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Orthogonality (programming)

About: Orthogonality (programming) is a(n) research topic. Over the lifetime, 425 publication(s) have been published within this topic receiving 6655 citation(s).

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Papers
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Journal ArticleDOI: 10.1145/352958.352963
Abstract: Spatio-temporal databases deal with geometries changing over time. The goal of our work is to provide a DBMS data model and query language capable of handling such time-dependent geometries, including those changing continuously that describe moving objects. Two fundamental abstractions are moving point and moving region, describing objects for which only the time-dependent position, or position and extent, respectively, are of interest. We propose to present such time-dependent geometries as attribute data types with suitable operations, that is, to provide an abstract data type extension to a DBMS data model and query language. This paper presents a design of such a system of abstract data types. It turns out that besides the main types of interest, moving point and moving region, a relatively large number of auxiliary data types are needed. For example, one needs a line type to represent the projection of a moving point into the plane, or a “moving real” to represent the time-dependent distance of two points. It then becomes crucial to achieve (i) orthogonality in the design of the system, i.e., type constructors can be applied unifomly; (ii) genericity and consistency of operations, i.e., operations range over as many types as possible and behave consistently; and (iii) closure and consistency between structure and operations of nontemporal and related temporal types. Satisfying these goal leads to a simple and expressive system of abstract data types that may be integrated into a query language to yield a powerful language for querying spatio-temporal data, including moving objects. The paper formally defines the types and operations, offers detailed insight into the considerations that went into the design, and exemplifies the use of the abstract data types using SQL. The paper offers a precise and conceptually clean foundation for implementing a spatio-temporal DBMS extension.

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Topics: Abstract data type (61%), Data type (58%), Data model (56%) ...read more

774 Citations


Open accessBook
Leland Wilkinson1Institutions (1)
01 Jan 1999-
Abstract: The Grammar of Graphics, or GOG, denotes a system with seven orthogonal components. By orthogonal, we mean there are seven graphical component sets whose elements are aspects of the general system and that every combination of aspects in the product of all these sets is meaningful. This sense of the word orthogonality, a term used by computer designers to describe a combinatoric system of components or building blocks, is in some sense similar to the orthogonal factorial analysis of variance (ANOVA), where factors have levels and all possible combinations of levels exist in the ANOVA design. If we interpret each combination of features in a GOG system as a point in a network, then the world described by GOG is represented in a seven-dimensional rectangular lattice.

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Topics: Orthogonality (programming) (54%), Graphics (50%)

596 Citations


Open accessJournal ArticleDOI: 10.1007/S12532-010-0017-1
Zaiwen Wen1, Donald Goldfarb1, Wotao Yin2Institutions (2)
Abstract: We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our algorithms are robust and very efficient due to their ability or exploit special structures, such as sparsity and constraint orthogonality in these problems.

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  • Table 4 Computational results on the BIQ problems
    Table 4 Computational results on the BIQ problems
  • Fig. 4 Performance profiles of two variants of SDPAD for the BIQ problems
    Fig. 4 Performance profiles of two variants of SDPAD for the BIQ problems
  • Fig. 1 Performance profiles of two variants of SDPAD for frequency assignment problems
    Fig. 1 Performance profiles of two variants of SDPAD for frequency assignment problems
  • Table 2 Computational results on computing θ(G)
    Table 2 Computational results on computing θ(G)
  • Table 3 Computational results on computing θ+(G)
    Table 3 Computational results on computing θ+(G)
  • + 3

Topics: Augmented Lagrangian method (64%), Quadratic programming (63%), Semidefinite programming (63%) ...read more

376 Citations


Open accessJournal ArticleDOI: 10.1109/78.668551
Abstract: This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

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  • Fig. 4. (a) Basic structure of a DMT-based digital transceiver. (b) Frequency response of a typical ADSL channel (CSA Loop 1).
    Fig. 4. (a) Basic structure of a DMT-based digital transceiver. (b) Frequency response of a typical ADSL channel (CSA Loop 1).
  • Fig. 9. (a) ICI and (b) ISI performance of 32, 64, and 128 DFT for CSA Loop 1.
    Fig. 9. (a) ICI and (b) ISI performance of 32, 64, and 128 DFT for CSA Loop 1.
  • Fig. 14. Time–frequency energy pattern of a frequency hopped spread spectrum.
    Fig. 14. Time–frequency energy pattern of a frequency hopped spread spectrum.
  • Fig. 15. Frequency hopping-based LPI detector.
    Fig. 15. Frequency hopping-based LPI detector.
  • Fig. 1. (a) Maximally decimatedM -band FIR PR-QMF filter bank structure (analysis/synthesis configuration). (b)M -band transmultiplexer structure (synthesis/analysis filter bank configuration ion).
    Fig. 1. (a) Maximally decimatedM -band FIR PR-QMF filter bank structure (analysis/synthesis configuration). (b)M -band transmultiplexer structure (synthesis/analysis filter bank configuration ion).
  • + 9

Topics: Filter bank (58%), Filter (video) (53%), Communications system (53%) ...read more

265 Citations


Proceedings ArticleDOI: 10.1109/ICASSP.2002.1005793
01 Jan 2002-

205 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202132
202017
201928
201814
201712
201614

Top Attributes

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Topic's top 5 most impactful authors

Ion Ivan

6 papers, 19 citations

Francis Tin-Loi

3 papers, 47 citations

Ying Jun Zhang

3 papers, 14 citations

Thomas Vetterlein

3 papers, 4 citations

Saharon Shelah

2 papers, 10 citations

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