Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data

2006 ◽  
pp. 27-35 ◽  
Author(s):  
R. R. Coifman
Keyword(s):  
Harmonic Analysis ◽  
High Dimensions ◽  
Definition Of

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

scholarly journals Petrochemical Production Big Data and its Four Typical Application Paradigms

2021 ◽  
Vol 11 (04) ◽  
pp. 15-25
Author(s):  
Hu Shaolin ◽  
Zhang Qinghua ◽  
Su Naiquan ◽  
Li Xiwu
Keyword(s):  
Big Data ◽  
Petrochemical Industry ◽  
Time Span ◽  
High Dimensions ◽  
Petrochemical Production ◽  
Data Set ◽  
Typical Application ◽  
Wide Range ◽  
Definition Of ◽  
Descriptive Definition

In recent years, the big data has attracted more and more attention. It can bring us more information and broader perspective to analyse and deal with problems than the conventional situation. However, so far, there is no widely acceptable and measurable definition for the term “big data”. For example, what significant features a data set needs to have can be called big data, and how large a data set is can be called big data, and so on. Although the "5V" description widely used in textbooks has been tried to solve the above problems in many big data literatures, "5V" still has significant shortcomings and limitations, and is not suitable for completely describing big data problems in practical fields such as industrial production. Therefore, this paper creatively puts forward the new concept of data cloud and the data cloud-based "3M" descriptive definition of big data, which refers to a wide range of data sources (Multisource), ultra-high dimensions (Multi-dimensional) and a long enough time span (Multi-spatiotemporal). Based on the 3M description of big data, this paper sets up four typical application paradigms for the production big data, analyses the typical application of four paradigms of big data, and lays the foundation for applications of big data from petrochemical industry.

scholarly journals Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods

2005 ◽  
Vol 102 (21) ◽  
pp. 7432-7437 ◽  
Author(s):  
R. R. Coifman ◽  
S. Lafon ◽  
A. B. Lee ◽  
M. Maggioni ◽  
B. Nadler ◽  
...  
Keyword(s):  
Harmonic Analysis ◽  
Multiscale Methods ◽  
Definition Of

scholarly journals Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps

2005 ◽  
Vol 102 (21) ◽  
pp. 7426-7431 ◽  
Author(s):  
R. R. Coifman ◽  
S. Lafon ◽  
A. B. Lee ◽  
M. Maggioni ◽  
B. Nadler ◽  
...  
Keyword(s):  
Harmonic Analysis ◽  
Diffusion Maps ◽  
Definition Of

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

Initial Polymerization Sites Indicated During Mitochondrial Oxidation of Diaminobenzidine after Toluene Treatment

1977 ◽  
Vol 35 ◽  
pp. 408-409
Author(s):  
W. A. Shannon ◽  
M. A. Matlib
Keyword(s):  
Membrane Permeability ◽  
Cytochrome Oxidase ◽  
Rat Liver ◽  
Precise Definition ◽  
Cytochemical Localization ◽  
Oxidative Reaction ◽  
Mitochondrial Oxidation ◽  
Definition Of ◽  
Exogenous Substrates

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.

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