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A harmonic analysis method adapted to capturing slow variations of tidal amplitudes and phases

CONTINENTAL SHELF RESEARCH 2018年 164卷 37-44页

作者： Guo, Zheng Pan, Haidong Cao, Anzhou Lv, Xianqing Ocean Univ China Phys Oceanog Lab Qingdao Collaborat Innovat Ctr Marine Sci & Techn Qingdao Peoples R China Qingdao Natl Lab Marine Sci & Technol Qingdao Peoples R China Zhejiang Univ Ocean Coll Zhoushan Peoples R China

Harmonic analysis (HA) is a widely used tool in the study of tides. To capture the slow variation of tidal amplitudes and phases revealed in recent research, namely, variations on a timescale of multiple months or longer, an empirical HA approach is presented and validated in this study. This empirical HA relies only on a knowledge of tidal frequencies and allows post facto analysis of dynamics. In essence, it is incorporation of piecewise linear functions into the conventional HA through the least squares matrix, permitting slow variations in amplitudes and phases. The advantage of linear functions over other functions such as cubic splines lies in their simple calculation and avoidance of artificial oscillation. In the approach, independent points (IPs) are selected to define the sub-domains for the piecewise functions. Tests with synthetic hourly water levels and application in practical contexts show that the new approach with sufficient IPs is able to reproduce the evolution of tidal amplitudes and phases. Its performance can be further improved by selecting suitable number of IPs for different constituents. In contrast, the more traditional method, for capturing slow variations using HA, of splitting the record into segments to perform HA always provides an average picture and loses variation of tidal amplitudes and phases near the beginning and end of a record.

关键词： Tides Harmonic analysis piecewise linear functions Independent points Slow variation Amplitudes and phases

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On variance component estimation with pseudo-observations

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GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS 2018年第2期9卷 317-334页

作者： Mysen, E. NMA Geodet Inst N-3507 Honefoss Norway

A common approach in geodesy is to rescale observation noise covariance blocks to compensate for errors in stochastic modelling. Each block represents a batch of observations, which is assumed to depend on parameters that are specific to that batch only, and on global parameters that may also be involved in other batches. In the presented work, the covariance rescaling using variance component estimation is given in a form that depends explicitly on the number of batch specific parameters. A transformation of the observations is applied to demonstrate that variance component estimation based on batch estimates of global parameters does not utilize the available information.

关键词： Variance component estimation piecewise linear functions Degrees of freedom Pseudo-observations Completeness

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Neuromorphic Cellular Neural Network Processor for Intelligent Internet-of-Things

Neuromorphic Cellular Neural Network Processor for Intellige...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Villemur, M. Julian, P. Figliola, T. Andreou, A. G. Univ Nacl Sur CONICET Dept Ingn Elect & Comp Inst Invest Ingn Elect Alfredo Desages San Andres 800 RA-8000 Bahia Blanca Buenos Aires Argentina Johns Hopkins Univ Dept Elect & Comp Engn 3400 North Charles Univ Baltimore MD 21218 USA

ISBN: (纸本)9781538648810

We discuss the architecture, implementation and testing of a neuromorphic Cellular Neural Network (CNN) processor for intelligent IoT devices. The processor is based on a simplicial piecewise linear CNN architecture that allows implementation of linear and nolinear CNNs. A linear array of 64 processing element (PE) with column-shared computation resources, tightly coupled to two data memory caches was synthesized and fabricated in a 55nm CMOS technology using custom layout libraries. The fabricated chip achieves an overall performance of 2.95 TOPS/W with dynamic energy dissipation efficiency of 86.4fJ per OP at V=500mV. The processor can implement different types of processing on 2D data arrays, such as gray-scale morphology, gradient flow, median filters, and approximate Gaussian filters, among others.

关键词： Neuromorphic CNN IoT low power piecewise linear functions

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Algorithm for Searching an Equilibrium in a Routing Game with piecewise Constant Cost functions

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INTERNATIONAL GAME THEORY REVIEW 2018年第4期20卷

作者： Parfenov, Andrey St Petersburg State Univ St Petersburg Russia St Petersburg Inst Econ & Math St Petersburg Russia

We consider nonatomic routing games which are used to model transportation systems with a large number of agents and suggest an algorithm to search for the user equilibrium in such games, which is a generalization of the notion of Nash equilibrium. In general, finding a user equilibrium in routing games is computationally a hard problem. We consider the following subclass of routing games: games with piecewise constant cost functions, and construct an algorithm finding equilibrium in such games. This algorithm is based on the potential function method and the method of piecewise linear (PWL) costs enumeration which finds min-cost flow in a network with PWL cost functions. If each cost function increases, then the complexity of our algorithm is polynomial in the parameters of the network. But if some cost functions have decreasing points, then the complexity is exponential by the number of such points.

关键词： Nonatomic routing games user equilibrium piecewise linear functions min-cost network flow

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Macroscopic urban dynamics: Analytical and numerical comparisons of existing models

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2017年 101卷 245-267页

作者： Mariotte, Guilhem Leclercqa, Ludovic Laval, Jorge A. Univ Lyon ENTPE IFSTTAR LICIT F-69518 Lyon France Georgia Inst Technol Sch Civil & Environm Engn Atlanta GA 30332 USA

Large-scale network modeling using the Macroscopic Fundamental Diagram (MFD) is widely based on the single-reservoir model, where the variation of the accumulation of circulating vehicles in the reservoir equals inflow minus outflow. However, inconsistent lags for information propagation between boundaries may be observed with this single accumulation-based model. For example, outflow is reacting too fast when inflow varies rapidly, whereas this information should be carried by vehicles that are never driving faster than the free-flow speed. To overcome this limitation, a trip-based model has been recently proposed, but whose solution cannot be obtained analytically. In this paper we compare both models under piecewise linear MFD and a piece wise constant demand. These assumptions allow to establish the exact solution of the accumulation-based model, and continuous approximations of the trip-based model at any order using Taylor series. Moreover, a flexible event-based simulation framework is implemented to solve the latter model, making it a promising tool to account for heterogeneity in distance traveled. Thanks to these resolution schemes we are able to measure the inaccuracy of the accumulation-based approach when the demand varies rapidly, and propose a validity domain for this model. Other applications with different trip lengths and supply limitations are also discussed. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Macroscopic modeling Single-reservoir Trip length Analytical resolution piecewise linear functions

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ON THE EVENTUAL PERIODICITY OF piecewise linear CHAOTIC MAPS

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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2017年第3期95卷 467-475页

作者： Khan, M. Ali Rajan, Ashvin V. Johns Hopkins Univ Dept Econ Baltimore MD 21218 USA 3935 Cloverhill Rd Baltimore MD 21218 USA

We present a family of continuous piecewise linear maps of the unit interval into itself that are all chaotic in the sense of Li and Yorke ['Period three implies chaos', Amer. Math. Monthly 82 (1975), 985-992] and for which almost every point (in the sense of Lebesgue) in the unit interval is an eventually periodic point of period p, p >= 3, for a member of the family.

关键词： Li-Yorke chaos piecewise linear functions eventual convergence almost everywhere convergence dynamical systems rationalisability

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Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2017年第2期172卷 554-577页

作者： Mordukhovich, B. S. Sarabi, M. E. Wayne State Univ Detroit MI 48202 USA RUDN Univ Moscow 117198 Russia Miami Univ Oxford OH 45056 USA

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise linear functions recently obtained by the authors. We mainly focus here on establishing relationships between full stability of local minimizers in composite optimization and Robinson's strong regularity of associated (linearized and nonlinearized) KKT systems. Finally, we address Lipschitzian stability of parametric variational systems with convex piecewise linear potentials.

关键词： Variational analysis and optimization piecewise linear functions Second-order subdifferentials Nondegeneracy Full stability of local minimizers Strong regularity of KKT systems Lipschitzian stability of parametric variational systems

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STRUCTURAL INVESTIGATION OF piecewise linearIZED NETWORK FLOW PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2016年第4期26卷 2863-2886页

作者： Liers, Frauke Merkert, Maximilian Friedrich Alexander Univ Erlangen Nurnberg Dept Math Lehrstuhl Wirtschmath Cauerstr 11 D-91058 Erlangen Germany

In this work we study polyhedra in the context of network flow problems, in which the flow value on each arc lies in one of several predefined intervals. This is motivated by nonlinear problems on transportation networks, where nonlinearities are handled by piecewise linear approximation or relaxation a common and established approach in many applications. Several methods for modeling piecewise linear functions which provide a complete description for a single network arc are known. However, in general this property is lost when considering multiple arcs. We show how to strengthen the formulation for specific substructures consisting of multiple arcs by linear inequalities. For the case of paths of degree-two nodes we give a complete description of the polyhedron projected to the integer variables. Our model is based on but not limited to the connection between binary variables and flow variables that is used in the multiple choice method or the convex combination method;we also show how to transfer our results to a formulation based on the incremental method. Computational results show that a state-of-the-art mixed-integer program solver greatly benefits from using our cutting planes for random and realistic network topologies.

关键词： combinatorial optimization complete description network flow problems piecewise linear functions

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Reduced Pairs of Compact Convex Sets and Ordered Median functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第2期171卷 354-364页

作者： Grzybowski, Jerzy Pallaschke, Diethard Urbanski, Ryszard Adam Mickiewicz Univ PL-61614 Poznan Poland Univ Karlsruhe KIT D-76128 Karlsruhe Germany

We prove that in finite dimensional spaces every ordered median function is the Minkowski dual of a reduced pair of polytopes. This implies a very general theorem on the representation of an ordered median function as a uniquely determined difference of two sublinear functions up to adding and subtracting one and the same arbitrary sublinear function.

关键词： Minkowski duality Reduced pairs of compact convex sets piecewise linear functions

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Standard deviation of recurrence times for piecewise linear transformations

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ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2017年第1期10卷

作者： Ismael, Mimoon Nillsen, Rodney Williams, Graham Univ Anbar Dept Pure Math Al Anbar Iraq Univ Wollongong Sch Math & Appl Stat Wollongong NSW 2522 Australia Univ Wollongong Fac Business Wollongong NSW 2522 Australia

This paper is concerned with dynamical systems of the form (X, f), where X is a bounded interval and f comes from a class of measure-preserving, piecewise linear transformations on X. If A subset of X is a Borel set and x is an element of A, the Poincar ' e recurrence time of x relative to A is defined to be the minimum of {n : n is an element of N and f(n)(x) is an element of A}, if the minimum exists, and 8 otherwise. The mean of the recurrence time is finite and is given by Kac's recurrence formula. In general, the standard deviation of the recurrence times need not be finite but, for the systems considered here, a bound for the standard deviation is derived.

关键词： Dynamical systems piecewise linear functions recurrence times standard deviation Kac's formula

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