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Average case complexity of linear multivariate problems I. Theory

1992
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Journal of Complexity
*

We study the average case

doi:10.1016/0885-064x(92)90001-r
fatcat:cap4dlcbfngktnrgo6hut5vd5i
*complexity*of linear*multivariate*problems, that is, the approximation of continuous linear operators on functions of d variables. ... Tractability of a linear*multivariate*problem means that the average case*complexity*of computing an E-approximation is O((l/~)p) with p independent of d. ... Part I deals with the*theory*of linear*multivariate*problems. Part II will deal with applications of the theoretical results to concrete linear*multivariate*problems. ...##
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Multivariate complex B-splines and Dirichlet averages

2010
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Journal of Approximation Theory
*

Based on this generalization several identities of

doi:10.1016/j.jat.2009.05.002
fatcat:wf7k5uq5djdzvjdjqlx5dcwu74
*multivariate**complex*B-splines are presented. ... The notion of a*complex*B-spline is extended to a*multivariate*setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and*multivariate*B-splines. ...*Multivariate**complex*B-splines In this section, we introduce*multivariate**complex*B-splines using a geometrically inspired definition by means of so-called ridge functions and an identity that is known ...##
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Real-Symmetric Extensions of Invertible Tuples of Multivariable Continuous Functions

2011
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Complex Analysis and Operator Theory
*

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Estimation of Multivariate Complex Normal Covariance Matrices Under an Invariant Quadratic Loss

2010
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Communications in Statistics - Theory and Methods
*

The problem of estimating

doi:10.1080/03610920802265194
fatcat:bktjmfkftzf7hksxuohszc5c4e
*multivariate**complex*normal covariance matrices is considered under an invariant quadratic loss function. ... Improved estimators include the best triangular equivariant estimators and*complex*analogues of estimators for*multivariate*real normal covariance matrices by Haff [1980, Ann. Statist. 8:586-597]. ... INTRODUCTION The*theory*of*complex*random matrices plays a vital role in multidimensional signal processing algorithms[see Maiward and Kraus (1994) , Tague and Caldwell (1994) , Ratnarajah and Vaillancourt ...##
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Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights

2013
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Journal of combinatorial theory. Series B (Print)
*

We find zero-free regions in the

doi:10.1016/j.jctb.2012.08.002
fatcat:ov6ukn6tmnfq5jmzlorgeywhli
*complex*plane at large |q| for the*multivariate*Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) Z_G(q,w) of a graph G with ... general*complex*edge weights w = w_e. ... (7.8) It then follows from the Yang-Lee [36]*theory*of phase transitions that there will be*complex*zeros of the partition function arbitrarily close (as G grows) to the phase-transition point (q, ...##
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Analysis on network properties of multivariate mixed air traffic management technical support system based on complex network theory

2016
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Wuli xuebao
*

Air traffic management technical support system provides communication, navigation and surveillance service for air traffic management system and air traffic controller. The failures of some facilities may lead to large delay, even affect air transportation safety. In order to improve the ability of air traffic management technical support system to respond to emergencies, a network model of air traffic management technical support system is presented. The network model of air traffic

doi:10.7498/aps.65.140203
fatcat:by7gkzyyhzes3mekam56ecqzly
## more »

... technical support system is established according to the effective coverage of communication, navigation and surveillance facilities, the position of air traffic management technical support system and air route network. Flexibility, robustness and efficiency are used to measure the network. The measure index of air traffic management technical support system network includes degree, degree distribution, strength, clustering coefficient, network performance, betweenness centrality, average shortest path and diameter. For Beijing, Shanghai, Guangzhou, Kunming, Shenyang and Lanzhou flight information regions, the air traffic management technical support networks are built by using the data of air traffic support facilities, air route, air traffic flow, etc. The average degrees, degree distributions, degree-degree correlations, clustering coefficients, average shortest paths and diameters of these netwoks are comparatively analyzed. The results show that the degrees of most nodes are between two and four. The network has a power law distribution, which is the same as that of air transportation network. The degree-degree correlation of air traffic management technical support system network is not assortative nor disassortative mixing, which has random network characteristics. The clustering coefficients of several air traffic management technical support system networks are between 0.25 and 0.39. The clustering value is lower than that of air transportation network. The shortest paths of air traffic management technical support system networks are between 3.16 and 5.05. The average shortest paths of these networks are all 3.4, which exhibits small world characteristics. Network attack based on degrees of priority and random is conducted to several flight information regions of air traffic management technical support network, showing the network is vulnerable. The network performance decreases quickly after degree priority attack. Some key nodes play an important role in the network. The network survivability can be improved after targeted immunized key nodes. The network performance can be improved by using more satellites based air traffic management technical support system. These rules provide theoretical support for improving and expanding air traffic management technical support system, and have practical significance for reducing the influence of emergency on air traffic management system support ability and ensuring the continuous safety of air traffic.##
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THE INFORMATION THEORY AND COGNITIVE TECHNOLOGIES IN MODELING COMPLEX MULTIVARIABLE DYNAMIC TECHNICAL SYSTEMS

Теория информации и когнитивные технологии в моделировании сложных многопараметрических динамических технических систем

2016
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Polythematic Online Scientific Journal of Kuban State Agrarian University
*

Теория информации и когнитивные технологии в моделировании сложных многопараметрических динамических технических систем

On the other hand, the phenomenological information model can be sufficient to determine the rational design features and parameters of the modes of operation of

doi:10.21515/1990-4665-121-002
fatcat:dzuwwrsrnngzjo4jhipa4jng7q
*complex*technical systems. ... It is proposed to use a new universal innovative method of artificial intelligence for creating phenomenological models of*complex*technical systems: automated system-cognitive analysis (ASC-analysis) ...##
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Preface: Multivariate algorithms and information-based complexity
[chapter]

2020
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Multivariate Algorithms and Information-Based Complexity
*

The field of information-based

doi:10.1515/9783110635461-201
fatcat:tv4wjvc4tfbfppffzld4re33iu
*complexity*(IBC), founded by Traub and Wozniakowski in the 1980s, analyzes the information*complexity*for*multivariate*problems and determines how it depends on d and ε. ... The authors of this book include several of the invited speakers in the workshop*Multivariate*Algorithms and Information-Based*Complexity*, which was part of the RICAM Special Semester on*Multivariate*Algorithms ... VI | Preface:*Multivariate*algorithms and information-based*complexity*namely the quality of random information in approximation and integration problems. ...##
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Page 14 of Contemporary Psychology Vol. 21, Issue 1
[page]

1976
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Contemporary Psychology
*

The book is more success- ful in the first respect than in the second,

*Multivariate**theories*have a breadth lacking in univariate*theories*. ... And, are*multivariate**theory*and re- search useful in studying a wide range of behaviors? ...##
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Page 2335 of Mathematical Reviews Vol. , Issue 81F
[page]

1981
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Mathematical Reviews
*

P. 81f:62091 Locally most powerful and other tests for independence in

*multivariate*populations. Analytic function methods in probability*theory*(Proc. Colloq. ... Methods of*Complex*Anal. in the*Theory*of Probab. and Statist., Kossuth L. Univ. Debrecen, Debrecen, 1977), pp. 99-121, Colloq. Math. Soc. Janos Bolyai, 21, North-Holland, Amsterdam, 1979. ...##
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Page 148 of Mathematical Reviews Vol. 33, Issue 1
[page]

1967
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Mathematical Reviews
*

A

*complex**multivariate*linear regression*theory*, based on the*complex**multivariate*Gaussian distribution considered by Goodman [same Ann. 34 (1963), 152-177; MR 26 #3148], is developed, leading to results ... P. 822 Some extensions of the Wishart and*multivariate*t-distributions in the*complex*case. J. Indian Statist. Assoc. 2 (1964), 131-136. ...##
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Linear Model Theory: Univariate, Multivariate, and Mixed Models

2007
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Technometrics
*

Most books on the subject have historically discussed univariate,

doi:10.1198/tech.2007.s478
fatcat:2pnzemta5bc3bgpqhbihxthq4i
*multivariate*, and mixed linear models separately, whereas Linear Model*Theory*: Univariate,*Multivariate*, and Mixed Models presents a unified ... Linear Model*Theory*: Univariate,*Multivariate*, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. ... Models with*complex*predictors,*complex*responses, or both, motivate the presentation. Contents: Preface. PART I: MODELS AND EXAMPLES. Exercises. 14. ...##
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Page 981 of Mathematical Reviews Vol. , Issue 85c
[page]

1985
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Mathematical Reviews
*

ISBN 0-8218-5006-7 This book contains a very comprehensive treatment of most of the author’s original results in the

*theory*of*complex*integral rep- resentation of cardinal spline functions. ... arising in approxi- mation*theory*. ...##
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A 'Univariate' Symposium on Multivariate Psychology

1976
*
Contemporary Psychology
*

The book is more success- ful in the first respect than in the second,

doi:10.1037/014831
fatcat:jfxxvzgbkzcb5cwhaw4cvv7cli
*Multivariate**theories*have a breadth lacking in univariate*theories*. ... And, are*multivariate**theory*and re- search useful in studying a wide range of behaviors? ...##
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Page 2304 of Mathematical Reviews Vol. 58, Issue 3
[page]

1979
*
Mathematical Reviews
*

Rosenbrock [State-space and

*multivariable**theory*, Wiley, New York, 1970; MR 48 #3550] is equivalent to defining the set of zeros of G(s) as the set {t,} of*complex*numbers ¢, for which rank N(t;)< p(N( ... Kaczorek (Warsaw) Vandewalle, Joos; Dewilde, P. 58 #15395 A local I/O structure*theory*for*multivariable*systems and its application to minimal cascade realization. IEEE Trans. ...
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