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"Recursive algorithms"
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Technical Note: Recursive Algorithm for Inbreeding Coefficients Assuming Nonzero Inbreeding of Unknown Parents
A recursive algorithm to calculate inbreeding coefficients was modified to account for nonzero inbreeding of unknown parents. The modification was done by changing one part of a recursive formula in which the inbreeding of an animal with at least one unknown parent is not zero and replacing it by the mean inbreeding of all animals born the same year. The algorithm is iterative. Testing involved 17million US Holsteins. Convergence was reached in 6 rounds. The computing time per round was 4min, twice as fast as the VanRaden algorithm based on the tabular method. The recursive algorithm is very simple; however, it requires that the recursion takes into account the order of animals. After a simple modification, the algorithm provides a very good approximation of inbreeding when the pedigree is unordered.
Journal Article
A Prime-Representing Constant
We present a constant and a recursive relation to define a sequence fn such that the floor of fn is the nth prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.
Journal Article
Research on the Implementation of Recursive Algorithm Based on C Language
In the utilization of C language, it often appears that the function calls itself directly or indirectly, that is, the function calls itself recursively. The recursive solution of the same kind of problem can be expressed by recursion, and the specific problem can be reduced by recursion. Based on this, this paper first analyses the concept and function of C language recursion, then studies the process description of recursion algorithm, and finally gives the implementation strategy of C language recursion algorithm.
Journal Article
ISOLATED RUPTURE DEGREE OF TREES AND GEAR GRAPHS
The isolated rupture degree for a connected graph G is defined as ir(G) = max{i(G-S)-|S|-m(G-S) : S ∈ C(G)}, where i(G-S) and m(G-S), respectively, denote the number of components which are isolated vertices and the order of a largest component in G - S. C(G) denotes the set of all cut-sets of G. The isolated rupture degree is a new graph parameter which can be used to measure the vulnerability of networks. In this paper, we firstly give a recursive algorithm for computing the isolated rupture degree of trees, and determine the maximum and minimum isolated rupture degree of trees with given order and maximum degree. Then, the exact value of isolated rupture degree of gear graphs are given. In the final, we determine the rupture degree of the Cartesian product of two special graphs and a special permutation graph.
Journal Article
The problem of researching a recursive society: Algorithms, data coils and the looping of the social
This commentary article outlines and explores the key problem that faces anyone interested in researching and understanding what might be thought of as a recursive society. It reflects on the problem that is posed by the layering of multiple feedback loops as a result of algorithmic sorting and data processes. This article is concerned with the difficulties of understanding the social where recursive algorithmic processes have repeatedly shaped outcomes, practices, relations and actions over time. This is not just about the sinking of algorithms into the everyday, it is about the way that loop-upon-loop of data processes lead to the social world itself being recursive. This repeated looping is described here as a kind of data coiling. The article argues for a focus on recursivity and for an engagement with the conceptual problems and questions that this notion implies.
Journal Article
A Recursive Parameter Estimation Algorithm for Modeling Signals with Multi-frequencies
In this paper, we focus on the modeling problem of the multi-frequency signals which contain many different frequency components. Based on the Newton search and the measured data, a Newton recursive parameter estimation algorithm is developed to estimate the amplitude, the angular frequency and the phase of a multi-frequency signal. In order to improve the performance of the identification algorithm, a convergence factor is introduced in the Hessian matrix of the developed Newton recursive method. The numerical examples verify that the proposed algorithm is effective for modeling the multi-frequency sine signals.
Journal Article
Nested particle filters for online parameter estimation in discrete-time state-space Markov models
We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs two layers of particle filters to approximate the posterior probability measure of the static parameters and the dynamic state variables of the system of interest, in a vein similar to the recent \"sequential Monte Carlo square\" (SMC2) algorithm. However, unlike the SMC2 scheme, the proposed technique operates in a purely recursive manner. In particular, the computational complexity of the recursive steps of the method introduced herein is constant over time. We analyse the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters computed via the proposed scheme. As a result, we prove, under regularity assumptions, that the approximation errors vanish asymptotically in Lp (p ≥ 1) with convergence rate proportional to $\\frac{1}{\\sqrt{\\mathrm{N}}}+\\frac{1}{\\sqrt{\\mathrm{M}}}$, where N is the number of Monte Carlo samples in the parameter space and N × M is the number of samples in the state space. This result also holds for the approximation of the joint posterior distribution of the parameters and the state variables. We discuss the relationship between the SMC2 algorithm and the new recursive method and present a simple example in order to illustrate some of the theoretical findings with computer simulations.
Journal Article
Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications
Two novel algorithms for the fast computation of the Zernike and Pseudo-Zernike moments are presented in this paper. The proposed algorithms are very useful, particularly in the case of using the computed moments, as discriminative features in pattern classification applications, where the computation of single moments of several orders is required. The derivation of the algorithms is based on the elimination of the factorial computations, by computing recursively the fractional terms of the orthogonal polynomials being used. The newly introduced algorithms are compared to the direct methods, which are the only methods that permit the computation of single moments of any order. The computational complexity of the proposed method is O(
p
2
) in multiplications, with
p
being the moment order, while the corresponding complexity of the direct method is O(
p
3
). Appropriate experiments justify the superiority of the proposed recursive algorithms over the direct ones, establishing them as alternative to the original algorithms, for the fast computation of the Zernike and Pseudo-Zernike moments.
Journal Article