The asymptotic analysis of a class of binomial sums that arise in information theory can be performed in a simple way by means of singularity analysis of generating functions. The method developed extends the range of...
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The asymptotic analysis of a class of binomial sums that arise in information theory can be performed in a simple way by means of singularity analysis of generating functions. The method developed extends the range of applicability of singularity analysis techniques to combinatorial sums involving transcendental elements like logarithms or fractional powers. (C) 1999-Elsevier Science B.V. All rights reserved.
We prove the worst-case upper bound 1.5045..(n) for the time complexity of 3-SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic t...
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We prove the worst-case upper bound 1.5045..(n) for the time complexity of 3-SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2- and 3-clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3-clause-sets and can be applied also to arbitrary trees. (C) 1999 Elsevier Science B.V. All rights reserved.
Given a set of n elements each of which is either red or blue, Boyer and Moore's MJRTY algorithm uses pairwise equal/not equal color comparisons to determine the majority color. We analyze the average behavior of ...
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Given a set of n elements each of which is either red or blue, Boyer and Moore's MJRTY algorithm uses pairwise equal/not equal color comparisons to determine the majority color. We analyze the average behavior of their algorithm, proving that if all 2(n) possible inputs are equally likely, the average number of color comparisons used is n - root 2n/pi + O(1) with variance (pi - 2)n/pi - root 2n/pi + O(1). (C) 2013 Elsevier B.V. All rights reserved.
A generalization of the particle swarm optimization (PSO) algorithm is presented in this paper. The novel optimizer, the Generalized PSO (GPSO), is inspired by linear control theory. It enables direct control over the...
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A generalization of the particle swarm optimization (PSO) algorithm is presented in this paper. The novel optimizer, the Generalized PSO (GPSO), is inspired by linear control theory. It enables direct control over the key aspects of particle dynamics during the optimization process. A detailed theoretical and empirical analysis is presented, and parameter-tuning schemes are proposed. GPSO is compared to the classical PSO and genetic algorithm (GA) on a set of benchmark problems. The results clearly demonstrate the effectiveness of the proposed algorithm. Finally, an application of the GPSO algorithm to the fine-tuning of the support vector machines classifier for electrical machines fault detection is presented. (C) 2011 Elsevier Inc. All rights reserved.
An algorithm for the scheduling of events in a discrete-event simulation system, due to J. O. Henriksen, is presented. An O(n<span class="mn" id="MathJax-Span-11" style="font-size: 7
The average-case complexity of BIT algorithm, a version of move-to-front (MTF) algorithm, was analyzed. A theorem showed that the cost of BIT is asymptotically better than that of MTF. Another theorem verified that th...
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The average-case complexity of BIT algorithm, a version of move-to-front (MTF) algorithm, was analyzed. A theorem showed that the cost of BIT is asymptotically better than that of MTF. Another theorem verified that the overwork of BIT is at least 1.5 times that of MTF. A function was structured so as to determine values of length t for which BIT performs better than MTF given a sequence Z of requests, if L, the size of size n, is initialized at random.
A complete characterization of a digital tree, also called a trie, is presented from the depth viewpoint in a Markovian framework, that is, under the assumption that symbols in a key are Markov-dependent. The main fin...
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A complete characterization of a digital tree, also called a trie, is presented from the depth viewpoint in a Markovian framework, that is, under the assumption that symbols in a key are Markov-dependent. The main findings show that asymptotically, as the number of keys n tends to infinity, the average depth becomes ED(n) approximately 1/*** n + c', and the variance is var D(n) approximately alpha log n + c", where h1 is the entropy of the (Markovian-dependent) alphabet, and alpha is a parameter of the probabilistic model. The symmetric independent model has alpha = 0, hence in this case var D(n) = O(1). Limiting distribution is also derived for the depth D(n), and in particular, it is shown that D(n) tends to the normal distribution in all cases except the symmetric independent model. These results extend all previous analyses since most of them have been limited to independent models.
We address the problem of modeling energy resource allocation, including dispatch, storage, and the long-term investments in new technologies, capturing different sources of uncertainty such as energy from wind, deman...
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We address the problem of modeling energy resource allocation, including dispatch, storage, and the long-term investments in new technologies, capturing different sources of uncertainty such as energy from wind, demands, prices, and rainfall. We also wish to model long-term investment decisions in the presence of uncertainty. Accurately modeling the value of all investments, such as wind turbines and solar panels, requires handling fine-grained temporal variability and uncertainty in wind and solar in the presence of storage. We propose a modeling and algorithmic strategy based on the framework of approximate dynamic programming (ADP) that can model these problems at hourly time increments over an entire year or several decades. We demonstrate the methodology using both spatially aggregate and disaggregate representations of energy supply and demand. This paper describes the initial proof of concept experiments for an ADP-based model called SMART;we describe the modeling and algorithmic strategy and provide comparisons against a deterministic benchmark as well as initial experiments on stochastic data sets.
The result of birthday problem is of fundamental importance and has many applications in diverse areas, analyzing the discrete logarithm problem in particular. The birthday problem can be modeled as sampling balls wit...
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The result of birthday problem is of fundamental importance and has many applications in diverse areas, analyzing the discrete logarithm problem in particular. The birthday problem can be modeled as sampling balls with replacement until one is sampled twice. In the classical scenario, balls are sampled uniformly. Inspired by the analysis of algorithms solving certain discrete logarithms, Galbraith and Holmes considered the non-uniform birthday problem and gave an estimate on the number of sampling before having a collision up to the dominating term. In this paper, we give a refined analysis to the non-uniform birthday problem, and apply it to the analysis of an algorithm solving certain discrete logarithm problem. Experiment results suggest that parameter selection following this refined analysis performs better than related work. (C) 2021 Elsevier B.V. All rights reserved.
Options are popular and important financial instruments in world financial markets. One of the simplest options is European call option, which is a contract giving its holder the right, but not the obligation, to buy ...
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Options are popular and important financial instruments in world financial markets. One of the simplest options is European call option, which is a contract giving its holder the right, but not the obligation, to buy a stock or other financial asset at some point in the future (called the expiration date) for a specified price X (called the strike price). The payoff of an option is the amount of money its holder makes on the contract. Suppose that we have a European option on a stock, and the stock price S is more than the strike price X on the expiration date. Then, we can make some money by exercising the option to buy the stock and selling the stock immediately at the market price. Hence, the payoff of a European option is given by (S — X)~+ = max{S — X, 0}. The price of the option is usually much less than the actual price of the underlying stock. Therefore, options hedge risk more cheaply than stocks only, and provide a chance to get large profit with a small amount of money if one's speculation is good.
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