The increasing amount of PV (photo-voltaic) power plants comes along with an increased instability in the power grid due to the high uncertainty of the PV power production. As a stabilizing measure, grid operators int...
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The increasing amount of PV (photo-voltaic) power plants comes along with an increased instability in the power grid due to the high uncertainty of the PV power production. As a stabilizing measure, grid operators introduce regulations on the injected power profiles comprising the obligation to declare in advance the predicted power production as well as penalties which apply in case these previously declared production profiles were not respected. In order to meet these regulations power plant owners are forced to invest into expensive storage capacities. In this work an algorithm is proposed which allows to determine the optimal battery size that maximizes the to-be-expected revenue of such an installation for a given regulative framework. Moreover the scheme explicitly takes into account the uncertainty in the PV power production and it provides guaranteed lower bounds on the to-be-expected revenue at a configurable probability. The underlying method allowing to achieve these objectives is a randomized algorithm. The principle of this method is to compute probabilistic guarantees for respecting a binary constraint, considering only a limited number of uncertainty scenarios. (C) 2017 Elsevier Ltd. All rights reserved.
The study conducts a bibliometric review of artificial intelligence applications in two areas: the entrepreneurial finance literature, and the corporate finance literature with implications for entrepreneurship. A rig...
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The study conducts a bibliometric review of artificial intelligence applications in two areas: the entrepreneurial finance literature, and the corporate finance literature with implications for entrepreneurship. A rigorous search and screening of the web of science core collection identified 1,890 journal articles for analysis. The bibliometrics provide a detailed view of the knowledge field, indicating underdeveloped research directions. An important contribution comes from insights through artificial intelligence methods in entrepreneurship. The results demonstrate a high representation of artificial neural networks, deep neural networks, and support vector machines across almost all identified topic niches. In contrast, applications of topic modeling, fuzzy neural networks, and growing hierarchical self-organizing maps are rare. Additionally, we take a broader view by addressing the problem of applying artificial intelligence in economic science. Specifically, we present the foundational paradigm and a bespoke demonstration of the Monte Carlo randomized algorithm.
A randomized algorithm for computing a maximum flow is presented. For an n-vertex m-edge network, the running time is O (nm + n(2)(log n)(2)) with probability at]east 1 - 2(-)root nm. The algorithm is always correct, ...
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A randomized algorithm for computing a maximum flow is presented. For an n-vertex m-edge network, the running time is O (nm + n(2)(log n)(2)) with probability at]east 1 - 2(-)root nm. The algorithm is always correct, and in the worst case runs in O(nm log n) time. The only use of randomization is to randomly permute the adjacency lists of the network vertices at the start of the execution. The analysis introduces the notion of premature target relabeling (PTR) events and shows that each PTR event contributes O (log n) amortized time to the overall running rime. The number of PTR events is always O (nm);however, it is shown that when the adjacency lists are randomly permuted, then this quantity is O (n(3)/(2)m(1/2) + n(2) log n) with high probability.
Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of th...
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Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of these algorithms are provided. Numerical experiments are given to test the proposed randomized algorithms.
Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy sol...
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Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares problems faster than standard direct methods based on QR factorization. Recently, Meier et al. demonstrated numerical instabilities in a version of sketch-and-precondition in floating point arithmetic. The work of Meier et al. raises the question, is there a randomized least-squares solver that is both fast and stable? This paper resolves this question in the affirmative by proving that iterative sketching, appropriately implemented, is forward stable. Numerical experiments confirm the theoretical findings, demonstrating that iterative sketching is stable and faster than QR-based solvers for large problem instances.
We consider the online metric matching problem in which we are given a metric space, k of whose points are designated as servers. Over time, up to k requests arrive at an arbitrary subset of points in the metric space...
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We consider the online metric matching problem in which we are given a metric space, k of whose points are designated as servers. Over time, up to k requests arrive at an arbitrary subset of points in the metric space, and each request must be matched to a server immediately upon arrival, subject to the constraint that at most one request is matched to any particular server. Matching decisions are irrevocable and the goal is to minimize the sum of distances between the requests and their matched servers. We give an O(log(2) k)-competitive randomized algorithm for the online metric matching problem. This improves upon the best known guarantee of O(log(3) k) on the competitive factor due to Meyerson, Nanavati and Poplawski (SODA '06, pp. 954-959, 2006). It is known that for this problem no deterministic algorithm can have a competitive better than 2k-1, and that no randomized algorithm can have a competitive ratio better than lnk.
This paper shows that many robust control problems can be formulated as constrained optimization problems and can be tackled by using randomized algorithms. Two different approaches in searching reliable solutions to ...
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This paper shows that many robust control problems can be formulated as constrained optimization problems and can be tackled by using randomized algorithms. Two different approaches in searching reliable solutions to robustness analysis problems under constraints are proposed, and the minimum computational efforts for achieving certain reliability and accuracy are investigated and bounds for sample size are derived. Moreover, the existing order statistics distribution theory is extended to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints.
The key objects in the group-theoretic approach to matrix multiplication are subsets of a group satisfying the so-called triple product property (TPP). In this paper, we focus on the problem of efficiently finding the...
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The key objects in the group-theoretic approach to matrix multiplication are subsets of a group satisfying the so-called triple product property (TPP). In this paper, we focus on the problem of efficiently finding the triple product property triples. We deduce and present some new characteristics of the triple product property. Using these new characteristics, we firstly propose an efficient deterministic algorithm in which a screening process based on historical information is designed to reduce the search space. In contrast to some of the recent heuristic search methods, the proposed deterministic algorithm can search all kinds of TPP triples in a highly efficient way with the help of a novel representation for subsets and a Moving I principle. In addition, we also propose an efficient randomized algorithm for finding TPP triples, which adopts a greedy randomized strategy to randomly generate possible TPP candidates. Experimental results demonstrate that our proposed deterministic algorithm can achieve a huge speed-up in terms of running time compared with the existing deterministic algorithm, and the proposed randomized algorithm outperforms other existing approaches for finding TPP triples. (C) 2018 Elsevier B.V. All rights reserved.
We present a randomized linear-time algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered linear-time algorithm ...
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We present a randomized linear-time algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered linear-time algorithm for verifying a minimum spanning tree. Our computational model is a unit-cost random-access machine with the restriction that the only operations allowed on edge weights are binary comparisons.
In this paper, we present some single-pass randomized algorithms to compute LU decomposition. These algorithms need only one pass over the original matrix and hence are very suitable for extremely large and high-dimen...
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In this paper, we present some single-pass randomized algorithms to compute LU decomposition. These algorithms need only one pass over the original matrix and hence are very suitable for extremely large and high-dimensional matrix stored outside of core memory or generated in a streaming fashion. Rigorous error bounds and complexity of these algorithms are provided. Numerical experiments show that these single-pass algorithms have the similar accuracy and runtime (excluding the cost of matrix transfer) compared with the state-of-the-art randomized algorithms for LU decomposition. (C) 2020 Elsevier Inc. All rights reserved.
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