The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw (1984)). Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms...
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ISBN:
(数字)9783790826043
ISBN:
(纸本)9783790826036
The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw (1984)). Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rousseeuw and Van Driessen (1999) is used. The FASTMCD algorithm is affine equivariant but not permutation invariant. Recently a deterministic algorithm, denoted as DetMCD, is developed which does not use random subsets and which is much faster (Hubert et al. (2010)). In this paper DetMCD is illustrated in a calibration framework. We focus on robust principal component regression and partial least squares regression, two very popular regression techniques for collinear data. We also apply DetMCD on data with missing elements after plugging it into the M-RPCR technique of Serneels and Verdonck (2009).
of input values and can be detected using pairwise test sets that cover each pair of input values. The generation of pairwise test sets with a minimal size is an NP-complete problem which implies that many algorithms ...
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ISBN:
(纸本)9781424486298
of input values and can be detected using pairwise test sets that cover each pair of input values. The generation of pairwise test sets with a minimal size is an NP-complete problem which implies that many algorithms are either expensive or based on a random process. In this paper we present a deterministic algorithm that exploits our observation that the pairwise testing problem can be modeled as a k-partite graph problem. We calculate the test set using well investigated graph algorithms that take advantage of properties of k-partite graphs. We present evaluation results that prove the applicability of our algorithm and discuss possible improvement of our approach.
Distance-2-Dispersion (D-2-D) problem aims to disperse k mobile robots starting from an arbitrary initial configuration on an anonymous port-labeled graph G with n nodes such that no two robots occupy adjacent nodes i...
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ISBN:
(纸本)9783031522123;9783031522130
Distance-2-Dispersion (D-2-D) problem aims to disperse k mobile robots starting from an arbitrary initial configuration on an anonymous port-labeled graph G with n nodes such that no two robots occupy adjacent nodes in the final configuration, though multiple robots may occupy a single node if there is no other empty node whose all adjacent nodes are also empty. In the existing literature, this problem is solved starting from a rooted configuration for k(>= 1) robots using O(m Delta) synchronous rounds with a total of O(log n) memory per robot, where m is the number of edges and Delta is the maximum degree of the graph. In this work, we start with k > n mobile robots and improve the run time to O(m) starting from a rooted configuration using the same amount of memory per robot. Further, we achieve D-2-D for an arbitrary initial configuration in O(pm) rounds using O(log n) memory per robot, where p is the number of nodes containing robots in the initial configuration. Both the algorithms terminate without any global knowledge of m, n, Delta, k, p. As we start with k > n robots, the nodes occupied by robots in the final configuration form a maximal independent set of the graph.
A team of mobile agents with different labels, starting from different nodes of an unknown anonymous network, must meet at the same node and declare that they all met. This task of gathering was traditionally consider...
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A team of mobile agents with different labels, starting from different nodes of an unknown anonymous network, must meet at the same node and declare that they all met. This task of gathering was traditionally considered assuming that agents at the same node can exchange information. We ask if this ability of talking is needed. The answer turns out to be no. We design two deterministic algorithms that accomplish gathering in a much weaker model. We only assume that each agent knows how many agents are at the node that it currently occupies. Our first algorithm assumes that agents know some upper bound N on the size of the network, and works in time polynomial in N and in the length l of the smallest label. Our second algorithm does not assume any knowledge about the network, but its complexity is at least exponential in the size of the network and in the labels of agents. Its purpose is to show feasibility of gathering under this harsher scenario. As a by-product we solve, in the same weak model, the fundamental problem of leader election among agents. As an application we solve the gossiping problem in this model: if each agent has a message, all agents can learn all messages. This is perhaps our most surprising finding: agents without any transmitting devices can solve the most general information exchange problem if they can count the number of agents present at visited nodes.
In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G = (V, E), where the graph's nodes are...
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ISBN:
(纸本)9783031210167;9783031210174
In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G = (V, E), where the graph's nodes are not labeled. The edges incident to a node v with degree d are labeled with port numbers in the range {0, 1,..., d - 1} at v. The robots have unique IDs in the range [0, L], where L >= k, and are initially placed at a source node s. Each robot knows only its ID, however, it does not know the IDs of the other robots or the values of L or k. The task of the dispersion was traditionally achieved based on the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them, and (b) any two robots in the network can exchange messages between them. This paper investigates whether this communication ability among co-located robots is absolutely necessary to achieve the dispersion. We established that even in the absence of the ability of communication, the task of the dispersion by a set of mobile robots can be achieved in a much weaker model, where a robot at a node v has the access of following very restricted information at the beginning of any round: (1) am I alone at v? (2) did the number of robots at v increase or decrease compared to the previous round? We propose a deterministic distributed algorithm that achieves the dispersion on any given graph G = (V, E) in time O (k log L + k(2) log Delta), where. is the maximum degree of a node in G. Further, each robot uses O(log L + log Delta) additional memory. We also prove that the task of the dispersion cannot be achieved by a set of mobile robots with o(log L + log Delta) additional memory.
It has been known that the primes are infinite in number but the exact sequence of primes is not predictable. Prime numbers and computers have been linked since the 1950s. Computer security authorities use extremely l...
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ISBN:
(纸本)9781479965854
It has been known that the primes are infinite in number but the exact sequence of primes is not predictable. Prime numbers and computers have been linked since the 1950s. Computer security authorities use extremely large prime numbers when they devise cryptographs, like RSA (short for Rivest, Shamir, and Adleman) algorithm, for protecting vital information that is transmitted between computers. There are many primality testing algorithms including mathematical models and computer programs. However, they are very time and energy consuming when the given number n is very large. In this paper, we propose a Compute Unified Device Architecture (CUDA)-accelerated deterministic algorithm to determine whether an input number is prime or composite much faster to save energy. We develop and implement the proposed algorithm using a system with an 8-core CPU and a 448-core GPu. Experimental results indicate that up to 45x speedup and 88% energy saving can be achieved for 20-digit decimal numbers.
This paper deals with the development of methodology suited for design of computation algorithm which is able to determine power losses of electronic systems based on measured temperature distribution. Second part of ...
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ISBN:
(纸本)9788026102762
This paper deals with the development of methodology suited for design of computation algorithm which is able to determine power losses of electronic systems based on measured temperature distribution. Second part of paper is given to development of methodology for optimal selection of mentioned active components for thermal simulation model of given electronic system. Finally experimental verification of proposed methodology is presented.
The aim of the dispersion problem is to place a set of k (= n, it is guaranteed that the nodes with robots form a maximal independent set of the underlying network. The graph G = (V, E) is a port-labelled graph having...
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ISBN:
(纸本)9783031377648;9783031377655
The aim of the dispersion problem is to place a set of k (<= n) mobile robots in the nodes of an unknown graph consisting of n nodes such that in the final configuration each node contains at most one robot, starting from any arbitrary initial configuration of the robots on the graph. In this work, we propose a variant of the dispersion problem, namely Distance-2-Dispersion, in short, D-2-D, where we start with any number of robots, and put an additional constraint that no two adjacent nodes contain robots in the final configuration. However, if a maximal independent set is already formed by the nodes which contain a robot each, then any other unsettled robot, if exists, will not find a node to settle. Hence we allow multiple robots to sit on some nodes only if there is no place to sit. If k >= n, it is guaranteed that the nodes with robots form a maximal independent set of the underlying network. The graph G = (V, E) is a port-labelled graph having n nodes and m edges, where nodes are anonymous. The robots have unique ids in the range [1, L], where L >= k. Co-located robots can communicate among themselves. We provide an algorithm that solves D-2-D starting from a rooted configuration (i.e., initially all the robots are co-located) and terminates after 2 Delta(8m - 3n + 3) synchronous rounds using O(log Delta) memory per robot without using any global knowledge of the graph parameters m, n and Delta, the maximum degree of the graph. We also provide Omega(m Delta) lower bound on the number of rounds for the D-2-D problem.
In this paper, we mainly study the law of stock price changes and the fitting method of it. After introducing the key point of fractal and Genetic algorithm, we focus on explaining the inverse problems of piecewise fr...
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ISBN:
(纸本)9780769531199
In this paper, we mainly study the law of stock price changes and the fitting method of it. After introducing the key point of fractal and Genetic algorithm, we focus on explaining the inverse problems of piecewise fractal interpolation theoretically first. Then, based on the theory, we analyze a large amount of stock price data, calculate all the values of parameters in the model, and finally get an image of the attractor. The result is comparatively satisfying, so that this algorithm is very effective.
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