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SYMBOL ERROR RATE CURVES FOR M-QAM SIGNALS WITH MULTIPLE COCHANNEL INTERFERERS

IEEE TRANSACTIONS ON COMMUNICATIONS 1988年第8期36卷 980-983页

作者： COCO, RA AT&T Bell Laboratories MA USA

A recursive algorithm for determining the probability of symbol error in an M-QAM system, subject to multiple-cochannel interferers, is presented. In particular, a recursive formula is derived for determining the symbol-error-rate (SER) of an M-QAM system subject to both multiple-sinusoidal and similar, independent QAM interferers. The result is expected to prove useful in the analysis of such systems exposed to ever-increasing interference.

关键词： recurrence formula recursive algorithms Quadrature amplitude modulation Analysis systems Curves SAFETY EVALUATION REPORT signals

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COMBINATORIAL AND NONCOMMUTATIVE LIST-PROCESSING AND ASSOCIATED GRAPHS

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JOURNAL OF MATHEMATICAL CHEMISTRY 1992年第1-3期11卷 133-144页

作者： DJURASOVIC, M STIPCEVIC, Z 1. Institut za Fiziku Prirodno-matemati?ki Fakultet Vojvode Putnika 43 71000 Sarajevo Yugoslavia

Recently the authors have proposed a list-processing approach to the modeling of algebraic quantum field theory methods in quantum mechanics in which the noncommutative algebra of quantum-mechanical operators is emulated by lists. The processing produces reordered sequences of elements of a ring with a unit commutator and generates dynamic structures which, for some initial arrangements, correspond to partially ordered graphs characterized by recurrence relations and combinatorial identities. Likewise, in another list-processing application to physical problems, a simulation of Feynman diagrams hinged on predominantly combinatorial aspects and demanded explicit generation of certain combinatorial objects. This motivated an investigation into the combinatorial nature of noncommutative list-processing and of recursive algorithms for explicit construction of combinatorial lists, which we now present. The emphasis is also placed on the consideration of associated graphs and the graph-theoretic origin of the appearance of recurrence relations in the reordering theorems of the noncommutative algebra.

关键词： Feynman diagrams Area of annulus Quantum mechanics recursive algorithms Algebra LIST RINGS rings Recurrence relation

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TRACKING ERROR-BOUNDS OF ADAPTIVE NONSTATIONARY FILTERING

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AUTOMATICA 1985年第3期21卷 293-302页

作者： EWEDA, E MACCHI, O CNRS ECOLE SUPER ELECTSIGNAUX & SYST LABF-91190 GIF SUR YVETTEFRANCE

Adaptive filtering with error gradient algorithm and constant step-size is analyzed for a deterministic time variable optimum filtering vector. The unrealistic assumption of independent observations is replaced by a bounded memory model, largely justifiable in applications. Then the mean square tracking deviation (MSD) between the optimum vector and the algorithm output is proved to include two contributions; the stationary mode error, characteristic of convergence accuracy, which is proportional to the step-size; and the transient mode error, reflecting the rapidity of tracking, which is proportional to the squared ratio of the maximum optimum estimator increment to the step-size. This result agrees with the common intuition that there exists an optimum step-size which compromises between convergence accuracy and tracking speed.

关键词： Adaptive systems discrete time systems filtering least-squares estimation linear systems random processes recursive algorithms time-varying systems

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Limiting distributions for the costs of partial match retrievals in multidimensional tries

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RANDOM STRUCTURES & algorithms 2000年第3-4期17卷 428-459页

作者： Schachinger, W Univ Vienna Dept Stat & Decis Support Syst A-1210 Vienna Austria

In this paper we derive limiting distributions for the costs of partial match retrievals in K-d tries. We confine ourselves to the binary case (i.e., the alphabet, from which the letters of the keys are drawn, has cardinality 2), to dimension K = 2, and to the query pattern (*, S). The probabilistic model that we assume is the Bernoulli model: keys are sequences of i.i.d. random variables, which assume the values 0 and 1 with probability p and 1 - p, and are pairwise independent. In the symmetric case (p = 1/2) our analysis reveals convergence in distribution of properly normalized costs C-N, as N --> infinity (N is the number of keys), to the normal distribution, as well as convergence of the moments. We also consider two models dealing with flexible queries. The first, which we call "adapted," assumes that the decision, in which subtree of a node to continue the search, is made when we reach that node, independent of all other such decisions. The second model, which we call "predictable," assumes that that decision is made one step in advance, telling, if the search should be continued in both left (resp. both right) subtrees of the two sons, again independent of all other such decisions. In the symmetric case the limiting distributions are the same as before, and in the asymmetric case limiting distributions are given in terms of some nonnormal distribution mu (p), which is the unique solution of a certain stochastic fixed point equation. Again we also establish convergence of the moments. Furthermore we derive some properties of mu (p), from its fixed point equation, such as existence and infinite differentiability of the density, and analyticity of the moment generating function, and we also determine the support of mu (p). (C) 2000 John Wiley & Sons, Inc.

关键词： recursive algorithms trie K-d trie limit theorems multidimensional data partial match retrieval

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Splines - A perfect fit for signal and image processing

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IEEE SIGNAL PROCESSING MAGAZINE 1999年第6期16卷 22-38页

作者： Unser, M Swiss Fed Inst Technol CH-1015 Lausanne Switzerland

The article provides arguments in favor of an alternative approachthat uses splines, which is equally justifiable on a theoretical basis,and which offers many practical advantages. To reassure the reader whomay be afraid to enter new territory, it is emphasized that one is notlosing anything because the traditional theory is retained as aparticular case (i.e., a spline of infinite degree). The basiccomputational tools are also familiar to a signal processing audience(filters and recursive algorithms), even though their use in the presentcontext is less conventional. The article also brings out the connectionwith the multiresolution theory of the wavelet transform. This articleattempts to fulfil three goals. The first is to provide a tutorial onsplines that is geared to a signal processing audience. The second is togather all their important properties and provide an overview of themathematical and computational tools available; i.e., a road map for thepractitioner with references to the appropriate literature. The thirdgoal is to give a review of the primary applications of splines insignal and image processing

关键词： filtering theory image processing interpolation signal processing signal resolution signal sampling splines (mathematics) wavelet transforms computational tools digital filtering filters mathematical tools multiresolution theory recursive algorithms sign Image processing recursive algorithms Digital filters signal resolution filtering theory signal processing splines (mathematics) wavelet transforms Interpolation Filters signal sampling

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Stochastic approximation: a survey

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WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS 2010年第1期2卷 87-96页

作者： Kushner, Harold Brown Univ Appl Math Providence RI 02912 USA

Stochastic recursive algorithms, also known as stochastic approximation, take many forms and have numerous applications. It is the asymptotic properties that are of interest. The early history, starting with the work of Robbins and Monro, is discussed. An approach to proofs of convergence with probability one is illustrated by a stability-type argument. For general noise processes and algorithms, the most powerful current approach is what is called the ordinary differential equations (ODE) method. The algorithm is interpolated into a continuous-time process, which is shown to converge to the solution of an ODE, whose asymptotic properties are those of the algorithm. There are probability one and weak convergence methods, the latter being the easiest to use and the most powerful. After discussing the basic ideas and giving some standard proofs, extensions are outlined. These include multiple time scales, tracking of time changing systems, state-dependent noise, rate of convergence, and random direction methods for high-dimensional problems. (C) 2009 John Wiley & Sons, Inc.

关键词： stochastic approximation recursive algorithms weak convergence ODE methods asymptotic properties

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Computation of Open Gromov-Witten Invariants for Toric Calabi-Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture

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COMMUNICATIONS IN MATHEMATICAL PHYSICS 2015年第2期337卷 483-567页

作者： Eynard, B. Orantin, N. IPHT CEA Saclay Inst Phys Theor F-91191 Gif Sur Yvette France Inst Super Tecn Dept Matemat CAMGSD P-1049001 Lisbon Portugal

The BKMP conjecture (2006-2008) proposed a new method to compute closed and open Gromov-Witten invariants for every toric Calabi-Yau 3-folds, through a topological recursion based on mirror symmetry. So far, this conjecture has been verified to low genus for several toric CY3folds, and proved to all genus only for . In this article we prove the general case. Our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs: on the A-model side this is the localization formula, and on the B-model side the graphs encode the recursive algorithm of the topological recursion. One can slightly reorganize the set of graphs obtained in the B-side, so that it coincides with the one obtained by localization in the A-model. Then it suffices to compare the weights of vertices and edges of graphs on each side, which is done in two steps: the weights coincide in the large radius limit, due to the fact that the toric graph is the tropical limit of the mirror curve. Then the derivatives with respect to Kahler radius coincide due to the special geometry property implied by the topological recursion.

关键词： Recursion recursive algorithms sidings combinatorial sum Conjecture mirror symmetric Invariant

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Distributed Random-Fixed Projected Algorithm for Constrained Optimization Over Digraphs

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IFAC-PapersOnLine 2017年第1期50卷 14436-14441页

作者： Xie, Pei You, Keyou Song, Shiji Wu, Cheng Department of Automation Tsinghua University Tsinghua National Laboratory for Information Science and Technology Beijing100084 China

This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To collaboratively solve the optimization, most of the existing works require the interaction graph to be balanced or “doubly-stochastic” which is quite restrictive and not necessary as shown in this paper. We focus on an epigraph form of the original optimization to resolve the “unbalanced” problem, and design a novel two-step recursive algorithm with a simple structure. Under strongly connected digraphs, we prove that each node asymptotically converges to some common optimal solution. Finally, simulations are performed to illustrate the effectiveness of the proposed algorithms. © 2017

关键词： Constrained optimization Cost functions Directed graphs Graph theory Parallel algorithms Stochastic systems Constrained optimi zation problems Doubly stochastic Interaction graphs Optimal solutions recursive algorithms Simple structures Strongly connected unbalanced digraphs

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Computing minimum with primitive recursion over lists

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THEORETICAL COMPUTER SCIENCE 1996年第1-2期163卷 269-276页

作者： Fredholm, D UNIV STOCKHOLM DEPT MATH S-10691 STOCKHOLM SWEDEN

We show that there is no primitive recursive algorithm over the natural numbers and lists of natural numbers that computes the minimum of two numbers in time O(min), in call-by-value evaluation order. This is in contr... 详细信息

关键词： recursive algorithms LIST Natural number Primitive

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OPTIMIZATION WITH RESPECT TO COVARIANCE SEQUENCE PARAMETERS

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AUTOMATICA 1985年第6期21卷 671-675页

作者： STOICA, P SODERSTROM, T UNIV UPPSALA INST TECHNOLDEPT AUTOMAT CONTROL & SYST ANALS-75121 UPPSALASWEDEN

A general problem involving optimization of a covariance sequence is considered in the paper. One difficulty with this class of problems is to ensure that the covariance sequence is nonnegative definite (in other words, realizable). It is suggested that this difficulty can be overcome by reformulating the optimization problem in terms of the partial autocorrelation coefficients (PAC). One need only constrain these coefficients to lie in the range (−1, 1) to guarantee that the corresponding covariance sequence is nonnegative definite. The synthesis of a signal realizing the optimizing covariance sequence is also discussed. Special emphasis is given to the case when some of the PACs are either +1 or −1.

关键词： Correlation methods estimation optimization recursive algorithms signal processing time-series analysis

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