In the theory of stochastic processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process is a filtration associated to the process which records its "past behaviour" at each time. It is in a sense the simplest filtration available for studying the given process: all information concerning the process, and only that information, is available in the natural filtration. More formally, let (Ω, F, P) be a probability space; let (I, ≤) be a totally ordered index set; let (S, Σ) be a measurable space; let X : I × Ω → S be a stochastic process. Then the natural filtration of F with respect to X is defined to be the filtration F•X = (FiX)i∈I given by i.e., the smallest σ-algebra on Ω that contains all pre-images of Σ-measurable subsets of S for "times" j up to i. In many examples, the index set I is the natural numbers N (possibly including 0) or an interval [0, T] or [0, +∞); the state space S is often the real line R or Euclidean space Rn. Any stochastic process X is an adapted process with respect to its natural filtration. (Wikipedia).
Gravity Filtration and Vacuum Filtration
The first laboratory technique that we will learn together is a very simple one, filtration. This is how we separate a mixture of liquids and solids. There are two common ways a chemist will perform filtration, those being gravity filtration and vacuum filtration. These are very easy to un
From playlist Chemistry Laboratory Techniques
How Does Water Treatment Work | Environmental Chemistry | Chemistry | FuseSchool
Learn the basics about water treatment, as a part of environmental chemistry. Human beings have added to the natural water cycle by taking water from rivers for use in our towns and cities. We are taking a huge amount of water from natural sources to use in our homes and industries. Lo
From playlist CHEMISTRY: Environmental Chemistry
A rotating nozzle that can print with multiple different materials at the same time has been used to print helix shapes with intriguing properties. The researchers who developed the system have experimented with printing a kind of artificial muscle and with changing the properties a length
From playlist Technology
Geyser Exhibit I Exploratorium
Geyser is a working model of a natural geyser. A large bowl of water is supported over a long, thin tube which runs down to a glass chamber filled with water heated by a heating element. As the water in the chamber begins to boil, air and water are shot up the tube into the air. Cool water
From playlist Hands-on Exploratorium
Filtration | MIT Digital Lab Techniques Manual
Filtration The easiest way to separate a liquid from a solid? Filtration! Learn how to effectively carry out gravity and vacuum filtrations in this video. Created by Dr. Sarah Tabacco and Aaeyesha Siddiqui View the complete resource at: http://ocw.mit.edu/resources/res-5-0001-digital-la
From playlist MIT Digital Lab Techniques Manual
What Types of Chemical Industries Are There | Environmental Chemistry | Chemistry | FuseSchool
Learn the basics about different types of chemical industries, from agriculture to pharmaceutical to energy, and many other uses. In this video, we consider the environmental impact caused by a range of different types of chemical industries. Chemicals produced by the chemicals industry
From playlist CHEMISTRY: Environmental Chemistry
How Do Water Treatment Plants Work?
For most everyone around the world, turning on your tap and getting fresh clean water is just a way of life. While this might seem to be a simple fact of modern civilization, it's a relatively new innovation in the timeline of human development. Access to fresh water is one of the largest
From playlist Concerning Engineering
GCSE Science Revision Chemistry "Filtration and Crystallisation"
Find my revision workbook here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at filtration and crystallisation, which are both examples of physical separation methods. First, I discuss the substances that can be separated using filtration and how to set up filtrat
From playlist 9-1 GCSE Chemistry Paper 1 Atomic Structure and the Periodic Table
Parabolic Mirror professional mold SOLAR WATER Boiling System WITH A PARABOLIC MIRROR
This is a professionally made high quality solar parabolic mirror designed for sun concentration. http://www.greenpowerscience.com/SHOPHOME.html This demonstrates a simple use of the mirror. Easy portable water boiling. Not enough power to distill water rapidly but will work if you have th
From playlist SOLAR COOKING Solar Oven Solar Fresnel Lens Parabolic Mirror
2 Ruediger - Stochastic Integration & SDEs
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Richard Hain - 3/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives
Michael Lesnick (2/23/2022): Stability of 2-Parameter Persistent Homology
We show that the standard stability results for union-of-balls, Čech, and Rips persistent homology have natural analogues in the 2-parameter setting, formulated in terms of the multicover bifiltration and Sheehy's subdivision bifiltrations. Our results imply that these bifiltrations are r
From playlist AATRN 2022
P=WP=W: a strange identity for GL(2,ℂ)GL(2,C) - Mark deCataldo
Mark deCataldo Stony Brook University; Member, School of Mathematics November 24, 2014 Start with a compact Riemann surface XX and a complex reductive group GG, like GL(n,ℂ)GL(n,C). According to Hitchin-Simpson's ``non abelian Hodge theory", the pair (X,G)(X,G) comes with two new complex
From playlist Mathematics
I will discuss certain invariants of singularities, the Hodge ideals, that are defined in the context of Saito’s theory of mixed Hodge modules. They can be considered as higher order analogues of the multiplier ideals, invariants that have had a lot of applications in complex geometry. I w
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
Bala Krishnamoorthy (9/16/20): Steinhaus filtration and stable paths in the Mapper
Title: Steinhaus Filtration and Stable Paths in the Mapper Abstract: Two central concepts of topological data analysis are persistence and the Mapper construction. Persistence employs a sequence of objects built on data called a filtration. A Mapper produces insightful summaries of data,
From playlist AATRN 2020
Floer Cohomology and Arc Spaces - Mark McLean
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Floer Cohomology and Arc Spaces Speaker: Mark McLean Affiliation: Stony Brook University Date: June 12, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Hodge theory, between algebraicity and transcendence (Lecture 1) by Bruno Klingler
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
How to Design and Construct a Glass Faucet | How It's Made
Glass faucets elevate indoor plumbing to an art form! See how they're made. Stream Full Episodes of How It's Made: https://www.sciencechannel.com/tv-shows/how-its-made/ Subscribe to Science Channel: http://bit.ly/SubscribeScience Like us on Facebook: https://www.facebook.com/ScienceCha
From playlist How It's Made
Infinite-Dimensional Geometric Invariant Theory and Gauged Gromov–Witten... by Dan Halpern-Leistner
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023