Related papers: A Functional Block Decomposition Method for Automa…
In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…
Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…
The decomposition of multiport interferometers is a fundamental tool in quantum optics and computing. This note aims to serve as a concise reference for performing the decomposition according to the most common design approaches, offering a…
Many complex real-world tasks are composed of several levels of sub-tasks. Humans leverage these hierarchical structures to accelerate the learning process and achieve better generalization. In this work, we study the inductive bias and…
Interpretation of deep learning remains a very challenging problem. Although the Class Activation Map (CAM) is widely used to interpret deep model predictions by highlighting object location, it fails to provide insight into the salient…
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a…
Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional…
When using heterogeneous hardware other than CPUs, barriers of technical skills such as OpenCL are high. Based on that, I have proposed environment adaptive software that enables automatic conversion, configuration, and high-performance…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We present a multipole expansion theory for optical force exerting on a particle immersed in generic monochromatic free-space optical field. Based on the theory, we have, for the first time, successfully decomposed the optical force on a…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm,…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…