Topological vector spaces

Biorthogonal system

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).

Video thumbnail

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

Video thumbnail

The Brain and Language

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

Introduction to Biopsychology

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Related pages

Linear span | Indexed family | Mathematics | Dual system | Kernel (algebra) | Orthogonal basis | Topological vector space | Kronecker delta