다양체
메모
- homology manifolds
- topological/smooth/PL manifolds
리뷰, 에세이, 강의노트
- Quinn, History of manifolds
관련도서
- James, I. M., ed. 1999. History of Topology. Amsterdam: North-Holland. http://www.ams.org/mathscinet-getitem?mr=1674906.
- Scholz, Erhard. 1999. “The Concept of Manifold, 1850–1950.” In History of Topology, 25–64. Amsterdam: North-Holland.
노트
- Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance.[1]
- In the same vein, the Japanese word "多様体" (tayōtai) also encompasses both manifold and variety.[1]
- The name manifold comes from Riemann's original German term, Mannigfaltigkeit, which William Kingdon Clifford translated as "manifoldness".[1]
- Riemann's intuitive notion of a Mannigfaltigkeit evolved into what is today formalized as a manifold.[1]
- The way these connect to one another dictates the control options of a manifold.[2]
- A Drilled manifold, on the other hand, is made with a single slab drilled with holes for passages.[2]
- Following up on the math-y stuff from my last post, I'm going to be taking a look at another concept that pops up in ML: manifolds.[3]
- For example, all "cat images" might lie on a lower-dimensional manifold compared to say their original 256x256x3 image dimensions.[3]
- Okay, that's all well and good, but that still doesn't answer the question: what is a manifold?[3]
- A manifold is a topological space that "locally" resembles Euclidean space.[3]
- The carburetor or the fuel injectors spray fuel droplets into the air in the manifold.[4]
- Comparison of a stock intake manifold for a Volkswagen 1.8T engine (top) to a custom-built one used in competition (bottom).[4]
- In the custom-built manifold, the runners to the intake ports on the cylinder head are much wider and more gently tapered.[4]
- This high-pressure air begins to equalize with lower-pressure air in the manifold.[4]
- To make use of the idea of a manifold a transition from the local to the global point of view is usually made.[5]
- For a disconnected manifold the components are usually taken to be of the same dimension.[5]
- A connected manifold without boundary is called open if it is non-compact, and closed if it is compact.[5]
- The global specification of a manifold is accomplished by an atlas: A set of charts covering the manifold.[5]
- The car's infotainment computer directs vehicle controllers that talk to valves that move the air through a manifold.[6]
- As a result, the company had to shut down one manifold, which effectively branches into several lines carrying propellant to four thrusters.[6]
- One of the goals of topology is to find ways of distinguishing manifolds.[7]
- For instance, a circle is topologically the same as any closed loop, no matter how different these two manifolds may appear.[7]
- As a topological space, a manifold can be compact or noncompact, and connected or disconnected.[7]
- Commonly, the unqualified term "manifold"is used to mean "manifold with boundary." This is the usage followed in this work.[7]
- Here we will focus on the general notion of a manifold.[8]
- At best, we can only talk about isomorphisms of manifolds.[8]
- An atlas is not considered an essential part of the structure of a manifold: two different atlases may yield the same manifold structure.[8]
- Morphisms of manifolds are here called smooth maps, and isomorphisms are called diffeomorphisms.[8]
- This step aims to approximate the manifolds of the datasets.[9]
- Then, we cluster those networks simultaneously based on the distances in the common manifold.[9]
- I claim that a super useful step in answering this question is understanding what a manifold is.[10]
- Visualize examples of manifolds in various contexts.[10]
- To be a manifold, there’s one important rule that needs to be satisfied.[10]
- Suppose there is a small ant walking along a manifold in three dimensions.[10]
- The course will start by introducing the concept of a manifold (without recourse to an embedding into an ambient space).[11]
- Colour qualities form a two-dimensional manifold (cf.[11]
- In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.[12]
- Two-dimensional manifolds are also called surfaces.[12]
- A Riemannian metric on a manifold allows distances and angles to be measured.[12]
- A surface is a two dimensional manifold, meaning that it locally resembles the Euclidean plane near each point.[12]
- A, B are the n by m PC matrices that span the task-specific manifolds A and B; the corresponding PC neural modes are their column vectors.[13]
- In dPCA, the rank m of the n by n matrix A is chosen as the desired dimensionality of the manifold.[13]
- As before, the chosen manifold dimensionality was m = 12, although the results held for m = 8, 15 (see Supplementary Fig.[13]
- Cognate with Middle High German manecvalt (“manifold”), Icelandic margfaldr (“multiple”).[14]
- To make manifold; multiply.[14]
- Direct mounted 2 valve manifold delivered with 2 bolts and one PTFE gasket.[15]
- with pages giving succinct and precise of important concepts in the theory of manifolds.[16]
- The term manifold is derived from Riemann's original German term, Mannigfaltigkeit.[17]
- Riemann's intuitive notion of a Mannigfaltigkeit evolved into what is formalised today as the concept of manifold.[17]
- A manifold, also a differentiable manifold, is defined as a topological space that is locally equivalent to the Euclidean space.[17]
- This amounts to say that each point of the manifold belongs to an open set which is homeomorphic to an open set of the Euclidean space.[17]
- As many of the results in the paper come from this embedding, it is important to actually note what the structure of this manifold is.[18]
- Moreover, the density within the manifold is not shown in any of the plots as well.[18]
- Using this projection, we visualized the density of points within the manifold.[18]
- By construction, the high-dimensional data manifold produced by the model is continuous.[18]
소스
- ↑ 1.0 1.1 1.2 1.3 History of manifolds and varieties
- ↑ 2.0 2.1 The Benefits and Uses of Manifold Blocks
- ↑ 3.0 3.1 3.2 3.3 Manifolds: A Gentle Introduction
- ↑ 4.0 4.1 4.2 4.3 Inlet manifold
- ↑ 5.0 5.1 5.2 5.3 Encyclopedia of Mathematics
- ↑ 6.0 6.1 Definition of Manifold by Merriam-Webster
- ↑ 7.0 7.1 7.2 7.3 Manifold -- from Wolfram MathWorld
- ↑ 8.0 8.1 8.2 8.3 manifold in nLab
- ↑ 9.0 9.1 ManiNetCluster: a novel manifold learning approach to reveal the functional links between gene networks
- ↑ 10.0 10.1 10.2 10.3 Manifolds in Data Science — A Brief Overview
- ↑ 11.0 11.1 MA3H5 Manifolds
- ↑ 12.0 12.1 12.2 12.3 Wikipedia
- ↑ 13.0 13.1 13.2 Cortical population activity within a preserved neural manifold underlies multiple motor behaviors
- ↑ 14.0 14.1 Wiktionary
- ↑ Manifold for pressure transmitter
- ↑ Manifold Atlas
- ↑ 17.0 17.1 17.2 17.3 Differentiable Manifold - an overview
- ↑ 18.0 18.1 18.2 18.3 The manifold structure of limb coordination in walking Drosophila