arXiv subjects

J. S. Murguia

Publications and source records attributed to J. S. Murguia.

12 recordsLinked to original sources

arXiv2021

Multifractal analysis of the symmetry of a strictly isospectral energy landscape on a square lattice

We use the Holder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and periodic in the two Cartesian directions, with the symmetry group $P_{4mm}$. The resulting parametric isospectral potential display a P_m symmetry for values of the parameter moderately close to the singular value gamma_s. However, at large values of the parameter, visually around gamma=gamma_s+110, the original symmetry is recovered. For a much higher precision value of the parameter for this symmetry recovery, we show that the multifractal spectrum of the parametric potential can be conveniently used. In the latter case, we obtain gamma=gamma_s+201.085 for three decimal digits precision.

cond-mat.other↗

arXiv2014

The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circular-like trajectories have been obtained and analyzed with the scaling statistical method of detrended fluctuation analysis optimized via a wavelet transform. In this way, we determined the Hurst parameters, in two orthogonal directions, which characterize the nature of the motion of live diatoms in light microscopy experiments. We have found mean values of these directional Hurst parameters between 0.70 and 0.63 with overall standard errors below 0.15. These numerical values give evidence that the motion of Nitzschia sp. diatoms is of persistent type and suggest an active cell motility with a kind of memory associated with long-range correlations on the path of their trajectories. For the collected statistics, we also find that the values of the Hurst exponents depend on the number of abrupt turns that occur in the diatom trajectory and on the type of wavelet, although their mean values do not change much

q-bio.QM↗

arXiv2013

Scaling analyses based on wavelet transforms for the Talbot effect

The fractal properties of the transverse Talbot images are analysed with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a characteristic feature of these Talbot images. The tau scaling exponents of the q moments are linear in q within the two methods, which proves the monofractality of the transverse diffractive paraxial field in the case of these images

physics.optics↗

arXiv2012

Multifractal analyses of row sum signals of elementary cellular automata

We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial multifractal time series of three different binomial parameters and find that the WTMM method indicates an enhanced difference between the fractal components than the known theoretical result. Next, we make use of the same methods for the time series of the row sum signals of the two complementary ECA pairs of rules (90,165) and (150,105) for ten initial conditions going from a single 1 in the central position up to a set of ten 1's covering the ten central positions in the first row. Since the members of the pairs are actually similar from the statistical point of view, we can check which method is the most stable numerically by recording the differences provided by the methods between the two members of the pairs for various important quantities of the scaling analyses, such as the multifractal support, the most frequent Holder exponent, and the Hurst exponent and considering as the better one the method that provides the minimum differences. According to this criterion, our results show that the MFDFA performs better than WT-MFDFA and WTMM in the case of the multifractal support, while for the other two scaling parameters the WT-MFDFA is the best. The employed set of initial conditions does not generate any specific trend in the values of the multifractal parameters

nlin.CG↗

arXiv2010

Improvement and analysis of a pseudo random bit generator by means of cellular automata

In this paper, we implement a revised pseudo random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix H_N with the aim of calculating the pseudo random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix H_N is revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST)

physics.comp-ph↗

arXiv2010

Detection of mixed-culture growth in the total biomass data by wavelet transforms

We have shown elsewhere that the presence of mixed-culture growth of microbial species in fermentation processes can be detected with high accuracy by employing the wavelet transform. This is achieved because the crosses in the different growth processes contributing to the total biomass signal appear as singularities that are very well evidenced through their singularity cones in the wavelet transform. However, we used very simple two-species cases. In this work, we extend the wavelet method to a more complicated illustrative fermentation case of three microbial species for which we employ several wavelets of different number of vanishing moments in order to eliminate possible numerical artifacts. Working in this way allows to filter in a more precise way the numerical values of the Hölder exponents. Therefore, we were able to determine the characteristic Hölder exponents for the corresponding crossing singularities of the microbial growth processes and their stability logarithmic scale ranges up to the first decimal in the value of the characteristic exponents. Since calibrating the mixed microbial growth by means of their Hölder exponents could have potential industrial applications, the dependence of the Hölder exponents on the kinetic and physical parameters of the growth models remains as a future experimental task

q-bio.QM↗

arXiv2009

A simple circuit realization of the tent map

We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values

nlin.CD↗

arXiv2009

Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA

In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background at^b through the direct fitting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parameters

nlin.CG↗

arXiv2008

Application of multifractal wavelet analysis to spontaneous fermentation processes

An algorithm is presented here to get more detailed information, of mixed culture type, based exclusively on the biomass concentration data for fermentation processes. The analysis is performed with only the on-line measurements of the redox potential being available. It is a two-step procedure which includes an Artificial Neural Network (ANN) that relates the redox potential to the biomass concentrations in the first step. Next, a multifractal wavelet analysis is performed using the biomass estimates of the process. In this context, our results show that the redox potential is a valuable indicator of microorganism metabolic activity during the spontaneous fermentation. In this paper, the detailed design of the multifractal wavelet analysis is presented, as well as its direct experimental application at the laboratory level

physics.bio-ph↗

arXiv2006

Self-image effects for diffraction and dispersion

Excerpt: We apply the wavelet transform to the fractal Talbot effect in both diffraction and fiber dispersion. In the first case, the self similar character of the transverse paraxial field at irrational multiples of the Talbot distance is confirmed, whereas in the second case it is shown that the field is not self similar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed out

physics.optics↗

arXiv2006

Niederhauser's model for epilepsy and wavelet methods

Wavelets and wavelet transforms (WT) could be a very useful tool to analyze electroencephalogram (EEG) signals. To illustrate the WT method we make use of a simple electric circuit model introduced by Niederhauser, which is used to produce EEG-like signals, particularly during an epileptic seizure. The original model is modified to resemble the 10-20 derivation of the EEG measurements. WT is used to study the main features of these signals

physics.med-ph↗

arXiv2005

Talbot effect for dispersion in linear optical fibers and a wavelet approach

We shortly recall the mathematical and physical aspects of Talbot's self-imaging effect occurring in near-field diffraction. In the rational paraxial approximation, the Talbot images are formed at distances z=p/q, where p and q are coprimes, and are superpositions of q equally spaced images of the original binary transmission (Ronchi) grating. This interpretation offers the possibility to express the Talbot effect through Gauss sums. Here, we pay attention to the Talbot effect in the case of dispersion in optical fibers presenting our considerations based on the close relationships of the mathematical representations of diffraction and dispersion. Although dispersion deals with continuous functions, such as gaussian and supergaussian pulses, whereas in diffraction one frequently deals with discontinuous functions, the mathematical correspondence enables one to characterize the Talbot effect in the two cases with minor differences. In addition, we apply, for the first time to our knowledge, the wavelet transform to the fractal Talbot effect in both diffraction and fiber dispersion. In the first case, the self similar character of the transverse paraxial field at irrational multiples of the Talbot distance is confirmed, whereas in the second case it is shown that the field is not self similar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed out

physics.optics↗