Results 11  20
of
1,137
The History of Histograms (abridged)
 PROC. OF VLDB CONFERENCE
, 2003
"... The history of histograms is long and rich, full of detailed information in every step. It includes the course of histograms in diFFerent scientific fields, the successes and failures of histograms in approximating and compressing information, their adoption by industry, and solutions that hav ..."
Abstract

Cited by 115 (0 self)
 Add to MetaCart
(Show Context)
The history of histograms is long and rich, full of detailed information in every step. It includes the course of histograms in diFFerent scientific fields, the successes and failures of histograms in approximating and compressing information, their adoption by industry, and solutions that have been given on a great variety of histogramrelated problems. In this paper and in the same spirit of the histogram techniques themselves, we compress their entire history (including their "future history" as currently anticipated) in the given/fixed space budget, mostly recording details for the periods, events, and results with the highest (personallybiased) interest. In a limited set of experiments, the semantic distance between the compressed and the full form of the history was found relatively small!
Optimal Sequences, Power Control, and User Capacity of Synchronous CDMA Systems with Linear MMSE Multiuser Receivers
 IEEE TRANS. INFORM. THEORY
, 1999
"... There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjuncti ..."
Abstract

Cited by 102 (5 self)
 Add to MetaCart
There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (SCDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its qualityofservice (QoS) requirement (expressed in terms of its desired signaltointerference ratio) met. Our characterization allows us to describe the user capacity through a simple effective bandwidth characterization: Users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity.
A unified framework for optimizing linear nonregenerative multicarrier MIMO relay communication systems
 IEEE TRANS. SIGNAL PROCESS
, 2009
"... In this paper, we develop a unified framework for linear nonregenerative multicarrier multipleinput multipleoutput (MIMO) relay communications in the absence of the direct source–destination link. This unified framework classifies most commonly used design objectives such as the minimal meansqu ..."
Abstract

Cited by 93 (50 self)
 Add to MetaCart
(Show Context)
In this paper, we develop a unified framework for linear nonregenerative multicarrier multipleinput multipleoutput (MIMO) relay communications in the absence of the direct source–destination link. This unified framework classifies most commonly used design objectives such as the minimal meansquare error and the maximal mutual information into two categories: Schurconcave and Schurconvex functions. We prove that for Schurconcave objective functions, the optimal source precoding matrix and relay amplifying matrix jointly diagonalize the source–relay–destination channel matrix and convert the multicarrier MIMO relay channel into parallel singleinput singleoutput (SISO) relay channels. While for Schurconvex objectives, such joint diagonalization occurs after a specific rotation of the source precoding matrix. After the optimal structure of the source and relay matrices is determined, the linear nonregenerative relay design problem boils down to the issue of power loading among the resulting SISO relay channels. We show that this power loading problem can be efficiently solved by an alternating technique. Numerical examples demonstrate the effectiveness of the proposed framework.
Asymptotically Optimal Importance Sampling and Stratification for Pricing PathDependent Options
 Mathematical Finance
, 1999
"... This paper develops a variance reduction technique for Monte Carlo simulations of pathdependent options driven by highdimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of dri ..."
Abstract

Cited by 90 (13 self)
 Add to MetaCart
This paper develops a variance reduction technique for Monte Carlo simulations of pathdependent options driven by highdimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which maximizes the product of probability and payoffthe most important path. The directions used for stratified sampling are optimal for a quadratic approximation to the integrand or payoff function. Indeed, under differentiability assumptions our importance sampling method eliminates variability due to the linear part of the payoff function, and stratification eliminates much of the variability due to the quadratic part of the payoff. The two parts of the method are linked because the asymptotically optimal drift vector frequently provides a particularly effective direction for stratification. We illustrate the use of the method with pathdependent options, a stochastic volatility model, and interest rate derivatives. The method reveals novel features of the structure of their payoffs. KEY WORDS: Monte Carlo methods, variance reduction, large deviations, Laplace principle 1. INTRODUCTION This paper develops a variance reduction technique for Monte Carlo simulations driven by highdimensional Gaussian vectors, with particular emphasis on the pricing of pathdependent options. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to...
Universality of Serial Histograms
, 1993
"... Many current relational database systems use some form of histograms to approximate the frequency distribution of values in the attributes of relations and based on them estimate query result sizes and access plan costs. The errors that exist in the histogram approximations directly or transitively ..."
Abstract

Cited by 89 (11 self)
 Add to MetaCart
Many current relational database systems use some form of histograms to approximate the frequency distribution of values in the attributes of relations and based on them estimate query result sizes and access plan costs. The errors that exist in the histogram approximations directly or transitively affect many estimates derived by the database system. We identify the class of serial histograms and demonstrate that they are optimal for reducing the query result size error for several classes of queries when the actual query result size (and hence the value of that error) reaches some extreme. Specifically, serial histograms are shown to be optimal for arbitrary tree equalityjoin queries when the query result size is maximized, whether or not the attribute independence assumption holds, and when the query result size is minimized and the attribute independence assumption holds. We also show that the expected error for any such query is always zero under all histograms, and thus argue that histograms should be chosen based on the reduction of the extremecases error, since reduction of the expected error is meaningless.
On Deterministic Traffic Regulation and Service Guarantees: A Systematic Approach by Filtering
 IEEE Transactions on Information Theory
, 1997
"... In this paper, we develop a filtering theory for deterministic traffic regulation and service guarantees under the (min; +)algebra. We show that traffic regulators that generate fupper constrained outputs can be implemented optimally by a linear time invariant filter with the impulse response f ..."
Abstract

Cited by 85 (4 self)
 Add to MetaCart
(Show Context)
In this paper, we develop a filtering theory for deterministic traffic regulation and service guarantees under the (min; +)algebra. We show that traffic regulators that generate fupper constrained outputs can be implemented optimally by a linear time invariant filter with the impulse response f under the (min; +)algebra, where f is the subadditive closure defined in the paper. Analogous to the classical filtering theory, there is an associate calculus, including feedback, concatenation, "filter bank summation" and performance bounds. The calculus is also applicable to the recently developed concept of service curves that can be used for deriving deterministic service guarantees. Our filtering approach not only yields easier proofs for more general results than those in the literature, but also allows us to design traffic regulators via systematic methods such as concatenation, filter bank summation, linear system realization, and FIRIIR realization. We illustrate the use of ...
Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback
, 2001
"... Abstract—We consider the capacity of a narrowband point to point communication system employing multipleelement antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while a ..."
Abstract

Cited by 84 (6 self)
 Add to MetaCart
(Show Context)
Abstract—We consider the capacity of a narrowband point to point communication system employing multipleelement antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while at the transmitter the channel matrix is modeled as consisting of zero mean complex jointly Gaussian random variables with known covariances. Specifically we assume a channel matrix with i.i.d. rows and correlated columns, a common model for downlink transmission. We determine the optimal transmit precoding strategy to maximize the Shannon capacity of such a system. We also derive closed form necessary and sufficient conditions on the spatial covariance for when the maximum capacity is achieved by beamforming. The conditions for optimality of beamforming agree with the notion of waterfilling over multiple degrees of freedom. I.
Designing Structured Tight Frames via an Alternating Projection Method
, 2003
"... Tight frames, also known as general WelchBoundEquality sequences, generalize orthonormal systems. Numerous applicationsincluding communications, coding and sparse approximationrequire finitedimensional tight frames that possess additional structural properties. This paper proposes an alterna ..."
Abstract

Cited by 84 (10 self)
 Add to MetaCart
Tight frames, also known as general WelchBoundEquality sequences, generalize orthonormal systems. Numerous applicationsincluding communications, coding and sparse approximationrequire finitedimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems, which includes the frame design problem. To apply this method, one only needs to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate
On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
Abstract

Cited by 78 (3 self)
 Add to MetaCart
We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
Random Walks on Weighted Graphs, and Applications to Online Algorithms (Extended
 Journal of the ACM
, 1990
"... We study the design and analysis of randomized online algorithms. ..."
Abstract

Cited by 78 (2 self)
 Add to MetaCart
We study the design and analysis of randomized online algorithms.