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Randomness is Linear in Space

1996
*
Journal of computer and system sciences (Print)
*

We show that any

doi:10.1006/jcss.1996.0004
fatcat:lqufc26t5ffx5jp2fkwqqmnit4
*randomized*algorithm that runs*in**space*S and time T and uses poly(S)*random*bits can be simulated using only O(S)*random*bits*in**space*S and time T + poly(S). ... A deterministic simulation*in**space*S follows. ... Several classes of*randomized*algorithms run naturally*in**linear**space*and thus can be simulated using only a*linear*number of*random*bits. ...##
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Equicontinuity, affine mean ergodic theorem and linear equations in random normed spaces

1976
*
Proceedings of the American Mathematical Society
*

The aim of this paper

doi:10.1090/s0002-9939-1976-0473883-3
fatcat:i54cedu2k5gzdkgtmreicjzb7e
*is*to give a characterization of equicontinuous families of*linear*operators*in**random*normed*spaces*which generalizes the normed*spaces*case. ...*In*this note*is*given a characterization of equicontinuous families of*linear*operators on such*spaces*. ... The aim of this paper*is*to give a characterization of equicontinuous families of*linear*operators*in**random*normed*spaces*which generalizes the normed*spaces*case. ...##
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Equicontinuity, Affine Mean Ergodic Theorem and Linear Equations in Random Normed Spaces

1976
*
Proceedings of the American Mathematical Society
*

The aim of this paper

doi:10.2307/2041210
fatcat:hv66casbifghdisueamtdz6fr4
*is*to give a characterization of equicontinuous families of*linear*operators*in**random*normed*spaces*which generalizes the normed*spaces*case. ...*In*this note*is*given a characterization of equicontinuous families of*linear*operators on such*spaces*. ... The aim of this paper*is*to give a characterization of equicontinuous families of*linear*operators*in**random*normed*spaces*which generalizes the normed*spaces*case. ...##
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Convergence for martingale sequences of random bounded operators

2018
*
VNU Journal of Science Mathematics - Physics
*

*In*this paper, we study the convergence for martingale sequences of

*random*bounded operators. The condition for the existence of such a infinite product

*is*established ... then {‖ ‖, ≥ 1}

*is*bounded

*in*probability. By Theorem 5.4 [5] ,

*is*

*random*bounded

*linear*operator. ... Y said to be a

*random*operator, where 0 L ( ) Y stands for the

*space*of Yvalued

*random*variables and

*is*equipped with the topology of convergence

*in*probability.

*linear*and continuous then it

*is*called ...

##
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Linear and Nonlinear Random Walks in 1d, 2d and 3d Space

2019
*
Global Journal of Astronomy and Applied Physics
*

*In*[3] we considered a visual model of a 3D

*random*

*linear*and nonlinear walk

*in*an octahedron. ... The construction of an octahedron using small cubes can be obtained by considering a

*random*walk

*in*three-dimensional (3D)

*space*. ...

*in*Figure 2)

*random*walk and arithmetic figures given

*in*this paper show various geometric properties and nonlinear effects of 1D, 2D and 3D spaces.In 1D

*space*with a

*linear*

*random*walk a

*linear*arithmetic ...

##
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Stochastic convergence of weighted sums in normed linear spaces

1975
*
Journal of Multivariate Analysis
*

If h

doi:10.1016/0047-259x(75)90027-5
fatcat:um7kk6tibvfnle6p4lavwidvlu
*is*a Bore1 function from X into another normed*linear**space*Y, then h(V)*is*a*random*element*in*Y whenever V*is*a*random*element*in*X. ... Another useful property*is*that V*is*a*random*element*in*X if and only if f( I')*is*a*random*variable for fe X*, where X**is*the set of all continuous,*linear*functionals on X. ...##
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On non-L0-linear perturbations of random isometries in random normed modules

2014
*
Journal of Inequalities and Applications
*

The purpose of this paper

doi:10.1186/1029-242x-2014-496
fatcat:xsglrmroafafxgiiwklfoxhpva
*is*to study non-L 0 -*linear*perturbations of*random*isometries*in**random*normed modules. ...*In*this paper, we first establish the Mazur-Ulam theorem*in**random*normed modules. ...*in*an original*random*normed*space*(briefly, an RN*space*)*is*a nonnegative*random*variable defined on some probability*space*. ...##
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Random Projections for Non-linear Dimensionality Reduction

2016
*
International Journal of Machine Learning and Computing
*

An innovative method framework that combines

doi:10.18178/ijmlc.2016.6.4.601
fatcat:pxtyyhnlhfaffooow3pj2wvkma
*random*projections and non-*linear*dimensionality reduction methods*is*proposed*in*this paper to increase computational speed and reduce memory usage, while ... Illustrations with various combinations of*random*projections and non-*linear*dimensionality reduction methods tested on a hand-written digits dataset are also given*in*this paper to demonstrate that this ... Additionally, we also observed empirically that performing non-*linear*dimensionality reduction*in*the randomly projected feature*space**is*faster than that*in*the original feature*space*. ...##
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ABSTRACT RANDOM LINEAR OPERATORS ON PROBABILISTIC UNITARY SPACES

2016
*
Journal of the Korean Mathematical Society
*

*In*this paper, we are concerned with abstract

*random*

*linear*operators on probabilistic unitary

*spaces*which are a generalization of generalized

*random*

*linear*operators on a Hilbert

*space*defined

*in*[25 ... Key words and phrases. probabilistic

*linear*

*space*, probabilistic unitary

*space*, probabilistic Hilbert

*space*, abstract

*random*

*linear*operator, abstract

*random*bounded

*linear*operator, abstract

*random*symmetric ... This research

*is*funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED)under grand number 101.03-2013. ...

##
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Limit theorems for randomly weighted sums of random elements in normed linear spaces

1988
*
Journal of Multivariate Analysis
*

INTRODUCTION If E denotes a separable normed

doi:10.1016/0047-259x(88)90158-3
fatcat:mziqufmpkfffraplem4nygmukm
*linear**space*with norm 1) .I), and (52, A, P)*is*a probability*space*, a*random*element V*in*E*is*a function from B into E which*is*A-measurable with respect ...*In*this paper, an extension of the original result of Rohatgi for randomly weighted sums of*random*elements*in*a normed*linear**space*(not necessarily a Banach*space*) without geometric conditions*is*obtained ...##
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Simple Constructions of Almost k-wise Independent Random Variables

1992
*
Random structures & algorithms (Print)
*

The number of bits used to specify a point

doi:10.1002/rsa.3240030308
fatcat:qoi76lbbefbhdfcslprogdg6ry
*in*the sample*space**is*O(loglogn+k+log $), where c*is*the statistical difference between of the distribution induced on any k bit locations and the uniform distribution ... Two of our constructions are based on bit sequences which are widely believed to posses "*randomness*properties" and our results can be viewed as an explanation and establishment of these beliefs. ...*Linear*Tests The heart of each of our constructions*is*a sample*space*which*is*very close to*random*with respect to "*linear*Boolean tests" (i.e., tests which take the exclusive-or of the bits*in*some fixed ...##
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Kernel principal component analysis for stochastic input model generation

2011
*
Journal of Computational Physics
*

*In*addition, polynomial chaos (PC) expansion

*is*used to represent the

*random*coefficients

*in*KPCA which provides a parametric stochastic input model. ...

*In*other words, it only preserves the second-order statistics (covariance) of a

*random*field, which

*is*insufficient for reproducing complex structures. ... However, the

*random*expansion coefficients of the

*linear*PCA

*in*the feature

*space*are assumed i.i.d. standard normal

*random*variables. ...

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Rapid cardiac MRI using random radial trajectories

2008
*
2008 National Radio Science Conference
*

We introduce using Sparse MRI with

doi:10.1109/nrsc.2008.4542382
fatcat:2cvy6homczfwhasf47djrkmdqi
*random*radial trajectories*in*order to allow MRI images reconstruction from a small number of acquired k-*space*data, so fulfilling the demands of dynamic MRI. ... Images reconstruction*is*performed using the non-*linear*L1 norm reconstruction. Entropy*is*computed for the reconstructed images, as a quantitative measure for the reconstructed image quality. ... Non-*linear*conjugate gradient reconstruction using (c) non-*random*radial kspace,*random*radial k-*space*with (d) variance = 0.5, (e) variance = 1, (f) variance = 2, (g) linearly increasing variance*in*the ...##
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Generalization of Coloring Linear Transformation

2019
*
Transactions of the VŠB: Technical University of Ostrava, Civil Engineering Series
*

The paper

doi:10.31490/tces-2018-0013
fatcat:dpqfj74tgzg47llhpg4l5atdq4
*is*focused on the technique of*linear*transformation between correlated and uncorrelated Gaussian*random*vectors, which*is*more or less commonly used*in*the reliability analysis of structures ... The proposed generalized*linear*transformation*is*able to rotate the transformation randomly, which may be desired*in*order to remove unwanted directional bias. ... Note that D*is*reduced to common Euclidean distance*in*Z*space*. ...##
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On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules

2013
*
Journal of Function Spaces and Applications
*

Finally, to connect module homomorphism between

doi:10.1155/2013/989102
fatcat:grdlqlgxojez7lcapq4kbhafnm
*random*normed modules with*linear*operators between ordinary normed*spaces*, we give a proof with better readability of the known result connecting*random*... Riesz representation theorem*in*complete*random*inner product modules under two kinds of topologies. ... Acknowledgment The author would like to thank Professor Quanhua Xu for kindly providing the reference [6]*in*February 2012, which makes us know, for the first time, the excellent work of Haydon, Levy ...
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