegner cycles for Bianchi modular forms by Guhan Venkat
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Projectile Motion is the branch of physics that studies how projectiles (bullets, cannonballs, arrows) move once fired. In the military, for example, projectile motion tells a soldier how far up to aim a cannon to hit a target. In basketball, if each player was a living calculator and coul
From playlist Fun
Learn how to solve an equation by completing the square
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done
From playlist Solve a Quadratic by Completing the Square | x^2+bx+c
Solve a quadratic equation by completing the square with imaginary solutions
👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done
From playlist Solve a Quadratic by Completing the Square | x^2+bx+c
Philippe michel - 2/4 Automorphic forms for GL(2)
Philippe michel - Automorphic forms for GL(2)
From playlist École d'été 2014 - Théorie analytique des nombres
Philippe Michel - 4/4 Automorphic forms for GL(2)
Philippe Michel - Automorphic forms for GL(2)
From playlist École d'été 2014 - Théorie analytique des nombres
The PROOF: e and pi are transcendental
Today’s video is dedicated to introducing you to two of the holy grails of mathematics, proofs that e and pi are transcendental numbers. For the longest time I was convinced that these proofs were simply out of reach of a self-contained episode of Mathologer, and I even said so in a video
From playlist Recent videos
Factoring a quadratic by diamond method
👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe
From playlist Factor Quadratic Expressions | Difference of Two Squares
Integral points and curves on moduli of local systems - Junho Peter Whang
Special Seminar Topic: Integral points and curves on moduli of local systems Speaker: Junho Peter Whang Affiliation: Princeton University Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Summary for solving a quadratic
👉Learn how to solve quadratic functions. Quadratic equations are equations whose highest power in the variable(s) is 2. They are of the form y = ax^2 + bx + c. There are various techniques which can be applied in solving quadratic equations. Some of the techniques includes factoring and th
From playlist Solve Quadratic Equations by Factoring
Ch5Pr7: Average value and length of a function
A projectile's position is given in parametric form. From this we deduce it's time until impact, impact speed, average height and arc length. This is Chapter 5 Problem 7 from the MATH1231/1241 Calculus notes. Presented by Dr. John Steele from UNSW, Australia.
From playlist Mathematics 1B (Calculus)
How to Solve Quadratics Without a Formula
An explanation of an overlooked method for solving quadratics, and an argument for reshaping how we think of and teach mathematics from a high school math teacher. Foundational Videos Link: (Coming Later!) Contents 00:00 - Introduction 00:35 - Foundation Pre-Check 01:06 - Cancelling 02:2
From playlist Summer of Math Exposition 2 videos
Firing rate models - networks by Bard Ermentrout
Dynamics of Complex Systems - 2017 DATES: 10 May 2017 to 08 July 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore This Summer Program on Dynamics of Complex Systems is second in the series. The theme for the program this year is Mathematical Biology. Over the past decades, the focus o
From playlist Dynamics of Complex Systems - 2017
X. Yuan - On the arithmetic degree of Shimura curves
The goal of this talk is to introduce a Gross--Zagier type formula, which relates the arithmetic self-intersection number of the Hodge bundle of a quaternionic Shimura curve over a totally real field to the logarithmic derivative of the Dedekind zeta function of the base field at 2. The pr
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Learn how to mentally factor a trinomial and solve the quadratic equation
we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods
From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c