The Information Uncertainty Principle
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The document discusses uncertainty principles in filter bank design and wavelet transforms. It explores different mathematical groups that model transformations and their associated uncertainty principles. Several approaches are discussed for finding functions that minimize joint uncertainty, including solutions for the 1D and 2D affine groups. Future work is proposed to find minimizers for other groups and apply these concepts to problems like segmentation.
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This document discusses stability estimates for identifying point sources using measurements from the Helmholtz equation. It begins by introducing the inverse problem of determining source terms from boundary measurements of the electromagnetic field. It then proves identifiability, showing that a single boundary measurement can uniquely determine the sources. Next, it establishes a local Lipschitz stability result, demonstrating continuous dependence of the sources on the measurements. Finally, it proposes a numerical inversion algorithm using a reciprocity gap concept to quickly and stably identify multiple sources.
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I am Jayson L. I am a Signals and Systems Homework Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Sheffield. I have been helping students with their homework for the past 7 years. I solve homework related to Signals and Systems.
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발표자: 정연우(서울대 박사과정)
발표일: 2018.7.
유사한 이미지 검색을 위해 neural network를 이용해 이미지의 embedding을 학습시킨다. 기존 연구에서는 검색 속도 증가를 위해 binary code의 hamming distance를 활용하지만 여전히 전체 데이터 셋을 검색해야 하며 정확도가 떨어지는 다는 단점이 있다. 이 논문에서는 sparse한 binary code를 학습하여 검색 정확도가 떨어지지 않으면서 검색 속도도 향상시키는 해쉬 테이블을 생성한다. 또한 mini-batch 상에서 optimal한 sparse binary code를 minimum cost flow problem을 통해 찾을 수 있음을 보였다. 우리의 방법은 Cifar-100과 ImageNet에서 precision@k, NMI에서 최고의 검색 정확도를 보였으며 각각 98× 와 478×의 검색 속도 증가가 있었다.
Introduction to Real Analysis 4th Edition Bartle Solutions Manual
Full download : https://goo.gl/VYHVDD Introduction to Real Analysis 4th Edition Bartle Solutions Manual
Chapter 3 projection
The document discusses projection methods for solving functional equations. Projection methods work by specifying a basis of functions and "projecting" the functional equation against that basis to find the parameters. This allows approximating different objects like decision rules or value functions. The document focuses on spectral methods that use global basis functions and covers various basis options like monomials, trigonometric series, Jacobi polynomials and Chebyshev polynomials. It also discusses how to generalize the basis to multidimensional problems, including using tensor products and Smolyak's algorithm to reduce the number of basis elements.
A New Lagrangian Relaxation Approach To The Generalized Assignment Problem
This summary provides the key details about a new Lagrangian relaxation approach to solving the generalized assignment problem (GAP) in 3 sentences:
The approach reformulates GAP into an equivalent problem by introducing auxiliary variables and coupling constraints, then relaxes the coupling constraints. This results in subproblems where the constraint structures of GAP are both active, providing stronger lower bounds than traditional approaches. The method was tested on small problems and shown to generate upper bounds more easily than traditional Lagrangian relaxation approaches for GAP.
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The Information Uncertainty Principle
- 1. Certainty & Uncertainty in Filter Bank Design Methodology Chen Sagiv
- 2. Joint work with: Nir Sochen Yehoshua Zeevi Peter Maass & Dirk Lorenz Stephan Dahlke
- 3. The Motivation: Maximal Accuracy Minimal Uncertainty location frequency scale orientation
- 4. The Motivation Image features
- 13. The Weyl-Heisenberg Group: Generators Commutation Relation
- 25. “ Solution” #2: Subspace Solution [ T s11 ,T s12 ],[T s11 ,T s21 ], [ T s11 ,T b1 ], [T s12 ,T b2 ] [T s22 ,T s21 ],[T s22 ,T s12 ], [ T s22 ,T b2 ], [T s21 ,T b1 ] i , s.t.
- 33. Thank You