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optimal cubature formulas for calculation of multidimensional integrals in weighted Sobolev spaces

SIBERIAN MATHEMATICAL JOURNAL 2016年第3期57卷 425-441页

作者： Boikov, I. V. Penza State Univ Penza Russia

optimal cubature formulas are constructed for calculations of multidimensional integrals in weighted Sobolev spaces. We consider some classes of functions defined in the cube Omega = [-1, 1] (l) , l = 1, 2,..., and having bounded partial derivatives up to the order r in Omega and the derivatives of jth order (r < j a parts per thousand currency sign s) whose modulus tends to infinity as power functions of the form (d(x, D"))(-(j-r)), where x a Omega D", x = (x (1),..., x (l) ), D" = a,Omega, and d(x, D") is the distance from x to D".

关键词： weighted Sobolev space cubature formula optimal algorithm

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optimal DATA EXCHANGE algorithmS ON STAR GRAPHS

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1994年第3期27卷 21-25页

作者： COOLSAET, K FACK, V STATE UNIV GHENT DEPT APPL MATH & COMP SCIB-9000 GHENTBELGIUM

Star graphs, as discussed in [1], are considered to be attractive alternatives for hypercubes. In this paper, we discuss optimal data exchange algorithms for star graphs of small dimension (n less-than-or-equal-to 6). In particular we study odd-distance and total exchange algorithms, using the tabular method introduced in [2]. The algorithms use no intermediate buffering of messages.

关键词： TOTAL EXCHANGE ODD-DISTANCE DATA EXCHANGE optimal algorithm STAR GRAPH

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Exact and optimal Conversion of a Hole-free 2d Digital Object into a Union of Balls in Polynomial Time 2nd

Exact and Optimal Conversion of a Hole-free 2d Digital Objec...

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2nd International Conference on Discrete Geometry and Mathematical Morphology (DGMM)

作者： Sivignon, Isabelle Univ Grenoble Alpes CNRS Grenoble INP GIPSA Lab F-38000 Grenoble France

ISBN: (纸本)9783031198960;9783031198977

This paper addresses the problem of converting a 2d digital object, i.e. a set S of points in Z(2), into a finite union of balls B centered on R-2, such that the digitization of B is exactly S and the cardinality of B is minimum. We prove that, for the specific case of 2d hole-free digital objects, there exists a greedy polynomial-time algorithm. The algorithm is based on the same principle as the simple greedy optimal algorithm for the interval cover problem. After bringing to light under which conditions the latter algorithm can be extended to tree-like structures, we show that such a structure can be defined for any hole-free 2d digital object, so that the extended algorithm applies.

关键词： Digital object Union of balls Covering optimal algorithm Arborescence

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optimal Copyset in Distributed Object Storage

Optimal Copyset in Distributed Object Storage

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9th IEEE International Conference on Big Data (IEEE BigData)

作者： Huo, Yaoguang Ma, Junfeng Li, Hui Yang, Xin Wang, Han Meng, Xiangzhen Peking Univ Shenzhen Grad Sch Shenzhen Peoples R China China Acad Informat & Commun Technol Beijing Peoples R China

ISBN: (纸本)9781665439022

In distributed storage systems, the replication mechanisms are usually used to ensure system reliability and data availability. Random replication is widely used in cloud storage systems to prevent data loss. Copyset Replication (CR) as a replication strategy, makes a nearly optimal trade-off between the number of scattered nodes and the probability of data loss. Compared with random replication, CR greatly reduces the probability of data loss caused by node failure. However, CR's random selection strategy makes it difficult to select the optimal copyset based on data characteristics such as calculation and storage. In response to this problem of CR, the optimal Copyset Replication (OCR) proposed in this paper can select the optimal copyset according to the specified data characteristics and its corresponding node conditions. Finally, combined with Cyberspace Mimicry Defense (CMD), we implemented OCR in a distributed object storage system and conducted related experiments. When the calculation type data reaches 300,000, the experimental results prove that compared with CR randomly selecting copyset, OCR reduces the data processing time by nearly 10% through selecting the optimal copyset. By setting relevant parameters, OCR can also ensure that the data distribution of each node is relatively uniform, and avoid data skew.

关键词： Copyset Replication optimal algorithm data loss Object Storage Service Cyberspace Mimic Defense

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optimal LQG control and stability of networked robot system with data dropout

Optimal LQG control and stability of networked robot system ...

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IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Liu, Qiao He, Ke-xue Jiang, Liang-zhong Changsha Univ Sci & Technol Elect & Informat Engn Coll Changsha 410076 Peoples R China S China Univ Technol Dept Mech Engn Guangzhou 510640 Peoples R China

ISBN: (纸本)9781424402588

By modeling the networked robot system (NRS) that drops packets randomly, we considered the problem of optimal linear quadratic Gaussian (LQG) control and analyzed the stability of a NRS. We presented a mathematical model based on a packet-based setting, extended the familiar LQG separation principle that allows us to solve this problem using a standard LQR state-feedback design, proposed an optimal algorithm irrespective of the packet drop pattern by constructing an encoder for the unreliable channel and designing the decoder that uses the information it receives across the link to construct an estimate of the state of the networked robot. For the case of packet drops occurring according to a Markov chain, the stability analysis was carried out. Because the separation theorem for linear systems and quadratic cost does not apply to the general framework of NRSs, we used the uncertainty threshold principle to show that under certain conditions there was a rate for dropped packets for which an undisturbed networked control system with imperfect state observation was mean square stable, used a sub-optimal method to simplify the calculation of the estimator and controller, got the solution to the Riccati-like equation and guaranteed the mean square stability of the NRS with perfect state information. This design does not assume any statistical model of the packet drop events and can be implemented as a small modification of an existing LQG control design.

关键词： LQG control networked robot system (NRS) data dropout stability analysis optimal algorithm

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optimal Self Boundary Recognition with Two-Hop Information for Ad Hoc Networks

Optimal Self Boundary Recognition with Two-Hop Information f...

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IEEE Wireless Communications and Networking Conference (WCNC)

作者： Chen, Yen-Hsu Chung, Wei-Ho Ni, Guo-Kai Zhang, Hongke Kuo, Sy-Yen Natl Taiwan Univ Dept Elect Engn Taipei 10764 Taiwan

ISBN: (纸本)9781467304375;9781467304368

The ad hoc network is composed of multiple sensor nodes to serve various applications, such as data collection or environmental monitoring. In many applications, the sensor nodes near the boundary of the deployment region provide biased or low-quality information because they have limited number of neighboring nodes and only partial information is available. Hence, the boundary recognition is an important issue in the ad hoc networks. By the statistical approach in high node density networks, Fekete's pioneer work identified the boundary node by number of neighboring nodes and using a specific threshold. By exploiting the number of nodes in the two-hop region, our proposed algorithm has significant improvement of boundary recognition contrasted with Fekete's algorithm in the low-density network. Given the information topology and the cost function, the analyses provide a framework to obtain the optimal threshold for boundary recognition. Besides, the simulation results reveal the proposed algorithm has greater than 90% detection rate and lower than 10% false alarm rate.

关键词： ad hoc networks boiundary recognition decision optimal algorithm

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optimal ERROR AND GMDH PREDICTORS - A COMPARISON WITH SOME STATISTICAL TECHNIQUES

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INTERNATIONAL JOURNAL OF FORECASTING 1987年第2期3卷 313-328页

作者： VICINO, A TEMPO, R GENESIO, R MILANESE, M POLITECN TORINO I-10129 TURIN ITALY

This paper presents some results obtained in time series forecasting using two nonstandard approaches and compares them with those obtained by usual statistical techniques. In particular, a new method based on recent results of the General Theory of optimal algorithm is considered. This method may be useful when no reliable statistical hypotheses can be made or when a limited number of observations is available. Moreover, a nonlinear modelling technique based on Group Method of Data Handling (GMDH) is also considered to derive forecasts. The well-known Wolf Sunspot Numbers and Annual Canadian Lynx Trappings series are analyzed; the optimal Error Predictor is also applied to a recently published demographic series on Australian Births. The reported results show that the optimal Error and GMDH predictors provide accurate one step ahead forecasts with respect to those obtained by some linear and nonlinear statistical models. Furthermore, the optimal Error Predictor shows very good performances in multistep forecasting.

关键词： optimal algorithm Time series GMDH Application Comparative methods Lead time

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ON optimal HEURISTIC RANDOMIZED SEMIDECISION PROCEDURES, WITH APPLICATION TO PROOF COMPLEXITY

ON OPTIMAL HEURISTIC RANDOMIZED SEMIDECISION PROCEDURES, WIT...

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27th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Hirsch, Edward A. Itsykson, Dmitry Steklov Inst Math St Petersburg 27 Fontanka St Petersburg 191023 Russia

ISBN: (纸本)9783939897163

The existence of a (p-) optimal propositional proof system is a major open question in (proof) complexity;many people conjecture that such systems do not exist. Krajicek and Pudlak [KP89] show that this question is equivalent to the existence of an algorithm that is optimal(1) on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false "theorems" (according to any polynomial-time samplable distribution on non-tautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems.

关键词： propositional proof complexity optimal algorithm

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optimal Implementation of Elliptic Curve Cryptography

Optimal Implementation of Elliptic Curve Cryptography

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IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI)

作者： Lv, Hongqiang Li, Hui Yi, Junkai Lu, Hao Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing Peoples R China

ISBN: (纸本)9781479905300;9781479905294

The most time-consuming operation in the Elliptic Curve Cryptography (ECC) calculation is scalar multiplication. Scalar multiplication plays a major role in ECC. Currently, there are several optimization algorithms for point scalar multiplication which have either high computational complexity or additional storage requirement. They are all unsuitable for further applying. In this paper, we present a new compatible optimal algorithm which improves the efficiency by generating a special random number k as the scalar. The experimental results show that the processes of encryption and decryption have been speed up significantly in the same condition.

关键词： Elliptic Curve Cryptography scalar multiplication optimal algorithm random number

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optimal packet scheduling in tree-structured LEO satellite clusters

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MOBILE NETWORKS & APPLICATIONS 2004年第4期9卷 289-295页

作者： Bonuccelli, MA Martelli, F Pelagatti, S Univ Pisa Dipartimento Informat I-56127 Pisa Italy CNR ISTI I-56124 Pisa Italy

Clusters of mobile (LEO) satellites, flying at a non-geostationary orbit, have been recently proposed, designed and made operational for achieving a global coverage of roaming users. An example of these is Teledesic. The satellites of these clusters are equipped with a radio frequency switch and connected via intersatellite links to form a specific topology. Uncoordinated packet transmission in these systems may result in collisions. Collided packets must be retransmitted, with an obvious degradation in performance, in terms of both bandwidth usage and delay. This performance degradation can be overcome by a proper scheduling of the packets. In this paper, we consider optimal (namely minimum length) packet scheduling in LEO satellite clusters. We present a preprocessing algorithm which, together with the optimal, polynomial time, packet scheduling algorithm for isolated satellites, produces an optimal schedule in tree-connected clusters. The overall algorithm inherit the time complexity of the optimal one for isolated systems, and is O(N-4) for a cluster serving N roaming users.

关键词： LEO satellite clusters TDMA packet scheduling optimal algorithm

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