Accurate and fast recognition of fiber intrusion signals has always been a fundamental task in the Optical Fiber Pre-warning System (OFPS). However, currently existing recognition models tend to focus on one aspect an...
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Accurate and fast recognition of fiber intrusion signals has always been a fundamental task in the Optical Fiber Pre-warning System (OFPS). However, currently existing recognition models tend to focus on one aspect and lack a comprehensive approach. In this paper, a dropout-based Stochastic Configuration Network (SCN) optical fiber intrusion signal recognition model is first proposed, which is named DropoutSCN. By combining dropout with randomized algorithm models, it not only enhances the fast learning ability, but also improves the generalization performance of the recognition model. In the experiment, compared with traditional Artificial Neural Network (ANN), Random Vector Functional Link (RVFL), and original SCN models, the DropoutSCN model proposed in this paper has the lowest rootmean-square error (RMSE). In terms of time efficiency, it reduces the time delay by about 2.5 times compared with the traditional ANN. In addition, this paper applies dropout to SCN, which provides a feasible thinking and reference for the study of randomized algorithm models.
We propose the pass-efficient truncated UTV algorithm, a faster variant of the TUXV algorithm for low-rank approximations. Compared with the TUXV algorithm, data transfer and the complexity of the proposed algorithm a...
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We propose the pass-efficient truncated UTV algorithm, a faster variant of the TUXV algorithm for low-rank approximations. Compared with the TUXV algorithm, data transfer and the complexity of the proposed algorithm are reduced. Therefore, our algorithm is suitable for large matrices stored out of memory or generated by streaming data. We also develop residual error upper bounds and singular value approximation error bounds for the pass-efficient truncated UTV algorithm. Numerical experiments are reported to demonstrate the efficiency and effectiveness of our algorithm.
Property testing is a rapid growing field in theoretical computer science. It considers the following task: given a function f over a domain D, a property P and a parameter 0 0, and present the first property tester ...
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Property testing is a rapid growing field in theoretical computer science. It considers the following task: given a function f over a domain D, a property P and a parameter 0 < epsilon < 1, by examining function values of f over o(vertical bar D vertical bar) elements in D, determine whether f satisfies P or differs from any one which satisfies P in at least epsilon vertical bar D vertical bar elements. An algorithm that fulfills this task is called a property tester. We focus on tree-likeness of quartet topologies, which is a combinatorial property originating from evolutionary tree construction. The input function is f(Q), which assigns one of the three possible topologies for every quartet over an n-taxon set S. We say that fQ satisfies tree-likeness if there exists an evolutionary tree T whose induced quartet topologies coincide with f(Q). In this paper, we prove the existence of a set of quartet topologies of error number at least c((n)(4)) for some constant c > 0, and present the first property tester for tree-likeness of quartet topologies. Our property tester makes at most O(n(3)/epsilon) queries, and is of one-sided error and non-adaptive.
In this paper we consider a variant of the well-known Achlioptas process for graphs adapted to monotone Boolean functions. Fix a number of choices r is an element of N and a sequence of increasing functions (f(n))(n &...
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In this paper we consider a variant of the well-known Achlioptas process for graphs adapted to monotone Boolean functions. Fix a number of choices r is an element of N and a sequence of increasing functions (f(n))(n >= 1) such that, for every n >= 1, f(n) : {0, 1}(n) (sic) {0, 1}. Given n bits which are all initially equal to 0, at each step r 0-bits are sampled uniformly at random and are proposed to an agent. Then, the agent selects one of the proposed bits and turns it from 0 to 1 with the goal to reach f(n)(-1) (1) as quickly as possible. We nearly characterize the conditions on (f(n))(n >= 1) under which an acceleration by a factor of r(1+ o(1)) is possible and underline the wide applicability of our results by giving examples from the fields of Boolean functions and graph theory.
Consider a team of kappa <= n autonomous mobile robots initially placed at a node of an arbitrary graph G with n nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a conf...
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Consider a team of kappa <= n autonomous mobile robots initially placed at a node of an arbitrary graph G with n nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a configuration in which each robot is at a distinct node of the graph. If the robots are anonymous, i.e., they do not have any unique identifiers, then the problem is not solvable by any deterministic algorithm. However, the problem can be solved even by anonymous robots if each robot is given access to a fair coin which they can use to generate random bits. In this setting, it is known that the robots require O(log.) bits of memory to achieve dispersion, where. is the maximum degree of G. On the other hand, the best known memory upper bound is min{Delta,max{log Delta, log D}} (D = diameter of G), which can be omega(log Delta), depending on the values of Delta and D. In this paper, we close this gap by presenting an optimal algorithm requiring O(log Delta) bits of memory. (c) 2023 Elsevier B.V. All rights reserved.
作者:
Xu, RenjieWei, TongWei, YiminYan, HongFudan Univ
Sch Math Sci Shanghai 200433 Peoples R China Fudan Univ
Inst Sci & Technol Brain Inspired Intelligence Shanghai 200433 Peoples R China Fudan Univ
Sch Math Sci Shanghai Key Lab Contemporary Appl Math Shanghai 200433 Peoples R China City Univ Hong Kong
Ctr Intelligent Multidimens Data Anal Dept Elect Engn Hong Kong Peoples R China
Matrix factorization in the context of dual numbers has found applications, in recent years, in fields such as kinematics and computer graphics. In this paper, we develop an efficient approach for handling large-scale...
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Matrix factorization in the context of dual numbers has found applications, in recent years, in fields such as kinematics and computer graphics. In this paper, we develop an efficient approach for handling large-scale data low-rank approximation problems using the UTV decomposition of dual matrices (DUTV). Theoretically, we propose an explicit expression for the DUTV and provide necessary and sufficient conditions for its existence. During this process, we also discovered that the general low-rank model for dual matrices can be solved by the Sylvester equation. In numerical experiments, the DUTV algorithm outperforms the dual matrix SVD algorithm in terms of speed and maintains effective performance in wave recognition. Subsequently, we utilize the DUTV algorithm to validate brain functional circuits in large-scale task-state functional magnetic resonance imaging data. Successfully identifying three types of wave signals, the DUTV method provides substantial empirical evidence for cognitive neuroscience theories.
We present a sequential method for approximating an unknown function sequentially using random noisy samples. Unlike the traditional function approximation methods, the current method constructs the approximation usin...
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We present a sequential method for approximating an unknown function sequentially using random noisy samples. Unlike the traditional function approximation methods, the current method constructs the approximation using one sample at a time. This results in a simple numerical implementation using only vector operations and avoids the need to store the entire data set. The method is thus particularly suitable when data set is exceedingly large. Furthermore, we present a general theoretical framework to define and interpret the method. Both upper and lower bounds of the method are established for the expectation of the results. Numerical examples are provided to verify the theoretical findings. (C) 2018 Elsevier Inc. All rights reserved.
This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph's minimum cut form an extremely small fraction of the graph's edges. U...
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This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph's minimum cut form an extremely small fraction of the graph's edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n(2)log(3)n) time, a significant improvement over the previous (O) over tilde(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in RNC with n(2) processors;this gives the first proof that the minimum cut problem can be solved in RNC. The algorithm does more than find a single minimum cut;it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of cu of the minimum cut's in expected (O) over tilde(n(2 alpha)) time, or in RNC with n(2 alpha) processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected (O) over tilde(n(2(r-1))) time, or in RNC with n(2(r-1)) processors. The ''trace'' of the algorithm's execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the more standard cactus representation for minimum cuts.
We consider the following resource constrained scheduling problem. We are given m identical processors, s resources R-1, ..., R-s with upper bounds b(1), ..., b(s), n independent jobs T-1, ..., T-n of unit length, whe...
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We consider the following resource constrained scheduling problem. We are given m identical processors, s resources R-1, ..., R-s with upper bounds b(1), ..., b(s), n independent jobs T-1, ..., T-n of unit length, where each job T-j has a start time r(j) is an element of N, requires one processor and an amount R-i(j) is an element of {0, 1} of resource R-i, i = 1, ..., s. The optimization problem is to schedule the jobs at discrete times in N subject to the processor, resource and start-time constraints so that the latest scheduling time is minimum. Multidimensional bin packing is a special case of this problem. Resource constrained scheduling can be relaxed in a natural way when one allows the scheduling of fraction of jobs. Let C-opt (resp. C) be the minimum schedule size for the integral (resp. fractional scheduling). While the computation of C-opt is a NP-hard problem, C can be computed by linear programming in polynomial time. In case of zero start times Rock and Schmidt (1983) showed for the integral problem a polynomial-time approximation within (m/2)C-opt and de la Vega and Lueker (1981), improving a classical result of Garey et al. (1976), gave for every is an element of > 0 a linear time algorithm with an asymptotic approximation guarantee of (s + epsilon)C-opt. The main contributions of this paper include the first polynomial-time algorithm approximating C-opt for every epsilon is an element of(0, 1) within a factor of 1 + epsilon for instances with b(i) = Omega(epsilon(-2)log(Cs)) for all i and m = Omega(epsilon(-2) logC), and a proof that the achieved approximation under the given conditions is best possible, unless P = NP. Furthermore, in some cases we give for every fixed alpha > 1 a parallel 2 alpha-factor approximation algorithm.
In this paper, we show that there is a 5/2 l .ln(1+ kappa)-competitive randomized algorithm for the kappa-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth l when n = kappa + 1 where n is the ...
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In this paper, we show that there is a 5/2 l .ln(1+ kappa)-competitive randomized algorithm for the kappa-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth l when n = kappa + 1 where n is the number of points in the metric space, which improved previous best competitive ratio 12l ln(1 + 4l (1 + k)) by Bansal et al. (FOCS, pp 267-276, 2011).
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