Solutions of the motivic ADHM recursion formula
Mozgovoy, Sergey
2011-01-01
We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of Higgs moduli spaces conjectured by Hausel and Rodriguez-Villegas. We solve also the twisted motivic ADHM recursion formula. As a byproduct we obtain a conjectural formula for the motives of twisted Higgs moduli spaces, which generalizes the conjecture of Hausel and Rodriguez-Villegas.
Recursive formulae for the multiplicative partition function
Jun Kyo Kim
1999-01-01
Full Text Available For a positive integer n, let f(n be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition function f(n.
Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas
Godlin, Benny; Makowsky, Johann A
2008-01-01
Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.
RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION
许进
2004-01-01
A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.
A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables
Reynaldo Iracheta
2015-12-01
Full Text Available This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT to obtain accurate transient responses in the time domain.
Recursive generation of one-loop SM amplitudes
Actis, Stefano [Paul Scherrer Institut, Wuerenlingen (Switzerland); Paul Scherrer Institut, Villigen (Switzerland); Denner, Ansgar; Hofer, Lars; Scharf, Andreas [Universitaet Wuerzburg (Germany); Uccirati, Sandro [Universita di Torino, Turin (Italy)
2013-07-01
We introduce the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the full Standard Model, including electroweak corrections. The presented algorithm for the calculation of one-loop amplitudes uses Dyson-Schwinger recursion relations to determine the coefficients of the tensor integrals. As a first application of Recola we discuss Z+2jets production at the LHC and present results for the next-to-leading-order electroweak corrections to the dominant partonic channels.
Use of the recursion formula of the Gompertz survival function to evaluate life-table data.
Bassukas, I D
1996-08-29
The recursion formula of the Gompertz function is an established method for the analysis of growth processes. In the present study the recursion formula of the Gompertz survival function 1n S(t + s) = a + b x ln S(t) is introduced for the analysis of survival data, where S(t) is the survival fraction at age 1, s is the constant age increment between two consecutive measurements of the survival fraction and a and b are parameters. With the help of this method--and provided stroboscopial measurements of rates of survival are available--the Gompertz survival function, instead of the corresponding mortality function, can be determined directly using linear regression analysis. The application of the present algorithm is demonstrated by analysing two sets of data taken from the literature (survival of Drosophila imagoes and of female centenarians) using linear regression analysis to fit survival or mortality rates to the corresponding models. In both cases the quality of fit was superior by using the algorithm presently introduced. Moreover, survival functions calculated from the fits to the mortality law only poorly predict the survival data. On the contrary, the results of the present method not only fit to the measurements, but, for both sets of data the mortality parameters calculated by the present method are essentially identical to those obtained by a corresponding application of a non-linear Marquardt-Levenberg algorithm to fit the same sets of data to the explicit form of the Gompertz survival function. Taking into consideration the advantages of using a linear fit (goodness-of-fit test and efficient statistical comparison of survival patterns) the method of the recursion formula of the Gompertz survival function is the most preferable method to fit survival data to the Gompertz function.
Recursion Formulae for Obtaining Surfaces with Constant Mean Curvature in R2,1
TIAN Yong-Bo; NAN Zhi-Jie; TIAN Chou
2007-01-01
Though the B(a)cklund transformation on time-like surfaces with constant mean curvature surfaces in R2,1 has been obtained,it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the B(a)cklund transformation is used.For sake of this,in this article,some special work is done to reform the B(a)cklund transformation to a recursion formula,by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.
Recursive Model System for Trip Generation and Trip Chaining
Goulias, Konstadinos G.; KITAMURA, Ryuichi
1991-01-01
A model system is developed to describe both trip generation and trip chaining in a coherent manner. A recursive structure is adopted to represent the generation of trips for different purposes, and the number of trip chains is expressed as a function of the numbers of trips by purpose. The model system offers theoretically consistent coefficient values and quantifies the relationship between the number of trips and the number of trip chains, and can be used in the conventional forecasting pr...
Accelerated Recursion Formulas for Lucas Sequences%Lucas序列的加速递推公式
孙星怡; 孙智宏
2016-01-01
Let {Un(P,Q)} be the Lucas sequence given by U0 =0,U1 =1 and Un+1 =PUn-QUn-1(n≥1). In this paper, using an inversion formula due to Z H Sun, we obtain some combinatorial identities and acceler-ated recursion formulas for Un ( P,Q) .%设Lucas序列｛Un （ P，Q）｝由U0＝0，U1＝1和Un＋1＝PUn －QUn－1给出，利用孙智宏的一个反演公式得出一些组合恒等式与Un （ P，Q）的加速递推公式。
Lim, Jun-Seok; Pang, Hee-Suk
2016-01-01
In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.
D. Veestraeten
2015-01-01
Sums of the parabolic cylinder function for, in absolute value, growing half-integer and integer orders emerge in numerous fields such as time-series analysis, quantum optics and transmission in wireless channels. This paper derives recursion formulas for the parabolic cylinder function with integer
Fine tuning points of generating function construction for linear recursions
Yolcu, Bahar; Demiralp, Metin
2014-10-01
Recursions are quite important mathematical tools since many systems are mathematically modelled to ultimately take us to these equations because of their rather easy algebraic natures. They fit computer programming needs quite well in many circumstances to produce solutions. However, it is generally desired to find the asymptotic behaviour of the general term in the relevant sequence for convergence and therefore practicality issues. One of the general tendencies to find the general term asymptotic behaviour, when its ordering number grows unboundedly, is the integral representation over a generating function which does not depend on individual sequence elements. This is tried to be done almost for all types of recursions, even though the linear cases gain more importance than the others because they can be more effectively investigated by using many linear algebraic tools. Despite this may seem somehow to be rather trivial, there are a lot of theoretical fine tuning issues in the construction of true integral representations over true intervals on real axis or paths in complex domains. This work is devoted to focus on this issue starting from scratch for better understanding of the matter. The example cases are chosen to best illuminate the situations to get information for future generalization even though the work can be considered at somehow introductory level.
Yuan, Yan; Ding, Yi
2012-01-01
of the multi-state weighted k-out-of-n systems. The well known universal generating function (UGF) approach was also used as a counterpart to compare with the developed recursive algorithms, which is not very efficient. In this paper a transformation of the conventional UGF formula is proposed to develop a UGF......A multi-state k-out-of-n system model provides a flexible tool for evaluating vulnerability and reliability of critical infrastructures such as electric power systems. The multi-state weighted k-out-of-n system model is the generalization of the multi-state k-out-of-n system model, where...
Recursive inter-generational utility in global climate risk modeling
Minh, Ha-Duong [Centre International de Recherche sur l' Environnement et le Developpement (CIRED-CNRS), 75 - Paris (France); Treich, N. [Institut National de Recherches Agronomiques (INRA-LEERNA), 31 - Toulouse (France)
2003-07-01
This paper distinguishes relative risk aversion and resistance to inter-temporal substitution in climate risk modeling. Stochastic recursive preferences are introduced in a stylized numeric climate-economy model using preliminary IPCC 1998 scenarios. It shows that higher risk aversion increases the optimal carbon tax. Higher resistance to inter-temporal substitution alone has the same effect as increasing the discount rate, provided that the risk is not too large. We discuss implications of these findings for the debate upon discounting and sustainability under uncertainty. (author)
XU Jin
2016-01-01
In this paper, two recursion formulae of chromatic polynomial of a maximal planar graphG are obtained: whend(G)=4, let4vW be a 4-wheel ofG with wheel-centerv and wheel-cyclev1v2v3v4v1, then 1324(,4)((){,},4)((){,},4)fGfGvvvfGvvv=-+-oo; whend(G)=5, let5vW a 5-wheel ofG with wheel-centerv and wheel-cyclev1v2v3v4v5v1, then1114132231353(,4)[(,4)({,},4)][(,4)({,},4)][(,4)fGfGfGvvvvfGfGvvvvfG=-+-+UU314({},4)]fGvv-U,()125{,}G=G-vovv,()()224335{,}, {,}G=G-vovvG=G-vovv, where“o”denotes the operation of vertex contraction. Moreover, the application of the above formulae to the proof of Four-Color Conjecture is investigated. By using these formulae, the proof of Four-Color Conjecture boils down to the study on a special class of graphs, viz., 4-chromatic-funnel pseudo uniquely-4-colorable maximal planar graphs.
Recursive generation of one-loop amplitudes in the Standard Model
Actis, Stefano; Hofer, Lars; Scharf, Andreas; Uccirati, Sandro
2012-01-01
We introduce the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the Standard Model. Tree-level amplitudes are constructed using off-shell currents instead of Feynman diagrams as basic building blocks. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are calculated similarly to the tree-level amplitudes by recursive construction of loop off-shell currents. We introduce a novel algorithm for the treatment of colour, assigning a colour structure to each off-shell current which enables us to recursively construct the colour structure of the amplitude efficiently. Recola is interfaced with a tensor-integral library and provides complete one-loop Standard Model amplitudes including rational terms and counterterms. As a first application we consider Z+2jets production at the LHC and calculate with Recola the next-to-leading-order electroweak corrections to the dominant partonic channels.
递推公式定义的数列极限%Limit of a Sequence for the Recursion Formula
成凯歌
2016-01-01
极限论是高等数学的重要组成部分，数列极限作为一类重要的极限，不仅是极限论的先导，而且在经济和数学领域中发挥着重要的作用。求数列极限是极限问题的一个重要方面，其方法既复杂又多样，并且和数列的表达方式密切相关。通过对递推公式定义的数列的研究，得到了这类数列极限的计算方法。%The limit theory is one important part of higher mathematics.The limit of sequence,as one type of the core limits,is not only the forerunner of the limit theory, but also plays an important role in the field of economics and mathematics.The determination of the limit of sequence,as one important part of limit problem,is complex and diverse in its approaches,and closely related to the ways of expression of a sequence.After the study of the sequence defined by recursion formula,the method for calculating its limit is obtained.
Oliva, Paulo Borges
2002-01-01
Modified bar recursion is a variant of Spector's bar recursion which can be used to give a realizability interpretation of the classical axiom of dependent choice. This realizability allows for the extraction of witnesses from proofs of forall-exists-formulas in classical analysis. In this talk I...... shall report on results regarding the relationship between modified and Spector's bar recursion. I shall also show that a seemingly weak form of modified bar recursion is as strong as "full" modified bar recursion in higher types....
Jeffrey eWatumull
2014-01-01
Full Text Available It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauser, Chomsky, and Fitch’s (2002 articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language—the faculty of language in the narrow sense (FLN—is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded—existent or nonexistent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension; definition by induction (i.e., rules strongly generative of structure; and mathematical induction (i.e., rules for the principled—and potentially unbounded—expansion of strongly generated structure. By these necessary and sufficient criteria, the grammars of all natural
高焕江; 闫淑芳
2012-01-01
运用周期数列以及线性递推数列的相关知识,构造出一类特殊分式递推数列的通项公式。%Based on the knowledge of periodic sequence and linear recursive sequence,we get the general term formula of a kind of special fractional recursive sequence.
二维递归序列的渐近性%Asymptotics on Two-dimensional Recursion Sequences
乌云高娃; 王天明
2007-01-01
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.
z. talebi
2014-07-01
Full Text Available Digital image has special cryptography algorithms for its specific properties. A mathematics sequence in most image cryptography has been used for image scrambling. The used mathematics sequence has a recursive equation which it has some coefficients that changes of these coefficients can generate different sequences. Performance of this sequence in image cryptography is evaluated with different standard criteria. Due to complexity of system and no direct relation between the coefficient and evaluation criteria, selection of the suitable coefficient is not easily possible. In this article, by considering a general form of recursive equation and define a fitness function, the proper coefficients are calculated by genetic algorithm that satisfies the evaluation criteria. The experimental results show that recursive equation that is computed by the genetic algorithm has satisfactory performance from some schemes.
Gracios-Marin, C.A.; Nuno-de-la-Parra, P.; Vega-Lebrum, Carlos [Universidad Popular Autonoma del Estado de Puebla, 21 Sur 1103 Col, Puebla, Pue, 72220 Santiago (Mexico); Munoz-Hernandez, G.A.; Estevez-Carreon, J. [Instituto Tecnologico de Puebla, Av. Tecnologico 420. Col. Maravillas, Puebla, Pue (Mexico); Diaz-Sanchez, A. [INAOE. - Luis Enrique Erro. No. 1, Tonantzintla, Puebla (Mexico)
2009-07-15
A new decision feedback extension (DFE) and an alternative application to schedule industrial processes are presented. The DFE is defined as a recursive decision feedback extension (RDFE), where the recursive part is developed to assign the probability of occurrence in the operation of a set of machines working together using an objective function of production. The fundaments of fuzzy factors and the principle of maximum membership function are used to develop the new extension. At last, RDFE is proposed to generate a fuzzy scheduler, which is used to apply an intelligent control scheme to a hydropower station. (author)
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2015-01-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2016-02-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Cocks, Orrin G.
1976-01-01
The principle of mathematical induction is often too sophisticated to use in freshman and sophomore courses. The well-ordering principle can be used to prove theorems such as the formula for the sum of the first n positive integers. (SD)
Generating function formula of heat transfer in harmonic networks
Saito, Keiji; Dhar, Abhishek
2011-04-01
We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which NL are connected to a bath at temperature TL and NR are connected to a bath at temperature TR. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for NL≠NR and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.
Goodstein, R L
2010-01-01
Recursive analysis develops natural number computations into a framework appropriate for real numbers. This text is based upon primary recursive arithmetic and presents a unique combination of classical analysis and intuitional analysis. Written by a master in the field, it is suitable for graduate students of mathematics and computer science and can be read without a detailed knowledge of recursive arithmetic.Introductory chapters on recursive convergence and recursive and relative continuity are succeeded by explorations of recursive and relative differentiability, the relative integral, and
Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.
2002-01-01
The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the nonl
Feynman formulas for semigroups generated by an iterated Laplace operator
Buzinov, M. S.
2017-04-01
In the present paper, we find representations of a one-parameter semigroup generated by a finite sum of iterated Laplace operators and an additive perturbation (the potential). Such semigroups and the evolution equations corresponding to them find applications in the field of physics, chemistry, biology, and pattern recognition. The representations mentioned above are obtained in the form of Feynman formulas, i.e., in the form of a limit of multiple integrals as the multiplicity tends to infinity. The term "Feynman formula" was proposed by Smolyanov. Smolyanov's approach uses Chernoff's theorems. A simple form of representations thus obtained enables one to use them for numerical modeling the dynamics of the evolution system as a method for the approximation of solutions of equations. The problems considered in this note can be treated using the approach suggested by Remizov (see also the monograph of Smolyanov and Shavgulidze on path integrals). The representations (of semigroups) obtained in this way are more complicated than those given by the Feynman formulas; however, it is possible to bypass some analytical difficulties.
NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS
无
2001-01-01
An expose about covering method on differential equations was given. The general formulae to determine nonlocal symmetries were derived which are analogous to the prolongation formulae of generalized symmetries. In addition, a new definition of nonlocal recursion operators was proposed, which gave a satisfactory explalnation in covering theory for the integro-differcntial recursion operators.
On the Relation between Spector's Bar Recursion and Modified Bar Recursion
Oliva, Paulo Borges
2002-01-01
We introduce a variant of Spector's Bar Recursion in finite types to give a realizability interpretation of the classical axiom of dependent choice allowing for the extraction of witnesses from proofs of Sigma_1 formulas in classical analysis. We also give a bar recursive definition of the fan...... functional and study the relationship of our variant of Bar Recursion with others....
Roberts, Eric S
1986-01-01
Concentrating on the practical value of recursion, this text, the first of its kind, is essential to computer science students' education. In this text, students will learn the concept and programming applications of recursive thinking. This will ultimately prepare students for advanced topics in computer science such as compiler construction, formal language theory, and the mathematical foundations of computer science.
1/f{sup {alpha}} fractal noise generation from Gruenwald-Letnikov formula
Rodriguez, Eduardo [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F. 09340 (Mexico)], E-mail: rofe@xanum.uam.mx; Echeverria, Juan Carlos; Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F. 09340 (Mexico)
2009-01-30
This communication presents a recursive algorithm for generating streams of 1/f{sup {alpha}} fractal noise, by means of fractional integration/differentiation of a white noise signal. The quality of correlated and anticorrelated noise obtained by this approach is evaluated by applying detrended fluctuation analysis.
Chinea, Alejandro
2009-01-01
Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not only for being extremely complex information processing models, but also because of a computational expensive learning phase. The most popular training method for these models is back-propagation through the structure. This algorithm has been revealed not to be the most appropriate for structured processing due to problems of convergence, while more sophisticated training methods enhance the speed of convergence at the expense of increasing significantly the computational cost. In this paper, we firstly perform an analysis of the underlying principles behind these models aimed at understanding their computational power. Secondly, we propose an approximate second order stochastic learning algorithm. The proposed algorithm dynamically adapts the learning rate throughout the tra...
Kaneko, K
1998-01-01
Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for t...
Using Spreadsheets to Help Students Think Recursively
Webber, Robert P.
2012-01-01
Spreadsheets lend themselves naturally to recursive computations, since a formula can be defined as a function of one of more preceding cells. A hypothesized closed form for the "n"th term of a recursive sequence can be tested easily by using a spreadsheet to compute a large number of the terms. Similarly, a conjecture about the limit of a series…
Isaacson, Joel
2016-01-01
Recursive distinctioning (RD) is a name coined by Joel Isaacson in his original patent document describing how fundamental patterns of process arise from the systematic application of operations of distinction and description upon themselves. Recursive distinctioning means just what it says. A pattern of distinctions is given in a space based on a graphical structure (such as a line of print or a planar lattice or given graph). Each node of the graph is occupied by a letter from some arbitrary alphabet. A specialized alphabet is given that can indicate distinctions about neighbors of a given node. The neighbors of a node are all nodes that are connected to the given node by edges in the graph. The letters in the specialized alphabet (call it SA) are used to describe the states of the letters in the given graph and at each stage in the recursion, letters in SA are written at all nodes in the graph, describing its previous state. The recursive structure that results from the iteration of descriptions is called ...
RECURSIVE SYSTEM IDENTIFICATION
Han-Fu Chen
2009-01-01
Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive.This paper demonstrates the recent progress in recursive system identification.The recursive identifi-cation algorithms are presented not only for linear systems (multivariate ARMAX systems) but also for nonlinear systems such as the Hammerstein and Wiener systems, and the non-linear ARX systems.The estimates generated by the algorithms are online updated and converge a.s.to the true values as time tends to infinity.
Daya Sagar, B S
2010-02-01
Spatial interpolation is one of the demanding techniques in Geographic Information Science (GISci) to generate interpolated maps in a continuous manner by using two discrete spatial and/or temporal data sets. Noise-free data (thematic layers) depicting a specific theme at varied spatial or temporal resolutions consist of connected components either in aggregated or in disaggregated forms. This short paper provides a simple framework: 1) to categorize the connected components of layered sets of two different time instants through their spatial relationships and the Hausdorff distances between the companion-connected components and 2) to generate sequential maps (interpolations) between the discrete thematic maps. Development of the median set, using Hausdorff erosion and dilation distances to interpolate between temporal frames, is demonstrated on lake geometries mapped at two different times and also on the bubonic plague epidemic spread data available for 11 consecutive years. We documented the significantly fair quality of the median sets generated for epidemic data between alternative years by visually comparing the interpolated maps with actual maps. They can be used to visualize (animate) the spatiotemporal behavior of a specific theme in a continuous sequence.
Redox cycling and generation of reactive oxygen species in commercial infant formulas.
Boatright, William L; Crum, Andrea D
2016-04-01
Three nationally prominent commercial powdered infant formulas generated hydrogen peroxide, ranging from 10.46 to 11.62 μM, when prepared according to the manufacturer's instructions. Treating infant formulas with the chelating agent diethylene triamine pentaacetic acid (DTPA) significantly reduced H2O2 generation. In contrast, the addition of disodium ethylenediaminetetraacetic acid (EDTA) elevated the level of H2O2 generated in the same infant formulas by approximately 3- to 4-fold above the untreated infant formulas. The infant formulas contained ascorbate radicals ranging from about 138 nM to 40 nM. Treatment with catalase reduced the ascorbate radical contents by as much as 67%. Treatment with DTPA further reduced ascorbate radical signals to below quantifiable levels in most samples, further implicating the involvement of transition metal redox cycling in reactive oxygen species (ROS) formation. Supportive evidence of the generation of ROS is provided using luminol-enhanced luminescence (LEL) in both model mixtures of ascorbic acid and in commercial infant formulas.
Müller, Gert; Sacks, Gerald
1990-01-01
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
Thermodynamic formula for the cumulant generating function of time-averaged current.
Nemoto, Takahiro; Sasa, Shin-ichi
2011-12-01
The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under nonequilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.
Textbook examples of recursion
Knuth, Donald E
2008-01-01
We discuss properties of recursive schemas related to McCarthy's ``91 function'' and to Takeuchi's triple recursion. Several theorems are proposed as interesting candidates for machine verification, and some intriguing open questions are raised.
Generating and ranking of Dyck words
Kasa, Zoltan
2010-01-01
A new algorithm to generate all Dyck words is presented, which is used in ranking and unranking Dyck words. We emphasize the importance of using Dyck words in encoding objects related to Catalan numbers. As a consequence of formulas used in the ranking algorithm we can obtain a recursive formula for the nth Catalan number.
丁玖; 陈清祥
2007-01-01
Using the principle of the method of undetermined coefficients and the technique of upper triangular systems of linear algebraic equations, a simple and direct iterative numerical procedure was proposed to obtain particular solutions for various types of inhomogeneous elliptic partial differential equations. This procedure employs the power series expansion of both the source function of the partial differential equation and the solution, and the problem of finding a particular solution is equivalent to solving a triangular system of linear algebraic equations. In the special case of polynomial source functions, we are often led to solving a finite triangular system. To demonstrate the effectiveness of the proposed scheme, recursive formulas for some elliptic equations were developed. Coupled with existing boundary methods for solving boundary value problems of homogeneous equations, the proposed method can be used to solve various types of partial differential equations.%对某些具有多项式右端项的非齐次椭圆型偏微分方程,利用基于待定系数法原理而得到的一些直接迭代程式,就可以快速得到精确的多项式函数特解.我们对对流-反应方程、轴对称Poisson方程、轴对称Helmholtz型方程等给出了显式迭代公式,它们本质上等价于解对应的决定特解多项式系数的上三角型线性方程组.这些特解可用于工程上常用的"基本解方法"来数值求解有关的偏微分方程边值问题.
General Recursion and Formal Topology
Silvio Valentini
2010-12-01
Full Text Available It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.
Recursive Lexicographical Search
Iskhakov, Fedor; Rust, John; Schjerning, Bertel
2016-01-01
(MPE) of these games, much less all of them. We propose a fast and robust generalization of backward induction we call state recursion that operates on a decomposition of the overall DDG into a finite number of more tractable stage games, which can be solved recursively. We provide conditions under...... which state recursion finds at least one MPE of the overall DDG and introduce a recursive lexicographic search (RLS) algorithm that systematically and efficiently uses state recursion to find all MPE of the overall game in a finite number of steps. We apply RLS to find all MPE of a dynamic model...
Sirunyan, A M; Tumasyan, A; Adam, W; Asilar, E; Bergauer, T; Brandstetter, J; Brondolin, E; Dragicevic, M; Erö, J; Flechl, M; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; König, A; Krätschmer, I; Liko, D; Matsushita, T; Mikulec, I; Rabady, D; Rad, N; Rahbaran, B; Rohringer, H; Schieck, J; Strauss, J; Waltenberger, W; Wulz, C-E; Chekhovsky, V; Dvornikov, O; Dydyshka, Y; Emeliantchik, I; Litomin, A; Makarenko, V; Mossolov, V; Stefanovitch, R; Suarez Gonzalez, J; Zykunov, V; Shumeiko, N; Alderweireldt, S; De Wolf, E A; Janssen, X; Lauwers, J; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Abu Zeid, S; Blekman, F; D'Hondt, J; Daci, N; De Bruyn, I; Deroover, K; Lowette, S; Moortgat, S; Moreels, L; Olbrechts, A; Python, Q; Skovpen, K; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Parijs, I; Brun, H; Clerbaux, B; De Lentdecker, G; Delannoy, H; Fasanella, G; Favart, L; Goldouzian, R; Grebenyuk, A; Karapostoli, G; Lenzi, T; Léonard, A; Luetic, J; Maerschalk, T; Marinov, A; Randle-Conde, A; Seva, T; Vander Velde, C; Vanlaer, P; Vannerom, D; Yonamine, R; Zenoni, F; Zhang, F; Cimmino, A; Cornelis, T; Dobur, D; Fagot, A; Gul, M; Khvastunov, I; Poyraz, D; Salva, S; Schöfbeck, R; Tytgat, M; Van Driessche, W; Yazgan, E; Zaganidis, N; Bakhshiansohi, H; Beluffi, C; Bondu, O; Brochet, S; Bruno, G; Caudron, A; De Visscher, S; Delaere, C; Delcourt, M; Francois, B; Giammanco, A; Jafari, A; Komm, M; Krintiras, G; Lemaitre, V; Magitteri, A; Mertens, A; Musich, M; Piotrzkowski, K; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Wertz, S; Beliy, N; Aldá Júnior, W L; Alves, F L; Alves, G A; Brito, L; Hensel, C; Moraes, A; Pol, M E; Rebello Teles, P; Belchior Batista Das Chagas, E; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; Da Silveira, G G; De Jesus Damiao, D; De Oliveira Martins, C; De Souza, S Fonseca; Huertas Guativa, L M; Malbouisson, H; Matos Figueiredo, D; Mora Herrera, C; Mundim, L; Nogima, H; Prado Da Silva, W L; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Pereira, A Vilela; Ahuja, S; Bernardes, C A; Dogra, S; Fernandez Perez Tomei, T R; Gregores, E M; Mercadante, P G; Moon, C S; Novaes, S F; Padula, Sandra S; Romero Abad, D; Ruiz Vargas, J C; Aleksandrov, A; Hadjiiska, R; Iaydjiev, P; Rodozov, M; Stoykova, S; Sultanov, G; Vutova, M; Dimitrov, A; Glushkov, I; Litov, L; Pavlov, B; Petkov, P; Fang, W; Ahmad, M; Bian, J G; Chen, G M; Chen, H S; Chen, M; Chen, Y; Cheng, T; Jiang, C H; Leggat, D; Liu, Z; Romeo, F; Ruan, M; Shaheen, S M; Spiezia, A; Tao, J; Wang, C; Wang, Z; Zhang, H; Zhao, J; Ban, Y; Chen, G; Li, Q; Liu, S; Mao, Y; Qian, S J; Wang, D; Xu, Z; Avila, C; Cabrera, A; Chaparro Sierra, L F; Florez, C; Gomez, J P; González Hernández, C F; Ruiz Alvarez, J D; Sanabria, J C; Godinovic, N; Lelas, D; Puljak, I; Ribeiro Cipriano, P M; Sculac, T; Antunovic, Z; Kovac, M; Brigljevic, V; Ferencek, D; Kadija, K; Mesic, B; Susa, T; Attikis, A; Mavromanolakis, G; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Rykaczewski, H; Tsiakkouri, D; Finger, M; Finger, M; Carrera Jarrin, E; El-Khateeb, E; Elgammal, S; Mohamed, A; Kadastik, M; Perrini, L; Raidal, M; Tiko, A; Veelken, C; Eerola, P; Pekkanen, J; Voutilainen, M; Härkönen, J; Järvinen, T; Karimäki, V; Kinnunen, R; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Tuominiemi, J; Tuovinen, E; Wendland, L; Talvitie, J; Tuuva, T; Besancon, M; Couderc, F; Dejardin, M; Denegri, D; Fabbro, B; Faure, J L; Favaro, C; Ferri, F; Ganjour, S; Ghosh, S; Givernaud, A; Gras, P; de Monchenault, G Hamel; Jarry, P; Kucher, I; Locci, E; Machet, M; Malcles, J; Rander, J; Rosowsky, A; Titov, M; Abdulsalam, A; Antropov, I; Baffioni, S; Beaudette, F; Busson, P; Cadamuro, L; Chapon, E; Charlot, C; Davignon, O; de Cassagnac, R Granier; Jo, M; Lisniak, S; Miné, P; Nguyen, M; Ochando, C; Ortona, G; Paganini, P; Pigard, P; Regnard, S; Salerno, R; Sirois, Y; Strebler, T; Yilmaz, Y; Zabi, A; Zghiche, A; Agram, J-L; Andrea, J; Aubin, A; Bloch, D; Brom, J-M; Buttignol, M; Chabert, E C; Chanon, N; Collard, C; Conte, E; Coubez, X; Fontaine, J-C; Gelé, D; Goerlach, U; Jansová, M; Bihan, A-C Le; Van Hove, P; Gadrat, S; Beauceron, S; Bernet, C; Boudoul, G; Carrillo Montoya, C A; Chierici, R; Contardo, D; Courbon, B; Depasse, P; El Mamouni, H; Fan, J; Fay, J; Gascon, S; Gouzevitch, M; Grenier, G; Ille, B; Lagarde, F; Laktineh, I B; Lethuillier, M; Mirabito, L; Pequegnot, A L; Perries, S; Popov, A; Sabes, D; Sordini, V; Vander Donckt, M; Verdier, P; Viret, S; Toriashvili, T; Tsamalaidze, Z; Autermann, C; Beranek, S; Feld, L; Kiesel, M K; Klein, K; Lipinski, M; Preuten, M; Schomakers, C; Schulz, J; Verlage, T; Zhukov, V; Albert, A; Brodski, M; Dietz-Laursonn, E; Duchardt, D; Endres, M; Erdmann, M; Erdweg, S; Esch, T; Fischer, R
2017-01-01
Searches are presented for direct production of top or bottom squark pairs in proton-proton collisions at the CERN LHC. Two searches, based on complementary techniques, are performed in all-jet final states that are characterized by a significant imbalance in transverse momentum. An additional search requires the presence of a charged lepton isolated from other activity in the event. The data were collected in 2015 at a centre-of-mass energy of 13[Formula: see text] with the CMS detector and correspond to an integrated luminosity of 2.3[Formula: see text]. No statistically significant excess of events is found beyond the expected contribution from standard model processes. Exclusion limits are set in the context of simplified models of top or bottom squark pair production. Models with top and bottom squark masses up to 830 and 890[Formula: see text], respectively, are probed for light neutralinos. For models with top squark masses of 675[Formula: see text], neutralino masses up to 260[Formula: see text] are excluded at 95% confidence level.
Cumulant generating function formula of heat transfer in ballistic systems with lead-lead coupling
Li, Huanan; Agarwalla, Bijay Kumar; Wang, Jian-Sheng
2012-10-01
Based on a two-time observation protocol, we consider heat transfer in a given time interval tM in a lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using the nonequilibrium Green's function method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads, valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen fluctuation symmetry is explicitly verified. In addition, we briefly discuss Di Ventra's repartitioning trick regarding whether the repartitioning procedure of the total Hamiltonian affects the nonequilibrium steady-state current fluctuation. All kinds of properties of nonequilibrium current fluctuations, such as the fluctuation theorem in different time regimes, could be readily given according to these exact formulas.
A New Approach for Proving or Generating Combinatorial Identities
Gonzalez, Luis
2010-01-01
A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…
Recursions for statistical multiple alignment.
Hein, Jotun; Jensen, Jens Ledet; Pedersen, Christian N S
2003-12-09
Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne-Kishino-Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignment at nodes in a tree. Depending on whether the complete realization of this Markov chain is decomposed into the first transition and the rest of the realization or the last transition and the first part of the realization, two kinds of recursions are obtained that are computationally similar but probabilistically different. The running time of the algorithms is O(Pi id=1 Li), where Li is the length of the ith observed sequences and d is the number of sequences. An alternative recursion is also formulated that uses only a Markov chain involving the inner nodes of a tree.
Recursive Palindromic Smarandache Values
Earls, Jason
2005-01-01
In [1] Recursive Prime Numbers were studied and shown to be finite. This article deals with the same "recursive" topic, but applies the method to numbers whose Smarandache value, S(n), gives a palindromic number. Here, S(n) denotes the Smarandache function of least m such that n divides m!, and a palindrome is an integer that reads the same forwards and backwards (23432, for example). This sequence of recursive palindromic Smarandache values is shown to be finite...
On finitely recursive programs
Baselice, Sabrina; Criscuolo, Giovanni
2009-01-01
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable model semantics is highly undecidable. In this paper we prove that a larger class of programs, called finitely recursive programs, preserves most of the good properties of finitary programs under the stable model semantics, namely: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: We prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splittin...
Recursive quantum repeater networks
Van Meter, Rodney; Horsman, Clare
2011-01-01
Internet-scale quantum repeater networks will be heterogeneous in physical technology, repeater functionality, and management. The classical control necessary to use the network will therefore face similar issues as Internet data transmission. Many scalability and management problems that arose during the development of the Internet might have been solved in a more uniform fashion, improving flexibility and reducing redundant engineering effort. Quantum repeater network development is currently at the stage where we risk similar duplication when separate systems are combined. We propose a unifying framework that can be used with all existing repeater designs. We introduce the notion of a Quantum Recursive Network Architecture, developed from the emerging classical concept of 'recursive networks', extending recursive mechanisms from a focus on data forwarding to a more general distributed computing request framework. Recursion abstracts independent transit networks as single relay nodes, unifies software layer...
2013-01-01
There has been a recent spate of work on recursion as a central design feature of language. This short report points out that there is little evidence that unlimited recursion, understood as center-embedding, is typical of natural language syntax. Nevertheless, embedded pragmatic construals seem available in every language. Further, much deeper center-embedding can be found in dialogue or conversation structure than can be found in syntax. Existing accounts for the 'performance' limitations o...
Modification of the degree-day formula for diurnal meltwater generation and refreezing
Žaknić-Ćatović, Ana; Howard, Ken W. F.; Ćatović, Zlatko
2017-01-01
The standard degree-day, temperature-index approach to calculating snowmelt generation and refreezing (the SDD method) is convenient and popularly used but seriously miscalculates the volumes of water that change phase on days when temperatures fluctuate either side of the freezing point. Additionally, the SDD method does not provide any estimate of the duration of daily melting and refreezing events. A modified version of the standard formula is introduced (the MDD method) that overcomes such problems by removing dependence on a single temperature index (the average daily temperature estimated over a 24-h period beginning at midnight) and instead transfers reliance onto daily air temperature extremes (maximum and minimum temperatures) at known times of occurrence. In this way, the modified formula retains the simplicity of the standard approach while targeting those segments of the diurnal air temperature curve that directly relate to periods of melting and freezing. Newly introduced temperature and time degree-day parameters allow the duration of melting and refreezing events to be estimated. The MDD method was evaluated for two sites in the snow-belt region of Canada where the availability of hourly records of daily temperature allowed the required MDD input parameters to be calculated reliably and thus used for comparative purposes. During testing, the MDD input parameters were obtained from daily temperature extremes and their times of occurrence, using two alternative approaches to synthetic air temperature curve generation, one linear, the other trigonometric. Very good agreement was obtained in both cases and confirms the value of the MDD approach. However, there is no significant benefit to be gained by using air temperature approximating functions more complicated than the linear method for supplementing the missing continuous air temperature measurements. Finally, the MDD approach is not seen as a replacement for the regular SDD method, so much as tool
Recursive representation of Wronskians in confluent supersymmetric quantum mechanics
Contreras-Astorga, Alonso; Schulze-Halberg, Axel
2017-03-01
A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation.
Lowenthal, Francis
2010-11-01
This paper examines whether the recursive structure imbedded in some exercises used in the Non Verbal Communication Device (NVCD) approach is actually the factor that enables this approach to favor language acquisition and reacquisition in the case of children with cerebral lesions. For that a definition of the principle of recursion as it is used by logicians is presented. The two opposing approaches to the problem of language development are explained. For many authors such as Chomsky [1] the faculty of language is innate. This is known as the Standard Theory; the other researchers in this field, e.g. Bates and Elman [2], claim that language is entirely constructed by the young child: they thus speak of Language Acquisition. It is also shown that in both cases, a version of the principle of recursion is relevant for human language. The NVCD approach is defined and the results obtained in the domain of language while using this approach are presented: young subjects using this approach acquire a richer language structure or re-acquire such a structure in the case of cerebral lesions. Finally it is shown that exercises used in this framework imply the manipulation of recursive structures leading to regular grammars. It is thus hypothesized that language development could be favored using recursive structures with the young child. It could also be the case that the NVCD like exercises used with children lead to the elaboration of a regular language, as defined by Chomsky [3], which could be sufficient for language development but would not require full recursion. This double claim could reconcile Chomsky's approach with psychological observations made by adherents of the Language Acquisition approach, if it is confirmed by researches combining the use of NVCDs, psychometric methods and the use of Neural Networks. This paper thus suggests that a research group oriented towards this problematic should be organized.
Weighted Laplacians, cocycles and recursion relations
Krasnov, Kirill; Scarinci, Carlos
2013-11-01
Hodge's formula represents the gravitational MHV amplitude as the determinant of a minor of a certain matrix. When expanded, this determinant becomes a sum over weighted trees, which is the form of the MHV formula first obtained by Bern, Dixon, Perelstein, Rozowsky and rediscovered by Nguyen, Spradlin, Volovich and Wen. The gravity MHV amplitude satisfies the Britto, Cachazo, Feng and Witten recursion relation. The main building block of the MHV amplitude, the so-called half-soft function, satisfies a different, Berends-Giele-type recursion relation. We show that all these facts are illustrations to a more general story. We consider a weighted Laplacian for a complete graph of n vertices. The matrix tree theorem states that its diagonal minor determinants are all equal and given by a sum over spanning trees. We show that, for any choice of a cocycle on the graph, the minor determinants satisfy a Berends-Giele as well as Britto-Cachazo-Feng-Witten type recursion relation. Our proofs are purely combinatorial.
Generating matrix and sums of Fibonacci and Pell sequences
Ho, C. K.; Woon, H. S.; Chong, Chin-Yoon
2014-07-01
In this paper, we study the Fibonacci sequence and Pell sequence and developed generating matrices for them. First we proved two results on the even sum of the Fibonacci sequence and the Pell sequence, using the generating matrix approach. We then deduce the odd sums, some identities and recursive formulas for these two sequences.
2000-01-01
A method and an apparatus for recursive ultrasound imaging is presented. The method uses a Synthetic Transmit Aperture, but unlike previous approaches a new frame is created at every pulse emission. In receive, parallel beam forming is implemented. The beam formed RF data is added to the previously...
2000-01-01
A method and an apparatus for recursive ultrasound imaging is presented. The method uses a Synthetic Transmit Aperture, but unlike previous approaches a new frame is created at every pulse emission. In receive, parallel beam forming is implemented. The beam formed RF data is added to the previously...
Recursive Programming: A Clarification
Hove d'Ertsenryck, G.M.C. van den
2012-01-01
We show that the block concept, as it was introduced in ALGOL 60, and two of the three main techniques introduced by E. W. Dijkstra in his seminal article Recursive Programming to implement it, the so-called "static links" and "display", have been partly misunderstood. These misunderstandings may ha
Relatively Recursive Rational Choice.
1981-11-01
Rogers [19671, Ch.IX, pp.127-134 . tCf. Ch. 13 of Rogers [19671. **Gerald E. Sacks, Degrees of Unsolvability, Annals of Mathematics No. 55, Princeton...265. CI -17- References Kleene, Stephen Cole, and Enil L. Post [19541, "The Upper Semi-Lattice of Degrees of Recursive Unsolvability", Annals of Mathematics , Vol
Recursive Advice for Coordination
Terepeta, Michal Tomasz; Nielson, Hanne Riis; Nielson, Flemming
2012-01-01
makes analyzing such languages more difficult due to the fact that aspects can be recursive - advice from an aspect must itself be analyzed by aspects - as well as being simultaneously applicable in concurrent threads. Therefore the problem of reachability of various states of a system becomes much more...
An update of the generator of atmospheric muons from parametric formulas (MUPAGE)
Bazzotti, M.; Carminati, G.; Margiotta, A.; Spurio, M.
2010-04-01
We present a new version of the fast generator of atmospheric muons based on parametric formulas (MUPAGE). The parameterization of the deep sea muon flux relies on a primary Cosmic Ray flux and interaction model able to correctly reproduce the flux, the multiplicity distribution, the spatial distance between muons as measured by the underground MACRO experiment [1]. MUPAGE produces the event kinematics of the muon bundle on the surface of a user-defined cylinder, surrounding the virtual detector. The new version improves the possibility to select the total energy of the muons bundle, and the choice of a virtual cylinder of any dimensions. New version program summaryProgram title: MUPAGE Catalogue identifier: AEBT_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBT_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3421 No. of bytes in distributed program, including test data, etc.: 59 308 Distribution format: tar.gz Programming language: C++ Computer: The code has been developed and tested on Pentium M, 2.0 GHz; 2x Intel Xeon Quad Core, 2.33 GHz. Operating system: Scientific Linux 3.x; 4.x; 5.x; Slackware 12.0.0. RAM: 50 MB Supplementary material: The table mentioned in the "Summary of revisions" section, can be obtained here. Classification: 1.1, 11.3 External routines: ROOT ( http://root.cern.ch) Catalogue identifier of previous version: AEBT_v1_0 Journal reference of previous version: Comput. Phys. Comm. 179 (2008) 915 Does the new version supersede the previous version?: Yes Nature of problem: Fast simulation of atmospheric muon bundles for underwater/ice neutrino telescopes. Solution method: Atmospheric muon events are generated according to parametric formulas [2] giving the flux, the multiplicity, the radial distribution and the energy spectrum
Elimination and recursions in the scattering equations
Carlos Cardona
2016-05-01
Full Text Available We use the elimination theory to explicitly construct the (n−3! order polynomial in one of the variables of the scattering equations. The answer can be given either in terms of a determinant of Sylvester type of dimension (n−3! or a determinant of Bézout type of dimension (n−4!. We present a recursive formula for the Sylvester determinant. Expansion of the determinants yields expressions in terms of Plücker coordinates. Elimination of the rest of the variables of the scattering equations is also presented.
Stable Recursive Subhomogeneous Algebras
Liang, Hutian
2011-01-01
In this paper, we introduce stable recursive subhomogeneous algebras (SRSHAs), which is analogous to recursive subhomogeneous algebras (RSHAs) introduced by N. C. Phillips in the studies of free minimal integer actions on compact metric spaces. The difference between the stable version and the none stable version is that the irreducible representations of SRSHAs are infinite dimensional, but the irreducible representations of the RSHAs are finite dimensional. While RSHAs play an important role in the study of free minimal integer actions on compact metric spaces, SRSHAs play an analogous role in the study of free minimal actions by the group of the real numbers on compact metric spaces. In this paper, we show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and non-vanishing have topological stable rank one.
The spectral curve of the Eynard-Orantin recursion via the Laplace transform
Dumitrescu, Olivia; Safnuk, Brad; Sorkin, Adam
2012-01-01
The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of the original counting problem. We examine this construction using four concrete examples: Grothendieck's dessins d'enfants (or higher-genus analogue of the Catalan numbers), the intersection numbers of tautological cotangent classes on the moduli stack of stable pointed curves, single Hurwitz numbers, and the stationary Gromov-Witten invariants of the complex projective line.
Recursion theory for metamathematics
Smullyan, Raymond M
1993-01-01
This work is a sequel to the author''s Godel''s Incompleteness Theorems, though it can be read independently by anyone familiar with Godel''s incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
1981-11-01
Systems, Annals of Mathematics Studies, No.47, -10- Princeton University Press, [1961], finitary objects and discretized procedures, for the...Ph.D. Thesis, Yeshiva University. Church, Alonzo [1941], The Calculus of Lamda-Conversion, Annals of Mathematics Studies, No.6, Princeton University...Post, Emil L., and Stephen Cole Kleene, [1954], "The Upper Semi-Lattice of Degrees of Recursive Unsolvability", Annals of Mathematics , Vol.59, pp.379
The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion
Yi OUYANG
2007-01-01
Let (u)z be the universal norm distribution and M a fixed power of prime p. By using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurring in the canonical basis in the cohomology group H0(Gz,(u)z/M(u)z). We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in the theory of Euler systems. One certainly hopes this could lead to a new way to find new Euler systems.
A Construction of Ramsey Graph of R(4,5)by the Method of Recursive Generation%拉姆齐图R(4,5)的递阶生成
斯勤夫; 段禅伦
2004-01-01
对于已知经典的拉姆齐数,其对应的拉姆齐图R(3,3),R(3,4)R(3,5),R(3,6),R(3,7),R(3,8)和R(3,9)均可递阶生成.给出了一个通过R(4,4)图递阶生成的一个R(4,5)拉姆齐图,证明了R(4,5)≥25.同时发现修改所构造的R(4,5)图的10条拉姆齐临界边,该图将变为经典10-正则的R(4,5)图.%For the known classic Ramsey numbers,the Ramsey graphs of R(3,3),R(3,4),R(3,5),R(3,6),R(3,7) and R(3,8) can be constructed by the method of recursive generation.A construction of Ramsey graphs R(4,5) by the method of recursive generation is given and R(4,5) 25 is proved.Some critical edges are found in the graph,by changing the color of some critical edges,the Ramsey graph of R(4,5) will turn into a 10-regular symmetric cyclic Ramsey graph of R(4,5).
Matone, Marco
2016-11-01
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp (X) exp (Y)=exp (W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp (X) exp (Y) exp (Z)=exp (W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper.
Matone, Marco [Universita di Padova, Dipartimento di Fisica e Astronomia ' ' G. Galilei' ' , Padua (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padua (Italy)
2016-11-15
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp(X) exp(Y) = exp(W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp(X) exp(Y) exp(Z) = exp(W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper. (orig.)
Li, Huanan
2013-03-01
Based on a two-time observation protocol, we consider heat transfer in a given time interval tM in a lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using the nonequilibrium Green's function method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads, valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen fluctuation symmetry is explicitly verified. In addition, we briefly discuss Di Ventra's repartitioning trick regarding whether the repartitioning procedure of the total Hamiltonian affects the nonequilibrium steady-state current fluctuation. All kinds of properties of nonequilibrium current fluctuations, such as the fluctuation theorem in different time regimes, could be readily given according to these exact formulas. Finally a practical formalism dealing with cumulants of heat transfer across general nonlinear quantum systems is established based on field theoretical/algebraic method.
Recursively determined representing measures for bivariate truncated moment sequences
Curto, Raul E
2012-01-01
A theorem of Bayer and Teichmann implies that if a finite real multisequence \\beta = \\beta^(2d) has a representing measure, then the associated moment matrix M_d admits positive, recursively generated moment matrix extensions M_(d+1), M_(d+2),... For a bivariate recursively determinate M_d, we show that the existence of positive, recursively generated extensions M_(d+1),...,M_(2d-1) is sufficient for a measure. Examples illustrate that all of these extensions may be required to show that \\beta has a measure. We describe in detail a constructive procedure for determining whether such extensions exist. Under mild additional hypotheses, we show that M_d admits an extension M_(d+1) which has many of the properties of a positive, recursively generated extension.
Recursive processing of cyclic graphs.
Bianchini, Monica; Gori, Marco; Sarti, Lorenzo; Scarselli, Franco
2006-01-01
Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.
Recursive principal components analysis.
Voegtlin, Thomas
2005-10-01
A recurrent linear network can be trained with Oja's constrained Hebbian learning rule. As a result, the network learns to represent the temporal context associated to its input sequence. The operation performed by the network is a generalization of Principal Components Analysis (PCA) to time-series, called Recursive PCA. The representations learned by the network are adapted to the temporal statistics of the input. Moreover, sequences stored in the network may be retrieved explicitly, in the reverse order of presentation, thus providing a straight-forward neural implementation of a logical stack.
Recursive Concurrent Stochastic Games
Etessami, Kousha
2008-01-01
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [16,17] to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \\epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \\epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy r...
Explicit Formulae for the Continued Fraction Convergents of "Square Root of D"
Braza, Peter A.
2010-01-01
The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.
Recursive Polynomial Remainder Sequence and its Subresultants
Terui, Akira
2008-01-01
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial polynomials, a sequence of PRSs calculated "recursively" for the GCD and its derivative until a constant is derived, and recursive subresultants are defined by determinants representing the coefficients in recursive PRS as functions of coefficients of init...
Subresultants in Recursive Polynomial Remainder Sequence
Terui, Akira
2008-01-01
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate "recursively" with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresultants to be determinants representing the coefficients in recursive PRS by coefficients of initial po...
Lambda calculus with explicit recursion
Z.M. Ariola (Zena); J.W. Klop (Jan Willem)
1996-01-01
textabstractThis paper is concerned with the study of $lambda$-calculus with explicit recursion, namely of cyclic $lambda$-graphs. The starting point is to treat a $lambda$-graph as a system of recursion equations involving $lambda$-terms, and to manipulate such systems in an unrestricted manner,
Non-recursive expressions for even-index Bernoulli numbers: A remarkable sequence of determinants
Van Malderen, Renaat
2005-01-01
Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives explicit formulas for Bernoulli numbers of even index. The formulas contain a remarkable sequence of determinants. The value of these determinants for variable dimension is investigated.
Geometric Modelling by Recursively Cutting Vertices
吕伟; 梁友栋; 等
1989-01-01
In this paper,a new method for curve and surface modelling is introduced which generates curves and surfaces by recursively cutting and grinding polygons and polyhedra.It is a generalization of the existing corner-cutting methods.A lot of properties,such as geometric continuity,representation,shape-preserving,and the algorithm are studied which show that such curves and surfaces are suitable for geometric designs in CAD,computer graphics and their application fields.
Type Inference for Guarded Recursive Data Types
Stuckey, Peter J.; Sulzmann, Martin
2005-01-01
We consider type inference for guarded recursive data types (GRDTs) -- a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference. Inference is incomplete because the set of type constraints allowed to appear in the type system is only a subset of those type constraints generated by type inference. Hence, inference only succeeds if the program is sufficiently type annotated. We present refin...
Recursive Construction of Operator Product Expansion Coefficients
Holland, Jan; Hollands, Stefan
2015-06-01
We derive a novel formula for the derivative of operator product expansion (OPE) coefficients with respect to a coupling constant. The formula involves just the OPE coefficients themselves but no further input, and is in this sense self-consistent. Furthermore, unlike other formal identities of this general nature in quantum field theory (such as the formal expression for the Lagrangian perturbation of a correlation function), our formula requires no further UV-renormalization, i.e., it is completely well-defined from the start. This feature is a result of a cancelation of UV- and IR-divergences between various terms in our identity. Our proof, and an analysis of the features of the identity, is given for the example of massive, Euclidean theory in 4 dimensional Euclidean space. It relies on the renormalization group flow equation method and is valid to arbitrary, but finite orders in perturbation theory. The final formula, however, makes neither explicit reference to the renormalization group flow, nor to perturbation theory, and we conjecture that it also holds non-perturbatively. Our identity can be applied constructively because it gives a novel recursive algorithm for the computation of OPE coefficients to arbitrary (finite) perturbation order in terms of the zeroth order coefficients corresponding to the underlying free field theory, which in turn are trivial to obtain. We briefly illustrate the relation of this method to more standard methods for computing the OPE in some simple examples.
Ollongren, Alexander
2011-02-01
In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, the present author has discussed various significant requirements such a lingua should satisfy. The author's Lingua Cosmica is a (meta) system for annotating contents of possibly large-scale messages for ETI. LINCOS, based on formal constructive logic, was primarily designed for dealing with logic contents of messages but is also applicable for denoting structural properties of more general abstractions embedded in such messages. The present paper explains ways and means for achieving this for a special case: recursive entities. As usual two stages are involved: first the domain of discourse is enriched with suitable representations of the entities concerned, after which properties over them can be dealt with within the system itself. As a representative example the case of Russian dolls (Matrjoshka's) is discussed in some detail and relations with linguistic structures in natural languages are briefly exploited.
Linear recursive distributed representations.
Voegtlin, Thomas; Dominey, Peter F
2005-09-01
Connectionist networks have been criticized for their inability to represent complex structures with systematicity. That is, while they can be trained to represent and manipulate complex objects made of several constituents, they generally fail to generalize to novel combinations of the same constituents. This paper presents a modification of Pollack's Recursive Auto-Associative Memory (RAAM), that addresses this criticism. The network uses linear units and is trained with Oja's rule, in which it generalizes PCA to tree-structured data. Learned representations may be linearly combined, in order to represent new complex structures. This results in unprecedented generalization capabilities. Capacity is orders of magnitude higher than that of a RAAM trained with back-propagation. Moreover, regularities of the training set are preserved in the new formed objects. The formation of new structures displays developmental effects similar to those observed in children when learning to generalize about the argument structure of verbs.
Generating q-Commutator Identities and the q-BCH Formula
Andrea Bonfiglioli
2016-01-01
Full Text Available Motivated by the physical applications of q-calculus and of q-deformations, the aim of this paper is twofold. Firstly, we prove the q-deformed analogue of the celebrated theorem by Baker, Campbell, and Hausdorff for the product of two exponentials. We deal with the q-exponential function expq(x=∑n=0∞(xn/[n]q!, where [n]q=1+q+⋯+qn-1 denotes, as usual, the nth q-integer. We prove that if x and y are any noncommuting indeterminates, then expq(xexpq(y=expq(x+y+∑n=2∞Qn(x,y, where Qn(x,y is a sum of iterated q-commutators of x and y (on the right and on the left, possibly, where the q-commutator [y,x]q≔yx-qxy has always the innermost position. When [y,x]q=0, this expansion is consistent with the known result by Schützenberger-Cigler: expq(xexpq(y=expq(x+y. Our result improves and clarifies some existing results in the literature. Secondly, we provide an algorithmic procedure for obtaining identities between iterated q-commutators (of any length of x and y. These results can be used to obtain simplified presentation for the summands of the q-deformed Baker-Campbell-Hausdorff Formula.
On Fusing Recursive Traversals of K-d Trees
Rajbhandari, Samyam; Kim, Jinsung; Krishnamoorthy, Sriram; Pouchet, Louis-Noel; Rastello, Fabrice; Harrison, Robert J.; Sadayappan, Ponnuswamy
2016-03-17
Loop fusion is a key program transformation for data locality optimization that is implemented in production compilers. But optimizing compilers currently cannot exploit fusion opportunities across a set of recursive tree traversal computations with producer-consumer relationships. In this paper, we develop a compile-time approach to dependence characterization and program transformation to enable fusion across recursively specified traversals over k-ary trees. We present the FuseT source-to-source code transformation framework to automatically generate fused composite recursive operators from an input program containing a sequence of primitive recursive operators. We use our framework to implement fused operators for MADNESS, Multiresolution Adaptive Numerical Environment for Scientific Simulation. We show that locality optimization through fusion can offer more than an order of magnitude performance improvement.
Recursion as a Human Universal and as a Primitive
Boban Arsenijevic
2010-09-01
Full Text Available This contribution asks, in an empirical rather than formal perspective, whether a range of descriptive phenomena in grammar usually characterized in terms of ‘recursion’ actually exhibit recursion. It is concluded that empirical evidence does not support this customary assumption. Language, while formally recursive, need not be recursive in the underlying generative mechanisms of its grammar. Hence, while recursion may well be one of the hallmarks of human nature, grammar may not be the cognitive domain where it is found. Arguments for this claim are briefly exposed and then discussed with respect to a selection of talks from the DGfS workshop on Foundations of Language Comparison: Human Universals as Constraints on Language Diversity that led to this special issue.
Compact QED tree-level amplitudes from dressed BCFW recursion relations
Badger, Simon D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Henn, Johannes M. [Humboldt Univ., Berlin (Germany). Inst. fuer Physik
2010-05-15
We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N{sup 2}MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial. (orig.)
Topological recursion and mirror curves
Bouchard, Vincent
2012-01-01
We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov-Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the "remodeling conjecture" to the full free energies, including the constant contributions. In the process we study how the pair of pants decomposition of the mirror curves plays an important role in the topological recursion. We also show that the free energies are not, strictly speaking, symplectic invariants, and that the recursive construction of the free energies does not commute with certain limits of mirror curves.
Recursive Algorithm For Linear Regression
Varanasi, S. V.
1988-01-01
Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.
Maire, Murielle; Rega, Barbara; Cuvelier, Marie-Elisabeth; Soto, Paola; Giampaoli, Pierre
2013-12-15
This paper investigates the effect of ingredients on the reactions occurring during the making of sponge cake and leading to the generation of volatile compounds related to flavour quality. To obtain systems sensitive to lipid oxidation (LO), a formulation design was applied varying the composition of fatty matter and eggs. Oxidation of polyunsaturated fatty acids (PUFA) and formation of related volatile compounds were followed at the different steps of cake-making. Optimised dynamic Solid Phase Micro Extraction was applied to selectively extract either volatile or semi-volatile compounds directly from the baking vapours. We show for the first time that in the case of alveolar baked products, lipid oxidation occurs very early during the step of dough preparation and to a minor extent during the baking process. The generation of lipid oxidation compounds depends on PUFA content and on the presence of endogenous antioxidants in the raw matter. Egg yolk seemed to play a double role on reactivity: protecting unsaturated lipids from oxidation and being necessary to generate a broad class of compounds of the Maillard reaction during baking and linked to the typical flavour of sponge cake.
Features and Recursive Structure
Kuniya Nasukawa
2015-01-01
Full Text Available Based on the cross-linguistic tendency that weak vowels are realized with a central quality such as ə, ɨ, or ɯ, this paper attempts to account for this choice by proposing that the nucleus itself is one of the three monovalent vowel elements |A|, |I| and |U| which function as the building blocks of melodic structure. I claim that individual languages make a parametric choice to determine which of the three elements functions as the head of a nuclear expression. In addition, I show that elements can be freely concatenated to create melodic compounds. The resulting phonetic value of an element compound is determined by the specific elements it contains and by the head-dependency relations between those elements. This concatenation-based recursive mechanism of melodic structure can also be extended to levels above the segment, thus ultimately eliminating the need for syllabic constituents. This approach reinterprets the notion of minimalism in phonology by opposing the string-based flat structure.
Consciousness as recursive, spatiotemporal self-location.
Peters, Frederic
2010-07-01
At the phenomenal level, consciousness arises in a consistently coherent fashion as a singular, unified field of recursive self-awareness (subjectivity) with explicitly orientational characteristics--that of a subject located both spatially and temporally in an egocentrically-extended domain. Understanding these twin elements of consciousness begins with the recognition that ultimately (and most primitively), cognitive systems serve the biological self-regulatory regime in which they subsist. The psychological structures supporting self-located subjectivity involve an evolutionary elaboration of the two basic elements necessary for extending self-regulation into behavioral interaction with the environment: an orientative reference frame which consistently structures ongoing interaction in terms of controllable spatiotemporal parameters, and processing architecture that relates behavior to homeostatic needs via feedback. Over time, constant evolutionary pressures for energy efficiency have encouraged the emergence of anticipative feedforward processing mechanisms, and the elaboration, at the apex of the sensorimotor processing hierarchy, of self-activating, highly attenuated recursively-feedforward circuitry processing the basic orientational schema independent of external action output. As the primary reference frame of active waking cognition, this recursive self-locational schema processing generates a zone of subjective self-awareness in terms of which it feels like something to be oneself here and now. This is consciousness-as-subjectivity.
Explicit formula for the generating series of diagonal 3D rook paths
Bostan, Alin; van Hoeij, Mark; Pech, Lucien
2011-01-01
Let $a_n$ denote the number of ways in which a chess rook can move from a corner cell to the opposite corner cell of an $n \\times n \\times n$ three-dimensional chessboard, assuming that the piece moves closer to the goal cell at each step. We describe the computer-driven \\emph{discovery and proof} of the fact that the generating series $G(x)= \\sum_{n \\geq 0} a_n x^n$ admits the following explicit expression in terms of a Gaussian hypergeometric function: [G(x) = 1 + 6 \\cdot \\int_0^x \\frac{\\,\\pFq21{1/3}{2/3}{2} {\\frac{27 w(2-3w)}{(1-4w)^3}}}{(1-4w)(1-64w)} \\, dw.
Genome-wide identification of zero nucleotide recursive splicing in Drosophila.
Duff, Michael O; Olson, Sara; Wei, Xintao; Garrett, Sandra C; Osman, Ahmad; Bolisetty, Mohan; Plocik, Alex; Celniker, Susan E; Graveley, Brenton R
2015-05-21
Recursive splicing is a process in which large introns are removed in multiple steps by re-splicing at ratchet points--5' splice sites recreated after splicing. Recursive splicing was first identified in the Drosophila Ultrabithorax (Ubx) gene and only three additional Drosophila genes have since been experimentally shown to undergo recursive splicing. Here we identify 197 zero nucleotide exon ratchet points in 130 introns of 115 Drosophila genes from total RNA sequencing data generated from developmental time points, dissected tissues and cultured cells. The sequential nature of recursive splicing was confirmed by identification of lariat introns generated by splicing to and from the ratchet points. We also show that recursive splicing is a constitutive process, that depletion of U2AF inhibits recursive splicing, and that the sequence and function of ratchet points are evolutionarily conserved in Drosophila. Finally, we identify four recursively spliced human genes, one of which is also recursively spliced in Drosophila. Together, these results indicate that recursive splicing is commonly used in Drosophila, occurs in humans, and provides insight into the mechanisms by which some large introns are removed.
Paradoxical intention and recursive anxiety.
Ascher, L M; Schotte, D E
1999-06-01
The present study was designed to investigate a possible relationship between "recursive anxiety" and paradoxical intention. Groups of subjects were chosen from among individuals with public speaking concerns. and for whom fear of fear or recursive anxiety clearly represented an important element, or was completely absent from the clinical profile. These subjects were offered a standard in vivo treatment program for public speaking phobia with inclusion or exclusion of paradoxical intention. A 2 x 2 factorial design was employed. Those whose public speaking anxiety was complicated by recursive anxiety experienced greater improvement when paradoxical intention was included in the treatment program than when it was not employed. In contrast, individuals reporting simple public speaking phobia demonstrated greater success with a treatment program in which paradoxical intention was absent. Wegner's hypothesis of "ironic" cognitive processing was used to explain the proposed relationship between paradoxical intention and fear of fear.
Recursion Relations for Conformal Blocks
Penedones, João; Yamazaki, Masahito
2016-09-12
In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\\Delta$ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.
The language intersection problem for non-recursive context-free grammars
Nederhof, M.J.; Satta, G
2004-01-01
We prove that, given as input two context-free grammars, deciding non-emptiness of intersection of the two generated languages is PSPACE-complete if at least one grammar is non-recursive. The problem remains PSPACE-complete when both grammars are non-recursive and deterministic. Also investigated ar
Recursive-operator method in vibration problems for rod systems
Rozhkova, E. V.
2009-12-01
Using linear differential equations with constant coefficients describing one-dimensional dynamical processes as an example, we show that the solutions of these equations and systems are related to the solution of the corresponding numerical recursion relations and one does not have to compute the roots of the corresponding characteristic equations. The arbitrary functions occurring in the general solution of the homogeneous equations are determined by the initial and boundary conditions or are chosen from various classes of analytic functions. The solutions of the inhomogeneous equations are constructed in the form of integro-differential series acting on the right-hand side of the equation, and the coefficients of the series are determined from the same recursion relations. The convergence of formal solutions as series of a more general recursive-operator construction was proved in [1]. In the special case where the solutions of the equation can be represented in separated variables, the power series can be effectively summed, i.e., expressed in terms of elementary functions, and coincide with the known solutions. In this case, to determine the natural vibration frequencies, one obtains algebraic rather than transcendental equations, which permits exactly determining the imaginary and complex roots of these equations without using the graphic method [2, pp. 448-449]. The correctness of the obtained formulas (differentiation formulas, explicit expressions for the series coefficients, etc.) can be verified directly by appropriate substitutions; therefore, we do not prove them here.
Recursive Definitions of Monadic Functions
Alexander Krauss
2010-12-01
Full Text Available Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.
Recursive Definitions of Monadic Functions
Krauss, Alexander
2010-01-01
Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.
A recursive algorithm for Zernike polynomials
Davenport, J. W.
1982-01-01
The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.
Huttel, Hans; Srba, Jiri
2004-01-01
This paper introduces a process calculus with recursion which allows us to express an unbounded number of runs of the ping-pong protocols introduced by Dolev and Yao. We study the decidability issues associated with two common approaches to checking security properties, namely reachability analys...
Haydock's recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-01
Haydock's recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber's quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock's recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials {pn(E) } in energy variable E. The polynomials {pn(E) } are orthonormal with respect to the density of states n0(E) and energy eigenstate | E > is the generating function of {pn(E) } . The generality of Haydock's recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
InfoVis Interaction Techniques in Animation of Recursive Programs
Antonio Pérez-Carrasco
2010-02-01
Full Text Available Algorithm animations typically assist in educational tasks aimed simply at achieving understanding. Potentially, animations could assist in higher levels of cognition, such as the analysis level, but they usually fail in providing this support because they are not flexible or comprehensive enough. In particular, animations of recursion provided by educational systems hardly support the analysis of recursive algorithms. Here we show how to provide full support to the analysis of recursive algorithms. From a technical point of view, animations are enriched with interaction techniques inspired by the information visualization (InfoVis field. Interaction tasks are presented in seven categories, and deal with both static visualizations and dynamic animations. All of these features are implemented in the SRec system, and visualizations generated by SRec are used to illustrate the article.
Virasoro Constraints and Topological Recursion for Grothendieck's Dessin Counting
Kazarian, Maxim; Zograf, Peter
2015-08-01
We compute the number of coverings of with a given monodromy type over and given numbers of preimages of 0 and 1. We show that the generating function for these numbers enjoys several remarkable integrability properties: it obeys the Virasoro constraints, an evolution equation, the KP (Kadomtsev-Petviashvili) hierarchy and satisfies a topological recursion in the sense of Eynard-Orantin.
Martins, Mauricio Dias; Gingras, Bruno; Puig-Waldmueller, Estela; Fitch, W Tecumseh
2017-04-01
The human ability to process hierarchical structures has been a longstanding research topic. However, the nature of the cognitive machinery underlying this faculty remains controversial. Recursion, the ability to embed structures within structures of the same kind, has been proposed as a key component of our ability to parse and generate complex hierarchies. Here, we investigated the cognitive representation of both recursive and iterative processes in the auditory domain. The experiment used a two-alternative forced-choice paradigm: participants were exposed to three-step processes in which pure-tone sequences were built either through recursive or iterative processes, and had to choose the correct completion. Foils were constructed according to generative processes that did not match the previous steps. Both musicians and non-musicians were able to represent recursion in the auditory domain, although musicians performed better. We also observed that general 'musical' aptitudes played a role in both recursion and iteration, although the influence of musical training was somehow independent from melodic memory. Moreover, unlike iteration, recursion in audition was well correlated with its non-auditory (recursive) analogues in the visual and action sequencing domains. These results suggest that the cognitive machinery involved in establishing recursive representations is domain-general, even though this machinery requires access to information resulting from domain-specific processes. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.
TRANSIENT QUEUE SIZE DISTRIBUTION SOLUTION OF GEOM/G/1 QUEUE WITH FEEDBACK-A RECURSIVE METHOD
Chuanyi LUO; Yinghui TANG; Cailiang LI
2009-01-01
This paper considers the Geom/G/1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state N(0+) = I. Some new results about the recursive expression of the transient queue size distribution at any epoch n+ and the recursive formulae of the equilibrium distribution are obtained, Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n-, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M/G/1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network.
Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA
Conradie, Willem; Goranko, Valentin; Vakarelov, Dimiter
2010-01-01
The previously introduced algorithm SQEMA computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend SQEMA with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of m...
Recursive neural network rule extraction for data with mixed attributes.
Setiono, R; Baesens, B; Mues, C
2008-02-01
In this paper, we present a recursive algorithm for extracting classification rules from feedforward neural networks (NNs) that have been trained on data sets having both discrete and continuous attributes. The novelty of this algorithm lies in the conditions of the extracted rules: the rule conditions involving discrete attributes are disjoint from those involving continuous attributes. The algorithm starts by first generating rules with discrete attributes only to explain the classification process of the NN. If the accuracy of a rule with only discrete attributes is not satisfactory, the algorithm refines this rule by recursively generating more rules with discrete attributes not already present in the rule condition, or by generating a hyperplane involving only the continuous attributes. We show that for three real-life credit scoring data sets, the algorithm generates rules that are not only more accurate but also more comprehensible than those generated by other NN rule extraction methods.
Recursive simulation of quantum annealing
Sowa, A P; Samson, J H; Savel'ev, S E; Zagoskin, A M; Heidel, S; Zúñiga-Anaya, J C
2015-01-01
The evaluation of the performance of adiabatic annealers is hindered by lack of efficient algorithms for simulating their behaviour. We exploit the analyticity of the standard model for the adiabatic quantum process to develop an efficient recursive method for its numerical simulation in case of both unitary and non-unitary evolution. Numerical simulations show distinctly different distributions for the most important figure of merit of adiabatic quantum computing --- the success probability --- in these two cases.
Conrad, Florian
2011-01-01
An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.
Astrup Jensen, Bjarne
Makeham's formula is an actuarial formula expressing the present value of a payment stream in terms of its repayments instead of the payments themselves. The formula is largely neglected in the finance literature, but -- as this paper shows -- it has a number of useful applications in fixed income...... analysis. We use Makeham's formula to decompose the return on a bond investment into interest payments, realized capital gains and accrued capital gains for a variety of accounting rules for measuring accruals in order to study the theoretical properties of these accounting rules, their taxation...
Lang, Kenneth R
1978-01-01
This volume is a reference source of fundamental formulae in physics and astrophysics. In contrast to most of the usual compendia it carefully explains the physical assumptions entering the formulae. All the important results of physical theories are covered: electrodynamics, hydrodynamics, general relativity, atomic and nuclear physics, and so on. Over 2100 formulae are included, and the original papers for the formulae are cited together with papers on modern applications in a bibliography of over 1900 entries. For this new edition, a chapter on space, time, matter and cosmology has been included and the other chapters have been carefully revised.
Recursively-regular subdivisions and applications
Rafel Jaume
2016-05-01
Full Text Available We generalize regular subdivisions (polyhedral complexes resulting from the projection of the lower faces of a polyhedron introducing the class of recursively-regular subdivisions. Informally speaking, a recursively-regular subdivision is a subdivision that can be obtained by splitting some faces of a regular subdivision by other regular subdivisions (and continue recursively. We also define the finest regular coarsening and the regularity tree of a polyhedral complex. We prove that recursively-regular subdivisions are not necessarily connected by flips and that they are acyclic with respect to the in-front relation. We show that the finest regular coarsening of a subdivision can be efficiently computed, and that whether a subdivision is recursively regular can be efficiently decided. As an application, we also extend a theorem known since 1981 on illuminating space by cones and present connections of recursive regularity to tensegrity theory and graph-embedding problems.
On the Hosoya index of a family of deterministic recursive trees
Chen, Xufeng; Zhang, Jingyuan; Sun, Weigang
2017-01-01
In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O(log2 n) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index.
Adding Recursive Constructs to Bialgebraic Semantics
Klin, Bartek
2004-01-01
This paper aims at fitting a general class of recursive equations into the framework of ‘well-behaved' structural operational semantics, formalized as bialgebraic semantics by Turi and Plotkin. Rather than interpreting recursive constructs by means of operational rules, separate recursive equations...... are added to semantic descriptions of languages. The equations, together with the remaining rules, are then interpreted in a suitable category and merged by means of certain fixpoint constructions. For a class of recursive equations called regular unfolding rules, this construction yields distributive laws...
Weighted Hurwitz numbers and topological recursion: an overview
Alexandrov, A; Eynard, B; Harnad, J
2016-01-01
This is an overview and summary of results on weighted Hurwitz numbers and topological recursion. The parametric family of hypergeometric $\\tau$-functions of Toda type serving as generating functions for weighted Hurwitz numbers is recalled. In terms of this, the Baker function and its dual, the adapted basis of the space of formal power series in an auxiliary variable, and the recursion operators that relate these basis elements and their duals are derived. The $n$-pair correlators and multicurrent correlators, which serve as an alternative type of generating function for the weighted Hurwitz numbers, are defined in terms of the $\\tau$-function and expressed in terms of these bases. Fermionic VEV representations are provided for all these quantities. The Baker function is shown to satisfy the quantum spectral curve equation whose classical limit is derived and given a rational parametrization. Choosing the weight generating function as a polynomial, and requiring the number of nonzero "second" KP flow parame...
Riordon, Tim
1984-01-01
Describes activities designed to teach students about embedded recursion. Topics cover providing intuitions about embedded recursions, predicting embedded recursions, seeing patterns and processes, presenting graphic designs containing embedded copies of themselves, and exploring graphics, numerical, and word examples. Parts I and II are in…
Scattering amplitudes and BCFW recursion in twistor space
Mason, Lionel; Skinner, David
2010-01-01
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for n-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the mathcal{N} = 8 supergravity recursion and the MHV and overline {text{MHV}} amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N k MHV, the amplitudes are given by 2 n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in mathcal{N} = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.
Recursive Optimization of Digital Circuits
1990-12-14
capability will become increasingly important as the application-specific integrated circuit (ASIC) market continues to meet its rapid growth projections... market (ASIC) continues to grow (18). The recursive optimization system presented in this thesis was developed to inves- tigate a new approach to global...f)) (narg (bar arg)) (fO (divide f narg)) (f1 (divide f arg)) (gO (divide g narg)) (gi (divide g arg)) ( productO (mult fO gO)) (producti (mult fl gl
A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints
Ueno, Kenya
2009-01-01
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko [13]. Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give integrally matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy [15].
Evaluating functions using tail recursion and parameter substitution
Georges E. Alfaro Salazar
2016-03-01
Full Text Available This article shows a general way to implement recursive functions calculation by linear tail recursion. It emphasizes the use of tail recursion to perform computations efficiently.
Command Algebras, Recursion and Program Transformation
Hesselink, Wim H.
1990-01-01
Dijkstra's language of guarded commands is extended with recursion and transformed into algebra. The semantics is expressed in terms of weakest preconditions and weakest liberal preconditions. Extreme fixed points are used to deal with recursion. Unbounded nondeterminacy is allowed. The algebraic
The Recursive Paradigm: Suppose We Already Knew.
Maurer, Stephen B.
1995-01-01
Explains the recursive model in discrete mathematics through five examples and problems. Discusses the relationship between the recursive model, mathematical induction, and inductive reasoning and the relevance of these concepts in the school curriculum. Provides ideas for approaching this material with students. (Author/DDD)
Conjugate gradient algorithms using multiple recursions
Barth, T.; Manteuffel, T.
1996-12-31
Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuffel gave necessary and sufficient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all possible recursions. This became evident when Jagels and Reichel used an algorithm of Gragg for unitary matrices to demonstrate that the class of matrices for which a practical conjugate gradient algorithm exists can be extended to include unitary and shifted unitary matrices. The implementation uses short double recursions for the direction vectors. This motivates the study of multiple recursion algorithms.
Zhang, Biao; Xiong, Deyi; Su, Jinsong
2016-01-01
In this paper, we propose a bidimensional attention based recursive autoencoder (BattRAE) to integrate clues and sourcetarget interactions at multiple levels of granularity into bilingual phrase representations. We employ recursive autoencoders to generate tree structures of phrases with embeddings at different levels of granularity (e.g., words, sub-phrases and phrases). Over these embeddings on the source and target side, we introduce a bidimensional attention network to learn their interac...
Dunin-Barkowski, P.; Lewanski, D.; Popolitov, A.; Shadrin, S.
2015-01-01
In this paper, we present an example of a derivation of an ELSV-type formula using the methods of topological recursion. Namely, for orbifold Hurwitz numbers we give a new proof of the spectral curve topological recursion, in the sense of Chekhov, Eynard and Orantin, where the main new step compared
Topological recursion for Gaussian means and cohomological field theories
Andersen, Jørgen Ellegaard; Norbury, Paul; Penner, Robert C
2016-01-01
We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{disc}$ (discrete volumes), to express Gaussian means in all genera as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate topological recursion of the Gaussian model into recurrent relations for coefficients of this expansion proving their integrality and positivity. As an application, we find the coefficients in the first subleading order for ${\\mathcal M}_{g,1}$ for all $g$ in three ways: by using the refined Harer--Zagier recursion, by exploiting the Givental-type decomposition of KPMM, and by an explicit diagram counting.
Snezhana Georgieva Gocheva-Ilieva
2013-01-01
Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.
递推数列通项的矩阵解法%Matrix Theory and Recursive Sequences
龚丽燕; 陈益智; 蔡俊树
2014-01-01
In this paper , general term formulas for some recursive sequences are obtained with the corresponding matrices .Also ,some examples are illustrated .%分情形讨论递推数列求通项的问题，介绍相应的矩阵解法，并借助实例说明其应用。
Recursive sequences in first-year calculus
Krainer, Thomas
2016-02-01
This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.
The remodeling conjecture and the Faber-Pandharipande formula
Bouchard, Vincent; Marchal, Olivier; Sulkowski, Piotr
2011-01-01
In this note, we prove that the free energies F_g constructed from the Eynard-Orantin topological recursion applied to the curve mirror to C^3 reproduce the Faber-Pandharipande formula for genus g Gromov-Witten invariants of C^3. This completes the proof of the remodeling conjecture for C^3.
An extension of the formula for spreading speeds.
Weinberger, Hans F; Zhao, Xiao-Qiang
2010-01-01
A well-known formula for the spreading speed of a discrete-time recursion model is extended to a class of problems for which its validity was previously unknown. These include migration models with moderately fat tails or fat tails. Examples of such models are given.
Feynman formulae for evolution semigroups
Ya. A. Butko
2014-01-01
Full Text Available The paper systematically describes an approach to solution of initial and initial-boundary value problems for evolution equations based on the representation of the corresponding evolution semigroups with the help of Feynman formulae. The article discusses some of the methods of constructing Feynman formulae for different evolution semigroups, presents specific examples of solutions of evolution equations. In particular, Feynman formula is obtained for evolution semigroups generated by multiplicative perturbations of generators of some initial semigroups. In this case semigroups on a Banach space of continuous functions defined on an arbitrary metric space are considered; Feynman formulae are constructed with the help of operator families, which are Chernoff equivalent to the initial unperturbed semigroups. The present result generalizes the author's paper \\Feynman formula for semigroups with multiplicative perturbed generators" and some of the results of the joint with O.G. Smolyanov and R.L. Schilling paper \\Lagrangian and Hamiltonian Feynman formulae for some Feller processes and their perturbations". The approach to the construction of Feynman formulae for semigroups with multiplicative and additive perturbed generators is illustrated with examples of the Cauchy problem for the Schrodinger equation, the approximation of transition probabilities of some Markov processes.Further, a wider class of additive and multiplicative perturbations of a particular generator | the Laplace operator | is considered in the paper. And Feynman formula for the solution of the Cauchy problem for a second order parabolic equation with unbounded variable coefficients is proved. In addition, the article describes a method for constructing Feynman formulae for solutions of the Cauchy | Dirichlet problem for parabolic differential equations. The method is also illustrated by a second order parabolic equation with variable coefficients. These results generalize some
Denotational semantics of recursive types in synthetic guarded domain theory
Møgelberg, Rasmus Ejlers; Paviotti, Marco
2016-01-01
Guarded recursion is a form of recursion where recursive calls are guarded by delay modalities. Previous work has shown how guarded recursion is useful for reasoning operationally about programming languages with advanced features including general references, recursive types, countable non...... typed lambda calculus with fixed points). This model was intensional in that it could distinguish between computations computing the same result using a different number of fixed point unfoldings. In this work we show how also programming languages with recursive types can be given denotational...... semantics in type theory with guarded recursion. More precisely, we give a computationally adequate denotational semantics to the language FPC (simply typed lambda calculus extended with recursive types), modelling recursive types using guarded recursive types. The model is intensional in the same way...
Vicari, Giuseppe; Adenzato, Mauro
2014-05-01
In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle's analysis of intentional action. We then discuss evidence from cognitive science and neuroscience supporting the claim that motor-intentional recursion is language-independent and suggest some explanatory hypotheses: (1) linguistic recursion is embodied in sensory-motor processing; (2) linguistic and motor-intentional recursions are distinct and mutually independent mechanisms. Finally, we propose some reflections about the epistemic status of HCF as presenting an empirically falsifiable hypothesis, and on the possibility of testing recursion in different cognitive domains.
Simple Recursion Relations for General Field Theories
Cheung, Clifford; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-...
Gaussian process based recursive system identification
Prüher, Jakub; Šimandl, Miroslav
2014-12-01
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Interpretations of Recursion under Unbounded Nondeterminacy
Hesselink, Wim H.
1988-01-01
A language is constructed that supports arbitrary atomic statements, composition, alternatives, and mutual recursion in the presence of unbounded nondeterminacy. The concept of interpretation is defined axiomatically. By operational means a standard interpretation is constructed, which is proved to
Certain Binomial Sums with recursive coefficients
Kilic, Emrah
2010-01-01
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving binomial coefficients and Fibonacci type sequences.
Modular functors, cohomological field theories and topological recursion
Andersen, Jørgen Ellegaard; Orantin, Nicolas
2015-01-01
Given a topological modular functor $\\mathcal{V}$ in the sense of Walker \\cite{Walker}, we construct vector bundles over $\\overline{\\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction depends on a determination of the logarithm of the eigenvalues of the Dehn twist and central element actions. We show that the intersection of the Chern class with the $\\psi$-classes in $\\overline{\\mathcal{M}}_{g,n}$ is computed by the topological recursion of \\cite{EOFg}, for a local spectral curve that we describe. In particular, we show how the Verlinde formula for the dimensions $D_{\\vec{\\lambda}}(\\mathbf{\\Sigma}_{g,n}) = \\dim \\mathcal{V}_{\\vec{\\lambda}}(\\mathbf{\\Sigma}_{g,n})$ is retrieved from the topological recursion. We analyze the consequences of our result on two examples: modular functors associated to a finite group $G$ (for which $D_{\\vec{\\lambda}}(\\mathbf{\\Sigma}_{g,n})$ enumerates certain $G$-principle bundles over a genus $g$ surface with $n$ boundary condi...
Recursion theory computational aspects of definability
Chong, Chi Tat
2015-01-01
This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.
Recursive Inversion Of Externally Defined Linear Systems
Bach, Ralph E., Jr.; Baram, Yoram
1992-01-01
Technical memorandum discusses mathematical technique described in "Recursive Inversion by Finite-Impulse-Response Filters" (ARC-12247). Technique is recursive algorithm yielding finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Useful in such diverse applications as medical diagnoses, identification of military targets, geophysical exploration, and nondestructive testing.
Recursions for the Individual Risk Model
Jan Dhaene; Carmen Ribas; Raluca Vernic
2006-01-01
In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.
Period of the d-Sequence Based Random Number Generator
Thippireddy, Suresh; Chalasani, Sandeep
2007-01-01
This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.
On the appearance of primes in linear recursive sequences
Jaroma John H
2005-01-01
Full Text Available We present an application of difference equations to number theory by considering the set of linear second-order recursive relations, , U0 = 0, U1 = 1, and , , where R and Q are relatively prime integers and n ∈ {0,1,...}. These equations describe the set of extended Lucas sequences, or rather, the Lehmer sequences. We add that the rank of apparition of an odd prime p in a specific Lehmer sequence is the index of the first term that contains p as a divisor. In this paper, we obtain results that pertain to the rank of apparition of primes of the form 2n p ± 1. Upon doing so, we will also establish rank of apparition results under more explicit hypotheses for some notable special cases of the Lehmer sequences. Presently, there does not exist a closed formula that will produce the rank of apparition of an arbitrary prime in any of the aforementioned sequences.
Implicit learning of a recursive rule in an artificial grammar.
Poletiek, Fenna H
2002-11-01
Participants performed an artificial grammar learning task, in which the standard finite state grammar (J. Verb. Learn. Verb. Behavior 6 (1967) 855) was extended with a recursive rule generating self-embedded sequences. We studied the learnability of such a rule in two experiments. The results verify the general hypothesis that recursivity can be learned in an artificial grammar learning task. However this learning seems to be rather based on recognising chunks than on abstract rule induction. First, performance was better for strings with more than one level of self-embedding in the sequence, uncovering more clearly the self-embedding pattern. Second, the infinite repeatability of the recursive rule application was not spontaneously induced from the training, but it was when an additional cue about this possibility was given. Finally, participants were able to verbalise their knowledge of the fragments making up the sequences-especially in the crucial front and back positions-, whereas knowledge of the underlying structure, to the extent it was acquired, was not articulatable. The results are discussed in relation to previous studies on the implicit learnability of complex and abstract rules.
Recursive linearization of multibody dynamics equations of motion
Lin, Tsung-Chieh; Yae, K. Harold
1989-01-01
The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.
Recursion Of Binary Space As A Foundation Of Repeatable Programs
Jeremy Horne
2006-10-01
Full Text Available Every computation, including recursion, is based on natural philosophy. Our world may be expressed in terms of a binary logical space that contains functions that act simultaneously as objects and processes (operands and operators. This paper presents an outline of the results of research about that space and suggests routes for further inquiry. Binary logical space is generated sequentially from an origin in a standard coordinate system. At least one method exists to show that each of the resulting 16 functions repeats itself by repeatedly forward-feeding outputs of a function operating over two others as new operands of the original function until the original function appears as an output, thus behaving as an apparent homeostatic automaton. As any space of any dimension is composed of one or more of these functions, so the space is recursive, as well. Semantics gives meaning to recursive structures, computer programs and fundamental constituents of our universe being two examples. Such thoughts open inquiry into larger philosophical issues as free will and determinism.
A Recurrence Formula for Computing the Derivative of Composition of Functions
A. A. Taani
2007-01-01
Full Text Available A new recursion formula for computing the n − th derivative of the composition of two functions has been introduced in this contribution. The importance of this new formula is associated with its counterpart; Leibniz rule for finding the n − th derivative of the product of two functions. Furthermore the process of computing this formula has been presented in algorithmic format herein.
Explicit Formulas for Meixner Polynomials
Dmitry V. Kruchinin
2015-01-01
Full Text Available Using notions of composita and composition of generating functions, we show an easy way to obtain explicit formulas for some current polynomials. Particularly, we consider the Meixner polynomials of the first and second kinds.
Thorenz, Ute R; Kundel, Michael; Müller, Lars; Hoffmann, Thorsten
2012-11-01
In this work, we describe a simple diffusion capillary device for the generation of various organic test gases. Using a set of basic equations the output rate of the test gas devices can easily be predicted only based on the molecular formula and the boiling point of the compounds of interest. Since these parameters are easily accessible for a large number of potential analytes, even for those compounds which are typically not listed in physico-chemical handbooks or internet databases, the adjustment of the test gas source to the concentration range required for the individual analytical application is straightforward. The agreement of the predicted and measured values is shown to be valid for different groups of chemicals, such as halocarbons, alkanes, alkenes, and aromatic compounds and for different dimensions of the diffusion capillaries. The limits of the predictability of the output rates are explored and observed to result in an underprediction of the output rates when very thin capillaries are used. It is demonstrated that pressure variations are responsible for the observed deviation of the output rates. To overcome the influence of pressure variations and at the same time to establish a suitable test gas source for highly volatile compounds, also the usability of permeation sources is explored, for example for the generation of molecular bromine test gases.
Breastfeeding vs. Formula Feeding
... 1- to 2-Year-Old Breastfeeding vs. Formula Feeding KidsHealth > For Parents > Breastfeeding vs. Formula Feeding Print ... a lactation specialist. previous continue All About Formula Feeding Commercially prepared infant formulas are a nutritious alternative ...
Random recursive trees and the elephant random walk
Kürsten, Rüdiger
2016-03-01
One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.
Anharmonic resonances with recursive delay feedback
Goldobin, Denis S., E-mail: Denis.Goldobin@gmail.com [Department of Mathematics, University of Leicester, Leicester LE1 7RH (United Kingdom); Institute of Continuous Media Mechanics, UB RAS, Perm 614013 (Russian Federation)
2011-09-12
We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators. -- Highlights: → We construct general theory of noisy limit-cycle oscillators with linear feedback. → We focus on coherence and 'reliability' of oscillators. → For recursive delay feedback control the theory shows importance of anharmonicity. → Anharmonic resonances are studied both numerically and analytically.
Recursion and feedback in image algebra
Ritter, Gerhard X.; Davidson, Jennifer L.
1991-04-01
Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.
Recursively arbitrarily vertex-decomposable suns
Olivier Baudon
2011-01-01
Full Text Available A graph \\(G = (V,E\\ is arbitrarily vertex decomposable if for any sequence \\(\\tau\\ of positive integers adding up to \\(|V|\\, there is a sequence of vertex-disjoint subsets of \\(V\\ whose orders are given by \\(\\tau\\, and which induce connected graphs. The aim of this paper is to study the recursive version of this problem on a special class of graphs called suns. This paper is a complement of [O. Baudon, F. Gilbert, M. Woźniak, Recursively arbitrarily vertex-decomposable graphs, research report, 2010].
On-shell recursion relations for gravity
Hall, Anthony
2008-06-01
We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo to show that graviton tree amplitudes are well behaved under large complex deformations of the momenta of a pair of like-helicity gravitons. This shows that Britto-Cachazo-Feng-Witten recursion relations for gravity amplitudes can be constructed using such shifts, providing an alternative proof to the recent one by Arkani-Hamed and Kaplan. By using auxiliary recursion relations the cancellations which are hidden when using covariant Feynman diagrams become manifest.
New recursive algorithm for matrix inversion
Cao Jianshu; Wang Xuegang
2008-01-01
To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms (called algorithms Ⅰ and Ⅱ, respectively)are presented. Algorithm Ⅰ is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm Ⅱ, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm Ⅰ. The implementation, for algorithm Ⅱ or Ⅰ, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.
Adaptable Iterative and Recursive Kalman Filter Schemes
Zanetti, Renato
2014-01-01
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
A Survey on Teaching and Learning Recursive Programming
Christian RINDERKNECHT
2014-01-01
.... After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some...
The recursion operator for a constrained CKP hierarchy
Li, Chuanzhong; He, Jingsong; Cheng, Yi
2010-01-01
This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition $q=r$.
The recursion operator for a constrained CKP hierarchy
Li, Chuanzhong; Tian, Kelei; He, Jingsong; Cheng, Yi
2010-01-01
This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition $q=r$.
Traceable Recursion with Graphical Illustration for Novice Programmers
Sa, Leonardo; Hsin, Wen-Jung
2010-01-01
Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion…
A Survey on Teaching and Learning Recursive Programming
Rinderknecht, Christian
2014-01-01
We survey the literature about the teaching and learning of recursive programming. After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some programming methodology, as well as the functional and imperative…
Convergence of a Linear Recursive Sequence
Tay, E. G.; Toh, T. L.; Dong, F. M.; Lee, T. Y.
2004-01-01
A necessary and sufficient condition is found for a linear recursive sequence to be convergent, no matter what initial values are given. Its limit is also obtained when the sequence is convergent. Methods from various areas of mathematics are used to obtain the results.
Recursive Filtering And Smoothing In Robot Dynamics
Rodriguez, Guillermo
1992-01-01
Techniques developed originally for electronic systems also useful for multibody mechanical systems. Report summarizes methods developed to solve nonlinear forward-dynamics problem for robot of multiple-link arms connected by joints. Primary objective to show equivalence between recursive methods of dynamical analysis and some filtering and smoothing techniques from state-estimation theory.
Recursions for the Individual Risk Model
Dhaene, J.; Ribas, C.; Vernic, R.
2006-01-01
In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with
The Language Faculty that Wasn't: A Usage-Based Account of Natural Language Recursion
Morten H Christiansen
2015-08-01
Full Text Available In the generative tradition, the language faculty has been shrinking—perhaps to include only the mechanism of recursion. This paper argues that even this view of the language faculty is too expansive. We first argue that a language faculty is difficult to reconcile with evolutionary considerations. We then focus on recursion as a detailed case study, arguing that our ability to process recursive structure does not rely on recursion as a property of the grammar, but instead emerge gradually by piggybacking on domain-general sequence learning abilities. Evidence from genetics, comparative work on non-human primates, and cognitive neuroscience suggests that humans have evolved complex sequence learning skills, which were subsequently pressed into service to accommodate language. Constraints on sequence learning therefore have played an important role in shaping the cultural evolution of linguistic structure, including our limited abilities for processing recursive structure. Finally, we re-evaluate some of the key considerations that have often been taken to require the postulation of a language faculty.
The language faculty that wasn't: a usage-based account of natural language recursion.
Christiansen, Morten H; Chater, Nick
2015-01-01
In the generative tradition, the language faculty has been shrinking-perhaps to include only the mechanism of recursion. This paper argues that even this view of the language faculty is too expansive. We first argue that a language faculty is difficult to reconcile with evolutionary considerations. We then focus on recursion as a detailed case study, arguing that our ability to process recursive structure does not rely on recursion as a property of the grammar, but instead emerges gradually by piggybacking on domain-general sequence learning abilities. Evidence from genetics, comparative work on non-human primates, and cognitive neuroscience suggests that humans have evolved complex sequence learning skills, which were subsequently pressed into service to accommodate language. Constraints on sequence learning therefore have played an important role in shaping the cultural evolution of linguistic structure, including our limited abilities for processing recursive structure. Finally, we re-evaluate some of the key considerations that have often been taken to require the postulation of a language faculty.
Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Penner, Robert C.
relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary length and point......We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in [1]. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion...
Analysis of litter size and average litter weight in pigs using a recursive model
Varona, Luis; Sorensen, Daniel; Thompson, Robin
2007-01-01
An analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM) is presented. The RMM establishes a one-way link from litter size to average piglet weight. It is shown that there is a one......-to-one correspondence between the parameters of SMM and RMM and that they generate equivalent likelihoods. As parameterized in this work, the RMM tests for the presence of a recursive relationship between additive genetic values, permanent environmental effects, and specific environmental effects of litter size...
Madsen, Kenneth Lindegaard; Herlo, Rasmus
2017-01-01
The shape and composition of a membrane directly regulate the localization, activity, and signaling properties of membrane associated proteins. Proteins that both sense and generate membrane curvature, e.g., through amphiphilic insertion motifs, potentially engage in recursive binding dynamics, w...
Generalized Klein-Nishina formula
Krajewska, K; Kamiński, J Z
2015-01-01
The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cut-off frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties.
Recursions for Statistical Multiple Alignment
Hein, Jotun; Pedersen, Christian Nørgaard Storm; Jensen, Jens Ledet
2002-01-01
Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne–Kishino–Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignm...
Chair, Noureddine, E-mail: n.chair@ju.edu.jo
2014-02-15
We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given.
... child. Does using infant formula increase risk for dental fluorosis? Because most infant formulas contain low levels of ... I use affect my child’s chance of getting dental fluorosis? Three types of infant formula are available in ...
Breastfeeding vs. Formula Feeding
... A What's in this article? All About Breastfeeding Breastfeeding Challenges All About Formula Feeding Formula Feeding Challenges Making a Choice en español Lactancia materna versus lactancia artificial Choosing whether to breastfeed or formula feed their ...
Spectral functions and time evolution from the Chebyshev recursion
Wolf, F. Alexander; Justiniano, Jorge A.; McCulloch, Ian P.; Schollwöck, Ulrich
2015-03-01
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of T =0 many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor ˜1/6 . We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time-evolution algorithm that instead of the group operator e-i H t only involves the action of the generator H . For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within the dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from H than time evolution algorithms when fixing a given amount of created entanglement.
Parsimonious extreme learning machine using recursive orthogonal least squares.
Wang, Ning; Er, Meng Joo; Han, Min
2014-10-01
Novel constructive and destructive parsimonious extreme learning machines (CP- and DP-ELM) are proposed in this paper. By virtue of the proposed ELMs, parsimonious structure and excellent generalization of multiinput-multioutput single hidden-layer feedforward networks (SLFNs) are obtained. The proposed ELMs are developed by innovative decomposition of the recursive orthogonal least squares procedure into sequential partial orthogonalization (SPO). The salient features of the proposed approaches are as follows: 1) Initial hidden nodes are randomly generated by the ELM methodology and recursively orthogonalized into an upper triangular matrix with dramatic reduction in matrix size; 2) the constructive SPO in the CP-ELM focuses on the partial matrix with the subcolumn of the selected regressor including nonzeros as the first column while the destructive SPO in the DP-ELM operates on the partial matrix including elements determined by the removed regressor; 3) termination criteria for CP- and DP-ELM are simplified by the additional residual error reduction method; and 4) the output weights of the SLFN need not be solved in the model selection procedure and is derived from the final upper triangular equation by backward substitution. Both single- and multi-output real-world regression data sets are used to verify the effectiveness and superiority of the CP- and DP-ELM in terms of parsimonious architecture and generalization accuracy. Innovative applications to nonlinear time-series modeling demonstrate superior identification results.
Cosmic Acceleration from Causal Backreaction with Recursive Nonlinearities
Bochner, Brett
2013-01-01
We revisit the causal backreaction paradigm, in which the need for Dark Energy is eliminated via the generation of an apparent cosmic acceleration from the causal flow of inhomogeneity information coming in towards each observer from distant structure-forming regions. This second-generation formalism incorporates "recursive nonlinearities": the process by which already-established metric perturbations will then act to slow down all future flows of inhomogeneity information. Here, the long-range effects of causal backreaction are now damped, weakening its impact for models that were previously best-fit cosmologies. Nevertheless, we find that causal backreaction can be recovered as a replacement for Dark Energy via the adoption of larger values for the dimensionless `strength' of the clustering evolution functions being modeled -- a change justified by the hierarchical nature of clustering and virialization in the universe, occurring on multiple cosmic length scales simultaneously. With this, and with one new m...
Recursive double-size fixed precision arithmetic
Chabot, Christophe; Fousse, Laurent; Giorgi, Pascal
2011-01-01
This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture).
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
Methods for assessing movement path recursion with application to African buffalo in South Africa
Bar-David, S.; Bar-David, I.; Cross, P.C.; Ryan, S.J.; Knechtel, C.U.; Getz, W.M.
2009-01-01
Recent developments of automated methods for monitoring animal movement, e.g., global positioning systems (GPS) technology, yield high-resolution spatiotemporal data. To gain insights into the processes creating movement patterns, we present two new techniques for extracting information from these data on repeated visits to a particular site or patch ("recursions"). Identification of such patches and quantification of recursion pathways, when combined with patch-related ecological data, should contribute to our understanding of the habitat requirements of large herbivores, of factors governing their space-use patterns, and their interactions with the ecosystem. We begin by presenting output from a simple spatial model that simulates movements of large-herbivore groups based on minimal parameters: resource availability and rates of resource recovery after a local depletion. We then present the details of our new techniques of analyses (recursion analysis and circle analysis) and apply them to data generated by our model, as well as two sets of empirical data on movements of African buffalo (Syncerus coffer): the first collected in Klaserie Private Nature Reserve and the second in Kruger National Park, South Africa. Our recursion analyses of model outputs provide us with a basis for inferring aspects of the processes governing the production of buffalo recursion patterns, particularly the potential influence of resource recovery rate. Although the focus of our simulations was a comparison of movement patterns produced by different resource recovery rates, we conclude our paper with a comprehensive discussion of how recursion analyses can be used when appropriate ecological data are available to elucidate various factors influencing movement. Inter alia, these include the various limiting and preferred resources, parasites, and topographical and landscape factors. ?? 2009 by the Ecological Society of America.
Recursively arbitrarily vertex-decomposable graphs
Olivier Baudon
2012-01-01
Full Text Available A graph \\(G = (V;E\\ is arbitrarily vertex decomposable if for any sequence \\(\\tau\\ of positive integers adding up to \\(|V|\\, there is a sequence of vertex-disjoint subsets of \\(V\\ whose orders are given by \\(\\tau\\, and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs called balloons.
FRPA: A Framework for Recursive Parallel Algorithms
2015-05-01
value of designing a programming language such as NESL from the ground up for its ability to be optimized for teaching and prototyping parallel...observations that communication costs often dominate computation costs. Previous work [1]–[3] demonstrates that carefully choosing which divide-and-conquer...pabilities, we present a detailed analysis of two al- gorithms: Strassen-Winograd [1] and Communication - Optimal Parallel Recursive Rectangular Matrix
Feature Weight Tuning for Recursive Neural Networks
2014-01-01
This paper addresses how a recursive neural network model can automatically leave out useless information and emphasize important evidence, in other words, to perform "weight tuning" for higher-level representation acquisition. We propose two models, Weighted Neural Network (WNN) and Binary-Expectation Neural Network (BENN), which automatically control how much one specific unit contributes to the higher-level representation. The proposed model can be viewed as incorporating a more powerful c...
A NEW RECURSIVE ALGORITHM FOR MULTIUSER DETECTION
Wang Lei; Zheng Baoyu; Li Lei; Chen Chao
2009-01-01
Based on the synthesis and analysis of recursive receivers,a new algorithm,namely partial grouping maximization likelihood algorithm,is proposed to achieve satisfactory performance with moderate computational complexity.During the analysis,some interesting properties shared by the proposed procedures are described.Finally,the performance assessment shows that the new scheme is superior to the linear detector and ordinary grouping algorithm,and achieves a bit-error rate close to that of the optimum receiver.
Linearly recursive sequences and Dynkin diagrams
Reutenauer, Christophe
2012-01-01
Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\\em frieze}; these sequences are given by nonlinear recursions (with division), and the fact that they are integers is a consequence of the Laurent phenomenon of Fomin and Zelevinsky. If the sequences satisfy a linear recursion with constant coefficients, then the graph must be a Dynkin diagram or an extended Dynkin diagram, with an acyclic orientation. The converse also holds: the sequences of the frieze associated to an oriented Dynkin or Euclidean diagram satisfy linear recursions, and are even $\\mathbb N$-rational. One uses in the proof objects called $SL_2$-{\\em tilings of the plane}, which are fillings of the discrete plane such that each adjacent 2 by 2 minor is equal to 1. These objects, which have applications in the theory of cluster algebras, are interesting for themselves. S...
Updating Recursive XML Views of Relations
Byron Choi; Gao Cong; Wenfei Fan; Stratis D. Viglas
2008-01-01
This paper investigates the view update problem for XML views published from relational data. We consider XML views defined in terms of mappings directed by possibly recursive DTDs compressed into DAGs and stored in relations.We provide new techniques to efficiently support XML view updates specified in terms of Xpath expressions with recursion and complex filters. The interaction between Xpath recursion and DAG compression of XML views makes the analysis of the XML view update problem rather intriguing. Furthermore, many issues are still open even for relational view updates,and need to be explored. In response to these, on the XML side, we revise the notion of side effects and update semantics based on the semantics of XML views, and present efficient algorithms to translate XML updates to relational view updates.On the relational side, we propose a mild condition on SPJ views, and show that under this condition the analysis of deletions on relational views becomes PTIME while the insertion analysis is NP-complete. We develop an efficient algorithm to process relational view deletions, and a heuristic algorithm to handle view insertions. Finally, we present an experimental study to verify the effectiveness of our techniques.
A Recursive Framework for Automatic Face Tracking
ZHUANGYueting; CHENJiashi; WUFei; ZHUQiang
2004-01-01
Human face modeling and tracking has always been an important problem for user interfaces, gesture recognition and surveillance. Our approach lies in two key techniques: sum-of-squared-difference (SSD) tracking and a recursive framework including a clever motion representation: twist. The recursive framework plays a pivotal role in the whole system: First, it stably maintains the 3D pose of the face according to the 2D observations. In the mean time, it predicts the new state and projects 3D structure from object coordinates to the feature trajectory in 2D image plane, which indicates a good initial position for 2D tracking in the next frame. The core idea is to propose a recursive framework (i.e. Extended Kalman filter, EKF)that treats the individual 2D trackers as a global 3D rigid structure, consequently solving the problems inherent in pure 2D tracking and avoiding feature loss. In the end, we will present several experimental results to validate our approach.
Recursive self-organizing network models.
Hammer, Barbara; Micheli, Alessio; Sperduti, Alessandro; Strickert, Marc
2004-01-01
Self-organizing models constitute valuable tools for data visualization, clustering, and data mining. Here, we focus on extensions of basic vector-based models by recursive computation in such a way that sequential and tree-structured data can be processed directly. The aim of this article is to give a unified review of important models recently proposed in literature, to investigate fundamental mathematical properties of these models, and to compare the approaches by experiments. We first review several models proposed in literature from a unifying perspective, thereby making use of an underlying general framework which also includes supervised recurrent and recursive models as special cases. We shortly discuss how the models can be related to different neuron lattices. Then, we investigate theoretical properties of the models in detail: we explicitly formalize how structures are internally stored in different context models and which similarity measures are induced by the recursive mapping onto the structures. We assess the representational capabilities of the models, and we shortly discuss the issues of topology preservation and noise tolerance. The models are compared in an experiment with time series data. Finally, we add an experiment for one context model for tree-structured data to demonstrate the capability to process complex structures.
Generating Function and Application%生成函数及其应用
陈军科
2011-01-01
The recurrence relations, recursive sequence and Bell series generating functions are studied. The generating function method and calculation skills are used and the formula is given. The basis for the computer problem-solving is provided.%研究了递推关系,递归数列及Bell级数的生成函数,使用生成函数的方法和计算技巧并给出了递推公式,为使用生成函数提供了依据.
On the appearance of primes in linear recursive sequences
John H. Jaroma
2005-05-01
Full Text Available We present an application of difference equations to number theory by considering the set of linear second-order recursive relations, Un+2(R,Q=RUn+1Ã¢ÂˆÂ’QUn, U0=0, U1=1, and Vn+2(R,Q=RVn+1Ã¢ÂˆÂ’QVn, V0=2,Ã¢Â€Â‰Ã¢Â€Â‰V1=R, where R and Q are relatively prime integers and nÃ¢ÂˆÂˆ{0,1,Ã¢Â€Â¦}. These equations describe the set of extended Lucas sequences, or rather, the Lehmer sequences. We add that the rank of apparition of an odd prime p in a specific Lehmer sequence is the index of the first term that contains p as a divisor. In this paper, we obtain results that pertain to the rank of apparition of primes of the form 2npÃ‚Â±1. Upon doing so, we will also establish rank of apparition results under more explicit hypotheses for some notable special cases of the Lehmer sequences. Presently, there does not exist a closed formula that will produce the rank of apparition of an arbitrary prime in any of the aforementioned sequences.
2008-01-01
<正>An equation which gives a general rule for a particular type of problem is called a formula. Frequently it is convenient to transform a formula,that is,express the formula with a dif- ferent subject.Consider the formula C=2πr;the subject is C.However,if we divide both sides by 2π:
Improved Undecidability Results for Reachability Games on Recursive Timed Automata
Shankara Narayanan Krishna
2014-08-01
Full Text Available We study reachability games on recursive timed automata (RTA that generalize Alur-Dill timed automata with recursive procedure invocation mechanism similar to recursive state machines. It is known that deciding the winner in reachability games on RTA is undecidable for automata with two or more clocks, while the problem is decidable for automata with only one clock. Ouaknine and Worrell recently proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. We revisited games on recursive timed automata with time-bounded restriction in the hope of recovering decidability. However, we found that the problem still remains undecidable for recursive timed automata with three or more clocks. Using similar proof techniques we characterize a decidability frontier for a generalization of RTA to recursive stopwatch automata.
Recursive Polynomial Remainder Sequence and the Nested Subresultants
Terui, Akira
2008-01-01
We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the size of the subresultant matrix drastically compared with the recursive subresultant proposed by the authors before, hence it is much more useful for investigation of the recursive PRS. Finally, we discuss usage of the reduced nested subresultant in approxima...
HURWITZ-HODGE INTEGRAL IDENTITIES FROM THE ORBIFOLD MARI(N)O-VAFA FORMULA
Chen ZHAO
2016-01-01
In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the poly-nomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral 〈τbLλgλ1〉aq.
Generating QCD amplitudes in the color-flow basis with MadGraph
Hagiwara, Kaoru
2010-01-01
We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as $gg\\rightarrow 5g$, $u\\bar{u}\\rightarrow 5g$ and $uu\\rightarrow uuggg$. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with Madgraph.
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
Sheftel, M. B.; Yazıcı, D.; Malykh, A. A.
2017-06-01
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian structures of the two-component general heavenly system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We discover that in the two-component form we have only a single nonlocal recursion operator. Composing the recursion operator with the first Hamiltonian operator we obtain second Hamiltonian operator. We check the Jacobi identities for the second Hamiltonian operator and compatibility of the two Hamiltonian structures using P. Olver's theory of functional multi-vectors. Our well-founded conjecture is that P. Olver's method works fine for nonlocal operators. We show that the general heavenly equation in the two-component form is a bi-Hamiltonian system integrable in the sense of Magri. We demonstrate how to obtain nonlocal Hamiltonian flows generated by local Hamiltonians by using formal adjoint recursion operator.
Rates of Convergence of Recursively Defined Sequences
Lambov, Branimir Zdravkov
2005-01-01
This paper gives a generalization of a result by Matiyasevich which gives explicit rates of convergence for monotone recursively defined sequences. The generalization is motivated by recent developments in fixed point theory and the search for applications of proof mining to the field. It relaxes...... the requirement for monotonicity to the form xn+1 ≤ (1+an)xn+bn where the parameter sequences have to be bounded in sum, and also provides means to treat computational errors. The paper also gives an example result, an application of proof mining to fixed point theory, that can be achieved by the means discussed...
Recursion equations in gauge field theories
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
Recursive backstepping control of chaotic Duffing oscillators
Harb, Ahmad M. [Jordan University of Science and Technology, EE Department, P.O. Box 3030, Irbid (Jordan)]. E-mail: aharb@just.edu.jo; Zaher, Ashraf A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States); Al-Qaisia, Ahmad A. [University of Jordan, ME Department, Amman (Jordan); Zohdy, Mohammad A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States)
2007-10-15
In this paper, the dynamics of a forced Duffing oscillator is studied by means of modern nonlinear, bifurcation and chaos theories and shows that the system is ultimately experiencing chaos. The main objective is to characterize and control chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.
Computability theory an introduction to recursion theory
Enderton, Herbert B
2010-01-01
Computability Theory: An Introduction to Recursion Theory, provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree str
Recursive training of neural networks for classification.
Aladjem, M
2000-01-01
A method for recursive training of neural networks for classification is proposed. It searches for the discriminant functions corresponding to several small local minima of the error function. The novelty of the proposed method lies in the transformation of the data into new training data with a deflated minimum of the error function and iteration to obtain the next solution. A simulation study and a character recognition application indicate that the proposed method has the potential to escape from local minima and to direct the local optimizer to new solutions.
Walkenbach, John
2013-01-01
Maximize the power of Excel 2013 formulas with this must-have Excel reference John Walkenbach, known as ""Mr. Spreadsheet,"" is a master at deciphering complex technical topics and Excel formulas are no exception. This fully updated book delivers more than 800 pages of Excel 2013 tips, tricks, and techniques for creating formulas that calculate, developing custom worksheet functions with VBA, debugging formulas, and much more. Demonstrates how to use all the latest features in Excel 2013 Shows how to create financial formulas and tap into the power of array formulas
Branching structure of uniform recursive trees
FENG; Qunqiang; SU; Chun; HU; Zhishui
2005-01-01
The branching structure of uniform recursive trees is investigated in this paper.Using the method of sums for a sequence of independent random variables, the distribution law of ηn, the number of branches of the uniform recursive tree of size n are given first. It is shown that the strong law of large numbers, the central limit theorem and the law of iterated logarithm for ηn follow easily from this method. Next it is shown that ηn and ξn, the depth of vertex n, have the same distribution, and the distribution law of ζn,m, the number of branches of size m, is also given, whose asymptotic distribution is the Poisson distribution with parameter λ = 1/m. In addition, the joint distribution and the asymptotic joint distribution of the numbers of various branches are given. Finally, it is proved that the size of the biggest branch tends to infinity almost sure as n -→∞.
On-shell recursion in string theory
Boels, Rutger H.; Marmiroli, Daniele; Obers, Niels A.
2010-10-01
We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.
Recursive support vector machines for dimensionality reduction.
Tao, Qing; Chu, Dejun; Wang, Jue
2008-01-01
The usual dimensionality reduction technique in supervised learning is mainly based on linear discriminant analysis (LDA), but it suffers from singularity or undersampled problems. On the other hand, a regular support vector machine (SVM) separates the data only in terms of one single direction of maximum margin, and the classification accuracy may be not good enough. In this letter, a recursive SVM (RSVM) is presented, in which several orthogonal directions that best separate the data with the maximum margin are obtained. Theoretical analysis shows that a completely orthogonal basis can be derived in feature subspace spanned by the training samples and the margin is decreasing along the recursive components in linearly separable cases. As a result, a new dimensionality reduction technique based on multilevel maximum margin components and then a classifier with high accuracy are achieved. Experiments in synthetic and several real data sets show that RSVM using multilevel maximum margin features can do efficient dimensionality reduction and outperform regular SVM in binary classification problems.
A self-applicable online partial evaluator for recursive flowchart languages
Glück, Robert
2012-01-01
This paper describes a self-applicable online partial evaluator for a ¿owchart language with recursive calls. Self-application of the partial evaluator yields generating extensions that are as ef¿cient as those reported in the literature for of¿ine partial evaluation. This result is remarkable...... because it has been assumed that online partial evaluation techniques unavoidably lead to inef¿cient and overgeneralized generating extensions. The purpose of this paper is not to determine which kind of partial evaluation is better, but to show how the problem can be solved by recursive polyvariant...... specialization. The design of the self-applicable online partial evaluator is based on a number of known techniques, but by combining them in a new way this result can be produced. The partial evaluator, its techniques, and its implementation are presented in full. Self-application according to all three...
Empirical results and formal approaches to recursion in acquisition.
Hollebrandse, Bartjan; Roeper, Thomas; Speas, Margareth; Roeper, Thomas
2014-01-01
We argue that the move from Direct recursion with conjunctive interpretation to Indirect recursion, where the Strong Minimalist Thesis requires that, at Phase boundaries, a semantic interpretation is necessary, provides the blueprint for the acquisition path. We provide an overview of experimental r
Empirical results and formal approaches to recursion in acquisition.
Hollebrandse, Bartjan; Roeper, Thomas; Speas, Margareth; Roeper, Thomas
2014-01-01
We argue that the move from Direct recursion with conjunctive interpretation to Indirect recursion, where the Strong Minimalist Thesis requires that, at Phase boundaries, a semantic interpretation is necessary, provides the blueprint for the acquisition path. We provide an overview of experimental r
Language, Mind, Practice: Families of Recursive Thinking in Human Reasoning
Josephson, Marika
2011-01-01
In 2002, Chomsky, Hauser, and Fitch asserted that recursion may be the one aspect of the human language faculty that makes human language unique in the narrow sense--unique to language and unique to human beings. They also argue somewhat more quietly (as do Pinker and Jackendoff 2005) that recursion may be possible outside of language: navigation,…
A recursive approach to mortality-linked derivative pricing
Shang, Z.; Goovaerts, M.; Dhaene, J.
2011-01-01
In this paper, we develop a recursive method to derive an exact numerical and nearly analytical representation of the Laplace transform of the transition density function with respect to the time variable for time-homogeneous diffusion processes. We further apply this recursion algorithm to the pric
Language, Mind, Practice: Families of Recursive Thinking in Human Reasoning
Josephson, Marika
2011-01-01
In 2002, Chomsky, Hauser, and Fitch asserted that recursion may be the one aspect of the human language faculty that makes human language unique in the narrow sense--unique to language and unique to human beings. They also argue somewhat more quietly (as do Pinker and Jackendoff 2005) that recursion may be possible outside of language: navigation,…
Recursive definition of global cellular-automata mappings
Feldberg, Rasmus; Knudsen, Carsten; Rasmussen, Steen
1994-01-01
A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping as...
Bivariate Recursive Equations on Excess-of-loss Reinsurance
Jing Ping YANG; Shi Hong CHENG; Xiao Qian WANG
2007-01-01
This paper investigates bivariate recursive equations on excess-of-loss reinsurance.For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1(a,b) family, bivariate recursive equations for the joint distribution of the cedent's aggregate claims and the reinsurer's aggre gate claims are obtained.
Identification and recovery of inward-recursion information%内-递推信息的辨识-还原
李豫颖; 阮群生; 张世良; 杨慧玲; 毛雁明
2011-01-01
信息传输过程中,存在信息元不断被丢失,生成具有递推特性的信息.应用具有动态特性的新数学工具P-集合,提出内-递推信息的概念,给出内-递推信息的结构、序定理、损失信息归并定理、辨识定理与还原定理.通过定义内-递推信息模与内-递推信息辨识度,得到内-递推信息的数值辨识与还原方法,给出内-递推信息的辨识准则,以及辨识与还原的应用.%Information which has a recursive characteristic in the process of transmission is generated because its information elements are continuously lost. By using P-sets which is a new mathematic tool and has dynamic characteristics, the concept of inward-recursion information is proposed, and the structure of inward-recursion is given. Theorems are obtained such as the sequence theorem of inward-recursion information, the merging theorem of loss information, identification and recovery theorems of inward-recursion information. By defining the modulus and the identification measure on inward-recursion information, the numerical value methods of identification and recovery are obtained. Also, the identification criterion of inward-recursion information is given. Finally, the application of identification and recovery is presented.
... based formulas. These formulas are made with cow's milk protein that has been changed to be more like ... be helpful for infants who have allergies to milk protein and for those with skin rashes or wheezing ...
Vandenplas,Yvan; DE GREEF, Elisabeth; Veereman, Gigi
2014-01-01
The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn’t. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota ...
Zhao, Bo; Bradbury, Katharine
2009-01-01
This paper designs a new equalization-aid formula based on fiscal gaps of local communities. When states are in transition to a new local aid formula, the issue of whether and how to hold existing aid harmless poses a challenge. The authors show that some previous studies and the formulas derived from them give differential weights to existing and…
Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian
2010-01-01
for Chargu´eraud and Pottier’s type and capability system including frame and anti-frame rules, based on the operational semantics and step-indexed heap relations. The worlds are constructed as a recursively defined predicate on a recursively defined metric space, which provides a considerably simpler...
Walkenbach, John
2011-01-01
Everything you need to know about* Mastering operators, error values, naming techniques, and absolute versus relative references* Debugging formulas and using the auditing tools* Importing and exporting XML files and mapping the data to specific cells* Using Excel 2003's rights management feature* Working magic with array formulas* Developing custom formulas to produce the results you needHere's the formula for Excel excellenceFormulas are the lifeblood of spreadsheets, and no one can bring a spreadsheet to life like John Walkenbach. In this detailed reference guide, he delves deeply into unde
Krishnan, M.; Bhowmik, B.; Tiwari, A. K.; Hazra, B.
2017-08-01
In this paper, a novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using recursive principal component analysis (RPCA) in conjunction with online damage indicators is proposed. In this method, the acceleration data is used to obtain recursive proper orthogonal modes in online using the rank-one perturbation method, and subsequently utilized to detect the change in the dynamic behavior of the vibrating system from its pristine state to contiguous linear/nonlinear-states that indicate damage. The RPCA algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants, using the rank-one perturbation method. An online condition indicator (CI) based on the L2 norm of the error between actual response and the response projected using recursive eigenvector matrix updates over successive iterations is proposed. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data. The proposed CI, named recursive residual error, is also adopted for simultaneous spatio-temporal damage detection. Numerical simulations performed on five-degree of freedom nonlinear system under white noise and El Centro excitations, with different levels of nonlinearity simulating the damage scenarios, demonstrate the robustness of the proposed algorithm. Successful results obtained from practical case studies involving experiments performed on a cantilever beam subjected to earthquake excitation, for full sensors and underdetermined cases; and data from recorded responses of the UCLA Factor building (full data and its subset) demonstrate the efficacy of the proposed methodology as an ideal candidate for real-time, reference free structural health monitoring.
Convergence of recursive functions on computers
Erivelton Geraldo Nepomuceno
2014-10-01
Full Text Available A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {f(n} is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set ⊂ ℚ of all numbers represented in a computer. However, as is not complete, the representation of f(n on is subject to an error. Then f(n and f(m are considered equal when its differences computed on are equal or lower than the sum of error of each f(n and f(m. An example is given to illustrate the use of the theorem.
Reasoning about Assignments in Recursive Data Structures
Tamalet, Alejandro; Madlener, Ken
This paper presents a framework to reason about the effects of assignments in recursive data structures. We define an operational semantics for a core language based on Meyer's ideas for a semantics for the object-oriented language Eiffel. A series of field accesses, e.g. f1 • f2 • ··· • fn , can be seen as a path on the heap. We provide rules that describe how these multidot expressions are affected by an assignment. Using multidot expressions to construct an abstraction of a list, we show the correctness of a list reversal algorithm. This approach does not require induction and the reasoning about the assignments is encapsulated in the mentioned rules. We also discuss how to use this approach when working with other data structures and how it compares to the inductive approach. The framework, rules and examples have been formalised and proven correct using the PVS proof assistant.
Recursive identification for EIV ARMAX systems
CHEN HanFu
2009-01-01
The input ukand output yk of the multivariate ARMAX system A(z)y_k = B(z)u_k+C(z)w_k are observed with noises:u_k~(ob)(△=)+εu_k and y_k~(ob)(△=)+εy_k,where ε_k~u and ε_k~y denote the observation noises.Such kind of systems are called errors-in-variables (EIV) systems.In the paper,recursive algorithms based on observations are proposed for estimating coefficients of A(z),B(z),C(z),and the covariance matrix Rw of w_k without requiring higher than the second order statistics.The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions.An Illustrative example is provided,and the simulation results are shown to be consistent with the theoretical analysis.
Recursive Partitioning Method on Competing Risk Outcomes
Xu, Wei; Che, Jiahua; Kong, Qin
2016-01-01
In some cancer clinical studies, researchers have interests to explore the risk factors associated with competing risk outcomes such as recurrence-free survival. We develop a novel recursive partitioning framework on competing risk data for both prognostic and predictive model constructions. We define specific splitting rules, pruning algorithm, and final tree selection algorithm for the competing risk tree models. This methodology is quite flexible that it can corporate both semiparametric method using Cox proportional hazards model and parametric competing risk model. Both prognostic and predictive tree models are developed to adjust for potential confounding factors. Extensive simulations show that our methods have well-controlled type I error and robust power performance. Finally, we apply both Cox proportional hazards model and flexible parametric model for prognostic tree development on a retrospective clinical study on oropharyngeal cancer patients. PMID:27486300
The Recursion Theorem and Infinite Sequences
Miller, Arnold W
2008-01-01
In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove that there exists an increasing sequence such that W_{e_n}={e_{n+1},e_{n+2},...} for every n. We call a nonempty computably enumerable set A self-constructing if W_e=A for every e in A. We show that every nonempty computable enumerable set which is disjoint from an infinite computable set is one-one equivalent to a self-constructing set
On semantics and applications of guarded recursion
Bizjak, Aleš
2016-01-01
chapter we study a simply typed calculus with additional "later" and "constant" modalities and a guarded fixed-point combinator. These are used for encoding and working with guarded recursive and coinductive types in a modular way. We develop a normalising operational semantics, provide an adequate...... denotational model and a logic for reasoning about program equivalence. In the last three chapters we study syntax and semantics of a dependent type theory with a family of later modalities indexed by the set of clocks, and clock quantifiers. In the fourth and fifth chapters we provide two model constructions......, one using a family of presheaf categories and one using a generalisation of the category of partial equilogical spaces. These model constructions are used to design the rules and prove consistency of the type theory presented in the last chapter. The type theory is a version of polymorphic dependent...
Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind
Arslan, Burcu; Hohenberger, Annette; Verbrugge, Rineke
2017-01-01
In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6–6;5 years) and one older (6;7–8;10 years). Although second-order syntactic recursion is significantly correlated with the second-order false belief task, results of ordinal logistic regressions revealed that the main predictor of second-order false belief reasoning is complex working memory span. Unlike simple working memory and second-order syntactic recursion tasks, the complex working memory task required processing information serially with additional reasoning demands that require complex working memory strategies. Based on our results, we propose that children’s second-order theory of mind develops when they have efficient reasoning rules to process embedded beliefs serially, thus overcoming a possible serial processing bottleneck. PMID:28072823
Polynomiality of Hurwitz numbers, Bouchard-Mari\\~no conjecture, and a new proof of the ELSV formula
Dunin-Barkowski, Petr; Orantin, Nicolas; Shadrin, Sergey; Spitz, Loek
2013-01-01
In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formula). Then, using this polynomiality we give a new prove of the Bouchard-Mari\\~no conjecture. After that, using the correspondence between the Givental group action and the topological recursion coming from matrix models, we prove the equivalence of the Bouchard-Mari\\~no conjecture and the ELSV formula (it is a refinement of an argument by Eynard).
Application of Time Recursive Processing for the Development of a Time/Phase Shifter
D. M. Perisic
2017-06-01
Full Text Available This paper describes a powerful digital time and/or phase shifter of pulse rates, based on Time Recursive Processing. It can function either as a time shifter or as a phase shifter. The circuit can generate precise shifting for a pulse rate with a constant input period, but it is also capable to shift a pulse rate whose period is a ramp function. Besides that, the shifter can be used in tracking and prediction applications. The shifter is described by recursive equations as a linear discrete system. All mathematical analyses are made using the Z transform. Computer simulations are employed to prove the correctness of the mathematical analysis. The realization of the shifter is described and, to demonstrate the shifter functioning, actual oscilloscope screenshots are presented.
Multi-policy improvement in stochastic optimization with forward recursive function criteria
Chang, Hyeong Soo
2005-05-01
Iwamoto recently established a formal transformation via an invariant imbedding to construct a controlled Markov chain that can be solved in a backward manner, as in backward induction for finite-horizon Markov decision processes (MDPs), for a given controlled Markov chain with non-additive forward recursive objective function criterion. Chang et al. presented formal methods, called "parallel rollout" and "policy switching," of combining given multiple policies in MDPs and showed that the policies generated by both methods improve all of the policies that the methods combine. This brief paper extends the methods of parallel rollout and policy switching for forward recursive objective function criteria and shows that the similar property holds as in MDPs. We further discuss how to implement these methods via simulation.
Recursive estimation of prior probabilities using the mixture approach
Kazakos, D.
1974-01-01
The problem of estimating the prior probabilities q sub k of a mixture of known density functions f sub k(X), based on a sequence of N statistically independent observations is considered. It is shown that for very mild restrictions on f sub k(X), the maximum likelihood estimate of Q is asymptotically efficient. A recursive algorithm for estimating Q is proposed, analyzed, and optimized. For the M = 2 case, it is possible for the recursive algorithm to achieve the same performance with the maximum likelihood one. For M 2, slightly inferior performance is the price for having a recursive algorithm. However, the loss is computable and tolerable.
Ward identity implies recursion relations in Yang-Mills theory
Chen, Gang
2012-07-01
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.
On the symmetries of some classes of recursive circulant graphs
Seyed Morteza Mirafzal
2014-03-01
Full Text Available A recursive-circulant $G(n; d$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$G(n; d$ is vertex-transitive, and has some strong hamiltonianproperties. $G(n; d$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. In this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. In particular, wewill find that the automorphism group of $G(2^m; 4$ is isomorphicwith the group $D_{2 cdot 2^m}$, the dihedral group of order $2^{m+1}
Spin-orbit coupling a recursion method approach
Huda, A U; Mookerjee, A; Paudyal, D
2003-01-01
Relativistic effects play a significant role in alloys of the heavier elements. The majority of earlier works on alloys had included the scalar relativistic corrections. We present here a methodology to take into account the spin-orbit coupling using the recursion method. The basis used for the representation of the Hamiltonian is the TB-LMTO, since its sparseness is an essential requirement for recursion. The recursion technique can then be extended to augmented space to deal with disordered alloys or rough surfaces.
Diagonally loaded SMI algorithm based on inverse matrix recursion
Cao Jianshu; Wang Xuegang
2007-01-01
The derivation of a diagonally loaded sample-matrix inversion (LSMI) algorithm on the busis of inverse matrix recursion (i.e. LSMI-IMR algorithm) is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, acorresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings.Simulations show that the LSMI-IMR algorithm is valid.
Recursive construction of operator product expansion coefficients
Holland, J
2014-01-01
We derive a novel formula for the derivative of operator product expansion (OPE) coefficients with respect to a coupling constant. The formula only involves the OPE coefficients themselves, and no further input, and is in this sense self-consistent. Furthermore, unlike other formal identities of this general nature in quantum field theory (such as the formal expression for the Lagrangian perturbation of a correlation function), our formula is completely well-defined from the start, i.e. requires no further UV-renormalization. This feature is a result of a cancelation of UV-divergences between various terms in our identity. Our proof, and an analysis of the features, of our identity is given for the example of massive, Euclidean $\\varphi^4$ theory in 4 dimensional Euclidean space, and relies heavily on the framework of the renormalization group flow equations. It is valid to arbitrary, but finite orders in perturbation theory. The final formula, however, makes no explicit reference to the renormalization group...
Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation
Laixiang Shan
2015-01-01
Full Text Available We present on-the-fly degeneralization algorithm used to transform generalized Büchi automata (GBA into Büchi Automata (BA different from the standard degeneralization algorithm. Contented situation, which is used to record what acceptance conditions are satisfiable during expanding LTL formulae, is attached to the states and transitions in the BA. In order to get the deterministic BA, the Shannon expansion is used recursively when we expand LTL formulae by applying the tableau rules. On-the-fly degeneralization algorithm is carried out in each step of the expansion of LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae. The temporary automata are stored as syntax directed acyclic graph in order to save storage space. These ideas are implemented in a conversion algorithm used to build a property automaton corresponding to the given LTL formulae. We compare our method to previous work and show that it is more efficient for four sets of random formulae generated by LBTT.
Infant feeding: formula, solids.
Barness, L A
1985-04-01
This article discusses and evaluates current formulas, traces their continual improvement (based largely on new information on breast milk composition), and then discusses the question of supplemental feedings.
Li Yinghong; Yang Wei
2009-01-01
@@ On the first day of November,when Jenson Button cheered his first Formula I World Championship 2009 at the final race of the season in Abu Dhabi,Chinese young university students were busy preparing for their own Formula event.According to a press conference on October 19,2009 in Beijing,the first Formula SAE-China (FSAE) event has set off,and will be officially launch its final race next year from October 14 to October 17 at Shanghai International Circuit,where will also be the Formula 12010 China stop again in next April.
Average weighted receiving time in recursive weighted Koch networks
DAI MEIFENG; YE DANDAN; LI XINGYI; HOU JIE
2016-06-01
Motivated by the empirical observation in airport networks and metabolic networks, we introduce the model of the recursive weighted Koch networks created by the recursive division method. As a fundamental dynamical process, random walks have received considerable interest in the scientific community. Then, we study the recursive weighted Koch networks on random walk i.e., the walker, at each step, starting from its current node, moves uniformly to any of itsneighbours. In order to study the model more conveniently, we use recursive division method again to calculate the sum of the mean weighted first-passing times for all nodes to absorption at the trap located in the merging node. It is showed that in a large network, the average weighted receiving time grows sublinearly with the network order.
On Measuring Non-Recursive Trade-Offs
Hermann Gruber
2009-07-01
Full Text Available We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems.
A Recursive Receding Horizon Planning for Unmanned Vehicles
National Aeronautics and Space Administration — This paper proposes a recursive receding horizon path planning algorithm for unmanned vehicles in nonuniform environments. In the proposed algorithm, the map is...
A novel extended kernel recursive least squares algorithm.
Zhu, Pingping; Chen, Badong; Príncipe, José C
2012-08-01
In this paper, a novel extended kernel recursive least squares algorithm is proposed combining the kernel recursive least squares algorithm and the Kalman filter or its extensions to estimate or predict signals. Unlike the extended kernel recursive least squares (Ex-KRLS) algorithm proposed by Liu, the state model of our algorithm is still constructed in the original state space and the hidden state is estimated using the Kalman filter. The measurement model used in hidden state estimation is learned by the kernel recursive least squares algorithm (KRLS) in reproducing kernel Hilbert space (RKHS). The novel algorithm has more flexible state and noise models. We apply this algorithm to vehicle tracking and the nonlinear Rayleigh fading channel tracking, and compare the tracking performances with other existing algorithms.
RECURSIVE CONVEYOR PROCESSES - THE MAIN PROPERTIES AND CHARACTERISTICS
Boris V. Kupriyanov
2015-01-01
Full Text Available In the article the formal model of recursive conveyor processes is considered. The main properties and characteristics ofthis type of processes are described andillustrated. Based on these properties splitting processes into classes is carried out.
Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields
Perdikaris, P.; Venturi, D.; Royset, J. O.; Karniadakis, G. E.
2015-01-01
We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders. PMID:26345079
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
HOPF ALGEBRAIC APPROACH TO THE n LINEARLY RECURSIVE SEQUENCES
LIANGGUI
1994-01-01
It is proved that a linearly recursive sequence of n indicea over field F(n≥1) is autorntatically a product of n lioearly recurplve sequencea of 1-lndex over F by the theory of Hopf algebras.By the way,the correspondence between the set of linearly recursive sequenoes of 1-index and F[X]0 is generalised to the case of n-index.
CONDITIONAL RECURSIVE EQUATIONS ON EXCESS-OF-LOSS REINSURANCE
YANG Jing-ping; WANG Xiao-qian; CHENG Shi-hong
2006-01-01
The marginal recursive equations on excess-of-loss reinsurance treaty are investignted, under the assumption that the number of claims belongs to the family consisting of Poisson, binomial and negative binomial, and that the severity distribution has bounded continuous density function. On conditional of the numbers of claims associated with the reinsurer and the cedent, some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.
Recursive least squares background prediction of univariate syndromic surveillance data
Burkom Howard; Najmi Amir-Homayoon
2009-01-01
Abstract Background Surveillance of univariate syndromic data as a means of potential indicator of developing public health conditions has been used extensively. This paper aims to improve the performance of detecting outbreaks by using a background forecasting algorithm based on the adaptive recursive least squares method combined with a novel treatment of the Day of the Week effect. Methods Previous work by the first author has suggested that univariate recursive least squares analysis of s...
Color-dressed recursive relations for multi-parton amplitudes
Duhr, C; Maltoni, F; Duhr, Claude; Hoeche, Stefan; Maltoni, Fabio
2006-01-01
Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.
Tube formula, Berezinians, and Dwork formula
Khudaverdian, Hovhannes M
2007-01-01
We consider an example of tubes of hypersurfaces in Euclidean space and generalise the tube formula to supercase. By this we assign to a point of the hypersurface in superspace a rational characteristic function. Does this rational function appear when we calculate the zeta-function of an arithmetic variety?
Recursive construction of perfect DNA molecules from imperfect oligonucleotides.
Linshiz, Gregory; Yehezkel, Tuval Ben; Kaplan, Shai; Gronau, Ilan; Ravid, Sivan; Adar, Rivka; Shapiro, Ehud
2008-01-01
Making faultless complex objects from potentially faulty building blocks is a fundamental challenge in computer engineering, nanotechnology and synthetic biology. Here, we show for the first time how recursion can be used to address this challenge and demonstrate a recursive procedure that constructs error-free DNA molecules and their libraries from error-prone oligonucleotides. Divide and Conquer (D&C), the quintessential recursive problem-solving technique, is applied in silico to divide the target DNA sequence into overlapping oligonucleotides short enough to be synthesized directly, albeit with errors; error-prone oligonucleotides are recursively combined in vitro, forming error-prone DNA molecules; error-free fragments of these molecules are then identified, extracted and used as new, typically longer and more accurate, inputs to another iteration of the recursive construction procedure; the entire process repeats until an error-free target molecule is formed. Our recursive construction procedure surpasses existing methods for de novo DNA synthesis in speed, precision, amenability to automation, ease of combining synthetic and natural DNA fragments, and ability to construct designer DNA libraries. It thus provides a novel and robust foundation for the design and construction of synthetic biological molecules and organisms.
Recursive implementations of temporal filters for image motion computation.
Clifford, C W; Langley, K
2000-05-01
Efficient algorithms for image motion computation are important for computer vision applications and the modelling of biological vision systems. Intensity-based image motion computation proceeds in two stages: the convolution of linear spatiotemporal filter kernels with the image sequence, followed by the non-linear combination of the filter outputs. If the spatiotemporal extent of the filter kernels is large, then the convolution stage can be very intensive computationally. One effective means of reducing the storage required and computation involved in implementing the temporal convolutions is the introduction of recursive filtering. Non-recursive methods require the number of frames of the image sequence stored at any given time to be equal to the temporal extent of the slowest temporal filter. In contrast, recursive methods encode recent stimulus history implicitly in the values of a small number of variables updated through a series of feedback equations. Recursive filtering reduces the number of values stored in memory during convolution and the number of mathematical operations involved in computing the filters' outputs. This paper extends previous recursive implementations of gradient- and correlation-based motion analysis algorithms [Fleet DJ, Langley K (1995) IEEE PAMI 17: 61-67; Clifford CWG, Ibbotson MR, Langley K (1997) Vis Neurosci 14: 741-749], describing a recursive implementation of causal band-pass temporal filters suitable for use in energy- and phase-based algorithms for image motion computation. It is shown that the filters' temporal frequency tuning curves fit psychophysical estimates of the temporal properties of human visual filters.
On the robustness of random Boolean formulae
Mozeika, Alexander; Saad, David [Non-linearity and Complexity Research Group, Aston University, Birmingham B4 7ET (United Kingdom); Raymond, Jack, E-mail: a.s.mozeika@aston.ac.u, E-mail: d.saad@aston.ac.u [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
2010-06-01
Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models.
The loading problem for recursive neural networks.
Gori, Marco; Sperduti, Alessandro
2005-10-01
The present work deals with one of the major and not yet completely understood topics of supervised connectionist models. Namely, it investigates the relationships between the difficulty of a given learning task and the chosen neural network architecture. These relationships have been investigated and nicely established for some interesting problems in the case of neural networks used for processing vectors and sequences, but only a few studies have dealt with loading problems involving graphical inputs. In this paper, we present sufficient conditions which guarantee the absence of local minima of the error function in the case of learning directed acyclic graphs with recursive neural networks. We introduce topological indices which can be directly calculated from the given training set and that allows us to design the neural architecture with local minima free error function. In particular, we conceive a reduction algorithm that involves both the information attached to the nodes and the topology, which enlarges significantly the class of the problems with unimodal error function previously proposed in the literature.
A bi-recursive neural network architecture for the prediction of protein coarse contact maps.
Vullo, Alessandro; Frasconi, Paolo
2002-01-01
Prediction of contact maps may be seen as a strategic step towards the solution of fundamental open problems in structural genomics. In this paper we focus on coarse grained maps that describe the spatial neighborhood relation between secondary structure elements (helices, strands, and coils) of a protein. We introduce a new machine learning approach for scoring candidate contact maps. The method combines a specialized noncausal recursive connectionist architecture and a heuristic graph search algorithm. The network is trained using candidate graphs generated during search. We show how the process of selecting and generating training examples is important for tuning the precision of the predictor.
Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions
Youneng Ma
2014-01-01
Full Text Available Partial fraction expansion (pfe is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles.
Rani K
2014-08-01
Full Text Available Photocopy documents are very common in our normal life. People are permitted to carry and present photocopied documents to avoid damages to the original documents. But this provision is misused for temporary benefits by fabricating fake photocopied documents. Fabrication of fake photocopied document is possible only in 2nd and higher order recursive order of photocopies. Whenever a photocopied document is submitted, it may be required to check its originality. When the document is 1st order photocopy, chances of fabrication may be ignored. On the other hand when the photocopy order is 2nd or above, probability of fabrication may be suspected. Hence when a photocopy document is presented, the recursive order number of photocopy is to be estimated to ascertain the originality. This requirement demands to investigate methods to estimate order number of photocopy. In this work, a voting based approach is used to detect the recursive order number of the photocopy document using probability distributions exponential, extreme values and lognormal distributions is proposed. A detailed experimentation is performed on a generated data set and the method exhibits efficiency close to 89%.
General forecasting correcting formula
Harin, Alexander
2009-01-01
A general forecasting correcting formula, as a framework for long-use and standardized forecasts, is created. The formula provides new forecasting resources and new possibilities for expansion of forecasting including economic forecasting into the areas of municipal needs, middle-size and small-size business and, even, to individual forecasting.
Mann, Allen L
2008-01-01
IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: ``Which IFG-formulas are equivalent to ordinary first-order formulas?'' We use the answer to show that the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure.
Formula misasi?! / Sten Soomlais
Soomlais, Sten
2008-01-01
Formula Student on kõrgkoolide masinaehituse ja/või autotehnika tudengite meeskondade vaheline iga-aastane tootearendusvõistlus, mis kujutab endast väikese vormelauto projekteerimist, ehitamist ja võidusõitmist ringrajal. Lisa: Formula Student Eestis
General forecasting correcting formula
2009-01-01
A general forecasting correcting formula, as a framework for long-use and standardized forecasts, is created. The formula provides new forecasting resources and new possibilities for expansion of forecasting including economic forecasting into the areas of municipal needs, middle-size and small-size business and, even, to individual forecasting.
Vandenplas, Yvan; De Greef, Elisabeth; Veereman, Gigi
2014-01-01
The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn't. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota resembling that of breastfed infants. They are added to infant formula because of their presence in breast milk. Infants on these supplemented formula have a lower stool pH, a better stool consistency and frequency and a higher concentration of bifidobacteria in their intestine compared to infants on a non-supplemented standard formula. Since most studies suggest a trend for beneficial clinical effects, and since these ingredients are very safe, prebiotics bring infant formula one step closer to breastmilk, the golden standard. However, despite the fact that adverse events are rare, the evidence on prebiotics of a significant health benefit throughout the alteration of the gut microbiota is limited.
Vandenplas, Yvan; Greef, Elisabeth De; Veereman, Gigi
2014-01-01
The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn’t. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota resembling that of breastfed infants. They are added to infant formula because of their presence in breast milk. Infants on these supplemented formula have a lower stool pH, a better stool consistency and frequency and a higher concentration of bifidobacteria in their intestine compared to infants on a non-supplemented standard formula. Since most studies suggest a trend for beneficial clinical effects, and since these ingredients are very safe, prebiotics bring infant formula one step closer to breastmilk, the golden standard. However, despite the fact that adverse events are rare, the evidence on prebiotics of a significant health benefit throughout the alteration of the gut microbiota is limited. PMID:25535999
Formula misasi?! / Sten Soomlais
Soomlais, Sten
2008-01-01
Formula Student on kõrgkoolide masinaehituse ja/või autotehnika tudengite meeskondade vaheline iga-aastane tootearendusvõistlus, mis kujutab endast väikese vormelauto projekteerimist, ehitamist ja võidusõitmist ringrajal. Lisa: Formula Student Eestis
Recursive recovery of Markov transition probabilities from boundary value data
Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)
1994-04-01
In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.
Some error bounds for K-iterated Gaussian recursive filters
Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia
2016-10-01
Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.
Recursion to food plants by free-ranging Bornean elephant
Megan English
2015-08-01
Full Text Available Plant recovery rates after herbivory are thought to be a key factor driving recursion by herbivores to sites and plants to optimise resource-use but have not been investigated as an explanation for recursion in large herbivores. We investigated the relationship between plant recovery and recursion by elephants (Elephas maximus borneensis in the Lower Kinabatangan Wildlife Sanctuary, Sabah. We identified 182 recently eaten food plants, from 30 species, along 14 × 50 m transects and measured their recovery growth each month over nine months or until they were re-browsed by elephants. The monthly growth in leaf and branch or shoot length for each plant was used to calculate the time required (months for each species to recover to its pre-eaten length. Elephant returned to all but two transects with 10 eaten plants, a further 26 plants died leaving 146 plants that could be re-eaten. Recursion occurred to 58% of all plants and 12 of the 30 species. Seventy-seven percent of the re-eaten plants were grasses. Recovery times to all plants varied from two to twenty months depending on the species. Recursion to all grasses coincided with plant recovery whereas recursion to most browsed plants occurred four to twelve months before they had recovered to their previous length. The small sample size of many browsed plants that received recursion and uneven plant species distribution across transects limits our ability to generalise for most browsed species but a prominent pattern in plant-scale recursion did emerge. Plant recovery time was a good predictor of time to recursion but varied as a function of growth form (grass, ginger, palm, liana and woody and differences between sites. Time to plant recursion coincided with plant recovery time for the elephant’s preferred food, grasses, and perhaps also gingers, but not the other browsed species. Elephants are bulk feeders so it is likely that they time their returns to bulk feed on these grass species when
Counting permutations with no long monotone subsequence via generating trees
Bousquet-Mélou, Mireille
2010-01-01
We recover Gessel's determinantal formula for the generating function of permutations with no ascending subsequence of length m+1. The starting point of our proof is the recursive construction of these permutations by insertion of the largest entry. This construction is of course extremely simple. The cost of this simplicity is that we need to take into account in the enumeration m-1 additional parameters --- namely, the positions of the leftmost increasing subsequences of length i, for i=2,...,m. This yields for the generating function a functional equation with m-1 "catalytic" variables, and the heart of the paper is the solution of this equation. We perform a similar task for involutions with no descending subsequence of length m+1, constructed recursively by adding a cycle containing the largest entry. We refine this result by keeping track of the number of fixed points. In passing, we prove that the ordinary generating functions of these families of permutations can be expressed as constant terms of rati...
A product formula and combinatorial field theory
Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I
2004-01-01
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
A Summation Formula for Macdonald Polynomials
de Gier, Jan; Wheeler, Michael
2016-03-01
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.
Keller, Kai Johannes
2010-01-01
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmer...
Readability Formulas: Pluses and Minuses.
Rygiel, Mary Ann
1982-01-01
Examines readability formulas and examples of their misuse. Analyzes an essay by George Orwell which was given a grade 10 readability level by one formula and discusses characteristics of Orwell's style that refute the accuracy of formula rating. (HTH)
Some Sum Formula for Generalized Lucas Numbers%广义Lucas数列的一些求和公式
陈小芳
2011-01-01
Defined by second linear recursion formula,Lucas sequence plays a significant role in theory research.In this paper, according some material on Lucas series, having researched unified formula problem of the generalized Lucas series equal length sub-sequence continuous items sum, we have given a more widely sum formula for generalized Lucas sequence and then we have adopted the recursive inductive method to prove.%由二次线性递推公式所定义的Lucas数列｛Ln}在数学的理论研究中有重要的作用.本文在已有的有关广义Lucas数列相关定理的基础上进一步推广,给出了更为广泛的广义Lucas数列的求和公式,采用了递推归纳的方法证明.
U.S. Department of Health & Human Services — This list includes products subject to recall since September 2010 related to infant formula distributed by Abbott. This list will be updated with publicly...
U.S. Department of Health & Human Services — This list includes products subject to recall since September 2010 related to infant formula distributed by Abbott. This list will be updated with publicly available...
Video game for learning and metaphorization of recursive algorithms
Ricardo Inacio Alvares Silva
2013-09-01
Full Text Available The learning of recursive algorithms in computer programming is problematic, because its execution and resolution is not natural to the thinking way people are trained and used to since young. As with other topics in algorithms, we use metaphors to make parallels between the abstract and the concrete to help in understanding the operation of recursive algorithms. However, the classic metaphors employed in this area, such as calculating factorial recursively and Towers of Hanoi game, may just confuse more or be insufficient. In this work, we produced a computer game to assist students in computer courses in learning recursive algorithms. It was designed to have regular video game characteristics, with narrative and classical gameplay elements, commonly found in this kind of product. Aiding to education occurs through metaphorization, or in other words, through experiences provided by game situations that refer to recursive algorithms. To this end, we designed and imbued in the game four valid metaphors related to the theory, and other minor references to the subject.
Localized Recursive Estimation in Energy Constrained Wireless Sensor Networks
Bang Wang
2006-06-01
Full Text Available This paper proposes a localized recursive estimation scheme for parameter estimation in wireless sensor networks. Given any parameter of a target occurring at some location and time, a number of sensors recursively estimate the parameter by using their local measurements of the parameter that is attenuated with the distance between a sensor and the target location and corrupted by noise. Compared with centralized estimation schemes that transmit all encoded measurements to a sink (or a fusion center, the recursive scheme needs only to transmit the final estimate to a sink. When the sink is faraway from the sensors and multihop communications have to be used, using localized recursive estimation can help to reduce energy consumption and reduce network traffic load. A sensor sequence with the fastest convergence rate is identified, by which the variance of estimation error reduces faster than all other sequences. In the case of adjustable transmission power, a heuristic has been proposed to find a sensor sequence with the minimum total transmission power when performing the recursive estimation. Numerical examples have been used to compare the performance of the proposed scheme with that of a centralized estimation scheme and have also shown the effectiveness of the proposed heuristic.
The redundancy of recursion and infinity for natural language.
Luuk, Erkki; Luuk, Hendrik
2011-02-01
An influential line of thought claims that natural language and arithmetic processing require recursion, a putative hallmark of human cognitive processing (Chomsky in Evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 45-61, 2010; Fitch et al. in Cognition 97(2):179-210, 2005; Hauser et al. in Science 298(5598):1569-1579, 2002). First, we question the need for recursion in human cognitive processing by arguing that a generally simpler and less resource demanding process--iteration--is sufficient to account for human natural language and arithmetic performance. We argue that the only motivation for recursion, the infinity in natural language and arithmetic competence, is equally approachable by iteration and recursion. Second, we submit that the infinity in natural language and arithmetic competence reduces to imagining infinite embedding or concatenation, which is completely independent from the ability to implement infinite processing, and thus, independent from both recursion and iteration. Furthermore, we claim that a property of natural language is physically uncountable finity and not discrete infinity.
Geometrization of Trace Formulas
Frenkel, Edward
2010-01-01
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.
Spin-1 Ising model on tetrahedron recursive lattices: Exact results
Jurčišinová, E.; Jurčišin, M.
2016-11-01
We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z = 6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.
Recursive modular modelling methodology for lumped-parameter dynamic systems.
Orsino, Renato Maia Matarazzo
2017-08-01
This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia-Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.
Termination Casts: A Flexible Approach to Termination with General Recursion
Aaron Stump
2010-12-01
Full Text Available This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form "Terminates t", expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.
Recursive Heaviside step functions and beginning of the universe
Shin, Changsoo; Kim, Seongjai
2017-04-01
This article introduces recursive Heaviside step functions, as a potential of the known universe, for the first time in the history of mathematics, science, and engineering. In modern cosmology, various bouncing models have been suggested based on the postulation that the current universe is the result of the collapse of a previous universe. However, all Big Bounce models leave unanswered the question of what powered inflation. Recursive Heaviside step functions are analyzed to represent the warpage of spacetime during the crunch-bounce transition. In particular, the time shift appeared during the transition is modeled in the form of recursive Heaviside step functions and suggested as a possible answer for the immeasurable energy appeared for the Big Bounce.
Theoretical properties of recursive neural networks with linear neurons.
Bianchini, M; Gori, M
2001-01-01
Recursive neural networks are a powerful tool for processing structured data, thus filling the gap between connectionism, which is usually related to poorly organized data, and a great variety of real-world problems, where the information is naturally encoded in the relationships among the basic entities. In this paper, some theoretical results about linear recursive neural networks are presented that allow one to establish conditions on their dynamical properties and their capability to encode and classify structured information. A lot of the limitations of the linear model, intrinsically related to recursive processing, are inherited by the general model, thus establishing their computational capabilities and range of applicability. As a byproduct of our study some connections with the classical linear system theory are given where the processing is extended from sequences to graphs.
Contextual processing of structured data by recursive cascade correlation.
Micheli, Alessio; Sona, Diego; Sperduti, Alessandro
2004-11-01
This paper propose a first approach to deal with contextual information in structured domains by recursive neural networks. The proposed model, i.e., contextual recursive cascade correlation (CRCC), a generalization of the recursive cascade correlation (RCC) model, is able to partially remove the causality assumption by exploiting contextual information stored in frozen units. We formally characterize the properties of CRCC showing that it is able to compute contextual transductions and also some causal supersource transductions that RCC cannot compute. Experimental results on controlled sequences and on a real-world task involving chemical structures confirm the computational limitations of RCC, while assessing the efficiency and efficacy of CRCC in dealing both with pure causal and contextual prediction tasks. Moreover, results obtained for the real-world task show the superiority of the proposed approach versus RCC when exploring a task for which it is not known whether the structural causality assumption holds.
Probability properties and fractal properties of statistically recursive sets
无
2001-01-01
In this paper we construct a class of statistically recursive sets K by statistical contraction operators and prove the convergence and the measurability of K. Many important sets are the special cases of K. Then we investigate the statistically self-similar measure (or set). We have found some sufficient conditions to ensure the statistically recursive set to be statistically self-similar. We also investigate the distribution PK-1. The zero-one laws and the support of PK-1 are obtained.Finally the Hausdorff dimension and Hausdorff exact measure function of a class of statistically recursive sets constructed by a collection of i.i.d. statistical contraction operators have been obtained.
From twistor string theory to recursion relations
Spradlin, Marcus; Volovich, Anastasia
2009-10-01
Witten’s twistor string theory gives rise to an enigmatic formula known as the “connected prescription” for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles we demonstrate explicitly that certain contour deformations rewrite the connected prescription as the Britto-Cachazo-Feng-Witten representation, thereby establishing a concrete link between Witten’s twistor string theory and the dual formulation for the S matrix of the N=4 SYM recently proposed by Arkani-Hamed Other choices of integration contour also give rise to “intermediate prescriptions.” We expect a similar though more intricate structure for more general amplitudes.
LU; Wenxuan
2006-01-01
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes.
Tan, Zhi-Zhong
2015-05-01
We develop a general recursion-transform (R-T) method for a two-dimensional resistor network with a zero resistor boundary. As applications of the R-T method, we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m×n resistor network with a null resistor and three arbitrary boundaries, a problem never solved before, since Green's function techniques and Laplacian matrix approaches are invalid in this case. Looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network. In this paper we obtain several general formulas of resistance between any two nodes in a nonregular m×n resistor network in both finite and infinite cases. In particular, 12 special cases are given by reducing one of the general formulas to understand its applications and meanings, and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network.
On a (2,2-rational recursive sequence
Ben Rhouma Mohamed
2005-01-01
Full Text Available We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+βyn/(1+yn-1 when the parameters α < 0 and β ∈ ℝ. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a + byn/(A + Byn-1, when the parameters a, b, A, B ∈ ℝ and abAB ≠ 0.
Detection of small target using recursive higher order statistics
Hou, Wang; Sun, Hongyuan; Lei, Zhihui
2014-02-01
In this paper, a recursive higher order statistics algorithm is proposed for small target detection in temporal domain. Firstly, the background of image sequence is normalized. Then, the higher order statistics are recursively solved in image sequence to obtain the feature image. Finally, the feature image is segmented with threshold to detect the small target. To validate the algorithm proposed in this paper, five simulated and one semi-simulation image sequences are created. The ROC curves are employed for evaluation of experimental results. Experiment results show that our method is very effective for small target detection.
Note on recursion relations for the Q -cut representation
Feng, Bo; He, Song; Huang, Rijun; Luo, Ming-xing
2017-01-01
In this note, we study the Q -cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., n-point one-loop integrand is constructed using tree-level amplitudes and m-point one-loop integrands with m ≤ n - 1. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original Q -cut construction, up to scale free terms.
THE PARALLEL RECURSIVE AP ADAPTIVE ALGORITHM BASED ON VOLTERRA SERIES
无
2005-01-01
Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identifies in parallel the Volterra kernel of each order, recursively estimate the inverse of the autocorrelation matrix for the Volterra input of each order, and remarkably improve the convergence speed of the identification process compared with the NLMS and conventional AP adaptive algorithm based on Volterra series. Simulation results indicate that the proposed method in this paper is efficient.
On-Shell Recursion Relations for Generic Theories
Cheung, Clifford
2008-01-01
We show that on-shell recursion relations hold for tree amplitudes in generic two derivative theories of multiple particle species and diverse spins. For example, in a gauge theory coupled to scalars and fermions, any amplitude with at least one gluon obeys a recursion relation. In (super)gravity coupled to scalars and fermions, the same holds for any amplitude with at least one graviton. This result pertains to a broad class of theories, including QCD, N=4 SYM, and N=8 supergravity.
Recursion relations and branching rules for simple Lie algebras
Lyakhovsky, V D
1995-01-01
The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights \\Gamma specific for each injection. The structure of \\Gamma is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for A_{3} \\oplus u(1) \\rightarrow B_{4} injection.
Topological recursion and a quantum curve for monotone Hurwitz numbers
Do, Norman; Dyer, Alastair; Mathews, Daniel V.
2017-10-01
Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In this paper, we prove that monotone Hurwitz numbers arise from the topological recursion of Eynard and Orantin applied to a particular spectral curve. We furthermore derive a quantum curve for monotone Hurwitz numbers. These results extend the collection of enumerative problems known to be governed by the paradigm of topological recursion and quantum curves, as well as the list of analogues between monotone Hurwitz numbers and their classical counterparts.
Chang, Chein-I
2017-01-01
This book explores recursive architectures in designing progressive hyperspectral imaging algorithms. In particular, it makes progressive imaging algorithms recursive by introducing the concept of Kalman filtering in algorithm design so that hyperspectral imagery can be processed not only progressively sample by sample or band by band but also recursively via recursive equations. This book can be considered a companion book of author’s books, Real-Time Progressive Hyperspectral Image Processing, published by Springer in 2016. Explores recursive structures in algorithm architecture Implements algorithmic recursive architecture in conjunction with progressive sample and band processing Derives Recursive Hyperspectral Sample Processing (RHSP) techniques according to Band-Interleaved Sample/Pixel (BIS/BIP) acquisition format Develops Recursive Hyperspectral Band Processing (RHBP) techniques according to Band SeQuential (BSQ) acquisition format for hyperspectral data.
Andersen, Bjarne Stig; Gunnels, John A.; Gustavson, Fred
2002-01-01
A new Recursive Packed Inverse Calculation Algorithm for symmetric positive definite matrices has been developed. The new Recursive Inverse Calculation algorithm uses minimal storage, \\$n(n+1)/2\\$, and has nearly the same performance as the LAPACK full storage algorithm using \\$n\\^2\\$ memory words....... New recursive packed BLAS needed for this algorithm have been developed too. Two transformation routines, from the LAPACK packed storage data format to the recursive storage data format were added to the package too....
The Pico's formula Generalization
Sergiu Cataranciuc; Marina Holban
2007-01-01
The Pico formula generalizations are obtained for area calculation of a polygon P through the determination of special nodes of the network in which this P is placed. The case of the polygon with rational coordinates of its vertexes is examined, as well as the case of the polygon with holes. In the case of three-dimensional space a formula of volume calculation for some polyhedrons, such as prism and tetrahedron is presented. On the basis of theoretic outcomes an algorithm that can be applied...
The Pico's formula Generalization
Sergiu Cataranciuc
2007-04-01
Full Text Available The Pico formula generalizations are obtained for area calculation of a polygon P through the determination of special nodes of the network in which this P is placed. The case of the polygon with rational coordinates of its vertexes is examined, as well as the case of the polygon with holes. In the case of three-dimensional space a formula of volume calculation for some polyhedrons, such as prism and tetrahedron is presented. On the basis of theoretic outcomes an algorithm that can be applied in calculation for areas of plane figure is elaborated.
Teaching and Learning Recursive Programming: A Review of the Research Literature
McCauley, Renée; Grissom, Scott; Fitzgerald, Sue; Murphy, Laurie
2015-01-01
Hundreds of articles have been published on the topics of teaching and learning recursion, yet fewer than 50 of them have published research results. This article surveys the computing education research literature and presents findings on challenges students encounter in learning recursion, mental models students develop as they learn recursion,…
Differential constraints for bounded recursive identification with multivariate splines
De Visser, C.C.; Chu, Q.P.; Mulder, J.A.
2011-01-01
The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able
A Survey on Teaching and Learning Recursive Programming
Christian RINDERKNECHT
2014-04-01
Full Text Available We survey the literature about the teaching and learning of recursive programming. After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some programming methodology, as well as the functional and imperative paradigms and the distinction between control flow vs. data flow. We follow the researchers in stating the problem with base cases, noting the similarity with induction in mathematics, making concrete analogies for recursion, using games, visualizations, animations, multimedia environments, intelligent tutoring systems and visual programming. We cover the usage in schools of the Logo programming language and the associated theoretical didactics, including a brief overview of the constructivist and constructionist theories of learning; we also sketch the learners' mental models which have been identified so far, and non-classical remedial strategies, such as kinesthesis and syntonicity. We append an extensive and carefully collated bibliography, which we hope will facilitate new research.
A nested recursive logit model for route choice analysis
Mai, Tien; Frejinger, Emma; Fosgerau, Mogens
2015-01-01
We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link...
Recursive Inversion By Finite-Impulse-Response Filters
Bach, Ralph E., Jr.; Baram, Yoram
1991-01-01
Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.
Recursive inversion of externally defined linear systems by FIR filters
Bach, Ralph E., Jr.; Baram, Yoram
1989-01-01
The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.
Knot Invariants from Topological Recursion on Augmentation Varieties
Gu, Jie; Klemm, Albrecht; Soroush, Masoud
2014-01-01
Using the duality between Wilson loop expectation values of SU(N) Chern-Simons theory on $S^3$ and topological open-string amplitudes on the local mirror of the resolved conifold, we study knots on $S^3$ and their invariants encoded in colored HOMFLY polynomials by means of topological recursion. In the context of the local mirror Calabi-Yau threefold of the resolved conifold, we generalize the topological recursion of the remodelled B-model in order to study branes beyond the class of toric Harvey-Lawson special Lagrangians -- as required for analyzing non-trivial knots on $S^3$. The basic ingredients for the proposed recursion are the spectral curve, given by the augmentation variety of the knot, and the calibrated annulus kernel, encoding the topological annulus amplitudes associated to the knot. We present an explicit construction of the calibrated annulus kernel for torus knots and demonstrate the validity of the topological recursion. We further argue that -- if an explicit form of the calibrated annulu...
Recursive representation of the torus 1-point conformal block
Hadasz, Leszek; Suchanek, Paulina
2009-01-01
The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by R. Poghossian. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.
Efficient Integrity Checking for Databases with Recursive Views
Martinenghi, Davide; Christiansen, Henning
2005-01-01
into incremental and optimized tests specialized for given update patterns. These tests may involve the introduction of new views, but for relevant cases of recursion, simplified integrity constraints are obtained that can be checked more efficiently than the original ones and without auxiliary views. Notably...
EVALUATION OF SOME PRODUCTION CHARACTERISTICS OF RECURSIVE CONVEYOR
Boris V. Kupriyanov
2016-01-01
Full Text Available We consider the two objectives of direct relevance to operational planning based on the model of recursive conveyor process. Calculate the Critical Operation of the conveyor and calculate the Load Factor of the equipment of the conveyor.
A nested recursive logit model for route choice analysis
Mai, Tien; Frejinger, Emma; Fosgerau, Mogens
2015-01-01
We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link...
A metric model of lambda calculus with guarded recursion
Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian
2010-01-01
We give a model for Nakano’s typed lambda calculus with guarded recursive definitions in a category of metric spaces. By proving a computational adequacy result that relates the interpretation with the operational semantics, we show that the model can be used to reason about contextual equivalence....
Velocity estimation using recursive ultrasound imaging and spatially encoded signals
Nikolov, Svetoslav; Gammelmark, Kim; Jensen, Jørgen Arendt
2000-01-01
Previously we have presented a recursive beamforming algorithm for synthetic transmit aperture focusing. At every emission a beamformed low-resolution image is added to an existing high-resolution one, and the low-resolution image from the previous emission with the current active element is subt...
RECURSIVE CLASSIFICATION OF MQAM SIGNALS BASED ON HIGHER ORDER CUMULANTS
Chen Weidong; Yang Shaoquan
2002-01-01
A new feature based on higher order cumulants is proposed for classification of MQAM signals. Theoretical analysis justify that the new feature is invariant with respect to translation (shift), scale and rotation transform of signal constellations, and can suppress color or white additive Gaussian noise. Computer simulation shows that the proposed recursive orderreduction based classification algorithm can classify MQAM signals with any order.
Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets
Kraft, Holger; Seifried, Frank Thomas; Steffensen, Mogens
2013-01-01
In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein–Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton–Jacobi–Bellman equation and provide a suitable verification theorem...
Pedestrian Path Prediction with Recursive Bayesian Filters: A Comparative Study
Schneider, N.; Gavrila, D.M.
2013-01-01
In the context of intelligent vehicles, we perform a comparative study on recursive Bayesian filters for pedestrian path prediction at short time horizons (< 2s). We consider Extended Kalman Filters (EKF) based on single dynamical models and Interacting Multiple Models (IMM) combining several such
Recursivity: A Working Paper on Rhetoric and "Mnesis"
Stormer, Nathan
2013-01-01
This essay proposes the genealogical study of remembering and forgetting as recursive rhetorical capacities that enable discourse to place itself in an ever-changing present. "Mnesis" is a meta-concept for the arrangements of remembering and forgetting that enable rhetoric to function. Most of the essay defines the materiality of "mnesis", first…
Accurate estimates of solutions of second order recursions
Mattheij, R.M.M.
1975-01-01
Two important types of two dimensional matrix-vector and second order scalar recursions are studied. Both types possess two kinds of solutions (to be called forward and backward dominant solutions). For the directions of these solutions sharp estimates are derived, from which the solutions themselve
Finite petri nets as models for recursive causal behaviour
Goltz, Ursula; Rensink, Arend
1994-01-01
Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a.nil | b.B)+c.nil. We will show that the answer depends on the chosen
Pedestrian Path Prediction with Recursive Bayesian Filters: A Comparative Study
Schneider, N.; Gavrila, D.M.
2013-01-01
In the context of intelligent vehicles, we perform a comparative study on recursive Bayesian filters for pedestrian path prediction at short time horizons (< 2s). We consider Extended Kalman Filters (EKF) based on single dynamical models and Interacting Multiple Models (IMM) combining several such b
Exploring the Recursive Nature of Food and Family Communication
Manning, Linda D.
2006-01-01
Family meals act as a barometer to signify the changing nature of family life. The primary objective of this activity is to allow students to experience the many ways in which a recursive relationship exists between the food families eat and the patterns of communication families enact. Through this activity, students experience how food and…
Recursive confidence band construction for an unknown distribution function.
Kiatsupaibul, Seksan; Hayter, Anthony J
2015-01-01
Given a sample X1,...,Xn of independent observations from an unknown continuous distribution function F, the problem of constructing a confidence band for F is considered, which is a fundamental problem in statistical inference. This confidence band provides simultaneous inferences on all quantiles and also on all of the cumulative probabilities of the distribution, and so they are among the most important inference procedures that address the issue of multiplicity. A fully nonparametric approach is taken where no assumptions are made about the distribution function F. Historical approaches to this problem, such as Kolmogorov's famous () procedure, represent some of the earliest inference methodologies that address the issue of multiplicity. This is because a confidence band at a given confidence level 1-α allows inferences on all of the quantiles of the distribution, and also on all of the cumulative probabilities, at that specified confidence level. In this paper it is shown how recursive methodologies can be employed to construct both one-sided and two-sided confidence bands of various types. The first approach operates by putting bounds on the cumulative probabilities at the data points, and a recursive integration approach is described. The second approach operates by providing bounds on certain specified quantiles of the distribution, and its implementation using recursive summations of multinomial probabilities is described. These recursive methodologies are illustrated with examples, and R code is available for their implementation.
A Decidable Recursive Logic for Weighted Transition Systems
Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian
2014-01-01
In this paper we develop and study the Recursive Weighted Logic (RWL), a multi-modal logic that expresses qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems labelled with actions and real-valued quantities representing the costs of ...
Step-indexed Kripke models over recursive worlds
Birkedal, Lars; Reus, Bernhard; Schwinghammer, Jan
2011-01-01
worlds that are recursively defined in a category of metric spaces. In this paper, we broaden the scope of this technique from the original domain-theoretic setting to an elementary, operational one based on step indexing. The resulting method is widely applicable and leads to simple, succinct models...
Semantics Boosts Syntax in Artificial Grammar Learning Tasks with Recursion
Fedor, Anna; Varga, Mate; Szathmary, Eors
2012-01-01
Center-embedded recursion (CER) in natural language is exemplified by sentences such as "The malt that the rat ate lay in the house." Parsing center-embedded structures is in the focus of attention because this could be one of the cognitive capacities that make humans distinct from all other animals. The ability to parse CER is usually…
Kastening
2000-04-01
The free energy of a multicomponent scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys nonlinear functional differential equations which are turned into recursion relations for the connected Green's functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Green's functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multiloop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are nonperturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.
Zhu, Binqi; Gao, Yesheng; Wang, Kaizhi; Liu, Xingzhao
2016-04-01
A computational method for suppressing clutter and generating clear microwave images of targets is proposed in this paper, which combines synthetic aperture radar (SAR) principles with recursive method and waveform design theory, and it is suitable for SAR for special applications. The nonlinear recursive model is introduced into the SAR operation principle, and the cubature Kalman filter algorithm is used to estimate target and clutter responses in each azimuth position based on their previous states, which are both assumed to be Gaussian distributions. NP criteria-based optimal waveforms are designed repeatedly as the sensor flies along its azimuth path and are used as the transmitting signals. A clutter suppression filter is then designed and added to suppress the clutter response while maintaining most of the target response. Thus, with fewer disturbances from the clutter response, we can generate the SAR image with traditional azimuth matched filters. Our simulations show that the clutter suppression filter significantly reduces the clutter response, and our algorithm greatly improves the SINR of the SAR image based on different clutter suppression filter parameters. As such, this algorithm may be preferable for special target imaging when prior information on the target is available.
Research Timeline: Formulaic language
Wray, Alison
2013-01-01
Creating a timeline for formulaic language is far from simple, because several partially independent lines of research have contributed to the emerging picture. Each exhibits cycles of innovation and consolidation over time: domains take a leading role in developing new knowledge and then fall back, while another area comes to the fore. Thus, some…
Sears, Doug; Picus, Lawrence O.
1999-01-01
Recognizing that traditional salary bargaining is divisive and that teacher salaries should remain competitive, Temple City (California) Unified School District has been experimenting with formula-based compensation for the past four years. Primary benefits are lack of conflict over salary increases, which are determined before negotiating other…
The Formula Essay Reconsidered
Haluska, Jan
2012-01-01
Bruce Pirie offers the following criticism about formula essays: "What does a five-paragraph essay teach about writing? It teaches that there are rules, and that those rules take the shape of a preordained form, like a cookie-cutter, into which we can pour ideas and expect them to come out well shaped." He goes on to discredit such essays as being…
Comix, a New Matrix Element Generator
Gleisberg, Tanju; /SLAC; Hoche, Stefan; /Durham U., IPPP
2008-09-03
We present a new tree-level matrix element generator, based on the color dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and color sampling.
Contradiction and Kant's Formula of Universal Law
Kleingeld, Pauline
2017-01-01
Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the
Contradiction and Kant's Formula of Universal Law
Kleingeld, Pauline
2017-01-01
Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the
Contradiction and Kant's Formula of Universal Law
Kleingeld, Pauline
2017-01-01
Kant's most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the
Case Study: Enteral formula: Selecting the right formula for your ...
Renée Blaauw, Division of Human Nutrition, Stellenbosch University. Anna-Lena du Toit, Dietetics .... standard enteral formulae require specialized renal formulae. Respiratory. • Modified .... not yet referred for renal replacement therapy (RRT).
Recursive Estimation of Gauss-Markov Random Fields Indexed over 1-D Space
Vats, Divyanshu
2009-01-01
This paper presents optimal recursive estimators for vector valued Gauss-Markov random \\emph{fields} taking values in $\\R^M$ and indexed by (intervals of) $\\R$ or $\\Z$. These 1-D fields are often called reciprocal processes. They correspond to two point boundary value fields, i.e., they have boundary conditions given at the end points of the indexing interval. To obtain the recursive estimators, we derive two classes of recursive representations for reciprocal processes. The first class transforms the Gaussian reciprocal process into a Gauss-Markov \\emph{process}, from which we derive forward and backwards recursive representations. The second representation folds the index set and transforms the original \\emph{field} taking values in $\\R^M$ into a Markov \\emph{process} taking values in $\\R^{2M}$. The folding corresponds to recursing the reciprocal process from the boundary points and telescoping inwards. From these recursive representations, Kalman filters and recursive smoothers are promptly derived.
Alfredo Bregni
2013-04-01
innovation to the main process functioning. As a result, the proposed algorithm copes better with demand uncertainty, lowers the system nervousness and also removes the need for continuous forecast adjustments, thereby improving the ease in managing the material flow, allowing the development of new forms of collaboration among different supply chain partners and the creation of new business networks. The algorithm is presented in formulas to describe in detail each procedure step and calculations.
Recursive design of nonlinear H∞ excitation controller
无
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
Recursive Array Layouts and Fast Matrix Multiplication
2005-01-01
specialized not only for a specific memory architecture but also for a specific matrix size. The ATLAS project generates code for BLAS 3 routines based on...parallel, rely on good spa- tial and temporal locality of reference for their performance. Matrix multiplication (the BLAS 3 [14] dgemm routine) is a key...multiprocessors with multi-level memory hierarchies, the column-major layout assumed in the BLAS 3 library can produce unfavorable access patterns in the memory
General correcting formula of forecasting?
2009-01-01
A general correcting formula of forecasting (as a framework for long-use and standardized forecasts) is proposed. The formula provides new forecasting resources and areas of application including economic forecasting.
General correcting formula of forecasting?
Harin, Alexander
2009-01-01
A general correcting formula of forecasting (as a framework for long-use and standardized forecasts) is proposed. The formula provides new forecasting resources and areas of application including economic forecasting.
Recursive organizer (ROR): an analytic framework for sequence-based association analysis.
Zhao, Lue Ping; Huang, Xin
2013-07-01
The advent of next-generation sequencing technologies affords the ability to sequence thousands of subjects cost-effectively, and is revolutionizing the landscape of genetic research. With the evolving genotyping/sequencing technologies, it is not unrealistic to expect that we will soon obtain a pair of diploidic fully phased genome sequences from each subject in the near future. Here, in light of this potential, we propose an analytic framework called, recursive organizer (ROR), which recursively groups sequence variants based upon sequence similarities and their empirical disease associations, into fewer and potentially more interpretable super sequence variants (SSV). As an illustration, we applied ROR to assess an association between HLA-DRB1 and type 1 diabetes (T1D), discovering SSVs of HLA-DRB1 with sequence data from the Wellcome Trust Case Control Consortium. Specifically, ROR reduces 36 observed unique HLA-DRB1 sequences into 8 SSVs that empirically associate with T1D, a fourfold reduction of sequence complexity. Using HLA-DRB1 data from Type 1 Diabetes Genetics Consortium as cases and data from Fred Hutchinson Cancer Research Center as controls, we are able to validate associations of these SSVs with T1D. Further, SSVs consist of nine nucleotides, and each associates with its corresponding amino acids. Detailed examination of these selected amino acids reveals their potential functional roles in protein structures and possible implication to the mechanism of T1D.
New recursion relations and a flat space limit for AdS/CFT correlators
Raju, Suvrat
2012-06-01
We consider correlation functions of the stress-tensor or a conserved current in AdSd+1/CFTd computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree-level. These relations have an advantage over the Britto-Cachazo-Feng-Witten (BCFW)-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the d-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon, or graviton amplitude appears as its coefficient.
Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
Andersen, Jorgen E. [Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 Arhus C (Denmark); Chekhov, Leonid O. [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 (Russian Federation); School of Mathematics, Loughborough University, Leicestershire (United Kingdom); Penner, R.C., E-mail: rpenner@caltech.edu [Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 Arhus C (Denmark); Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA, 91125 (United States); Reidys, Christian M. [Department of Mathematics and Computer Science, University of Southern Denmark, DK-5230 Odense M (Denmark); Sulkowski, Piotr, E-mail: psulkows@theory.caltech.edu [Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA, 91125 (United States); Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1090 GL, Amsterdam (Netherlands); Faculty of Physics, University of Warsaw, ul. Hoza 69, 00-681 Warsaw (Poland)
2013-01-21
We introduce and study the Hermitian matrix model with potential V{sub s,t}(x)=x{sup 2}/2-stx/(1-tx), which enumerates the number of linear chord diagrams with no isolated vertices of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly in genus less than four.
Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
Andersen, Jørgen E; Penner, R C; Reidys, Christian M; Sułkowski, Piotr
2012-01-01
We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four.
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2016-01-01
Jet multiplicity distributions in top quark pair ([Formula: see text]) events are measured in pp collisions at a centre-of-mass energy of 8 TeV with the CMS detector at the LHC using a data set corresponding to an integrated luminosity of 19.7[Formula: see text]. The measurement is performed in the dilepton decay channels ([Formula: see text], [Formula: see text], and [Formula: see text]). The absolute and normalized differential cross sections for [Formula: see text] production are measured as a function of the jet multiplicity in the event for different jet transverse momentum thresholds and the kinematic properties of the leading additional jets. The differential [Formula: see text] and [Formula: see text] cross sections are presented for the first time as a function of the kinematic properties of the leading additional [Formula: see text] jets. Furthermore, the fraction of events without additional jets above a threshold is measured as a function of the transverse momenta of the leading additional jets and the scalar sum of the transverse momenta of all additional jets. The data are compared and found to be consistent with predictions from several perturbative quantum chromodynamics event generators and a next-to-leading order calculation.
Recursive utility in a Markov environment with stochastic growth.
Hansen, Lars Peter; Scheinkman, José A
2012-07-24
Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.
ETHICS AND KNOWLEDGE OF RECURSIVITY IN PSYCHOLOGISTS TRAINING
Ramón Sanz Ferramola
2008-07-01
Full Text Available This work deals with the characterization of psychology as a science and profession. Thisfeature is part of the Argentine academic tradition which goes from the origins of psychology as an undergraduate program by the end of the 1950s to the present day. In relation to this topic, four issues are analysed: a the knowledges of psychology showing the necessity of two epistemic dimensions closely related, namely the discursivity and recursivity, or knowledge and metaknowledge, b the role of psychology as a profession within the praxis, rather than in the poiesis, according to the Greek distinction between the implications of these two modalities of the “doing”, c the concurrence and difference of ethics and deontology, their roles, bounds and potentialities within the psychological field in general, and that of scientific-professional morality in particular, and d the definition and characterization of ethics and epistemology as knowledge of recursivity in psychologists’ training.
On a (2,2-rational recursive sequence
Azza K. Khalifa
2005-09-01
Full Text Available We investigate the asymptotic behavior of the recursive difference equation yn+1=(ÃŽÂ±+ÃŽÂ²yn/(1+ynÃ¢ÂˆÂ’1 when the parameters ÃŽÂ±<0 and ÃŽÂ²Ã¢ÂˆÂˆÃ¢Â„Â. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters ÃŽÂ± and ÃŽÂ². We also give a summary of results and open questions on the more general recursive sequences yn+1=(a+byn/(A+BynÃ¢ÂˆÂ’1, when the parameters a,b,A,BÃ¢ÂˆÂˆÃ¢Â„Â and abABÃ¢Â‰Â 0.
Recursive estimation of the conditional geometric median in Hilbert spaces
Cardot, Hervé; Zitt, Pierre-André
2012-01-01
A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirms the interest of this new and fast algorithm when the sample sizes are large. Finally, the ability of these recursive algorithms to deal with very high-dimensional data is illustrated on the robust estimation of television audience profiles conditional on the total time spent watching television over a period of 24 hours.
Recursive three-dimensional model reconstruction based on Kalman filtering.
Yu, Ying Kin; Wong, Kin Hong; Chang, Michael Ming Yuen
2005-06-01
A recursive two-step method to recover structure and motion from image sequences based on Kalman filtering is described in this paper. The algorithm consists of two major steps. The first step is an extended Kalman filter (EKF) for the estimation of the object's pose. The second step is a set of EKFs, one for each model point, for the refinement of the positions of the model features in the three-dimensional (3-D) space. These two steps alternate from frame to frame. The initial model converges to the final structure as the image sequence is scanned sequentially. The performance of the algorithm is demonstrated with both synthetic data and real-world objects. Analytical and empirical comparisons are made among our approach, the interleaved bundle adjustment method, and the Kalman filtering-based recursive algorithm by Azarbayejani and Pentland. Our approach outperformed the other two algorithms in terms of computation speed without loss in the quality of model reconstruction.
ROOM: A recursive object oriented method for information systems development
Thelliez, T.; Donahue, S.
1994-02-09
Although complementary for the development of complex systems, top-down structured design and object oriented approach are still opposed and not integrated. As the complexity of the systems are still growing, and the so-called software crisis still not solved, it is urgent to provide a framework mixing the two paradigms. This paper presents an elegant attempt in this direction through our Recursive Object-Oriented Method (ROOM) in which a top-down approach divides the complexity of the system and an object oriented method studies a given level of abstraction. Illustrating this recursive schema with a simple example, we demonstrate that we achieve the goal of creating loosely coupled and reusable components.
A recursion identity for formal iterated logarithms and iterated exponentials
Robinson, Thomas J
2010-01-01
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of logarithmic intertwining operators and logarithmic tensor category theory for modules for a vertex operator algebra. This extension has a variety of interesting arithmetic properties. We develop one such result here, the aforementioned recursive identity. We have applied this identity elsewhere to certain formal series expansions related to a general formal Taylor theorem and these series expansions in turn yield a sequence of combinatorial identities which have as special cases certain classical combinatorial identities involving (separately) the Stirling numbers of the first and second kinds.
BPSK Receiver Based on Recursive Adaptive Filter with Remodulation
N. Milosevic
2011-12-01
Full Text Available This paper proposes a new binary phase shift keying (BPSK signal receiver intended for reception under conditions of significant carrier frequency offsets. The recursive adaptive filter with least mean squares (LMS adaptation is used. The proposed receiver has a constant, defining the balance between the recursive and the nonrecursive part of the filter, whose proper choice allows a simple construction of the receiver. The correct choice of this parameter could result in unitary length of the filter. The proposed receiver has performance very close to the performance of the BPSK receiver with perfect frequency synchronization, in a wide range of frequency offsets (plus/minus quarter of the signal bandwidth. The results obtained by the software simulation are confirmed by the experimental results measured on the receiver realized with the universal software radio peripheral (USRP, with the baseband signal processing at personal computer (PC.
Development of a recursion RNG-based turbulence model
Zhou, YE; Vahala, George; Thangam, S.
1993-01-01
Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.
Distributed Recursive Least-Squares: Stability and Performance Analysis
Mateos, Gonzalo
2011-01-01
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying...
Encoding nondeterministic fuzzy tree automata into recursive neural networks.
Gori, Marco; Petrosino, Alfredo
2004-11-01
Fuzzy neural systems have been a subject of great interest in the last few years, due to their abilities to facilitate the exchange of information between symbolic and subsymbolic domains. However, the models in the literature are not able to deal with structured organization of information, that is typically required by symbolic processing. In many application domains, the patterns are not only structured, but a fuzziness degree is attached to each subsymbolic pattern primitive. The purpose of this paper is to show how recursive neural networks, properly conceived for dealing with structured information, can represent nondeterministic fuzzy frontier-to-root tree automata. Whereas available prior knowledge expressed in terms of fuzzy state transition rules are injected into a recursive network, unknown rules are supposed to be filled in by data-driven learning. We also prove the stability of the encoding algorithm, extending previous results on the injection of fuzzy finite-state dynamics in high-order recurrent networks.
Risk Assessment Algorithms Based On Recursive Neural Networks
De Lara, Alejandro Chinea Manrique
2007-01-01
The assessment of highly-risky situations at road intersections have been recently revealed as an important research topic within the context of the automotive industry. In this paper we shall introduce a novel approach to compute risk functions by using a combination of a highly non-linear processing model in conjunction with a powerful information encoding procedure. Specifically, the elements of information either static or dynamic that appear in a road intersection scene are encoded by using directed positional acyclic labeled graphs. The risk assessment problem is then reformulated in terms of an inductive learning task carried out by a recursive neural network. Recursive neural networks are connectionist models capable of solving supervised and non-supervised learning problems represented by directed ordered acyclic graphs. The potential of this novel approach is demonstrated through well predefined scenarios. The major difference of our approach compared to others is expressed by the fact of learning t...
Recursive Bayesian recurrent neural networks for time-series modeling.
Mirikitani, Derrick T; Nikolaev, Nikolay
2010-02-01
This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.
Processing directed acyclic graphs with recursive neural networks.
Bianchini, M; Gori, M; Scarselli, F
2001-01-01
Recursive neural networks are conceived for processing graphs and extend the well-known recurrent model for processing sequences. In Frasconi et al. (1998), recursive neural networks can deal only with directed ordered acyclic graphs (DOAGs), in which the children of any given node are ordered. While this assumption is reasonable in some applications, it introduces unnecessary constraints in others. In this paper, it is shown that the constraint on the ordering can be relaxed by using an appropriate weight sharing, that guarantees the independence of the network output with respect to the permutations of the arcs leaving from each node. The method can be used with graphs having low connectivity and, in particular, few outcoming arcs. Some theoretical properties of the proposed architecture are given. They guarantee that the approximation capabilities are maintained, despite the weight sharing.
Recursive algorithm for the two-stage EFOP estimation method
LUO GuiMing; HUANG Jian
2008-01-01
A recursive algorithm for the two-stage empirical frequency-domain optimal param-eter (EFOP) estimation method Was proposed. The EFOP method was a novel sys-tem identificallon method for Black-box models that combines time-domain esti-mation and frequency-domain estimation. It has improved anti-disturbance perfor-mance, and could precisely identify models with fewer sample numbers. The two-stage EFOP method based on the boot-strap technique was generally suitable for Black-box models, but it was an iterative method and takes too much computation work so that it did not work well online. A recursive algorithm was proposed for dis-turbed stochastic systems. Some simulation examples are included to demonstrate the validity of the new method.
Elucidating the stop bands of structurally colored systems through recursion
Amir, Ariel
2012-01-01
Interference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics; namely, specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer and solve it using recursion relations. We present experimental data for various beetles, whose optical structure resembles the proposed model. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursive relations. In order for these to converge, an infinitesimal amount of absorption needs to be present, reminiscent of the regularization procedures commonly used in physics calculations. Thus, using only the phenomenon of...
High resolution inverse scattering in two dimensions using recursive linearization
Borges, Carlos; Greengard, Leslie
2016-01-01
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems, for which we employ a recently developed, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately one million partial differential equations were ...
EEG and MEG source localization using recursively applied (RAP) MUSIC
Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [University of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.
1996-12-31
The multiple signal characterization (MUSIC) algorithm locates multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. A signal subspace is estimated from the data, then the algorithm scans a single dipole model through a three-dimensional head volume and computes projections onto this subspace. To locate the sources, the user must search the head volume for local peaks in the projection metric. Here we describe a novel extension of this approach which we refer to as RAP (Recursively APplied) MUSIC. This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections, which uses the metric of principal correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace. The dipolar orientations, a form of `diverse polarization,` are easily extracted using the associated principal vectors.
Twisting formula of epsilon factors
SAZZAD ALI BISWAS
2017-09-01
For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper, we give a generalized twisting formula of epsilon factorsvia local Jacobi sums.
Recursive bias estimation and L2 boosting
Hengartner, Nicolas W [Los Alamos National Laboratory; Cornillon, Pierre - Andre [INRA, FRANCE; Matzner - Lober, Eric [RENNE, FRANCE
2009-01-01
This paper presents a general iterative bias correction procedure for regression smoothers. This bias reduction schema is shown to correspond operationally to the L{sub 2} Boosting algorithm and provides a new statistical interpretation for L{sub 2} Boosting. We analyze the behavior of the Boosting algorithm applied to common smoothers S which we show depend on the spectrum of I - S. We present examples of common smoother for which Boosting generates a divergent sequence. The statistical interpretation suggest combining algorithm with an appropriate stopping rule for the iterative procedure. Finally we illustrate the practical finite sample performances of the iterative smoother via a simulation study.
Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
Bena, I; Kosower, D A
2004-01-01
Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.
Recursive fragmentation model with quark spin. Application to quark polarimetry
Artru, X
2010-01-01
An elementary recursive model accounting for the quark spin in the fragmentation of a quark into mesons is presented. The quark spin degree of freedom is represented by a two-components spinor. Spin one meson can be included. The model produces Collins effect and jet handedness. The influence of the initial quark polarisation decays exponentially with the rank of the meson, at dierent rates for longitudinal and transverse polarisations
The Recursive Thick Frontier Approach to Estimating Efficiency
Wagenvoort, Rien; Schure, Paul
1999-01-01
The traditional econometric techniques for frontier models, namely the Stochastic Frontier Approach (SFA), the Thick Frontier Approach (TFA) and the Distribution Free Approach (DFA) have in common that they depend on a priori assumptions that are, whether feasible or not, difficult to test. This paper introduces the Recursive Thick Frontier Approach (RTFA) to the estimation of technology parameters when panel data is available. Our approach is based on the assertion that if deviations from th...
Propagator-based methods for recursive subspace model identification
Mercère, Guillaume; Bako, Laurent; Lecoeuche, Stéphane
2008-01-01
International audience; The problem of the online identification of multi-input multi-output (MIMO) state-space models in the framework of discrete-time subspace methods is considered in this paper. Several algorithms, based on a recursive formulation of the MIMO output error state-space (MOESP) identification class, are developed. The main goals of the proposed methods are to circumvent the huge complexity of eigenvalues or singular values decomposition techniques used by the offline algorit...
Forms and Estimation Methods of Panel Recursive Dynamic Systems
Ghassan, Hassan B.
2000-01-01
The purpose of this paper is to study the model belongs to the family of structural equation models with data varying both across individuals (sectors) and in time. A complete theoretical analysis is developed in this work for the case of a dynamic recursive structure. Maximum likelihood estimation and SUR-GLS “Seemingly Unrelated Regressions-Generalized Least Square” estimators (iterated or not, with proper instruments and with Taylor’s transformation) are carefully used. These last converge...
Cascade recursion models of computing the temperatures of underground layers
HAN; Liqun; BI; Siwen; SONG; Shixin
2006-01-01
An RBF neural network was used to construct computational models of the underground temperatures of different layers, using ground-surface parameters and the temperatures of various underground layers. Because series recursion models also enable researchers to use above-ground surface parameters to compute the temperatures of different underground layers, this method provides a new way of using thermal infrared remote sensing to monitor the suture zones of large areas of blocks and to research thermal anomalies in geologic structures.
Multipath Convolutional-Recursive Neural Networks for Object Recognition
2014-01-01
Part 8: Pattern Recognition; International audience; Extracting good representations from images is essential for many computer vision tasks. While progress in deep learning shows the importance of learning hierarchical features, it is also important to learn features through multiple paths. This paper presents Multipath Convolutional-Recursive Neural Networks(M-CRNNs), a novel scheme which aims to learn image features from multiple paths using models based on combination of convolutional and...
Recursive Neural Networks Based on PSO for Image Parsing
2013-01-01
This paper presents an image parsing algorithm which is based on Particle Swarm Optimization (PSO) and Recursive Neural Networks (RNNs). State-of-the-art method such as traditional RNN-based parsing strategy uses L-BFGS over the complete data for learning the parameters. However, this could cause problems due to the nondifferentiable objective function. In order to solve this problem, the PSO algorithm has been employed to tune the weights of RNN for minimizing the objective. Experimental res...
Fixed point semantics and partial recursion in Coq
Bertot, Yves; Komendantsky, Vladimir
2008-01-01
International audience; We propose to use the Knaster-Tarski least fixed point theorem as a basis to define recursive functions in the Calculus of Inductive Constructions. This widens the class of functions that can be modelled in type-theory based theorem proving tools to potentially non-terminating functions. This is only possible if we extend the logical framework by adding some axioms of classical logic. We claim that the extended framework makes it possible to reason about terminating or...
Recursion relations for AdS/CFT correlators
Raju, Suvrat
2011-06-01
We expand on the results of our recent letter [Phys. Rev. Lett. 106, 091601 (2011)PRLTAO0031-900710.1103/PhysRevLett.106.091601], where we presented new recursion relations for correlation functions of the stress-tensor and conserved currents in conformal field theories with an AdSd+1 dual for d≥4. These recursion relations are derived by generalizing the Britto-Cachazo-Feng-Witten (BCFW) relations to amplitudes in anti-de Sitter space (AdS) that are dual to boundary correlators, and are usually computed perturbatively by Witten diagrams. Our results relate vacuum-correlation functions to integrated products of lower-point transition amplitudes, which correspond to correlators calculated between states dual to certain normalizable modes. We show that the set of “polarization vectors” for which amplitudes behave well under the BCFW extension is smaller than in flat-space. We describe how transition amplitudes for more general external polarizations can be constructed by combining answers obtained by different pairs of BCFW shifts. We then generalize these recursion relations to supersymmetric theories. In AdS, unlike flat-space, even maximal supersymmetry is insufficient to permit the computation of all correlators of operators in the same multiplet as a stress-tensor or conserved current. Finally, we work out some simple examples to verify our results.
Design of recursive variable digital filters with theoretically guaranteed stability
Deng, Tian-Bo
2016-12-01
Stability is one of the most concerned issues in designing a recursive variable digital filter (VDF). This is because the coefficients of a recursive VDF constantly vary in the tuning process, and updating the coefficients may incur instability. Thus, an appropriate measure needs to be taken for ensuring its stability. This paper presents a new coefficient transformation (CT) method for transforming the coefficients of a recursive transfer-function denominator into a set of new coefficients. From the viewpoint of conventional constant-coefficient filter (constant filter) design, the new coefficients can take arbitrary values without incurring instability. For designing a stable VDF, we apply this CT to the variable case and approximate each transformed coefficient as a distinct polynomial in the tuning parameter. Thus, we can change the filter coefficients by changing the value of the tuning parameter, and thus tune the magnitude response. Thanks to the proposed CT, updating the filter coefficients will never incur instability. This is the core part of the CT-based design approach. In this paper, we utilise a weighting function to ignore the transition-band errors and thus enhance the design accuracy of important frequency bands (passband and stopband). Moreover, the polynomials use different degrees so as to reduce the VDF complexity. Two design examples (lowpass VDF and bandpass VDF) are provided for verifying the design accuracy and checking the stability.
Explicit neural representations, recursive neural networks and conscious visual perception.
Pollen, Daniel A
2003-08-01
The fundamental question as to whether the neural correlates of any given conscious visual experience are expressed locally within a given cortical area or more globally within some widely distributed network remains unresolved. We inquire as to whether recursive processing-by which we mean the combined flow and integrated outcome of afferent and recurrent activity across a series of cortical areas-is essential for the emergence of conscious visual experience. If so, we further inquire as to whether such recursive processing is essential only for loops between extrastriate cortical areas explicitly representing experiences such as color or motion back to V1 or whether it is processing between still higher levels and the areas computing such explicit representations that is exclusively or additionally essential for visual experience. If recursive processing is not essential for the emergence of conscious visual experience, then it should also be possible to determine whether it is only the intracortical sensory processing within areas computing explicit sensory representations that is required for perceptual experience or whether it is the subsequent processing of the output of such areas within more anterior cortical regions that engenders perception. The present analysis suggests that the questions posed here may ultimately become experimentally resolvable. Whatever the outcome, the results will likely open new approaches to identify the neural correlates of conscious visual perception.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
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2017-01-01
This paper reports the measurement of [Formula: see text] meson production in proton-proton ([Formula: see text]) and proton-lead ([Formula: see text]) collisions at a center-of-mass energy per nucleon pair of [Formula: see text] by the CMS experiment at the LHC. The data samples used in the analysis correspond to integrated luminosities of 28[Formula: see text] and 35[Formula: see text] for [Formula: see text] and [Formula: see text] collisions, respectively. Prompt and nonprompt [Formula: see text] mesons, the latter produced in the decay of [Formula: see text] hadrons, are measured in their dimuon decay channels. Differential cross sections are measured in the transverse momentum range of [Formula: see text], and center-of-mass rapidity ranges of [Formula: see text] ([Formula: see text]) and [Formula: see text] ([Formula: see text]). The nuclear modification factor, [Formula: see text], is measured as a function of both [Formula: see text] and [Formula: see text]. Small modifications to the [Formula: see text] cross sections are observed in [Formula: see text] relative to [Formula: see text] collisions. The ratio of [Formula: see text] production cross sections in [Formula: see text]-going and Pb-going directions, [Formula: see text], studied as functions of [Formula: see text] and [Formula: see text], shows a significant decrease for increasing transverse energy deposited at large pseudorapidities. These results, which cover a wide kinematic range, provide new insight on the role of cold nuclear matter effects on prompt and nonprompt [Formula: see text] production.
Analysis of straightening formula
Devadatta M. Kulkarni
1988-01-01
standard bitableaux (or the set of standard monomials in minors gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step.
Del Moral Hernandez, Emilio
2005-01-01
This paper addresses recurrent neural architectures based on bifurcating nodes that exhibit chaotic dynamics, with local dynamics defined by first order parametric recursions. In the studied architectures, logistic recursive nodes interact through parametric coupling, they self organize, and the network evolves to global spatio-temporal period-2 attractors that encode stored patterns. The performance of associative memories arrangements is measured through the average error in pattern recovery, under several levels of prompting noise. The impact of the synaptic connections magnitude on architecture performance is analyzed in detail, through pattern recovery performance measures and basin of attraction characterization. The importance of a planned choice of the synaptic connections scale in RPEs architectures is shown. A strategy for minimizing pattern recovery degradation when the number of stored patterns increases is developed. Experimental results show the success of such strategy. Mechanisms for allowing the studied associative networks to deal with asynchronous changes in input patterns, and tools for the interconnection between different associative assemblies are developed. Finally, coupling in heterogeneous assemblies with diverse recursive maps is analyzed, and the associated synaptic connections are equated.
Pesin’s entropy formula for stochastic flows of diffeomorphisms
刘培东
1996-01-01
Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.
Eye Gaze Reveals a Fast, Parallel Extraction of the Syntax of Arithmetic Formulas
Schneider, Elisa; Maruyama, Masaki; Dehaene, Stanislas; Sigman, Mariano
2012-01-01
Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the…
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Pop, A; Poppenborg, H; Porteboeuf-Houssais, S; Porter, J; Pospisil, J; Pozdniakov, V; Prasad, S K; Preghenella, R; Prino, F; Pruneau, C A; Pshenichnov, I; Puccio, M; Puddu, G; Pujahari, P; Punin, V; Putschke, J; Qvigstad, H; Rachevski, A; Raha, S; Rajput, S; Rak, J; Rakotozafindrabe, A; Ramello, L; Rami, F; Rana, D B; Raniwala, R; Raniwala, S; Räsänen, S S; Rascanu, B T; Rathee, D; Ratza, V; Ravasenga, I; Read, K F; Redlich, K; Rehman, A; Reichelt, P; Reidt, F; Ren, X; Renfordt, R; Reolon, A R; Reshetin, A; Reygers, K; Riabov, V; Ricci, R A; Richert, T; Richter, M; Riedler, P; Riegler, W; Riggi, F; Ristea, C; Cahuantzi, M Rodríguez; Røed, K; Rogochaya, E; Rohr, D; Röhrich, D; Rokita, P S; Ronchetti, F; Ronflette, L; Rosnet, P; Rossi, A; Rotondi, A; Roukoutakis, F; Roy, A; Roy, C; Roy, P; Montero, A J Rubio; Rueda, O V; Rui, R; Russo, R; Rustamov, A; Ryabinkin, E; Ryabov, Y; Rybicki, A; Saarinen, S; Sadhu, S; Sadovsky, S; Šafařík, K; Saha, S K; Sahlmuller, B; Sahoo, B; Sahoo, P; Sahoo, R; 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2017-01-01
The invariant differential cross sections for inclusive [Formula: see text] and [Formula: see text] mesons at midrapidity were measured in pp collisions at [Formula: see text] TeV for transverse momenta [Formula: see text] GeV/c and [Formula: see text] GeV/c, respectively, using the ALICE detector. This large range in [Formula: see text] was achieved by combining various analysis techniques and different triggers involving the electromagnetic calorimeter (EMCal). In particular, a new single-cluster, shower-shape based method was developed for the identification of high-[Formula: see text] neutral pions, which exploits that the showers originating from their decay photons overlap in the EMCal. Above 4 GeV/[Formula: see text], the measured cross sections are found to exhibit a similar power-law behavior with an exponent of about 6.3. Next-to-leading-order perturbative QCD calculations differ from the measured cross sections by about 30% for the [Formula: see text], and between 30-50% for the [Formula: see text] meson, while generator-level simulations with PYTHIA 8.2 describe the data to better than 10-30%, except at [Formula: see text] GeV/[Formula: see text]. The new data can therefore be used to further improve the theoretical description of [Formula: see text] and [Formula: see text] meson production.
Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure
Danvy, Olivier; Schultz, Ulrik Pagh
1997-01-01
;rbæk's case study presented at PEPM '95, most polyvariant specializers for procedural programs operate on recursive equations. To this end, in a pre-processing phase, they lambda-lift source programs into recursive equations, As a result, residual programs are also expressed as recursive equations, often......Lambda-lifting a functional program transforms it into a set of recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.For lack of scope, recursive equations must carry around all...... with dozens of parameters, which most compilers do not handle efficiently. Lambda-dropping in a post-processing phase restores their block structure and lexical scope thereby significantly reducing both the compile time and the run time of residual programs....
Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure
Danvy, Olivier; Schultz, Ulrik Pagh
1999-01-01
;rbæk's case study presented at PEPM '95, most polyvariant specializers for procedural programs operate on recursive equations. To this end, in a pre-processing phase, they lambda-lift source programs into recursive equations, As a result, residual programs are also expressed as recursive equations, often......Lambda-lifting a functional program transforms it into a set of recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.For lack of scope, recursive equations must carry around all...... with dozens of parameters, which most compilers do not handle efficiently. Lambda-dropping in a post-processing phase restores their block structure and lexical scope thereby significantly reducing both the compile time and the run time of residual programs....
Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure
Danvy, Olivier; Schultz, Ulrik Pagh
1998-01-01
;rbæk's case study presented at PEPM '95, most polyvariant specializers for procedural programs operate on recursive equations. To this end, in a pre-processing phase, they lambda-lift source programs into recursive equations, As a result, residual programs are also expressed as recursive equations, often......Lambda-lifting a functional program transforms it into a set of recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.For lack of scope, recursive equations must carry around all...... with dozens of parameters, which most compilers do not handle efficiently. Lambda-dropping in a post-processing phase restores their block structure and lexical scope thereby significantly reducing both the compile time and the run time of residual programs....
Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
Birkedal, Lars; Mogelberg, R.E.
2013-01-01
points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions...... and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable......Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed...
Cho, Pyeong Whan; Szkudlarek, Emily; Tabor, Whitney
2016-01-01
Learning is typically understood as a process in which the behavior of an organism is progressively shaped until it closely approximates a target form. It is easy to comprehend how a motor skill or a vocabulary can be progressively learned—in each case, one can conceptualize a series of intermediate steps which lead to the formation of a proficient behavior. With grammar, it is more difficult to think in these terms. For example, center embedding recursive structures seem to involve a complex interplay between multiple symbolic rules which have to be in place simultaneously for the system to work at all, so it is not obvious how the mechanism could gradually come into being. Here, we offer empirical evidence from a new artificial language (or “artificial grammar”) learning paradigm, Locus Prediction, that, despite the conceptual conundrum, recursion acquisition occurs gradually, at least for a simple formal language. In particular, we focus on a variant of the simplest recursive language, anbn, and find evidence that (i) participants trained on two levels of structure (essentially ab and aabb) generalize to the next higher level (aaabbb) more readily than participants trained on one level of structure (ab) combined with a filler sentence; nevertheless, they do not generalize immediately; (ii) participants trained up to three levels (ab, aabb, aaabbb) generalize more readily to four levels than participants trained on two levels generalize to three; (iii) when we present the levels in succession, starting with the lower levels and including more and more of the higher levels, participants show evidence of transitioning between the levels gradually, exhibiting intermediate patterns of behavior on which they were not trained; (iv) the intermediate patterns of behavior are associated with perturbations of an attractor in the sense of dynamical systems theory. We argue that all of these behaviors indicate a theory of mental representation in which recursive
Cho, Pyeong Whan; Szkudlarek, Emily; Tabor, Whitney
2016-01-01
Learning is typically understood as a process in which the behavior of an organism is progressively shaped until it closely approximates a target form. It is easy to comprehend how a motor skill or a vocabulary can be progressively learned-in each case, one can conceptualize a series of intermediate steps which lead to the formation of a proficient behavior. With grammar, it is more difficult to think in these terms. For example, center embedding recursive structures seem to involve a complex interplay between multiple symbolic rules which have to be in place simultaneously for the system to work at all, so it is not obvious how the mechanism could gradually come into being. Here, we offer empirical evidence from a new artificial language (or "artificial grammar") learning paradigm, Locus Prediction, that, despite the conceptual conundrum, recursion acquisition occurs gradually, at least for a simple formal language. In particular, we focus on a variant of the simplest recursive language, a (n) b (n) , and find evidence that (i) participants trained on two levels of structure (essentially ab and aabb) generalize to the next higher level (aaabbb) more readily than participants trained on one level of structure (ab) combined with a filler sentence; nevertheless, they do not generalize immediately; (ii) participants trained up to three levels (ab, aabb, aaabbb) generalize more readily to four levels than participants trained on two levels generalize to three; (iii) when we present the levels in succession, starting with the lower levels and including more and more of the higher levels, participants show evidence of transitioning between the levels gradually, exhibiting intermediate patterns of behavior on which they were not trained; (iv) the intermediate patterns of behavior are associated with perturbations of an attractor in the sense of dynamical systems theory. We argue that all of these behaviors indicate a theory of mental representation in which recursive
Random forest methodology for model-based recursive partitioning: the mobForest package for R
Garge, Nikhil R; Bobashev, Georgiy; Eggleston, Barry
2013-01-01
Background Recursive partitioning is a non-parametric modeling technique, widely used in regression and classification problems. Model-based recursive partitioning is used to identify groups of observations with similar values of parameters of the model of interest. The mob() function in the party package in R implements model-based recursive partitioning method. This method produces predictions based on single tree models. Predictions obtained through single tree models are very sensitive to...
Recursive Architecture for the Forward and Inverse Modified Discrete Cosine Transfer
LUJunming; JIANGGuoxiong; LINZhenghui
2003-01-01
Recursive algorithms have been found very effective for realization using software and very large scale integrated circuit (VLSI) techniques. In this paper, an efficient recursive algorithm for the forward and inverse modified discrete cosine transfer (IMDCT) with arbitrary length is presented. This new recursive structure for the transform kernels of the MDCT and IMDCT can reduce the computational complexity. The proposed regular ar-chitecture is particularly suitable for parallel VLSI realiza-tion.
RecRWR: a recursive random walk method for improved identification of diseases.
Arrais, Joel Perdiz; Oliveira, José Luís
2015-01-01
High-throughput methods such as next-generation sequencing or DNA microarrays lack precision, as they return hundreds of genes for a single disease profile. Several computational methods applied to physical interaction of protein networks have been successfully used in identification of the best disease candidates for each expression profile. An open problem for these methods is the ability to combine and take advantage of the wealth of biomedical data publicly available. We propose an enhanced method to improve selection of the best disease targets for a multilayer biomedical network that integrates PPI data annotated with stable knowledge from OMIM diseases and GO biological processes. We present a comprehensive validation that demonstrates the advantage of the proposed approach, Recursive Random Walk with Restarts (RecRWR). The obtained results outline the superiority of the proposed approach, RecRWR, in identifying disease candidates, especially with high levels of biological noise and benefiting from all data available.
A Comparison of Evolutionary Algorithms for Tracking Time-Varying Recursive Systems
White Michael S
2003-01-01
Full Text Available A comparison is made of the behaviour of some evolutionary algorithms in time-varying adaptive recursive filter systems. Simulations show that an algorithm including random immigrants outperforms a more conventional algorithm using the breeder genetic algorithm as the mutation operator when the time variation is discontinuous, but neither algorithm performs well when the time variation is rapid but smooth. To meet this deficit, a new hybrid algorithm which uses a hill climber as an additional genetic operator, applied for several steps at each generation, is introduced. A comparison is made of the effect of applying the hill climbing operator a few times to all members of the population or a larger number of times solely to the best individual; it is found that applying to the whole population yields the better results, substantially improved compared with those obtained using earlier methods.
Nigel: A Systemic Grammar for Text Generation.
1983-02-01
in the logical component). Henrici [ Henrici 811 observes that "linear recursion is rather more troublesome" than recursion through embedding (which...notation defined by Henrici [ Henrici 81]. However, we have neither exhausted the grammar nor reached the lexicon. This section will present how the...Halliday, M. A. K., Language as Social Semiotic, University Park Press, Baltimore, 1978 [ Henrici 81] Henrici , A., "Some notes on the systemic generation of
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Digital Repository of Mathematical Formulae
Howard S. Cohl; McClain, Marjorie A.; Saunders, Bonita V.; Schubotz, Moritz; Williams, Janelle C.
2014-01-01
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed f...
一类双指标递归关系的求解方法%The Method of Solving a Type of Recursive Relations with Double Indexes
赵天玉; 郭金海
2011-01-01
递归关系不仅在数学中有广泛应用,而且在计算机算法设计与分析中也有广泛应用.在讨论两DNA序列间可能出现的比对数目时,得到比对数目满足的递归关系.对这种递归关系进行了推广,得到一类含四个参数的双指标递归关系模型.采用母函数方法,给出了这类递归关系模型的显式解表达式.%Recursive relations have the extensive applications both in mathematics and in designing and analyzing of computer algorithms. When discussing the number of possible alignments between two DNA sequences, we find a type of recursive relations which the number of alignments meets. This paper expanded these recursive relations, and got a type of recursive relations models with double indexes and including four parameters. Using generating function method,we gave the solutions of this type of models.
Asymptotic normality of recursive algorithms via martingale difference arrays
Werner Schachinger
2001-12-01
Full Text Available We propose martingale central limit theorems as an tool to prove asymptotic normality of the costs of certain recursive algorithms which are subjected to random input data. The recursive algorithms that we have in mind are such that if input data of size N produce random costs L N, then L N = D L n + L N-n +R N for N ≥ n 0 ≥2, where n follows a certain distribution P N on the integers {0, … ,N} and L k = D L k for k≥0. L n, L N-n and R N are independent, conditional on n, and R N are random variables, which may also depend on n, corresponding to the cost of splitting the input data of size N (into subsets of size n and N-n and combining the results of the recursive calls to yield the overall result. We construct a martingale difference array with rows converging to Z N:= [L N- EL N ] / [√ Var L N ]. Under certain compatibility assumptions on the sequence (P N N≥0 we show that a pair of sufficient conditions (of Lyapunov type for Z N → D N(0,1 can be restated as a pair of conditions regarding asymptotic relations between three sequences. All these sequences satisfy the same type of linear equation, that is also the defining equation for the sequence (EL N N≥0 and thus very likely a well studied object. In the case that the P N are binomial distributions with the same parameter p, and for deterministic R N, we demonstrate the power of this approach. We derive very general sufficient conditions in terms of the sequence (R N N≥0 (and for the scale R N =N α a characterization of those α leading to asymptotic normality of Z N.
Lessons in speed from Formula One.
2016-06-22
Could observing a sports team be the key to improving care in a time-critical hospital environment? Nick Evans, writing in Nursing Children and Young People, examines how a collaboration between a Formula One team and the University Hospital of Wales (UHW) generated ideas for clinicians to improve care. What similarities did the neonatal team at UHW spot between the sport and resuscitative care? And what changes did the hospital make following the collaboration?
Vision-based recursive estimation of rotorcraft obstacle locations
Leblanc, D. J.; Mcclamroch, N. H.
1992-01-01
The authors address vision-based passive ranging during nap-of-the-earth (NOE) rotorcraft flight. They consider the problem of estimating the relative location of identifiable features on nearby obstacles, assuming a sequence of noisy camera images and imperfect measurements of the camera's translation and rotation. An iterated extended Kalman filter is used to provide recursive range estimation. The correspondence problem is simplified by predicting and tracking each feature's image within the Kalman filter framework. Simulation results are presented which show convergent estimates and generally successful feature point tracking. Estimation performance degrades for features near the optical axis and for accelerating motions. Image tracking is also sensitive to angular rate.
Recursive estimation algorithms for power controls of wireless communication networks
Gang George YIN; Chin-An TAN; Le Yi WANG; Chengzhong XU
2008-01-01
Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access(DS/CDMA)channels.It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework.For effective solutions to this optimization problem in real time,recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components.Under broad conditions,convergence of the algorithms is established by using weak convergence methods.
Symmetries and (Related Recursion Operators of Linear Evolution Equations
Giampaolo Cicogna
2010-02-01
Full Text Available Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
Conventional Tanner Graph for Recursive onvolutional Codes and Associated Decoding
SUN Hong
2001-01-01
A different representation of recur-sive systematic convolutional (RSC) codes is pro-posed. This representation can be realized by a con-ventional Tanner graph. The graph becomes a treeby introducing hidden edge. It is shown that thesum-product algorithm applied to this graph modelis equivalent to the BCJR algorithm for turbo de-coding with lower computational complexity. Themessage-passing chain of the BCJR algorithm is pre-sented more exactly in the graph. In addition, theproposed representation of RSC codes provides an ef-ficient method to set up the trellis and the conven-tional Tanner graph for RSC codes provides directlythe architecture for decoding.
Recursive Subdivision of Urban Space and Zipf's law
Chen, Yanguang; Wang, Jiejing
2012-01-01
Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law and can be characterized with the rank-size rule. A model of spatial disaggregation of urban space is presented to depict the spatial regularity of urban growth. By recursive subdivision of space, an urban region can be geometrically divided into two parts,...
On the construction of a nonlinear recursive predictor
Voitcu, Ovidiu; Wong, Yau Shu
2006-06-01
In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.
Recursive Neural Networks Based on PSO for Image Parsing
Guo-Rong Cai
2013-01-01
Full Text Available This paper presents an image parsing algorithm which is based on Particle Swarm Optimization (PSO and Recursive Neural Networks (RNNs. State-of-the-art method such as traditional RNN-based parsing strategy uses L-BFGS over the complete data for learning the parameters. However, this could cause problems due to the nondifferentiable objective function. In order to solve this problem, the PSO algorithm has been employed to tune the weights of RNN for minimizing the objective. Experimental results obtained on the Stanford background dataset show that our PSO-based training algorithm outperforms traditional RNN, Pixel CRF, region-based energy, simultaneous MRF, and superpixel MRF.
Association-dissociation process with aging subunits: Recursive solution
Niedermayer, Thomas; Lipowsky, Reinhard
2015-11-01
The coupling of stochastic growth and shrinkage of one-dimensional structures to random aging of the constituting subunits defines the simple association-dissociation-aging process which captures the essential features of the nonequilibrium assembly of cytoskeletal filaments. Because of correlations, previously employed mean-field methods fail to correctly describe filament growth. We study an alternative formulation of the full master equation of the stochastic process. An ansatz for the steady-state solution leads to a recursion relation which allows for the calculation of all emergent quantities with increasing accuracy and in excellent agreement with stochastic simulations.
Recursive Algorithm and Alternate Operation Strategy in Sequential Tests
XU Hong-lin; CHEN Zhan-qi; GUO Lue
2009-01-01
Based on the sequential probability ratio test (SPRT) developed by Wald, an improved method for successful probability test of missile flight is proposed. A recursive algorithm and its program in Matlab are designed to calculate the real risk level of the sequential test decision and the average number of samples under various test conditions. A concept, that is "rejecting as soon as possible", is put forward and an alternate operation strategy is conducted. The simulation results show that it can reduce the test expenses.
Chambers, David W
2005-01-01
Groups naturally promote their strengths and prefer values and rules that give them an identity and an advantage. This shows up as generational tensions across cohorts who share common experiences, including common elders. Dramatic cultural events in America since 1925 can help create an understanding of the differing value structures of the Silents, the Boomers, Gen Xers, and the Millennials. Differences in how these generations see motivation and values, fundamental reality, relations with others, and work are presented, as are some applications of these differences to the dental profession.
Formula vs. Fractured Formula in Contest Persuasive Speaking.
Reynolds, Christina L.
In the past decade, contest persuasive speaking has become a product that student competitors produce and perform. A perversion of the contest formula has removed the element of persuasion from the formula. Competition rules suggest that a student's purposes in participating in forensics events should include inspiring, reinforcing, or changing…
Keller, Kai Johannes
2010-04-15
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)
Gianola Daniel
2010-01-01
Full Text Available Abstract Background The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL, calving difficulty (CD and stillbirth (SB. All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype. Methods Four models were compared in terms of goodness of fit and predictive ability: 1 standard mixed model (SMM, a model with unstructured (covariance matrices; 2 recursive mixed model 1 (RMM1, assuming that residual correlations are due to the recursive relationships between phenotypes; 3 RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4 RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes. Results For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB. Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible. Conclusions The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the
Recursive Feature Selection with Significant Variables of Support Vectors
Chen-An Tsai
2012-01-01
Full Text Available The development of DNA microarray makes researchers screen thousands of genes simultaneously and it also helps determine high- and low-expression level genes in normal and disease tissues. Selecting relevant genes for cancer classification is an important issue. Most of the gene selection methods use univariate ranking criteria and arbitrarily choose a threshold to choose genes. However, the parameter setting may not be compatible to the selected classification algorithms. In this paper, we propose a new gene selection method (SVM-t based on the use of t-statistics embedded in support vector machine. We compared the performance to two similar SVM-based methods: SVM recursive feature elimination (SVMRFE and recursive support vector machine (RSVM. The three methods were compared based on extensive simulation experiments and analyses of two published microarray datasets. In the simulation experiments, we found that the proposed method is more robust in selecting informative genes than SVMRFE and RSVM and capable to attain good classification performance when the variations of informative and noninformative genes are different. In the analysis of two microarray datasets, the proposed method yields better performance in identifying fewer genes with good prediction accuracy, compared to SVMRFE and RSVM.
Applications of recursive segmentation to the analysis of DNA sequences.
Li, Wentian; Bernaola-Galván, Pedro; Haghighi, Fatameh; Grosse, Ivo
2002-07-01
Recursive segmentation is a procedure that partitions a DNA sequence into domains with a homogeneous composition of the four nucleotides A, C, G and T. This procedure can also be applied to any sequence converted from a DNA sequence, such as to a binary strong(G + C)/weak(A + T) sequence, to a binary sequence indicating the presence or absence of the dinucleotide CpG, or to a sequence indicating both the base and the codon position information. We apply various conversion schemes in order to address the following five DNA sequence analysis problems: isochore mapping, CpG island detection, locating the origin and terminus of replication in bacterial genomes, finding complex repeats in telomere sequences, and delineating coding and noncoding regions. We find that the recursive segmentation procedure can successfully detect isochore borders, CpG islands, and the origin and terminus of replication, but it needs improvement for detecting complex repeats as well as borders between coding and noncoding regions.
Recursive dynamic mode decomposition of a transient cylinder wake
Noack, B R; Morzynski, M; Schmid, P J
2015-01-01
A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N-1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. RDMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al. 2012) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have pure frequency content while retaining a residual of comparable order as POD. In contrast to DMD with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit cycle resolution from the same snaphots. RDMD is proposed...
Implicit Artificial Syntax Processing: Genes, Preference, and Bounded Recursion
Vasiliki Folia
2011-06-01
Full Text Available The first objective of this study was to compare the brain network engaged by preference classification and the standard grammaticality classification after implicit artificial syntax acquisition by re-analyzing previously reported event-related fMRI data. The results show that preference and grammaticality classification engage virtually identical brain networks, including Broca’s region, consistent with previous behavioral findings. Moreover, the results showed that the effects related to artificial syntax in Broca’s region were essentially the same when masked with variability related to natural syntax processing in the same participants. The second objective was to explore CNTNAP2-related effects in implicit artificial syntax learning by analyzing behavioral and event-related fMRI data from a subsample. The CNTNAP2 gene has been linked to specific language impairment and is con-trolled by the FOXP2 transcription factor. CNTNAP2 is expressed in language related brain networks in the developing human brain and the FOXP2–CNTNAP2 pathway provides a mechanistic link between clinically distinct syndromes involving disrupted language. Finally, we discuss the implication of taking natural language to be a neurobiological system in terms of bounded recursion and suggest that the left inferior frontal region is a generic on-line sequence processor that unifies information from various sources in an incremental and recursive manner.
On-shell recursion relations for generic integrands
Boels, Rutger H
2016-01-01
The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut contributions needed to complete on-shell recursion relations for the integrand of scattering amplitudes in generic power-counting renormalisable theories at conjecturally any loop order. Our proposal meshes well with standard dimensional regularisation and applies in particular directly to much of the standard model of particle physics. Apart from a diagrammatic construction, at one loop order we provide a direct cross-check for box coefficients. Interestingly, at one loop our proposal can be related to a specific subset of all double unitarity cuts as well as tree-level poles by iterated recursion. We focus in particular on demonstrating the method in rational-term one-loop examples in pure Yang-Mills theory. For the finite amplitudes we present all-order arguments. First steps to...
Interacting via the Heap in the Presence of Recursion
Jurriaan Rot
2012-12-01
Full Text Available Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and local variables the interactions of a program with the heap can become rather complex, as an unbounded number of objects can be allocated either on the call stack using local variables, or, anonymously, on the heap using reference fields. As such a static analysis is, in general, undecidable. In this paper we study the verification of recursive programs with unbounded allocation of objects, in a simple imperative language for heap manipulation. We present an improved semantics for this language, using an abstraction that is precise. For any program with a bounded visible heap, meaning that the number of objects reachable from variables at any point of execution is bounded, this abstraction is a finitary representation of its behaviour, even though an unbounded number of objects can appear in the state. As a consequence, for such programs model checking is decidable. Finally we introduce a specification language for temporal properties of the heap, and discuss model checking these properties against heap-manipulating programs.
Recursive Subdivision of Urban Space and Zipf's law
Chen, Yanguang
2012-01-01
Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law and can be characterized with the rank-size rule. A model of spatial disaggregation of urban space is presented to depict the spatial regularity of urban growth. By recursive subdivision of space, an urban region can be geometrically divided into two parts, four parts, eight parts, and so on, and form a hierarchy with cascade structure. If we rank these parts by size, the portions will conform to the Zipf distribution. By means of GIS technique and remote sensing data, the model of recursive subdivision of urban space is applied to three cities of China. The results show that the intra-urban hierarchy complies with Zipf's law, and the values of the rank-size scaling exponent are very close to 1. The significance of this study lies in three aspects. First, it shows that the ...
Recursive subdivision of urban space and Zipf’s law
Chen, Yanguang; Wang, Jiejing
2014-02-01
Zipf’s law can be used to describe the rank-size distribution of cities in a region. It has seldom been employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf’s law and can be characterized with the rank-size rule. A model of spatial disaggregation of urban space is presented to depict the spatial regularity of urban growth. By recursive subdivision of space, an urban region can be geometrically divided into two parts, four parts, eight parts, and so on, and form a hierarchy with cascade structure. If we rank these parts by size, the portions will conform to the Zipf distribution. By means of the GIS technique and remote sensing data, the model of recursive subdivision of urban space is applied to three cities in China. The results show that the intra-urban hierarchy complies with Zipf’s law, and the values of the rank-size scaling exponent are very close to 1. The significance of this study lies in three aspects. First, it shows that the strict subdivision of space is an efficient approach to revealing spatial order of urban form. Second, it discloses the relationships between the urban space-filling process and the rank-size rule. Third, it suggests a new way of understanding fractals, Zipf’s law, and spatial organization of urban evolution.
Exploiting fine-grain parallelism in recursive LU factorization
Dongarra, Jack
2012-01-01
The LU factorization is an important numerical algorithm for solving system of linear equations. This paper proposes a novel approach for computing the LU factorization in parallel on multicore architectures. It improves the overall performance and also achieves the numerical quality of the standard LU factorization with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic and the atomicity of selecting the appropriate pivots. We remedy this in our new approach to LU factorization of (narrow and tall) panel submatrices. We use a parallel fine-grained recursive formulation of the factorization. It is based on conflict-free partitioning of the data and lock-less synchronization mechanisms. Our implementation lets the overall computation naturally flow with limited contention. Our recursive panel factorization provides the necessary performance increase for the inherently problematic portion of the LU factorization of square matrices. A large panel width results in larger Amdahl\\'s fraction as our experiments have revealed which is consistent with related efforts. The performance results of our implementation reveal superlinear speedup and far exceed what can be achieved with equivalent MKL and/or LAPACK routines. © 2012 The authors and IOS Press. All rights reserved.
Recursive mentalizing and common knowledge in the bystander effect.
Thomas, Kyle A; De Freitas, Julian; DeScioli, Peter; Pinker, Steven
2016-05-01
The more potential helpers there are, the less likely any individual is to help. A traditional explanation for this bystander effect is that responsibility diffuses across the multiple bystanders, diluting the responsibility of each. We investigate an alternative, which combines the volunteer's dilemma (each bystander is best off if another responds) with recursive theory of mind (each infers what the others know about what he knows) to predict that actors will strategically shirk when they think others feel compelled to help. In 3 experiments, participants responded to a (fictional) person who needed help from at least 1 volunteer. Participants were in groups of 2 or 5 and had varying information about whether other group members knew that help was needed. As predicted, people's decision to help zigzagged with the depth of their asymmetric, recursive knowledge (e.g., "John knows that Michael knows that John knows help is needed"), and replicated the classic bystander effect when they had common knowledge (everyone knowing what everyone knows). The results demonstrate that the bystander effect may result not from a mere diffusion of responsibility but specifically from actors' strategic computations.
Automatic line detection in document images using recursive morphological transforms
Kong, Bin; Chen, Su S.; Haralick, Robert M.; Phillips, Ihsin T.
1995-03-01
In this paper, we describe a system that detects lines of various types, e.g., solid lines and dotted lines, on document images. The main techniques are based on the recursive morphological transforms, namely the recursive opening and closing transforms. The advantages of the transforms are that they can perform binary opening and closing with any sized structuring element simultaneously in constant time per pixel, and that they offer a solution to morphological image analysis problems where the sizes of the structuring elements have to be determined after the examination of the image itself. The system is evaluated on about 1,200 totally ground-truthed IRS tax form images of different qualities. The line detection output is compared with a set of hand-drawn groundtruth lines. The statistics like the number and rate of correct detection, miss detection, and false alarm are calculated. The performance of 32 algorithms for solid line detection are compared to find the best one. The optimal algorithm tuning parameter settings could be estimated on the fly using a regression tree.
TWO REMARKS ON SCHWARZ FORMULA
Ding Xiaqi; Luo Peizhu
2005-01-01
This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense of Hua. Secondly the authors use the classical Schwarz formula to give a new proof of the zero free region of the Riemann zeta-function.
Oort, F.
2016-01-01
Let ϕ : S → T be a surjective holomorphic map between compact Riemann surfaces. There is a formula relating the various invariants involved: the genus of S, the genus of T, the degree of ϕ and the amount of ramification. Riemann used this formula in case T has genus zero. Contemporaries referred to
Algebraic Proofs over Noncommutative Formulas
Tzameret, Iddo
2010-01-01
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analogue of Frege proofs, different from that given in [BIKPRS96,GH03]. We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ("PC over ordered formulas", for short). This is an algebraic propositional proof system that operates with noncommutative polynomials in which the order of products in all monomials respects a fixed linear order on the variables, and where proof-lines are written as noncommutative formulas. We show that the latter proof system is strictly stronger than resolution, polynomial calculus and polynomial calculus with resolution (PCR) and admits polynomial-size refutations for the pigeonhole principle and the Tseitin's formulas. We...
Recursive subspace identification of linear and non-linear Wiener state-space models
Lovera, Marco; Gustafsson, Tony; Verhaegen, M.H.G.
2000-01-01
The problem of MIMO recursive identification is analyzed within the framework of subspace model identification (SMI) and the use of recent signal processing algorithms for the recursive update of the singular value decomposition (SVD) is proposed. To accommodate for arbitrary correlation of the dist
Time-area efficient multiplier-free recursive filter architectures for FPGA implementation
Shajaan, Mohammad; Sørensen, John Aasted
1996-01-01
Simultaneous design of multiplier-free recursive filters (IIR filters) and their hardware implementation in Xilinx field programmable gate array (XC4000) is presented. The hardware design methodology leads to high performance recursive filters with sampling frequencies in the interval 15-21 MHz (...
A Recursive Formulation of Cholesky Factorization of a Matrix in Packed Storage Format
Andersen, Bjarne Stig; Gustavson, Fred; Wasniewski, Jerzy
2001-01-01
A new compact way to store a symmetric or triangular matrix called RPF for Recursive Packed Format is fully described. Novel ways to transform RPF to and from standard packed format are included. A new algorithm, called RPC for Recursive Packed Cholesky that operates on the RPF format is presente...
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
1990-01-01
A new recursive prediction error routine is compared with the backpropagation method of training neural networks. Results based on simulated systems, the prediction of Canadian Lynx data and the modelling of an automotive diesel engine indicate that the recursive prediction error algorithm is far superior to backpropagation.
A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration
Cherabini, Luca; Danvy, Olivier
2011-01-01
We revisit both the usual ``going-up'' induction principle and Manna and Waldinger's ``going-down'' induction principle for primitive recursion,`a la Goedel, and primitive iteration, `a la Church. We use 'Kleene's trick' to show that primitive recursion and primitive iiteration are as expressive ...
The Paradigm Recursion: Is It More Accessible When Introduced in Middle School?
Gunion, Katherine; Milford, Todd; Stege, Ulrike
2009-01-01
Recursion is a programming paradigm as well as a problem solving strategy thought to be very challenging to grasp for university students. This article outlines a pilot study, which expands the age range of students exposed to the concept of recursion in computer science through instruction in a series of interesting and engaging activities. In…
A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration
Cherabini, Luca; Danvy, Olivier
2011-01-01
We revisit both the usual ``going-up'' induction principle and Manna and Waldinger's ``going-down'' induction principle for primitive recursion,`a la Goedel, and primitive iteration, `a la Church. We use 'Kleene's trick' to show that primitive recursion and primitive iiteration are as expressive...
Recursive functions of context free languages (Ⅱ)——Validity of CFPRF and CFRF definitions
董韫美
2002-01-01
In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed the relation between them and recursive functions defined on other domains. It is indicated that the functions of natural numbers and/or symbol strings (words) are functions of CFLs. Several frequently used primitive recursive functions on words were given, including logical connectives, conditional expressions. Also the powerful operators (bounded maximization and minimization operators) for constructing primitive recursive functions were defined. Two important nontrivial algorithms, the characteristic function of arbitrary CFL and the parse function of CFL sentences were constructed. Based on them, the method for extending or restricting function domain was described.``
Qiu, Chenlu
2011-01-01
This work studies the recursive robust principal components' analysis (PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background from moving foreground objects on-the-fly. The background sequence is well modeled as lying in a low dimensional subspace, that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. In this and many other applications, the foreground is an outlier for PCA but is actually the "signal of interest" for the application; where as the background is the corruption or noise. Thus our problem can also be interpreted as one of recursively recovering a time sequence of sparse signals in the presence of large but spatially correlated noise. This work has two key contributions. First, we provide a new way of looking at this problem and sh...
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
The Formula of Plague Narratives
Christensen, Jørgen Riber
2015-01-01
it is possible to establish a stable formula for plague narratives despite the spread over centuries and in different text types, and to explain this formula and possible variations of it. The initial and tentative hypothesis is that a formulaic narrative structure exists for accounts, both documentary...... and fictional, of epidemics. The samples include: Exodus, History of the Peloponnesian War, Samuel Pepys’ Diary, A Journal of the Plague Year, The Last Man, The Plague in Bergamo, Discipline and Punish: The Birth of the Prison, Doomsday, The Dead Zone, World War Z. An Oral History of the Zombie War, Pandemic...
Methods of Writing Constitutional Formulas
Raos, N.
2012-09-01
Full Text Available Chemical formulas, as well as any linguistic entity, have to fulfill two basic requirements – expressiveness and economy, i.e. they have to express the maximal meaning with minimal means. Besides, chemical formula, being a scientific notation, has not to convey vague and scientifically unapproved meanings. This article presents the development of various kinds of chemical formulas and discusses their meaning in the historical context. Special attention is paid to line notation, developed for computers (WLN, SMILES, InChI etc.. We also discuss Seymour B. Elk's "biparametric nomenclature", based on the concept of 3-simplex, which was claimed to be universally applicable to all classes of compounds.
APPLICABILITY OF SEDIMENT TRANSPORT FORMULAS
Chih Ted YANG; Caian HUANG
2001-01-01
The paper provides a comprehensive testing of the applicability of 13 sediment transport formulas under different flow and sediment conditions. The dimensionless parameters used for testing the reliability and sensitivity of formulas are dimensionless particle diameter, relative depth, Froude number, relative shear velocity, dimensionless unit stream power, and sediment concentration. A total of 3,391 sets of laboratory and river data are used in the tests. Engineers may find the test results useful to their selection of formulas under different flow and sediment conditions.
Tachibana, Takahiro [Waseda Univ., Tokyo (Japan). Advanced Research Center for Science and Engineering
1997-07-01
Wapstra and Audi`s Table is famous for evaluation of experimental data of atomic nuclear masses (1993/1995 version) which estimated about 2000 kinds of nuclei. The error of atomic mass of formula is 0.3 MeV-0.8 MeV. Four kinds of atomic mass formula: JM (Jaenecke and Masson), TUYY (Tachibana, Uno, Yamada and Yamada), FRDM (Moeller, Nix, Myers and Swiatecki) and ETFSI (Aboussir, Pearson, Dutta and Tondeur) and their properties (number of parameter and error etc.) were explained. An estimation method of theoretical error of mass formula was presented. It was estimated by the theoretical error of other surrounding nuclei. (S.Y.)
Convergence of Recursive Identification for ARMAX Process with Increasing Variances
JIN Ya; LUO Guiming
2007-01-01
The autoregressive moving average exogenous (ARMAX) model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inputs. In this paper we focus on a paramete estimate of the ARMAX model. Classical modeling methods are usually based on the assumption that the driven noise in the moving average (MA) part has bounded variances, while in the model considered here the variances of noise may increase by a power of log n. The plant parameters are identified by the recursive stochastic gradient algorithm. The diminishing excitation technique and some results of martingale difference theory are adopted in order to prove the convergence of the identification. Finally, some simulations are given to show the theoretical results.
Fractal and transfractal recursive scale-free nets
Rozenfeld, Hernan D [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Havlin, Shlomo [Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900 (Israel); Ben-Avraham, Daniel [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States)
2007-06-15
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some are fractals-possessing a finite fractal dimension-while others are small-world (their diameter grows logarithmically with their size) and are infinite-dimensional. We show how a useful measure of transfinite dimension may be defined and applied to the small-world nets. Concerning multiscaling, we show how first-passage time for diffusion and resistance between hubs (the most connected nodes) scale differently than for other nodes. Despite the different scalings, the Einstein relation between diffusion and conductivity holds separately for hubs and nodes. The transfinite exponents of small-world nets obey Einstein relations analogous to those in fractal nets.
Direct recursive identification of the Preisach hysteresis density function
Ruderman, Michael
2013-12-01
In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.
Recursive camera-motion estimation with the trifocal tensor.
Yu, Ying Kin; Wong, Kin Hong; Chang, Michael Ming Yuen; Or, Siu Hang
2006-10-01
In this paper, an innovative extended Kalman filter (EKF) algorithm for pose tracking using the trifocal tensor is proposed. In the EKF, a constant-velocity motion model is used as the dynamic system, and the trifocal-tensor constraint is incorporated into the measurement model. The proposed method has the advantages of those structure- and-motion-based approaches in that the pose sequence can be computed with no prior information on the scene structure. It also has the strengths of those model-based algorithms in which no updating of the three-dimensional (3-D) structure is necessary in the computation. This results in a stable, accurate, and efficient algorithm. Experimental results show that the proposed approach outperformed other existing EKFs that tackle the same problem. An extension to the pose-tracking algorithm has been made to demonstrate the application of the trifocal constraint to fast recursive 3-D structure recovery.
Spatially recursive filtering and smoothing for multibody dynamics
Rodriguez, G.
1988-01-01
Methods developed recently by the author to solve the problem of forward dynamics for nonlinear joint-connected multibody systems are summarized. Solution of this problem is of interest in such application areas as robotics, deploying structures, ground vehicles, and pointing of antennas and instrumented platforms. The problem is solved by the recursive filtering and smoothing techniques of state estimation theory. The filtering stage takes the applied joint moments as inputs to produce a sequence of spatial constraint forces acting at the joints of the system. The smoothing stage takes the innovations process resulting from the filter as an input and produces a set of spatial accelerations and a corresponding set of joint-angle accelerations.
Structure damage detection based on random forest recursive feature elimination
Zhou, Qifeng; Zhou, Hao; Zhou, Qingqing; Yang, Fan; Luo, Linkai
2014-05-01
Feature extraction is a key former step in structural damage detection. In this paper, a structural damage detection method based on wavelet packet decomposition (WPD) and random forest recursive feature elimination (RF-RFE) is proposed. In order to gain the most effective feature subset and to improve the identification accuracy a two-stage feature selection method is adopted after WPD. First, the damage features are sorted according to original random forest variable importance analysis. Second, using RF-RFE to eliminate the least important feature and reorder the feature list each time, then get the new feature importance sequence. Finally, k-nearest neighbor (KNN) algorithm, as a benchmark classifier, is used to evaluate the extracted feature subset. A four-storey steel shear building model is chosen as an example in method verification. The experimental results show that using the fewer features got from proposed method can achieve higher identification accuracy and reduce the detection time cost.
Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation
Namyong Kim
2016-06-01
Full Text Available The minimum error entropy (MEE algorithm is known to be superior in signal processing applications under impulsive noise. In this paper, based on the analysis of behavior of the optimum weight and the properties of robustness against impulsive noise, a normalized version of the MEE algorithm is proposed. The step size of the MEE algorithm is normalized with the power of input entropy that is estimated recursively for reducing its computational complexity. The proposed algorithm yields lower minimum MSE (mean squared error and faster convergence speed simultaneously than the original MEE algorithm does in the equalization simulation. On the condition of the same convergence speed, its performance enhancement in steady state MSE is above 3 dB.
Recursive Estimation for the Tracking of Radioactive Sources
Howse, J.W.; Muske, K.R.; Ticknor, L.O.
1999-02-01
This paper describes a recursive estimation algorithm used for tracking the physical location of radioactive sources in real-time as they are moved around in a facility. The al- gorithm is a nonlinear least squares estimation that mini- mizes the change in, the source location and the deviation between measurements and model predictions simultane- ously. The measurements used to estimate position consist of four count rates reported by four different gamma ray de tectors. There is an uncertainty in the source location due to the variance of the detected count rate. This work repre- sents part of a suite of tools which will partially automate security and safety assessments, allow some assessments to be done remotely, and provide additional sensor modalities with which to make assessments.
Toward An Ontology of Mutual Recursion: Models, Mind and Media
Mat Wall-Smith
2008-01-01
Full Text Available In Parables for the Virtual Massumi describes 'The Autonomy of Affect' in our ecology of thought (Massumi 2002 : 35. The object of Stiegler's Technics and Time is 'technics apprehended as the horizon of all possibility to come and all possibility of a future' (Stiegler 1998 : ix. The ecological dynamic described by the recursion between this 'affective autonomy' and a 'technical horizon of possibility' describes a metamodel of the relation between body and world, between perception and expression. I argue that this metamodel allows for the technical architectures that enshrine media processes and models as both the manifestation and modulation of the 'industry' or vitality of mind. I argue that these technical architectures are crucial to the creation and maintenance of dynamic ecologies of living.
Adaptive Hammerstein Predistorter Using the Recursive Prediction Error Method
LI Hui; WANG Desheng; CHEN Zhaowu
2008-01-01
The digital baseband predistorter is an effective technique to compensate for the nonlinearity of power amplifiers (Pas) with memory effects. However, most available adaptive predistorters based on direct learning architectures suffer from slow convergence speeds. In this paper, the recursive prediction error method is used to construct an adaptive Hammerstein predistorter based on the direct learning architecture,which is used to linearize the Wiener PA model. The effectiveness of the scheme is demonstrated on a digi-tal video broadcasting-terrestrial system. Simulation results show that the predistorter outperforms previous predistorters based on direct learning architectures in terms of convergence speed and linearization. A simi-lar algorithm can be applied to estimate the Wiener PA model, which will achieve high model accuracy.
Performance of a recursive algorithm for polynomial predistorter design
XU Ling-jun; WU Xiao-guang; WANG Yong; ZHANG Ping
2008-01-01
In this article, based on least square estimation, a recursive algorithm for indirect learning structure predistorter is introduced. Simulation results show that of all polynomial predistorter nonlinear terms, higher-order (higher than 7th-order) nonlinear terms are so minor that they can be omitted in practical predistorter design. So, it is unnecessary to construct predistorter with higher-order polynomials, and the algorithm will always be stable. Further results show that even when 15th-order polynomial model is used, the algorithm is convergent after 10 iterations, and it can improve out-band spectrum of 20 MHz bandwidth signal by 64 dB, with a 1.2×1011 matrix condition number.
Step-Indexed Normalization for a Language with General Recursion
Chris Casinghino
2012-02-01
Full Text Available The Trellys project has produced several designs for practical dependently typed languages. These languages are broken into two fragments—a _logical_ fragment where every term normalizes and which is consistent when interpreted as a logic, and a _programmatic_ fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard-Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment.
Chaotic spin-spin entanglement on a recursive lattice.
Chakhmakhchyan, Levon; Guérin, Stéphane; Leroy, Claude
2015-08-01
We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.
Applying recursive numerical integration techniques for solving high dimensional integrals
Ammon, Andreas [IVU Traffic Technologies AG, Berlin (Germany); Genz, Alan [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, Tobias [King' s College, London (United Kingdom). Dept. of Mathematics; Jansen, Karl; Volmer, Julia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, Hernan [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2016-11-15
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.
A Recursive Fuzzy System for Efficient Digital Image Stabilization
Nikolaos Kyriakoulis
2008-01-01
Full Text Available A novel digital image stabilization technique is proposed in this paper. It is based on a fuzzy Kalman compensation of the global motion vector (GMV, which is estimated in the log-polar plane. The GMV is extracted using four local motion vectors (LMVs computed on respective subimages in the logpolar plane. The fuzzy Kalman system consists of a fuzzy system with the Kalman filter's discrete time-invariant definition. Due to this inherited recursiveness, the output results into smoothed image sequences. The proposed stabilization system aims to compensate any oscillations of the frame absolute positions, based on the motion estimation in the log-polar domain, filtered by the fuzzy Kalman system, and thus the advantages of both the fuzzy Kalman system and the log-polar transformation are exploited. The described technique produces optimal results in terms of the output quality and the level of compensation.
Binary recursive partitioning: background, methods, and application to psychology.
Merkle, Edgar C; Shaffer, Victoria A
2011-02-01
Binary recursive partitioning (BRP) is a computationally intensive statistical method that can be used in situations where linear models are often used. Instead of imposing many assumptions to arrive at a tractable statistical model, BRP simply seeks to accurately predict a response variable based on values of predictor variables. The method outputs a decision tree depicting the predictor variables that were related to the response variable, along with the nature of the variables' relationships. No significance tests are involved, and the tree's 'goodness' is judged based on its predictive accuracy. In this paper, we describe BRP methods in a detailed manner and illustrate their use in psychological research. We also provide R code for carrying out the methods.
Models for Prediction, Explanation and Control: Recursive Bayesian Networks
Lorenzo Casini
2011-01-01
Full Text Available The Recursive Bayesian Net (RBN formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular how a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis.
Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods
Bhatnagar, S; Prashanth, L A
2013-01-01
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...
Applying recursive numerical integration techniques for solving high dimensional integrals
Ammon, Andreas; Hartung, Tobias; Jansen, Karl; Leövey, Hernan; Volmer, Julia
2016-01-01
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points $m$ that is at least exponential.
Multiple-resolution clustering for recursive divide and conquer
Noel, Steven E.; Szu, Harold H.
1997-04-01
In recent work, a recursive divide-and-conquer approach was developed for path-minimization problems such as the traveling salesman problem (TSP). The approach is based on multiple-resolution clustering to decompose a problem into minimally-dependent parts. It is particularly effective for large-scale, fractal data sets, which exhibit clustering on all scales, and hence at all resolutions. This leads to the application of wavelets for performing the necessary multiple-resolution clustering. While the general topic of multiple-resolution clustering via wavelets is relatively immature, it has been explored for certain specific applications. However, nothing in the literature addresses the specific type of multiple-resolution clustering needed for the divide-and-conquer approach. That is the primary goal of this paper.
A Recursive Algorithm for the Reduction of Block Diagrams
Trond Andresen
1991-01-01
Full Text Available A recursive algorithm to compute input-output relationships in a network of rational transfer functions (a block diagram is derived. Initially all transfer functions are disconnected. For each step in the algorithm, a new transfer function in the network is connected to the system. One application of the algorithm is to find the transfer matrix of a linear multivariable system given on state space form. The algorithm is advantageous when one needs repeated computations of a transfer matrix in a multivariable system for successive changes in one or a few parameters in the system. The transfer matrix for a multivariable linear system with one time delay, and the exact frequency response in the case of several time delays, are derived.
VLSI neural system architecture for finite ring recursive reduction.
Zhang, D; Jullien, G A
1996-12-01
The use of neural-like networks to implement finite ring computations has been presented in a previous paper. This paper develops efficient VLSI neural system architecture for the finite ring recursive reduction (FRRR), including module reduction, MSB carry iteration and feedforward processing. These techniques deal with the basic principles involved in constructing a FRRR, and their implementations are efficiently matched to the VLSI medium. Compared with the other structure models for finite ring computation (e.g. modification of binary arithmetic logic and bit-steered ROM's), the FRRR structure has the lowest area complexity in silicon while maintaining a high throughput rate. Examples of several implementations are used to illustrate the effectiveness of the FRRR architecture.
Application of wavelet transform to recursive prediction of vibration signals
SUN Zhen-ming; WANG Ri-xin; JIANG Xing-wei; XU Min-qiang
2005-01-01
This paper investigates the characteristics of a non-stationary time series, which exists in mechanical fault diagnosis. Combining the characteristics with predictive efficiency, the limitation of the ARIMA model prediction method is analyzed. This model often is applied in the prediction of a non-stationary times series in present. Thus, a wavelet prediction method is introduced to solve non-stationary problems. The Mallat method,often used in signal processing, results form the decimation or the retention of one out of every two samples. Its advantage is that just enough information is kept to allow the exact reconstruction of the input series, but the disadvantage is a time-varying series on line cannot be pursued. Therefore, the authors present another method,à Trous method, which can be applied for recursive prediction in real-time sampling procedure.
An algebraic approach to analysis of recursive and concurrent programs
Terepeta, Michal Tomasz
This thesis focuses on formal techniques based on static program analysis, model checking and abstract interpretation that offer means for reasoning about software, verification of its properties and discovering potential bugs. First, we investigate an algebraic approach to static analysis...... the soundness or completeness results. Moreover, we present a new application of pushdown systems in the context of an aspect-oriented process calculus. The addition of aspect-oriented features makes it possible for a process to exhibit a recursive structure. We show how one can faithfully model and analyze...... present a compact data structure as well as efficient algorithms for the semiring operations. Apart from that, we discuss an improvement to Pre* and Post* algorithms for pushdown systems, making it possible to directly use program representations such as program graphs. We present a modular library...
Source localization using recursively applied and projected (RAP) MUSIC
Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [Univ. of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.
1998-03-01
A new method for source localization is described that is based on a modification of the well known multiple signal classification (MUSIC) algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace, but errors in the estimate can make location of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix, and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection is then performed in this reduced subspace. Using the metric of principal angles, the authors describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation, the authors demonstrate the improved Monte Carlo performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods, S and IES-MUSIC.
A recursive approach to the reduction of tensor Feynman integrals
Diakonidis, Theodoros; Riemann, Tord; Tausk, Bas
2010-01-01
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with shifted dimensions and indices, and then expressed by conventional scalars with generalized recurrence relations. The scheme is worked out explicitly for up to $n=6$ external legs and for tensor ranks $R\\leq n$. The tensors are represented by scalar one- to four-point functions in $d$ dimensions. For the evaluation of them, the Fortran code for the tensor reductions has to be linked with a package like QCDloop or LoopTools/FF. Typical numerical results are presented.
Learning to play Go using recursive neural networks.
Wu, Lin; Baldi, Pierre
2008-11-01
Go is an ancient board game that poses unique opportunities and challenges for artificial intelligence. Currently, there are no computer Go programs that can play at the level of a good human player. However, the emergence of large repositories of games is opening the door for new machine learning approaches to address this challenge. Here we develop a machine learning approach to Go, and related board games, focusing primarily on the problem of learning a good evaluation function in a scalable way. Scalability is essential at multiple levels, from the library of local tactical patterns, to the integration of patterns across the board, to the size of the board itself. The system we propose is capable of automatically learning the propensity of local patterns from a library of games. Propensity and other local tactical information are fed into recursive neural networks, derived from a probabilistic Bayesian network architecture. The recursive neural networks in turn integrate local information across the board in all four cardinal directions and produce local outputs that represent local territory ownership probabilities. The aggregation of these probabilities provides an effective strategic evaluation function that is an estimate of the expected area at the end, or at various other stages, of the game. Local area targets for training can be derived from datasets of games played by human players. In this approach, while requiring a learning time proportional to N(4), skills learned on a board of size N(2) can easily be transferred to boards of other sizes. A system trained using only 9 x 9 amateur game data performs surprisingly well on a test set derived from 19 x 19 professional game data. Possible directions for further improvements are briefly discussed.
CHY formula and MHV amplitudes
Du, Yi-jian; Wu, Yong-shi
2016-01-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.
Overview: Infant Formula and Fluorosis
... Journal Articles for Community Water Fluoridation Overview: Infant Formula and Fluorosis Recommend on Facebook Tweet Share Compartir ... file Microsoft PowerPoint file Microsoft Word file Microsoft Excel file Audio/Video file Apple Quicktime file RealPlayer ...
On generalizations of Verlinde's formula
Bántay, P
2000-01-01
It is shown that traces of mapping classes of finite order may be expressed by Verlinde-like formulae. The 3D topological argument is explained, and the resulting trace identities for modular matrix elements are presented.
FDA Abbott Infant Formula Recall
U.S. Department of Health & Human Services — On September 22, 2010, Abbott issued a voluntary recall of certain Similac powdered infant formula after identifying a common warehouse beetle (both larvae and...
Methods of Writing Constitutional Formulas
Raos, N; Miličević, A
2012-01-01
... – expressiveness and economy, i.e. they have to express the maximal meaning with minimal means. Besides, chemical formula, being a scientific notation, has not to convey vague and scientifically unapproved meanings...
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
Valle, Annalisa; Massaro, Davide; Castelli, Ilaria; Marchetti, Antonella
2015-01-01
This study explores the development of theory of mind, operationalized as recursive thinking ability, from adolescence to early adulthood (N = 110; young adolescents = 47; adolescents = 43; young adults = 20). The construct of theory of mind has been operationalized in two different ways: as the ability to recognize the correct mental state of a character, and as the ability to attribute the correct mental state in order to predict the character’s behaviour. The Imposing Memory Task, with five recursive thinking levels, and a third-order false-belief task with three recursive thinking levels (devised for this study) have been used. The relationship among working memory, executive functions, and linguistic skills are also analysed. Results show that subjects exhibit less understanding of elevated recursive thinking levels (third, fourth, and fifth) compared to the first and second levels. Working memory is correlated with total recursive thinking, whereas performance on the linguistic comprehension task is related to third level recursive thinking in both theory of mind tasks. An effect of age on third-order false-belief task performance was also found. A key finding of the present study is that the third-order false-belief task shows significant age differences in the application of recursive thinking that involves the prediction of others’ behaviour. In contrast, such an age effect is not observed in the Imposing Memory Task. These results may support the extension of the investigation of the third order false belief after childhood. PMID:27247645
Improving Scalability of Java Archive Search Engine through Recursion Conversion And Multithreading
Oscar Karnalim
2016-05-01
Full Text Available Based on the fact that bytecode always exists on Java archive, a bytecode based Java archive search engine had been developed [1, 2]. Although this system is quite effective, it still lack of scalability since many modules apply recursive calls and this system only utilizes one core (single thread. In this research, Java archive search engine architecture is redesigned in order to improve its scalability. All recursion are converted to iterative forms although most of these modules are logically recursive and quite difficult to convert (e.g. Tarjan’s strongly connected component algorithm. Recursion conversion can be conducted by following its respective recursive pattern. Each recursion is broke down to four parts (before and after actions of current and its children and converted to iteration with the help of caller reference. This conversion mechanism improves scalability by avoiding stack overflow error caused by method calls. System scalability is also improved by applying multithreading mechanism which successfully cut off its processing time. Shorter processing time may enable system to handle larger data. Multithreading is applied on major parts which are indexer, vector space model (VSM retriever, low-rank vector space model (LRVSM retriever, and semantic relatedness calculator (semantic relatedness calculator also involves multiprocess. The correctness of both recursion conversion and multithread design are proved by the fact that all implementation yield similar result.
Annalisa Valle
2015-02-01
Full Text Available This study explores the development of theory of mind, operationalized as recursive thinking ability, from adolescence to early adulthood (N = 110; young adolescents = 47; adolescents = 43; young adults = 20. The construct of theory of mind has been operationalized in two different ways: as the ability to recognize the correct mental state of a character, and as the ability to attribute the correct mental state in order to predict the character’s behaviour. The Imposing Memory Task, with five recursive thinking levels, and a third-order false-belief task with three recursive thinking levels (devised for this study have been used. The relationship among working memory, executive functions, and linguistic skills are also analysed. Results show that subjects exhibit less understanding of elevated recursive thinking levels (third, fourth, and fifth compared to the first and second levels. Working memory is correlated with total recursive thinking, whereas performance on the linguistic comprehension task is related to third level recursive thinking in both theory of mind tasks. An effect of age on third-order false-belief task performance was also found. A key finding of the present study is that the third-order false-belief task shows significant age differences in the application of recursive thinking that involves the prediction of others’ behaviour. In contrast, such an age effect is not observed in the Imposing Memory Task. These results may support the extension of the investigation of the third order false belief after childhood.
Valle, Annalisa; Massaro, Davide; Castelli, Ilaria; Marchetti, Antonella
2015-02-01
This study explores the development of theory of mind, operationalized as recursive thinking ability, from adolescence to early adulthood (N = 110; young adolescents = 47; adolescents = 43; young adults = 20). The construct of theory of mind has been operationalized in two different ways: as the ability to recognize the correct mental state of a character, and as the ability to attribute the correct mental state in order to predict the character's behaviour. The Imposing Memory Task, with five recursive thinking levels, and a third-order false-belief task with three recursive thinking levels (devised for this study) have been used. The relationship among working memory, executive functions, and linguistic skills are also analysed. Results show that subjects exhibit less understanding of elevated recursive thinking levels (third, fourth, and fifth) compared to the first and second levels. Working memory is correlated with total recursive thinking, whereas performance on the linguistic comprehension task is related to third level recursive thinking in both theory of mind tasks. An effect of age on third-order false-belief task performance was also found. A key finding of the present study is that the third-order false-belief task shows significant age differences in the application of recursive thinking that involves the prediction of others' behaviour. In contrast, such an age effect is not observed in the Imposing Memory Task. These results may support the extension of the investigation of the third order false belief after childhood.
LU分解递归算法的实现%IMPLEMENTATION OF RECURSIVE ALGORITHM FOR LU FACTORIZATION
陈建平
2004-01-01
Recursion leads to automatic matrix blocking in the computation of dense linear algebra. It makes a good use of memory hierarchies of today's high-performance computers and hence improves the efficiency of the algorithm. The recursive algorithm for LU factorization of matrix that is used to solve linear systems of equations is studied in this paper. A detailed derivation of the recursive algorithm is presented. FORTRAN90 language, which supports recursion as a language feature, is used to implement the algorithm. Experimental results show that the recursive algorithm is near 20% faster than the currently used block algorithm.
Unbounded random operators and Feynman formulae
Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G.
2016-12-01
We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one.
Dirac's monopole, quaternions, and the Zassenhaus formula
Soloviev, Michael A
2016-01-01
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by explicit calculation of the star product up to the second order in the Planck constant. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
New supplements to infant formulas.
Eshach Adiv, Orly; Berant, Moshe; Shamir, Raanan
2004-12-01
Foods, which, in addition to their nutritional attributes, contain also elements that are considered to be health-promoting, have been termed "functional foods". In this regard, human milk has gained recognition as being the ultimate functional food for infants - by its biological compatibility, nutritional value and the undisputed added value of its health promoting qualities. Intensive research activity has recently evolved in a quest to identify and define the components of human milk that might confer disease-preventing and health-enhancing properties and to determine the instances and clinical conditions in which these factors become particularly important. The outcome of such research would also provide a rationale for advocating the supplementation of commercial infant formulas with such substances. In effect, the body of data accumulated from scientific and clinical studies on nucleotides, probiotics, prebiotics and long-chain polyunsaturated fatty acids in human milk and as additives to infant formula, has become regarded as convincing enough by the infant formula industry so as to launch into the market formulas supplemented with one or more of these factors - in an effort to emulate human milk and its beneficial effects. The following review is intended for the reader to obtain a general idea of the new supplements that have been introduced to infant formulas. We summarize the pertinent experimental and clinical observations concerning each of the supplements, pointing out their potential specific benefits, their possible disadvantages and the issues that still remain unresolved.
Rong-Jian Chen
2010-01-01
Full Text Available This paper presents a new stream cipher for data security, which is based on permutation of the data and replacement of the data values. Permutation is done by scan patterns generated by the SCAN approach. The replacement of data values using variable ordered recursive cellular automata (CA substitutions. To achieve this aim, an encryption-specific SCAN technique was firstly developed, 2-D hybrid CA was next built, and then 1st-ordered and 2nd-ordered generalized CA transforms were introduced to build variable ordered recursive CA substitutions. The proposed stream cipher satisfies the properties of confusion and diffusion because of characteristics of the SCAN and the CA substitutions are flexible. Moreover, the characteristics of the proposed stream cipher are loss-less, symmetric private key, very large number of security keys (number of possible security keys is more than 9568 10 ~ 14785 10 - according to the size of the 2-D von Neumann CA, and key-dependent pixel value replacement. Experimental results obtained using some color images clearly demonstrate the strong performance of the proposed stream cipher. This paper also shows the DSP+FPGA implementation of the proposed stream cipher for the real-time image security.