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A New Method for Functional Arrays
 Journal of Functional Programming
, 1997
"... Arrays are probably the most widely used data structure in imperative programming languages, yet functional languages typically only support arrays in a limited manner, or prohibit them entirely. This is not too surprising, since most other mutable data structures, such as trees, have elegant immuta ..."
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Cited by 13 (0 self)
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Arrays are probably the most widely used data structure in imperative programming languages, yet functional languages typically only support arrays in a limited manner, or prohibit them entirely. This is not too surprising, since most other mutable data structures, such as trees, have elegant immutable analogues in the functional world, whereas arrays do not. Previous attempts at addressing the problem have suffered from one of three weaknesses, either that they don't support arrays as a persistent data structure (unlike the functional analogues of other imperative data structures), or that the range of operations is too restrictive to support some common array algorithms efficiently, or that they have performance problems. Our technique provides arrays as a true functional analogue of imperative arrays with the properties that functional programmers have come to expect from their data structures. To efficiently support array algorithms from the imperative world, we provide O(1) operations for singlethreaded array use. Fully persistent array use can also be provided at O(1) amortized cost, provided that the algorithm satisfies a simple requirement as to uniformity of access. For those algorithms which do not access the array uniformly or singlethreadedly, array reads or updates take at most O(log n) amortized time, where n is the size of the array. Experimental results indicate that the overheads of our technique are acceptable in practice for many applications.
Maximum principle and convergence of central schemes based on slope limiters ∗
, 2010
"... A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter which unfortunately red ..."
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Cited by 1 (1 self)
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A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter which unfortunately reduces the scheme to first order at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence.
1 Maximum Principle of Central Schemes
"... The NessyahuTadmor (NT) scheme is a simple yet robust second order nonoscillatory scheme, which relies on a piecewise linear reconstruction. A typical reconstruction choice is based on the standard minmod limiter. This choice gives a maximum principle for the scheme. However, it reduces the recons ..."
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The NessyahuTadmor (NT) scheme is a simple yet robust second order nonoscillatory scheme, which relies on a piecewise linear reconstruction. A typical reconstruction choice is based on the standard minmod limiter. This choice gives a maximum principle for the scheme. However, it reduces the reconstruction to first order at local extrema. In this paper we show that a maximum principle is still valid for second order schemes when a new limiter is used, MAPRlike [2]. To prove this result we require that the flux is kmonotone. We also show that the maximum principle implies the usual TVD bound. 1
Extremal Distributions in Information Theory and Hypothesis Testing
"... Many problems in Information Theory can be distilled to an optimization problem over a space of probability distributions. The most important examples are in communication theory, where it is necessary to maximize mutual information ..."
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Many problems in Information Theory can be distilled to an optimization problem over a space of probability distributions. The most important examples are in communication theory, where it is necessary to maximize mutual information
unknown title
, 2005
"... www.elsevier.com/locate/spa Worstcase largedeviation asymptotics with application to queueing and information theory ✩ Charuhas Pandit a, Sean Meyn b,∗ ..."
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www.elsevier.com/locate/spa Worstcase largedeviation asymptotics with application to queueing and information theory ✩ Charuhas Pandit a, Sean Meyn b,∗
NEW INEQUALITIES FOR CSISZÁR DIVERGENCE AND APPLICATIONS
"... Abstract. In this paper we point out some new inequalities for Csiszár fdivergence and apply them for particular instances of distances between two probability distributions. 1. ..."
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Abstract. In this paper we point out some new inequalities for Csiszár fdivergence and apply them for particular instances of distances between two probability distributions. 1.
57 SHRI NIKETAN COLONY
, 2005
"... ABSTRACT. In this note we establish new Čebyšev type integral inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities. ..."
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ABSTRACT. In this note we establish new Čebyšev type integral inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities.
ON AN INEQUALITY OF V. CSISZÁR AND T.F. MÓRI FOR CONCAVE FUNCTIONS OF TWO VARIABLES
"... vol. 8, iss. 3, art. 88, 2007 ..."