arXiv subjects

Radhakrishnan Nagarajan

Publications and source records attributed to Radhakrishnan Nagarajan.

25 records · Page 2Linked to original sources

arXiv2005

Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes

Detrended fluctuation analysis (DFA) has been used widely to determine possible long-range correlations in data obtained from diverse settings. In a recent study [1], uncorrelated random spikes superimposed on the long-range correlated noise (LR noise) were found to affect DFA scaling exponent estimates. In this brief communication, singular-value decomposition (SVD) filter is proposed to minimize the effect random spikes superimposed on LR noise, thus facilitating reliable estimation of the scaling exponents. The effectiveness of the proposed approach is demonstrated on random spikes sampled from normal and uniform distributions.

cond-mat.stat-mech↗

arXiv2005

Effect of coarse-graining on detrended fluctuation analysis

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting digital data is discretized in amplitude and time, and shall be referred to as coarse-grained realization in the present study. Since coarse-graining precedes scaling exponent analysis, it is important to understand its effects on scaling exponent estimators such as DFA. In this brief communication, k-means clustering is used to generate coarse-grained realizations of data sets with different correlation properties, namely: anti-correlated noise, long-range correlated noise and uncorrelated noise. It is shown that the coarse-graining can significantly affect the scaling exponent estimates. It is also shown that scaling exponent can be reliably estimated even at low levels of coarse-graining and the number of the clusters required varies across the data sets with different correlation properties.

cond-mat.stat-mech↗

arXiv2004

Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise

Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes [1]. However, recent studies have reported the susceptibility of DFA to trends [2] which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. Inspired by these reports, we propose a technique based on singular value-decomposition (SVD) of the trajectory matrix to minimize the effect of linear, power-law, periodic and also quasi-periodic trends superimposed on long-range correlated power-law noise. The effectiveness of the technique is demonstrated on publicly available data sets [2].

cond-mat.stat-mech↗

arXiv2004

Modeling Genetic Networks from Clonal Analysis

In this report a systematic approach is used to determine the approximate genetic network and robust dependencies underlying differentiation. The data considered is in the form of a binary matrix and represent the expression of the nine genes across the ninety-nine colonies. The report is divided into two parts: the first part identifies significant pair-wise dependencies from the given binary matrix using linear correlation and mutual information. A new method is proposed to determine statistically significant dependencies estimated using the mutual information measure. In the second, a Bayesian approach is used to obtain an approximate description (equivalence class) of network structures. The robustness of linear correlation, mutual information and the equivalence class of networks is investigated with perturbation and decreasing colony number. Perturbation of the data was achieved by generating bootstrap realizations. The results are refined with biological knowledge. It was found that certain dependencies in the network are immune to perturbation and decreasing colony number and may represent robust features, inherent in the differentiation program of osteoblast progenitor cells. The methods to be discussed are generic in nature and not restricted to the experimental paradigm addressed in this study.

q-bio.MN↗

arXiv2004

Minimizing the effect of sinusoidal trends in detrended fluctuation analysis

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log-log plots obtained by DFA and MF-DFA techniques.

cond-mat.stat-mech↗

arXiv2004

Evidence of crossover phenomena in wind speed data

In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a power-law decay characteristic of $1/f^α$ processes with possible long-range correlations. Conventional analysis using Hurst exponent estimators proved to be inconclusive. Subsequent analysis using detrended fluctuation analysis (DFA) revealed a crossover in the scaling exponent ($α$). At short time scales, a scaling exponent of $α\sim 1.4$ indicated that the data resembled Brownian noise, whereas for larger time scales the data exhibited long range correlations ($α\sim 0.7$). The scaling exponents obtained were similar across the three locations. Our findings suggest the possibility of multiple scaling exponents characteristic of multifractal signals.

physics.data-an↗

arXiv2004

A Multifractal Description of Wind Speed Records

In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^α$ processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis {\em MFDFA}. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model.

cond-mat.stat-mech↗