Nonlinear, multidimensional transformations and their applications to signal processing

Modeling a system based on time series is a complicated problem in general, especially when the time series is nonlinear and chaotic. The goal of the thesis is to introduce a method of prediction and modeling that exploits the property of recurrence in dynamical systems. A time series is said to be recurrent if keeps on visiting a particular neighborhood in the state space. The thesis demonstrates that the inherent redundancy structure of a well known topological technique known as delay embedding can be coupled with recurrence property to develop a new method of prediction. The modeling procedure empirically finds the recurrence neighborhoods from the signal, which are then subdivided into various equivalence classes based on their recurrence timings. A set of affine maps are then derived across these equivalence classes. This gives is a possibility of simplifying the dynamics in terms of affine transformations in small neighborhoods. The delay-embedding (done in a dimension much higher than the inherent dimension of the dynamics) is used as a scaffolding to analyze the global structure of the system. A projection to a lower dimension was followed to take care of the fundamental issues related to high dimensional models that describe a low dimensional dynamics. Local analysis of the system was done in the low dimensional projected space. A topological conjugacy of the recurrence neighborhoods in both the lower and the higher dimensional spaces are demonstrated. The proposed model uses a nonlinear generalization of a well known linear algebra technique named Singular Value Decomposition (SVD) for data analysis. The method of nonlinear SVD and its uses (i) to determine nonlinearity in a time series and (ii) to empirically arrive at an upper bound for the dimension of a manifold where the data resides are demonstrated. The proposed method of prediction and modeling was used for the analysis of (i) data generated by the Duffing oscillator and (ii) an Electrocardiogram (ECG) record. It is shown that the entire nonlinear structure can be deduced from one or few overlapping neighborhoods for these data. A method of stability analysis by studying the properties of affine maps specific to the neighborhoods are demonstrated for both these data. The thesis gives a theoretical justification for a well known experimental observation that the heart rate variability– a variability in beat-to-beat intervals of the heart is a necessity for healthy functioning of the heart. The relevance and contribution of the introduced method for biomedical signal processing is justified by using it successfully for analyzing a set of multi-channel physiological data

Rapid chaotic synchronization by intermittent driving signals

Abstract—Synchronization of two identical chaotic systems which starts with different initial conditions, by sending a part of state space to other in a continuous fashion is a well established procedure. This paper discusses synchronization by intermittent driving signals from a part of a system to the other system. Here we show numerical evidence that if we were to run the second system on its own until the intermittent information about the first is available, and replacing it, synchronization does take place but it takes a longer time. What we show is a method to speed up this procedure even when the intermittent signals are not that frequent. This has potential application in communication, especially in the area of cryptography. Details of procedure and possible application in cryptography are included in Ref. [8

Estimating the dimension of a manifold and finding local charts on it by using nonlinear single value decomposition

In this paper we propose a method of using nonlinear generalization of Singular Value Decomposition (SVD) to arrive at an upper bound for the dimension of a manifold which is embedded in some RN. We have assumed that the data about its co-ordinates is available. We would also assume that there exists at least one small neighborhood with sufficient number of data points. Given these conditions, we show a method to compute the dimension of a manifold. We begin by looking at the simple case when the manifold is in the form of a lower dimensional affine subspace. In this case, we show that the well known technique of SVD can be used to (i) calculate the dimension of the manifold and (ii) to get the equations which define the subspace. For the more general case, we have applied a nonlinear generalization of the SVD (i) to search for an upper bound for the dimension of the manifold and (ii) to find the equations for the local charts of the manifold. We have included a brief discussion about how this method would be highly useful in the context of the Takens’ embedding which is used in the analysis of a time series data from a dynamical system. We show a specific problem that has recently been found out when applying this method. One very effective solution is to develop a model which is based on local charts and for this purpose a good estimate of the underlying dimension of an embedded data is required

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Not AvailableSundarban area of West Bengal State in India is a complex-diverse-risk prone agro-ecosystem grappled with degraded soil, water logging, brackish ground water and marginal farm holdings. South west monsoon rain-fed paddy crop is the major production system and the farm families have to migrate to other areas for employment during the post-monsoon season. Farm pond based rain water harvesting and optimally utilizing it to cultivate vegetables and rearing fish in the pond would provide them employment, income and self-reliance on a sustainable basis is the solution. Rain water harvesting based production system models namely, land shaping for aqua-agri integration, brackishwater pond based polyculture and paddy-cum-fish farming were implemented to 370 beneficiary families to enhance the livelihood security at Kakdwip and Namkhana blocks of South 24 Parganas district of West Bengal. A set of 15 indicators were identified by the subject matter scientists to assess the outcome of the interventions in enhancing the livelihood security of farm families. Impact analysis was done using ‘before vs after’ and control vs treatment research design. Primary data were collected from the sample of 120 proportionate random sample beneficiary farm families using a structured questionnaire and focus group meetings. The findings substantially indicated that all the three farming models have contributed for enhancing the livelihood security levels of the farm families in terms of creation of livelihood asset mainly the farm pond, conservation of natural water for multiple cropping and aquaculture, enhanced capabilities, employment generation, improved production from the land/pond, enhanced income from farming, access to better market price, access to development institutions, minimization of migration during off-season, enhanced self-reliant, and social status of the farm families. The analyses have confirmed that all the three farming models have significantly contributed for the livelihood security of the coastal farm families (p<0.01). Therefore, the study suggested that the Government may evolve a scheme with inbuilt subsidy in up-scaling these models in the entire Sundarban region for enhancing the livelihood security of farm families.Not Availabl

YOGA PRACTICE AND BIOCHEMICAL AND PHYSIOLOGICAL ALTERATIONS IN NORMAL SUBJECTS

ABSTRACTObjective: To assess the effect of 45 minute yogic kriya (Surya Namaskar and Kapalbhati) for 30 days on various physiological and biochemicalparameters.Methods: About 20 Nursing College students of the Santosh Medical University, Ghaziabad, between the age group 17 and 21 years volunteered toparticipate in the study. They were divided into two Groups A and B. Group A students including 10 students in each group were subjected to 30 daysyoge kriya for 45 minutes for 6 days in a week. Statistical analysis: A student's t-test was used for comparing the means of pre- and post-yoga resultsof various parameters.Results: No significant difference was found in systolic blood pressure, pulse, body mass index, hemoglobin except for fasting blood sugar and diastolicblood pressure (p&lt;0.001) among the yoga subject while comparing with baseline values and control.Keywords: Yoga, Biochemical alterations, Physiological alterations, Surya Namaskar and Kapal Bhati

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How managers can build trust in strategic alliances: a meta-analysis on the central trust-building mechanisms

Trust is an important driver of superior alliance performance. Alliance managers are influential in this regard because trust requires active involvement, commitment and the dedicated support of the key actors involved in the strategic alliance. Despite the importance of trust for explaining alliance performance, little effort has been made to systematically investigate the mechanisms that managers can use to purposefully create trust in strategic alliances. We use Parkhe’s (1998b) theoretical framework to derive nine hypotheses that distinguish between process-based, characteristic-based and institutional-based trust-building mechanisms. Our meta-analysis of 64 empirical studies shows that trust is strongly related to alliance performance. Process-based mechanisms are more important for building trust than characteristic- and institutional-based mechanisms. The effects of prior ties and asset specificity are not as strong as expected and the impact of safeguards on trust is not well understood. Overall, theoretical trust research has outpaced empirical research by far and promising opportunities for future empirical research exist

Virtual Reality for Nondestructive Evaluation Applications

Gas transmission pipelines are often inspected and monitored using the magnetic flux leakage method [1]. An inspection vehicle known as a “pig” is launched into the pipeline and conveyed along the pipe by the pressure of natural gas. The pig contains a magnetizer, an array of sensors and a microprocessor-based data acquisition system for logging data. The data is subsequently retrieved and analyzed offline. The pipeline inspection results in the generation of a vast amount of data — in excess of 4 GB, even in compressed form. It is important that these data are presented in a suitable manner for evaluation by trained operator. Virtual reality (VR) display techniques represent an attractive mechanism for presenting this huge amount of data effectively. The application of VR techniques enables the operator to explore the virtual environment generated by the computer. This technique can serve as an important bridge between human operator and the computer. In this paper, we present some preliminary efforts in achieving this interface

Reaction rates and transport in neutron stars

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.