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Randomness is Linear in Space

Noam Nisan, David Zuckerman
1996 Journal of computer and system sciences (Print)  
We show that any 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.  ... 
doi:10.1006/jcss.1996.0004 fatcat:lqufc26t5ffx5jp2fkwqqmnit4

Equicontinuity, affine mean ergodic theorem and linear equations in random normed spaces

V. Radu
1976 Proceedings of the American Mathematical Society  
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.  ...  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.  ... 
doi:10.1090/s0002-9939-1976-0473883-3 fatcat:i54cedu2k5gzdkgtmreicjzb7e

Equicontinuity, Affine Mean Ergodic Theorem and Linear Equations in Random Normed Spaces

V. Radu
1976 Proceedings of the American Mathematical Society  
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.  ...  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.  ... 
doi:10.2307/2041210 fatcat:hv66casbifghdisueamtdz6fr4

Convergence for martingale sequences of random bounded operators

Cuong Tran Manh, Son Ta Cong, Oanh Le Thi
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  ... 
doi:10.25073/2588-1124/vnumap.4305 fatcat:lsgejfh6erg4zfoqnwklasdfoy

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  ... 
doi:10.46940/gjaap.01.1001 fatcat:oca2wbtn2rhi5etb67rk6tj26e

Stochastic convergence of weighted sums in normed linear spaces

R.L Taylor, W.J Padgett
1975 Journal of Multivariate Analysis  
If h 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.  ... 
doi:10.1016/0047-259x(75)90027-5 fatcat:um7kk6tibvfnle6p4lavwidvlu

On non-L0-linear perturbations of random isometries in random normed modules

Shien Zhao, Yuan Zhao, Minghua Yao
2014 Journal of Inequalities and Applications  
The purpose of this paper 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.  ... 
doi:10.1186/1029-242x-2014-496 fatcat:xsglrmroafafxgiiwklfoxhpva

Random Projections for Non-linear Dimensionality Reduction

Long Cheng, Chenyu You, Yani Guan
2016 International Journal of Machine Learning and Computing  
An innovative method framework that combines 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.  ... 
doi:10.18178/ijmlc.2016.6.4.601 fatcat:pxtyyhnlhfaffooow3pj2wvkma

ABSTRACT RANDOM LINEAR OPERATORS ON PROBABILISTIC UNITARY SPACES

Xuan Quy Tran, Hung Thang Dang, Thinh Nguyen
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.  ... 
doi:10.4134/jkms.2016.53.2.347 fatcat:42v3bmog25devmdfgxuzmn5lni

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

M.Ordóñez Cabrera
1988 Journal of Multivariate Analysis  
INTRODUCTION If E denotes a separable normed 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  ... 
doi:10.1016/0047-259x(88)90158-3 fatcat:mziqufmpkfffraplem4nygmukm

Simple Constructions of Almost k-wise Independent Random Variables

Noga Alon, Oded Goldreich, Johan Håstad, René Peralta
1992 Random structures & algorithms (Print)  
The number of bits used to specify a point 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  ... 
doi:10.1002/rsa.3240030308 fatcat:qoi76lbbefbhdfcslprogdg6ry

Kernel principal component analysis for stochastic input model generation

Xiang Ma, Nicholas Zabaras
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.  ... 
doi:10.1016/j.jcp.2011.05.037 fatcat:rmmiekbburhkja7u4o7tptgf2i

Rapid cardiac MRI using random radial trajectories

Shereen M. El-Metwally, Khaled Z. Abd-Ehnoniem, Abou-Bakr M. Youssef, Yasser M. Kadah
2008 2008 National Radio Science Conference  
We introduce using Sparse MRI with 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  ... 
doi:10.1109/nrsc.2008.4542382 fatcat:2cvy6homczfwhasf47djrkmdqi

Generalization of Coloring Linear Transformation

Lukas Novak, Miroslav Vorechovsky
2019 Transactions of the VŠB: Technical University of Ostrava, Civil Engineering Series  
The paper 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.  ... 
doi:10.31490/tces-2018-0013 fatcat:dpqfj74tgzg47llhpg4l5atdq4

On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules

Guo Tiexin
2013 Journal of Function Spaces and Applications  
Finally, to connect module homomorphism between 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  ... 
doi:10.1155/2013/989102 fatcat:grdlqlgxojez7lcapq4kbhafnm
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