Luis Scoccola Approximate and Discrete Vector Bundles in Theory and Applications
April 16th, 2021 Applied Topology in Albany (ATiA) Seminar
Speaker: Luis Scoccola (Michigan State University)
Title: Approximate and Discrete Vector Bundles in Theory and Applications
Abstract: Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In the first case, the characteristic classes of the bundle provide obstructions to global synchronization, while, in the second case, they provide topological information of the manifold beyond its homology, and in particular, give obstructions to dimensionality reduction. I will describe joint work with Jose Perea in which we propose several notions of approximate and discrete vector bundle, study the extent to which they determine true vector bundles, and give algorithms for the stable and consistent computation of low dimensional characteristic classes directly from these combinatorial representations. No previous knowledge of the theory of vector bundles will be assumed.
How to Convert Celsius to Fahrenheit | Math with Mr. J
Welcome to How to Convert Celsius to Fahrenheit with Mr. J! Need help with converting Celsius to Fahrenheit? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with Celsius to Fahrenheit conversions. Mr. J will go through converting Celsius to Fahrenheit examples and explain the formula for how to convert Celsius to Fahrenheit.
✅ Converting Fahrenheit to Celsius:
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Hopefully this video is what you're looking for when it comes to converting Celsius to Fahrenheit.
Approximate nearest neighbors and vector models, introduction to Annoy
Vector models are being used in a lot of different fields: natural language processing, recommender systems, computer vision, and other things. They are fast and convenient and are often state of the art in terms of accuracy. One of the challenges with vector models is that as the number of dimensions increase, finding similar items gets challenging. Erik developed a library called Annoy that uses a forest of random tree to do fast approximate nearest neighbor queries in high dimensional spaces. We will cover some specific applications of vector models with and how Annoy works.
Speaker Bio:
Erik Bernhardsson is the CTO at Better, a small startup in NYC working with mortgages. Before Better, he spent five years at Spotify managing teams working with machine learning and data analytics, in particular music recommendations.
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Red Ribbon Ube Ensaymada: Ube Brioche Buns (Kneaded By Hand) With Butter/Cheese | Cooking with Kurt
Learn how to make a Red Ribbon-Style Ube Ensaymada - soft and moist Filipino-Style brioche buns (we show how to knead the dough by hand!) filled with ube halaya and topped with sugar, butter and cheesy goodness! It's a delicious treat, perfect for breakfast with coffee or as a snack. Enjoy!
RECIPE:
NOTE: If you're using a stand mixer with a dough hook attachment, just add all the dough ingredients into your mixing bowl, and mix on medium speed (Level 4 on KitchenAid) for 15 - 20 minutes, till it passes the windowpane test - shown in video.
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Equipment:
Thermometer -
Brioche/ Tart Molds -
13 x 18-in Half Sheet Pans -
Flexible Dough Scraper -
Grater -
Pastry Brush -
Ingredients:
Brioche Dough:
2.75 cups all-purpose flour [330 g] -
1/2 cup whole milk [120 mL]
3 tbsp sugar [38 g]
1 tsp salt [6 g]
1 tablespoon instant yeast [7 g = 1/4 oz = 1 full envelope]
3 large eggs, cold from fridge [150 g without shell]
10 tablespoons unsalted butter, room temperature [142 g]
Filling:
1 cup ube halaya [240 mL] -
3 tbsp unsalted butter, room temperature [43 g]
1 tsp ube extract [5 mL] -
1/4 tsp salt [1.5 g]
Egg wash:
1 large egg [50 g without shell]
2 tsp of whole milk [10 mL]
Topping:
4 tbsp unsalted butter, room temperature [57 g]
4 tbsp powdered sugar [30 g]
2 cups grated edam or gouda cheese (queso de bola) [250 g]
*Disclaimer: Cooking with Kurt® is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. As an Amazon Associate, I earn from qualifying purchases.
PGT Agar Cups Recipe (Ez as 123)
Today's class is an introduction to Agar, what the benefits of using Agar are, and a recipe for how I make my agar cups that you can make at home using ingredients found at your local grocery stores.
Agar Agar -
Potato Flakes -
Corn Syrup -
2oz Ketchup Cups -
Media Bottle -
Digital Gram Scale -
Laser Thermometer Gun -
Mirro Pressure Cooker -
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Baking Icelandic THUNDER BREAD in an Oven (Cooks in ONLY 8 Hours!)
Jared's Junk Food: Icelandic Thunder Bread in the Oven
Recently I posted a video about Icelandic thunder bread, which is traditionally cooked with the earth. In this episode I try to recreate it with an oven.
Watch my full exploration about foods cooked by the earth here:
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