In mathematics, a biorthogonal system is a pair of indexed families of vectors such thatwhere and form a pair of topological vector spaces that are in duality, is a bilinear mapping and is the Kronecker delta. An example is the pair of sets of respectively left and right eigenvectors of a matrix, indexed by eigenvalue, if the eigenvalues are distinct. A biorthogonal system in which and is an orthonormal system. (Wikipedia).
Research Methods of Biopsychology
With some information regarding the organization of neurons and neural pathways, we are ready to start getting into some deeper topics. But before we do that, it will be useful to get a general sense of precisely how we learn about the things we will be discussing. The brain is complicated
From playlist Biopsychology
The way that humans communicate is very complex. We have an innate ability to understand and formulate language. As one might imagine, the accompanying brain activity is also quite complex, involving several different regions with very specific functions. Let's go in for a closer look! Wa
From playlist Biopsychology
The Sensorimotor System and Human Reflexes
We just learned all about how sensory information from the surroundings makes it to the brain, but once it's there, the brain has to then tell the body what to do to respond to its surroundings. This happens thanks to the sensorimotor system, so let's learn all about motor response now! W
From playlist Biopsychology
Neurotransmitters: Type, Structure, and Function
We know that neurotransmitters are signaling molecules that travel across the synaptic space to interact with receptors and propagate signals from one neuron to the next. But what are these molecules? What are their structures? How do they work? Let's get a closer look! Watch the whole Bi
From playlist Biopsychology
Complex ODEs: Asymptotics, Orthogonal Polynomials and Random Matrices - 15 May 2018
Centro di Ricerca Matematica Ennio De Giorgi http://crm.sns.it/event/429/ Complex ODEs: Asymptotics, Orthogonal Polynomials and Random Matrices An international interdisciplinary workshop, gathering experts in mathematics and mathematical physics, working on the theory of orthogonal and
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Staudinger Reactions - Bioothogonal before Click Chemistry
The original bioorthogonal chemistry using azides and their reaction phosphines to form aza-ylids, which can do bioconjugation reactions and other useful transformations in organic synthesis. The aza-ylid (aminophosphorane) generated can react directly with water in a hydrolysis reaction
From playlist Organic Chemistry Mechanisms
Daniel Remenik: The KPZ fixed point - Part 2
Abstract: In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in
From playlist Probability and Statistics
Daniel Remenik: The KPZ fixed point - Part 1
Abstract: In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in
From playlist Probability and Statistics
Let's learn all about the human brain! It's the most complex and fascinating object in the known universe. It's the source of our consciousness, so we wouldn't be much without it. This course will assume prior knowledge from my biochemistry, biology, and anatomy & physiology courses, so ma
From playlist Biopsychology
Angela Kunoth: 25+ Years of Wavelets for PDEs
Abstract: Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs,
From playlist Numerical Analysis and Scientific Computing
Maurice Duits -- CLTs for biorthogonal ensembles: Beyond the Strong Szegö Limit Theorem
The Strong Szegö Limit Theorem for Toeplitz determinants implies a CLT for linear statistics for eigenvalues of a CUE matrix. The first part of the talk will be an overview of results on various extensions of the Strong Szegö Limit theorem to determinants of truncated exponentials of ban
From playlist Columbia Probability Seminar
Suhasini Subba Rao: Reconciling the Gaussian and Whittle Likelihood with an application to ...
In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussia likelihood and the Whittle likelihood. We derive an exact,
From playlist Virtual Conference
Lec 1 | MIT 6.451 Principles of Digital Communication II
Introduction; Sampling Theorem and Orthonormal PAM/QAM; Capacity of AWGN Channels View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.451 Principles of Digital Communication II
Central Limit Theorems for linear statistics for biorthogonal ensembles - Maurice Duits
Maurice Duits SU April 2, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
The Structure and Physiology of the Human Brain
So we already learned all about the brain in the Anatomy & Physiology series, so if you missed that one, definitely check it out before moving forward with this playlist: https://www.youtube.com/watch?v=Eo3Dp0h5490 But if you're up to speed, let's do a quick review, introduce a couple new
From playlist Biopsychology
The Autonomic Nervous System: Sympathetic and Parasympathetic Divisions
We've learned quite a bit about the peripheral nervous system, which has a sensory division and a motor division. The latter is the one that tells the body what to do, and this is divided into the somatic nervous system, which involves voluntary motion, and the autonomic nervous system, wh
From playlist Anatomy & Physiology
The Urinary System - An Introduction | Physiology | Biology | FuseSchool
The Urinary System - An Introduction | Physiology | Biology | FuseSchool The urinary system is also known as the renal system and consists of the kidneys, the ureters, the bladder and the urethra. Your kidneys are bean shaped organs that are about the same size as a computer mouse. To fin
From playlist BIOLOGY: Physiology
The Psychology of Emotion and Stress
Humans, just like most other mammals, display a wide variety of emotional states. But what are emotions? Why do we have them? What purpose do they serve in an evolutionary context? Let's get to the bottom of emotions right now! Watch the whole Biopsychology playlist: http://bit.ly/ProfDav
From playlist Biopsychology
The Central Nervous System: The Brain and Spinal Cord
The nervous system is extremely complicated, but we should definitely know the basics, so let's dive in! It is comprised of two main divisions, the central nervous system, and the peripheral nervous system. The first of these is made up of the brain and spinal cord, and since the human bra
From playlist Anatomy & Physiology
RubyConf 2022: Helping Redistrict California with Ruby by Jeremy Evans
Every 10 years, after the federal census, California and most other states redraw the lines of various electoral districts to attempt to ensure the districts are fair and have roughly equal population. California uses a system written in Ruby for citizens to apply to become redistricting c
From playlist RubyConf 2022: Mini and Houston