Recursive Version Research Articles

Block-term tensor decomposition in array signal processing

The ability of tensor decomposition (TD)-based methods to recover latent information, including channel parameters and transmitted symbols in the array signal processing (ASP) context, in a deterministic manner and with little or no training overhead, fits well with the data efficiency needs of future-generation multi-user massive multiple-input multiple-output systems. However, such methods have mostly relied on a few classical TD models, notably the canonical polyadic decomposition (CPD), which can be quite restrictive in realistic scenarios. In this paper, a generalized CPD model, known as block-term decomposition (BTD), is re-visited in the context of ASP, and shown to be the natural choice in sensor arrays of increased dimensionality that also involve channel multipath. Semi-blind joint channel estimation/data detection (JCD) is addressed in this context via efficient algorithms that wed existing JCD schemes with BTD approximation. Robust to sensor failures and recursive versions are also developed. The special yet important case of the uniform rectangular array (URA) configuration is adopted to illustrate the ideas and results. The signal detection performance of the BTD-inspired semi-blind JCD schemes is evaluated under various conditions with the aid of simulations and seen to be favorably compared with that of the training-only-based solution.

A Study on the Sum of ‘m+1’ Consecutive Cullen Numbers

Objectives: To discover new formulae for the matrix form of the sum of m+1 Cullen numbers. This is an effort to explain the Recursive Matrix form formula and a few of its uses. Methods: Conclusions derived from theorems and the matching matrix representations of them. Additionally, a few apps are offered. The terminology of Cullen Numbers are utilised to demonstrate the main theorems. Additionally, algebraic simplifications and mathematical computations are used to derive the findings. Findings: A lemma is used to construct the formula for the Sum of m+1 consecutive Cullen Numbers. Here, the recursive and sum forms are obtained in matrix form. It also obtains the matrix representation of the sums of m+1 successive Cullen Numbers. Several intriguing correlations among Special Numbers, Cullen Numbers, and Carol Numbers are provided in the application section. Novelty: New formulas are obtained for the analysis. Research has recently discovered matrix representation with its recursive versions. Furthermore, there are many relationships between Cullen Numbers along with other peculiar numbers. Keywords: Cullen Numbers, Carol Numbers, Woodall Numbers, Sum of Cullen Number

Smooth least absolute deviation estimators for outlier-proof identification

The paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes of little use for reliably identifying systems in the presence of destructive measurement errors. Bearing in mind that the classic task of minimizing the quality functional of absolute deviations encounters fundamental analytical problems, it is proposed to use a dedicated iterative estimator for off-line evaluation of the parameters of the analyzed process. In addition, a simplified recursive version of the absolute deviation estimation procedure was developed, which allows for practical on-line tracking of the evolution of variable parameters of non-stationary systems. Importantly, a novel refinement of the discussed absolute deviation estimators was proposed to effectively overcome some inconvenient numerical effects. We also present an interesting comparison of the improved (by non-linear modification) iterative absolute-deviation estimator with the classical Gauss-Newton gradient algorithm, which leads to constructive conclusions. Finally, using computer simulations, the operation of the developed iterative and recursive estimators minimizing the absolute deviation is illustrated. The work ends with an indication of directions for further research.

The Recursive Structures of Manin Symbols over Q, Cusps and Elliptic Points on X0 (N)

Firstly, we present a more explicit formulation of the complete system D(N) of representatives of Manin’s symbols over Q, which was initially given by Shimura. Then, we establish a bijection between D(M)×D(N) and D(MN) for (M,N)=1, which reveals a recursive structure between Manin’s symbols of different levels. Based on Manin’s complete system Π(N) of representatives of cusps on X0(N) and Cremona’s characterization of the equivalence between cusps, we establish a bijection between a subset C(N) of D(N) and Π(N), and then establish a bijection between C(M)×C(N) and C(MN) for (M,N)=1. We also provide a recursive structure for elliptical points on X0(N). Based on these recursive structures, we obtain recursive algorithms for constructing Manin symbols over Q, cusps, and elliptical points on X0(N). This may give rise to more efficient algorithms for modular elliptic curves. As direct corollaries of these recursive structures, we present a recursive version of the genus formula and prove constructively formulas of the numbers of D(N), cusps, and elliptic points on X0(N).

Primitive recursive ordered fields and some applications

We establish primitive recursive (PR) versions of some known facts about computable ordered fields of reals and computable reals, and apply them to prove primitive recursiveness of several important problems in linear algebra and analysis. One of the central results of this paper is a partial PR analogue of Ershov–Madison’s theorem about real closures of computable ordered fields. It allows us, in particular, to obtain PR root-finding algorithms in the PR real and algebraic closures of PR fields with a certain property (PR splitting). We also relate the corresponding fields to the PR reals, as well as introduce and study the notion of a PR metric space. It enables us to derive sufficient conditions for PR computing of normal forms of matrices and solution operators of symmetric hyperbolic systems of PDEs. The methods represent a mix of symbolic and approximate algorithms.

A recursive low-pass filtering method for a commercial cooling fan tray parameter online estimation with measurement noise

Cooling fans are extensively used in industrial fields. However, performance degradation may cause serious damages to surrounding electronic devices. Hence, parameter identification and fan speed online diagnosis of the fan tray system are essential. To address parameter identification subject to measurement noise, an online filtering method is designed to alleviate the noise effect. A selection guide for the filtering coefficient is presented for improving the parameter identification results. Investigation shows that the filtering process for the nonlinear cooling fan parameter identification can be further reformulated by simple measurement equations. Based on this result, two well-known recursive algorithms can be integrated directly to realize the recursive version. Therefore, the limited on-board memory and computation time inefficiency issues can be solved for a cheap embedded system. Finally, numerical simulations as well as experiments are carried out to validate the feasibility of the proposed method for online parameters identification and speed diagnosis.

Real-time Change-Point Detection: A deep neural network-based adaptive approach for detecting changes in multivariate time series data

The behavior of a time series may be affected by various factors. Changes in mean, variance, frequency, and auto-correlation are the most common. Change-Point Detection (CPD) aims to track down abrupt statistical characteristic changes in time series that can benefit many applications in different domains. As demonstrated in recently introduced CPD methodologies, deep learning approaches have the potential to identify more subtle changes. However, due to improper handling of data and insufficient training, these methodologies generate more false alarms and are not efficient enough in detecting change-points. In real-time CPD algorithms, preprocessed data plays a vital role in increasing the algorithm’s efficiency and minimizing false alarm rates. Therefore, preprocessing of data should be a part of the algorithm, but in the existing methods, preprocessing of data is done initially, and then the whole dataset is passed to the CPD algorithm. A new three-phase architecture is proposed to address this issue, in which all phases, from preprocessing to CPD, work in an adaptive manner. The phases are integrated into a pipeline, allowing the algorithm to work in real-time. Our proposed strategy performs optimally and consistently based on performance metrics resulting from experiments on real-world datasets and artifacts. This work effectively addresses the issue of non-stationary data normalization using deep learning approaches. To reduce noise and outliers from the data, a recursive version of singular spectrum analysis is introduced. It is demonstrated that the method’s performance has significantly improved by combining adaptive preprocessing with deep learning CPD techniques.

Neural kernels for recursive support vector regression as a model for episodic memory

Retrieval of episodic memories requires intrinsic reactivation of neuronal activity patterns. The content of the memories is thereby assumed to be stored in synaptic connections. This paper proposes a theory in which these are the synaptic connections that specifically convey the temporal order information contained in the sequences of a neuronal reservoir to the sensory-motor cortical areas that give rise to the subjective impression of retrieval of sensory motor events. The theory is based on a novel recursive version of support vector regression that allows for efficient continuous learning that is only limited by the representational capacity of the reservoir. The paper argues that hippocampal theta sequences are a potential neural substrate underlying this reservoir. The theory is consistent with confabulations and post hoc alterations of existing memories.

Recursive and Non-Recursive Generalized Least-Squares Methods for Estimation of Time Series Models with Exogenous Variables

We present in this paper two generalized least-squares (GLS) methods for estimating regression coefficients of time series models with exogenous variables. The non-recursive GLS method is a generalization of the GLS method suggested by Cochrane and Orcutt (1949). The proposed GLS method consists of a sequence of four linear regressions. A first regression is fitted and provides residuals. These residuals are modeled as an autoregressive process and are used in a second regression (or autoregression) for obtaining estimators of autoregressive coefficients. These estimators are used to generate transformed endogenous and exogenous variables. A third regression makes use of the lagged values of these transformed variables to estimate the regression coefficients. The estimators of the regression coefficients are used to determine the true residuals which are modeled as an ARMA process which is finally used for obtaining the estimators of autoregressive and moving average parameters. The second GLS method is a recursive version of the first GLS method where the estimators are updated at each time point on receipt of the additional observations. The Simulation results based on different model structures with varying numbers of observations are used to compare the performance of our methods with that of exact maximum likelihood (EML) estimates.

The recursive variational Gaussian approximation (R-VGA)

We consider the problem of computing a Gaussian approximation to the posterior distribution of a parameter given N observations and a Gaussian prior. Owing to the need of processing large sample sizes N, a variety of approximate tractable methods revolving around online learning have flourished over the past decades. In the present work, we propose to use variational inference to compute a Gaussian approximation to the posterior through a single pass over the data. Our algorithm is a recursive version of variational Gaussian approximation we have called recursive variational Gaussian approximation. We start from the prior, and for each observation, we compute the nearest Gaussian approximation in the sense of Kullback–Leibler divergence to the posterior given this observation. In turn, this approximation is considered as the new prior when incorporating the next observation. This recursive version based on a sequence of optimal Gaussian approximations leads to a novel implicit update scheme which resembles the online Newton algorithm and which is shown to boil down to the Kalman filter for Bayesian linear regression. In the context of Bayesian logistic regression, the implicit scheme may be solved, and the algorithm is shown to perform better than the extended Kalman filter, while being less computationally demanding than its sampling counterparts.

Nonparametric recursive regression estimation on Riemannian Manifolds

The considerations of this paper are restricted to random variables with values on Riemannian manifolds M and hence we propose a geometric framework to estimate their recursive regression function. Suppose we are given observations (Xi,Yi)i=1⋯n, where Xi∈M and Yi∈R. In this work we define and study a new estimator of the regression function on Riemannian Manifold M. Precisely, we employ a recursive version of the Nadaraya–Watson estimator on Riemannian Manifolds. Under some assumptions in Riemannian Manifolds data analysis, we study the properties of a recursive family kernels regression. The bias, variance are computed explicitly.

Clearness index forecasting: A comparative study between a stochastic realization method and a machine learning algorithm

With the increase in solar energy penetration in electric power systems, it is necessary to predict future solar radiation. With this, the solar power generation capacity can be predicted, allowing accurate scheduling for other sources. The solar radiation or the clearness index (CI) prediction was already presented using classical time series methods, artificial intelligence algorithms, among other approaches. In this paper, two methods are proposed to predict the CI. The first one solves a stochastic realization problem to find a mathematical model for the stochastic process that describes the CI. Then, a state observer is implemented to predict its future values. The second one performs the k-Nearest Neighbors (k-NN) regression algorithm for time series forecasting using two different approaches: the traditional k-NN and a recursive version proposed by the authors. As far as the authors know, the statistical and the recursive k-NN methods are different from the ones found in the literature to predict the CI. The methods were implemented and compared for short and long-term predictions. The results illustrate that one approach is more accurate than the other, depending on the prediction horizon. The comparison between the methods for different horizons is another contribution of this paper.

Reduction of Impulsive Noise from Speech and Audio Signals by using Sd Rom Algorithm

Removal of noise is the heart for speech and audio signal processing. Impulse noise is one of the most important noise which corrupts different parts in speech and audio signals. To remove this type of noise from speech and audio signals the technique proposed in this work is signal dependent rank order mean (SD-ROM) method in recursive version. This technique is used to replace the impulse noise samples based on the neighbouring samples. It detects the impulse noise samples based on the rank ordered differences with threshold values. This technique doesn’t change the features and tonal quality of signal. Rank ordered differences is used for detecting the impulse noise samples in speech and audio signals. Once the sample is detected as corrupted sample, that sample is replaced with rank ordered mean value and this rank ordered mean value depends on the sliding window size and neighbouring samples. This technique shows good results in terms of signal to noise ratio (SNR) and peak signal to noise ratio (PSNR) when compared with other techniques. It mainly used for removal of impulse noises from speech and audio signals.

Recursive identification of errors-in-variables models with correlated output noise

Abstract The identification of Errors-in-variables (EIV) models refers to systems where the available measurements of their inputs and outputs are corrupted by additive noise. A large variety of solutions are available when dealing with this estimation problem, in particular when the corrupting noises are white processes. However, the number of available solutions decreases when the output noise is assumed as a colored process, which is a case of great practical interest. On the other hand, many applications require estimation algorithms to work on-line, tracking a dynamical system behavior for control, signal processing, or diagnosis. In many cases, they even have to take into account computational constraints. In this paper, we propose an estimation method that is able to both lay out an algorithm to solve the identification problem of EIV systems with arbitrarily correlated output noise and also provide an efficient recursive version that does not make use of variable size matrix inversions.

DISCOPOLIS 2.0: a new recursive version of the algorithm for uniform sampling of metabolic flux distributions with linear programming

DISCOPOLIS 2.0: a new recursive version of the algorithm for uniform sampling of metabolic flux distributions with linear programming

Tagging boosted hadronic objects with dynamical grooming

We evaluate the phenomenological applicability of the dynamical grooming technique, introduced in [1], to boosted W and top tagging at LHC conditions. An extension of our method intended for multi-prong decays with an internal mass scale, such as the top quark decay, is presented. First, we tackle the reconstruction of the mass distribution of W and top jets quantifying the smearing due to pileup. When compared to state-of-the-art grooming algorithms like SoftDrop and its recursive version, dynamical grooming shows an enhanced resilience to background fluctuations. In addition, we asses the discriminating power of dynamical grooming to distinguish W (top) jets from QCD ones by performing a two-step analysis: introduce a cut on the groomed mass around the W (top) mass peak followed by a restriction on the N-subjettinnes ratio $\tau_{21}$ ($\tau_{32}$). For W jets, the out-of-the-box version of dynamical grooming, free of ad-hoc parameters, results into a comparable performance to SoftDrop. Regarding the top tagger efficiency, 3-prong dynamical grooming, in spite of its simplicity, presents better performance than SoftDrop and similar results to Recursive SoftDrop.

Intelligent forecasting of time series based on evolving distributed Neuro‐Fuzzy network

AbstractAn evolving methodology based on Neuro‐Fuzzy Takagi‐Sugeno network (NF‐TS) for distributed forecasting of univariate time series, is proposed. First, the unobservable components, or hidden patterns, are extracted from experimental data of the time series. Then, a distributed forecasting is performed separately for each component, considering an evolving NF‐TS associated with each extracted pattern. The evolving NF‐TS uses components data to adapt and adjust its structure, as the number of fuzzy rules increases or decreases according the behavior of the unobservable components. A recursive version of singular spectral analysis (SSA) technique is formulated, as one of the main contributions of this article, and it is applied to extract the components. The efficiency of proposed methodology is illustrated from results of comparison to others state‐of‐the‐art techniques for forecasting of various univariate time series.

Online estimation of integrated squared density derivatives

Hall and Marron (1987) introduced kernel estimators of integrals of the squared m-order derivatives of a probability density. Mokkadem and Pelletier (2020) gave recursive versions of their estimators, but the main drawback of these estimators is that their update requires the use of all past data. The aim of this paper is the study of online versions of the estimators introduced by Hall and Marron (1987), that is of estimators which are not only recursive, but which also have the property that their update uses only the last available data. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987) and of Mokkadem and Pelletier (2020), our online estimators achieve the parametric rate n−1 when m=0 or when higher order kernels are used. For the case when the parametric rate is not obtained, we also study an online version of the estimator proposed by Jones and Sheather (1991). Finally, we provide recursive estimators of the optimal bandwidth in the framework of density estimation.

An Efficient Recursive Approach for Electromagnetic Scattering by Arbitrary-Shaped Multilayer Cylinders

We present a recursive version of the previously proposed fast algorithm for computation of the field scattered from arbitrary-shaped multilayer objects. As in the original version, the field at each layer is represented by a series of cylindrical functions with unknown coefficients. In order to determine these coefficients, a linear system of equations is obtained through a procedure based on the boundary conditions between the layers. Instead of solving this large system by applying conventional linear solvers as done in the original version, through an approach based on Thomas algorithm, we derive recursive expressions to compute the scattered field. While the accuracy of the results for both versions are almost the same, the recursive version has lower time and memory complexity. Hence, it supersedes the original version.

A bijective proof of the hook-length formula for skew shapes

Recently, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes. The formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook lengths in the denominator, like the classical hook-length formula due to Frame, Robinson and Thrall. In this paper, we present a simple bijection that proves an equivalent recursive version of Naruse’s result, in the same way that the celebrated hook-walk proof due to Greene, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-length formula for ordinary shapes.In particular, we also give a new bijective proof of the classical hook-length formula, quite different from the known proofs.