Sliding mode control for generalized robust synchronization of mismatched fractional order dynamical systems and its application to secure transmission of voice messages.

This paper proposes a generalized robust synchronization method for different dimensional fractional order dynamical systems with mismatched fractional derivatives in the presence of function uncertainty and external disturbance by a designing sliding mode controller. Based on the proposed theory of generalized robust synchronization criterion, a novel audio cryptosystem is proposed for sending or sharing voice messages secretly via insecure channel. Numerical examples are given to verify the potency of the proposed theories.

Controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion.

This paper presents a new set of sufficient conditions for controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion (fBm) in finite dimensional space using fractional calculus, fixed point technique and stochastic analysis approach. In particular, we discuss the complete controllability for nonlinear fractional stochastic integrodifferential systems under the proved result of the corresponding linear fractional system is controllable. Finally, an example is presented to illustrate the efficiency of the obtained theoretical results.

Dynamical Analysis of the Hindmarsh-Rose Neuron With Time Delays.

This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh-Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov-Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.

Synchronization of Markovian jumping inertial neural networks and its applications in image encryption.

This study is mainly concerned with the problem on synchronization criteria for Markovian jumping time delayed bidirectional associative memory neural networks and their applications in secure image communications. Based on the variable transformation method, the addressed second order differential equations are transformed into first order differential equations. Then, by constructing a suitable Lyapunov-Krasovskii functional and based on integral inequalities, the criteria which ensure the synchronization between the uncontrolled system and controlled system are established through designed feedback controllers and linear matrix inequalities. Further, the proposed results proved that the error system is globally asymptotically stable in the mean square. Moreover, numerical illustrations are provided to validate the effectiveness of the derived analytical results. Finally, the application of addressed system is explored via image encryption/decryption process.

A new thresholding technique based on fuzzy set as an application to leukocyte nucleus segmentation.

BACKGROUND AND OBJECTIVES: The main aim of this paper is to segment leukocytes in blood smear images using interval-valued intuitionistic fuzzy sets (IVIFSs). Generally, uncertainties occur in terms of vagueness through brightness levels of image. Processing of such uncertain images can be efficiently handled by using fuzzy sets, particularly IVIFSs. METHODS: Logarithmic membership function is utilized for computing membership values corresponding to intensities of the pixel. Non-membership function of IVIFS is constructed by using Yager generating function. By varying parameters, 256 IVIFSs are generated. An IVIFS is selected from 256 IVIFSs having maximizing ultrafuzziness along with varying threshold. Threshold is determined by finding an IVIFS with maximum similarity between ideal segmented and segmented results obtained from the proposed method. RESULTS: Quantitatively, the segmented images are evaluated using precision-recall, receiver operator characteristic curves, Jaccard coefficient and measure for structural similarity index along with the time taken for segmenting nucleus, and their results are compared with results of existing methods. Performance measures reveal that the proposed method seems to segment leukocytes better than other comparable methods. CONCLUSIONS: Segmentation of leukocytes using the proposed method helps the analyst in differentiating various types of leukocytes and in the determination of leukocyte count, and the counting is essential in finding out diseases related to reduction or surplus quantity of these cells.

Delay decomposition approach to [Formula: see text] filtering analysis of genetic oscillator networks with time-varying delays.

In this paper, the [Formula: see text] filtering problem is treated for N coupled genetic oscillator networks with time-varying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov-Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed [Formula: see text] performance. Second, based on the above analysis, the existence of the designed [Formula: see text] filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.

Pediatric brain tumors: An analysis of 5 years of data from a tertiary cancer care center, India.

BACKGROUND: Pediatric brain tumors are the most common solid tumors in children and a leading cause of mortality and morbidity in children worldwide. Even though there are enough data about the epidemiology of pediatric brain tumors in western population, there are only a few reports from developing countries like India. AIMS: To study the epidemiological patterns of brain tumors in children, to study the patterns of care, and to assess the treatment response. MATERIALS AND METHODS: A retrospective epidemiological approach is used. The records of children <18 years registered in our department from August 2006 to July 2011 diagnosed as primary brain tumors are selected. Data regarding age, sex, site of the tumor, clinical features, histology, treatment plan, and treatment response are collected. The World Health Organization classification of neoplasms was adopted. RESULTS: Of 250 cases, females (57%) slightly outnumbered males. The present study revealed that astrocytoma (52%) is the most common brain tumor in childhood. Surgery was the main modality of treatment. Chemotherapy was given to 16% of patients. Even though radiation therapy was offered to 74% of patients, only 42% completed radiotherapy. There was subjective clinical improvement in 68% of patient population after treatment. CONCLUSIONS: This is the second study from Tamil Nadu that deals with epidemiology of brain tumors. Multimodality management including surgery, chemotherapy, and radiation therapy remains the cornerstone in the management of pediatric brain tumors.

Admissibility analysis for discrete-time singular systems with randomly occurring uncertainties via delay-divisioning approach.

This paper deals with the problem of admissibility analysis for discrete-time singular system with time-delays. The uncertainties occurring in the system parameters are assumed to be random. By constructing Lyapunov functional, sufficient delay-dependent stochastic admissibility conditions are established via delay divisioning approach in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. Numerical examples and their simulation results are given to illustrate the effectiveness of the obtained theoretical results.

Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks.

The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov-Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.

An analysis of medulloblastoma: 10 year experience of a referral institution in South India.

BACKGROUND: Medulloblastoma is an embryonal tumor with aggressive behavior and is more commonly seen in children than adults. The aim of this study was to determine the epidemiological patterns of medulloblastoma in a tertiary care center in Southern India. MATERIALS AND METHODS: It is a retrospective study, in which the records of all the clinically diagnosed medulloblastoma cases in the last 10 years (2002-2012) were analyzed. RESULTS: A total of 58 cases were found, with the mean age at diagnosis being 10 years. There was a slight predilection for the male sex (58.62%). The first presenting symptom was mostly related to raise intracranial pressure and the mean duration of symptoms was 200 days. Nearly, 89.6% of patients were in Stage 0 and had a central tumor location. Multimodality treatment included surgery followed by craniospinal irradiation up to 36 gray followed by posterior fossa boost up to 54 gray. Median radiation therapy duration was 6.5 weeks and concurrent single agent vincristine was the most common chemotherapy used. Most of the patients showed only a partial response to treatment, mainly because of large tumors at presentation, which could be attributed to the lack of awareness, delayed medical attention and poor follow-up. CONCLUSION: Early diagnosis and treatment is the key to management of medulloblastoma, which still needs to be achieved. Bulky tumors have a poor outcome, efforts should be aimed at complete surgery and giving risk stratification based treatment. Resources need to be allocated to make more conformal methods of radiotherapy available, which will decrease the growth abnormalities and cognitive impairments.

Synchronization and an application of a novel fractional order King Cobra chaotic system.

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.

Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties.

This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov-Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.

Differential regulation of defense-related gene expression in response to red rot pathogen Colletotrichum falcatum infection in sugarcane.

Red rot is a serious disease of sugarcane caused by the fungus Colletotrichum falcatum imposing a considerable economic loss annually in all sugarcane-producing countries. In this study, we analyzed the early resistance response of sugarcane to red rot fungus by comparing the differences between control and inoculated stalk tissues. Differential display reverse transcription polymerase chain reaction (DD-RT-PCR) was employed to identify altered expression of genes in disease-resistant cv Co 93009, in response to pathogen infection. DD-RT-PCR identified 300 differentially expressed transcripts of which 112 were selected for further analysis. Cloning and sequence analysis of the isolated cDNA fragments resulted in functional categorization of these clones into five categories, of which the defense/stress/signaling group was the largest, with clones homologous to genes known to be actively involved in various pathogenesis-related functions in plant species. This group showed overexpression of several transcripts related to ethylene-mediated and jasmonic acid pathway of plant defense mechanisms. Of the 112 expressed sequence tags, validation of expression was carried out for five important genes whose role in plant defense mechanisms is well established. This is the first report of Colletotrichum-mediated gene regulation in sugarcane which has provided a set of candidate genes for detailed molecular dissection of signaling and defense responses in tropical sugarcane during the onset of red rot resistance.

State estimation for delayed genetic regulatory networks based on passivity theory.

This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov-Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.

State estimation for genetic regulatory networks with mode-dependent leakage delays, time-varying delays, and Markovian jumping parameters.

This paper considers the state estimation problem for Markovian jumping genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays. In order to approximate the true concentrations of the mRNA and protein, the state estimator is designed using available measurement outputs. The GRNs are composed of N modes. The system switches from one mode to another according to a Markovian chain with known transition probabilities. Based on the Lyapunov functionals, including triple integral terms, some inequalities, and a time-varying delay partitioning approach, delay-dependent criteria which employ all upper bounds of time delays of each mode are obtained in terms of linear matrix inequalities (LMIs). This guarantees that the estimation error dynamics can be globally asymptotically stable from solutions of LMIs. Finally, a numerical example is presented to demonstrate the efficiency of the proposed estimation scheme.

Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties.

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov-Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.

Comment on "Generalized projective synchronization in time-delayed systems: nonlinear observer approach" [Chaos 19, 013102 (2009); 20, 029902 (2010)].

In Chaos 19, 013102 (2009), the author proposed generalized projective synchronization for time delay systems using nonlinear observer and obtained sufficient condition to ensure projective synchronization for modulated time varying delay. There are concerns with the obtained conditions as the result was applicable only to trivial case of time varying delay τ[over dot](1)(t)=dτ(1)(t)/dt<1. In this paper, we note the drawbacks of the proposed sufficient condition. The new improved sufficient condition for ensuring the projective synchronization of time varying delayed systems is presented. The proposed new criteria have been verified by adopting the Ikeda system.

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay.

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.