Frequency Chaos Research Articles

Bacterial classification with convolutional neural networks based on different data reduction layers

For high accuracy classification of DNA sequences through Convolutional Neural Networks (CNNs), it is essential to use an efficient sequence representation that can accelerate similarity comparison between DNA sequences. In addition, CNN networks can be improved by avoiding the dimensionality problem associated with multi-layer CNN features. This paper presents a new approach for classification of bacterial DNA sequences based on a custom layer. A CNN is used with Frequency Chaos Game Representation (FCGR) of DNA. The FCGR is adopted as a sequence representation method with a suitable choice of the frequency k-lengthen words occurrence in DNA sequences. The DNA sequence is mapped using FCGR that produces an image of a gene sequence. This sequence displays both local and global patterns. A pre-trained CNN is built for image classification. First, the image is converted to feature maps through convolutional layers. This is sometimes followed by a down-sampling operation that reduces the spatial size of the feature map and removes redundant spatial information using the pooling layers. The Random Projection (RP) with an activation function, which carries data with a decent variety with some randomness, is suggested instead of the pooling layers. The feature reduction is achieved while keeping the high accuracy for classifying bacteria into taxonomic levels. The simulation results show that the proposed CNN based on RP has a trade-off between accuracy score and processing time.

Distinguishing between intra-genomic helitron families using time-frequency features and random forest approaches

Since its discovery in the promoter of ADC1 (Arginine Decarboxylase 1) gene in Arabidopsis thaliana, the helitron never stopped drawing the attention of researchers. Helitrons belong to the transposable elements (TEs) class II which transpose via a rolling circle mechanism; they are known as potential insertional mutagens. Given that these transposable elements do not have typical characteristics, their identification remains restricted to biological experiments. In addition, their distribution in the same genome is not uniform, which makes their classification a difficult task. Indeed, in the case of helitrons, the frequency of apparition in the same genome differs from one helitron type to another. In this framework, we propose two-steps based on-method to automatically identify and classify the helitron types. The spectral analysis method is then used to characterize these elements. This is done by the Smoothed Discrete Fourier Transform (SDFT) which permits the global localization of latent periodicities in helitrons’ signals. For each helitron type, we prove the presence of various periodicities indicating the existence of microsatellites and minisatellites. As an example, the short repetitive sequences with a size equal to 3 bp are found in the helitrons: HelitronY1_CE and HelitronY1A. In a second step, machine learning is used to classify the helitron families (10 classes) in the C.elegans genome. Subsequently, a prediction method of helitron types is proposed using the combination of features extracted from numerical helitron sequences (the Frequency Chaos Game Signals: FCGS2) and a machine learning technique (the Random Forest: RF). The helitrons features are obtained by the analysis techniques: SDFT (32 values) or CWT (Continuous Wavelet Transform, 64 values). Here, the helitrons database is randomly split into two datasets: training (80%) and testing (20%). As for the machine learning method, we use the Random Forest algorithm under the data analytics platform KNIME. In our prediction system, the features corresponding to the same genome (C.elegans) were proven to be sufficient for successful categorization of helitron families. The accuracy scores over 100 fold cross validation ranged from 78% to 94% with an overall score of 90%.

A combined support vector machine-FCGS classification based on the wavelet transform for Helitrons recognition in C.elegans

The Helitrons, an important sub-class of the transposable elements (TEs) class II, have been revealed in diverse eukaryotic genomes. They are mobile elements with great impact on genomic evolution. Till today, there is no systematic classification model of helitrons; that’s why we thought of creating an efficient automatic model to identify these sequences. This paper focuses on the discrimination between helitrons and non-helitrons using the Support Vector Machine (SVM). In this study, we use all the SVM kernels and the higher accuracy rates are obtained by reaching the optimal kernels-parameters (d, c and σ). Further, we introduce two methods to represent the genomic sequences in the form of features to be considered later for the classification task: (i) the temporal and the spectral features extracted from the Frequency Chaos Game Signals order 2 (FCGS2) (ii) the features extracted from the Continuous Wavelet Transform (CWT) applied to the FCGS2 signals. The dataset we used regards two types DNA classes in C.elegans: the helitrons and the repetitive DNA sequences that contain microsatellites and do not form helitrons. The classification results prove that the wavelet energy feature is more effective than the FCGS2 features in the helitron’s recognition system. The performance of our system achieves a high recognition rate (Globally accuracy rate) reaching the value of 92.27%.

Secure free-space communication, turbulence mitigation, and other applications using acousto-optic chaos.

Use of acousto-optic (A-O) chaos via the feedback loop in a Bragg cell for signal encryption began as a conceptual demonstration around 2008. Radio frequency (RF) chaos from a hybrid A-O feedback device may be used for secure communications of analog and digital signals. In this paper, modulation of RF chaos via first-order feedback is discussed with results corroborated by nonlinear dynamics, bifurcation maps, and Lyapunov analyses. Applications based on encryption with profiled optical beams, and extended to medical and embedded steganographic data, and video signals are discussed. It is shown that the resulting encryption is significantly robust with key tolerances potentially less than 0.1%. Results are also presented for the use of chaotic encryption for image restoration during propagation through atmospheric turbulence.

Helitron’s Periodicities Identification in C.Elegans based on the Smoothed Spectral Analysis and the Frequency Chaos Game Signal Coding

Helitrons are typical rolling circle transposons which make up the bulk of eukaryotic genomes. Unlike of other DNA transposons, these transposable elements (TEs), don’t create target site duplications or end in inverted repeats, which make them particular challenge to identify and more difficult to annotate. To date, these elements are not well studied; they only attracted the interest of researchers in biology. The focus of this paper is oriented towards identifying the helitrons in C.elegans genome in the perspective of signal processing. Aiming at the helitron's identification, a novel methodology including two steps is proposed: the coding and the spectral analysis. The first step consists in converting DNA into a 1-D signal based on the statistical features of the sequence (FCGS coding). As for the second step, it aims to identify the global periodicities in helitrons using the Smoothed Fourier Transform. The resulting spectrum and spectrogram are shown to present a specific signature of each helitron’s type.

Chaotic Dynamics of Colpitts Oscillator Under Control of MEMS Feedback

The nonlinear dynamics of Colpitts oscillator under control of MEMS varactor in feedback connectivity has been analyzed with objectives for generation and control of high frequency chaotic signals. The feedback signal derived from the capacitive divider in the standard Colpitts oscillator is modified by the MEMS varactor response mirrored by a voltage-controlled current multiplier. The latter implements MEMS capacitance multiplication and serves as a control parameter. The effects of voltage nonlinearity of the MEMS capacitance and the capacitance multiplication factor (α) have been analyzed by employing Lyapunov exponent, bifurcation diagram, phase portrait and Fourier transform methods. The modified feedback network facilitates high frequency chaos generation due to frequency doubling and high pass filtering effects of the MEMS capacitance. The latter emphasizes high frequency generation and attenuates lower frequencies. The variation of capacitance multiplication factor allows systematic changes in the qualitative nature of oscillator dynamics from a stable low frequency noisy state to Hopf bifurcation to period doubling/ tripling to chaos generation. The analysis suggests new MEMS based tuning and control of chaotic Colpitts oscillations.

Inferring Helitron Structures from 1D and 2D Representations Based on the Chaos Game Theory

This work introduces a new procedure to highlight helitron structures in the C. elegans DNA sequences. In this sense, the DNA strings are converted to numerical representations either in one or two dimensions. As a one dimensional coding, we choose the Frequency Chaos Game Signal (FCGS) which encodes the DNA based on the Chaos Game theory. Afterwards, a time–frequency representation – generated by the complex Morlet wavelet analysis – transforms the obtained signal into a 2D representation. Through the examples furnished in this paper, we demonstrate the accuracy of the method in emphasizing the helitron borders especially with high orders of FCGS. A comparison with the 2D spectrogram representation confirms the obtained results.

Emergence of complex dynamical behaviors in improved Colpitts oscillators: antimonotonicity, coexisting attractors, and metastable chaos

Emerging applications of chaotic oscillators require a classification and characterization of their complex behaviour with respect to their numerous parameters. In the present work, the dynamics of improved Colpitts oscillator is revisited based on a smooth (i.e. exponential) mathematical model of the system. In contrast to previous literature related to the improved Colpitts oscillator, the numerical simulations reveal very rich and striking phenomena including antimonotonicity, coexistence of attractors, and metastable chaos. Various complex dynamics regimes are characterized in terms of the system parameters by using bifurcation diagrams, Lyapunov exponents and phase space trajectory plots. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to validate the theoretical analysis. Owing to the richness of bifurcation modes observed in this work, the improved Colpitts oscillator may be useful in theoretical, numerical and experimental studies of various aspects of nonlinear dynamics in autonomous systems and related topics. It also has promising applications in the fields of High Frequency chaos based communications, sonar sensors as well as radar systems.

Wavelet analysis of frequency chaos game signal: a time-frequency signature of the C. elegans DNA.

Challenging tasks are encountered in the field of bioinformatics. The choice of the genomic sequence’s mapping technique is one the most fastidious tasks. It shows that a judicious choice would serve in examining periodic patterns distribution that concord with the underlying structure of genomes. Despite that, searching for a coding technique that can highlight all the information contained in the DNA has not yet attracted the attention it deserves. In this paper, we propose a new mapping technique based on the chaos game theory that we call the frequency chaos game signal (FCGS). The particularity of the FCGS coding resides in exploiting the statistical properties of the genomic sequence itself. This may reflect important structural and organizational features of DNA. To prove the usefulness of the FCGS approach in the detection of different local periodic patterns, we use the wavelet analysis because it provides access to information that can be obscured by other time-frequency methods such as the Fourier analysis. Thus, we apply the continuous wavelet transform (CWT) with the complex Morlet wavelet as a mother wavelet function. Scalograms that relate to the organism Caenorhabditis elegans (C. elegans) exhibit a multitude of periodic organization of specific DNA sequences.Electronic supplementary materialThe online version of this article (doi:10.1186/s13637-014-0016-z) contains supplementary material, which is available to authorized users.

Building Specific Signals from Frequency Chaos Game and Revealing Periodicities Using a Smoothed Fourier Analysis.

Investigating the roles and functions of DNA within genomes is becoming a primary focus of genomic research. Thus, the research works are moving towards cooperation between different scientific disciplines which aims at facilitating the interpretation of genetic information. In order to characterize the DNA of living organisms, signal processing tools appear to be very suitable for such study. However, a DNA sequence must be converted into a numerical sequence before processing; which defines the concept of DNA coding. In line with this, we propose a new one dimensional model based on the chaos game representation theory called Frequency Chaos Game Signal: FCGS. Then, we perform a Smoothed Fourier Transform to enhance hidden periodicities in the C.elegans DNA sequences. Through this study, we demonstrate the performance of our coding approach in highlighting characteristic periodicities. Indeed, several periodicities are shown to be involved in the 1D spectra and the 2D spectrograms of FCGSs. To investigate further about the contribution of our method in the enhancement of characteristic spectral attributes, a comparison with a range of binary indicators is established.

A Coding Technique Based on the Frequency Evolution Creates with a Time Frequency Analysis a New Genome's Landscape

In recent years, considerable effort has been devoted to study the biological data sets within the framework of the genomic signal processing field. However, the enormous amount of data deposited into public databases makes the search for useful information a difficult task. Effectively, the choice for a convenient analysis approach is not at all obvious at all. In this work, we provide a new way to map the genomes within the form of images. The mapping uses the Complex Morlet wavelet as analysis technique and the Frequency Chaos Game Signal (FCGS) as digital dataset. Before processing the wavelet analysis, we build the FCGS in such a way that we can follow the frequency evolution of nucleotides’ occurrence along the genome. The time-frequency analysis of the FCGS signals constitutes a pertinent tool for exploring the DNA structures in the C.elegans genome-wide landscape.

A Phylogenetic Analysis of the Brassicales Clade Based on an Alignment-Free Sequence Comparison Method

Phylogenetic analyses reveal the evolutionary derivation of species. A phylogenetic tree can be inferred from multiple sequence alignments of proteins or genes. The alignment of whole genome sequences of higher eukaryotes is a computational intensive and ambitious task as is the computation of phylogenetic trees based on these alignments. To overcome these limitations, we here used an alignment-free method to compare genomes of the Brassicales clade. For each nucleotide sequence a Chaos Game Representation (CGR) can be computed, which represents each nucleotide of the sequence as a point in a square defined by the four nucleotides as vertices. Each CGR is therefore a unique fingerprint of the underlying sequence. If the CGRs are divided by grid lines each grid square denotes the occurrence of oligonucleotides of a specific length in the sequence (Frequency Chaos Game Representation, FCGR). Here, we used distance measures between FCGRs to infer phylogenetic trees of Brassicales species. Three types of data were analyzed because of their different characteristics: (A) Whole genome assemblies as far as available for species belonging to the Malvidae taxon. (B) EST data of species of the Brassicales clade. (C) Mitochondrial genomes of the Rosids branch, a supergroup of the Malvidae. The trees reconstructed based on the Euclidean distance method are in general agreement with single gene trees. The Fitch–Margoliash and Neighbor joining algorithms resulted in similar to identical trees. Here, for the first time we have applied the bootstrap re-sampling concept to trees based on FCGRs to determine the support of the branchings. FCGRs have the advantage that they are fast to calculate, and can be used as additional information to alignment based data and morphological characteristics to improve the phylogenetic classification of species in ambiguous cases.

Nonlinear Analysis Based on Experiments of the Rotation Shaft System of Mine Drainage Motor and Pump

The experimental study results show that the system’s nonlinear characteristics, incluing the dynamic responses of the poincare mapping, the bifurcation plots, three-dimensional waterfalls diagrams etc. The effects factors of system experiment are studied and analyzed, including the misalignment and the rub-impact stiffness on system responses. So, the faults characteristics of the misalignment and the rub-impact of the rotation shaft-mechanical seal system on the drainge motor and drainge pump are also gained by the experiment. The dynamic performance of the system show nonlinear characteristics in different working conditions. The rotating shaft-mechanical seal system on the drainge motor and drainge pump can be optimization design and performance prediction based on the studied results of our work. The experiment’s results show that: the multiple frequencies are produced of the rotating shaft-mechanical seal system on drainge motor and drainge pump, and the frequencies of 1-time and 2-time are dominating components under the exciting force effects of misalignment and imbalance. At the fault state of misalignment coupling rub-impact, the multiple frequencies including 2-time, 3-time, 4-time and so on, will be induced under the critical speed. Over the value of the critical speed, will cause the phenomenon of frequency demultiplication and chaos. With rub-impact stiffness value increased, the phenomenon of frequency demultiplication and chaos are induced more frequently; with the degree of misalignment increased, the phenomena of chaos will decrease and the system will tend to be the stable state.

ANN based Genome Classifier using Frequency Chaos Game Representation

Classification of organisms into different categories using their genomic sequences has found its importance in the study of evolutionary characteristics of organisms and specific identification of previously unknown organisms in bio-diversity studies and related areas. Chaos game representation (CGR) uniquely represents DNA sequence in a visual format and reveals hidden patterns in it. Frequency CGR (FCGR) derived from CGR shows the frequency of sub-sequences present in the DNA sequence. In this paper, a novel method for classification of organisms based on a combination of FCGR and Artificial Neural network (ANN) is proposed. Eight categories, from the taxonomical distribution of Eukaryotic organisms are taken from NCBI and ANN is used for classification. Different con- figurations of ANN are tested and good accuracy is obtained. The way, the fractal nature of CGR helps in classification, is also investigated.

A survey of Wien bridge-based chaotic oscillators: Design and experimental issues

This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua’s circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode–inductor composite, in the inductorless form by using CFOA-based synthetic inductor.

Experimental observation of delay-induced radio frequency chaos in a transmission line oscillator

We report an experimental study of fast chaotic dynamics in a delay dynamical system. The system is an electronic device consisting of a length of coaxial cable terminated on one end with a diode and on the other with a negative resistor. When the negative resistance is large, the system evolves to a steady state. As the negative resistance is decreased, a Hopf bifurcation occurs. By varying the length of the transmission line we observe Hopf frequencies from 7-53 MHz. With the transmission line length fixed, we observe a period doubling route to chaos as the negative resistance is further reduced providing the first experimental confirmation of an existing theoretical model for nonlinear dynamics in transmission line oscillators [Corti et al., IEEE Trans. Circ. Syst., I: Fundam. Theory Appl. 41, 730 (1994)]. However, other experimental results indicate limitations to this model including an inability to predict the Hopf frequency or to produce realistic continuous wave forms. We extend the model to include finite bandwidth effects present in a real negative resistor. The resulting model is a neutral delay differential equation that provides better agreement with experimental results.

Limit cycle oscillating and chaos of the radiation field in a traveling wave tube amplifier

In this paper the evolution of the radiation field from frequency bifurcation to chaos and the temporal and frequency characteristics of the nonlinear unsteady states are investigated, based on the threshold analysis of nonlinear instability for the radiation field in a traveling wave tube amplifier. In the soft nonlinear regime,the nonlinear radiation field is characterized by limit cycle oscillations with frequency bifurcated, and the output power spectrum is discrete and asymmetric around the carrier frequency. This instability is intermittent so that the device can operate in expected steady states or limit cycle oscillation states by slightly adjusting the parameter. In the hard nonlinear regime in which the radiation field is characterized by randomly non-periodic oscillations with frequency chaos, the output power spectrum is continuous and wide, the components with a larger amplitude are restricted in the low-frequency range near zero. This instability is continuous so that it cannot be avoided by slightly adjusting the parameter.

Controlling high frequency chaos in circular YIG films

High power ferromagnetic resonance experiments involving thin circular YIG films produce chaotic oscillations with broad band frequency spectra in the 0.5–25 MHz range. To eliminate chaotic oscillations, a delayed feedback of the ac component of the ferromagnetic resonance signal was used to modulate one of the system parameters, the applied static magnetic field. The chaotic oscillations were converted to oscillations of reduced periodicity, and ultimately the quiescent state, as the gain in the feedback loop was increased. Similar results have been obtained in numerical simulations.

An experimental search for the conditions for the existence of chaotic states in Class C bipolar transistor RF amplifiers

An experimental search, supported by SPICE simulation, of certain configurations of Class C bipolar transistor RF amplifier suggests that frequency division and chaos can occur in this type of circuit. SPICE simulations, qualitatively supporting experimental observations of such frequency division and chaos, are resented. ossible mechanisms giving rise to the chaos are discussed. The importance of this henomenon for RF circuit designers is that such amplifiers can thereby generate a large amount of noise-like ower across a broad band of frequencies, thus giving rise to interference roblems in communication systems

EFFECTS OF LIGHT FEEDBACK ON CO2 LASER INSTABILITIES

The effects of transverse distribution of light field on CO2 laser instabilities are studied by means of light feedback. The phenomena of pulsing frequency shift and chaos in CO2 laser caused by light feedback are observed experimentally. The mechanism of laser instabilities resulting from the transverse distribution is discussed.