Parametric dictionary design for sparse coding

Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries

Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the motion of phase defects, while theory predicts a stationary transverse amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes. Stripes then show an oscillatory TAM whose frequency is incommensurate with the driving frequency. At higher a, the TAM undergoes a phase instability. At still higher a, edge dislocations form and fluid droplets are ejected. (3) Intermediate-nu fluids show a complex coexistence of squares and stripes, as well as stationary and oscillatory TAM instabilities of the stripes.Comment: REVTEX, with 3 separate uuencoded figures, to appear in Europhys. Let

Shear Behavior of Self Drilling Screws Used in Low Ductility Steel

The results of 264 shear tests conducted on self drilling screws are presented. The tests conducted include single screws in single shear, two screws in single shear, and single screws in double shear. The performance and behavior of self drilling screws in low ductility steel are compared to the performance and behavior of screws in normal ductility steel. Results are compared to the 1986 AISI specification with 1989 addenda, and the recently approved AISI specification for self drilling screws which will be included in the next edition of the AISI code. Also, new equations are presented for the tilting/bearing limit state for screws in single shear, and the bearing limit state for screws in double shear

Stub Column Study Using Welded, Cold-reduced Steel

The primary goal of the subject study was to investigate the behavior and load capacity of stub columns using cold-reduced, low-ductility steel versus un-reduced, normal-ductility steel. Specimens that were cold-reduced were also welded transversely across the entire stud cross section. Therefore, this study also yielded data with regard to the axial performance of welded studs. In addition, since stub columns were punched and un-punched, further conclusions can be drawn about the effect of a weld located at a web perforation. A total of 133 stub column tests were performed at the Dietrich Material Testing Laboratory in Hammond, Indiana, between December 14 and December 20 of 1993, and on January 27 of 1994. Tests were conducted using two procedures. The first test procedure used a track at each end of the stub column. The second test procedure did not use a track. Grouting or welding was not used in either test procedure. There was no need for special end preparations since specimens were cut with very close tolerances regarding end squareness. From the test data the following conclusions can be drawn. First, the presence of a weld in a stud had no effect on the stub column load capacity. Second, the presence of a weld at a knockout had no effect on the stub column load capacity. Third, reduced stub columns fared very favorably in load capacity when compared to the 1986 AISI specification as long as 75 percent of the yield strength is used per AISI Specification, Section A3.3.2. Fourth, it is recommended that Section A3.3.1 of the AISI Specification be changed to include steel having Fᵤ/Fᵧ ratios of 1. 01, elongations in a 2 in. gage length of three percent, and elongations in a 1/2 in. gage length of ten percent

Audio Signal Representations for Factorization in the sparse domain

International audienceIn this paper, a new class of audio representations is introduced, together with a corresponding fast decomposition algorithm. The main feature of these representations is that they are both sparse and approximately shift-invariant, which allows similarity search in a sparse domain. The common sparse support of detected similar patterns is then used to factorize their representations. The potential of this method for simultaneous structural analysis and compressing tasks is illustrated by preliminary experiments on simple musical data

Machine learning and the physical sciences

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences. This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges