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Papers by Sajini Anand P S
Acta Applicandae Mathematicae, Jan 23, 2010
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper demonstrates an application of nonlinear SVD to identify parameters when the signal is generated by a nonlinear transformation. Examples of maps (Logistic map and Henon map) and flows (Van der Pol oscillator and Duffing oscillator) are used to illustrate the method of nonlinear SVD to identify parameters. The paper presents the recovery of parameters in the following scenarios: (i) data generated by maps and flows, (ii) comparison of the method for both noisy and noise-free data, (iii) surrogate data analysis for both the noisy and noise-free cases. The paper includes two applications of the method: (i) Mathematical Modeling and (ii) Chaotic Cryptanalysis.
arXiv: Chaotic Dynamics, 2017
The paper introduces a novel topological method for prediction and modeling for a nonlinear time-... more The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few overlapping recurrence neighborhoods. The inherent redundancy structure of the delay embedding procedure and the property of recurrence are used to reduce the computational load, which is inevitable in nonlinear analysis. The modeling and prediction possibilities of the model are demonstrated using (i) a numerical data generated by a dynamical system: the Duffing oscillator and (ii) a real--life data: Electrocardiogram ECG data of a healthy human. A potential application of the proposed model is demonstrated for a multivariate cardiovascular data set that exhibits the property of recurrence. Real--time monitoring of cardiovascular signals are essential in clinical research and corruption of data are very common. It is a challenging task for a mod...
Modeling a system based on time series is a complicated problem in general, especially when the t... more 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 h...
2019 Fifteenth International Conference on Information Processing (ICINPRO), 2019
Management of containers and carriers in a supply chain that spreads across different intermodal ... more Management of containers and carriers in a supply chain that spreads across different intermodal legs of ocean, land, river, rail and air transport is a challenging task in the shipping industry. During the intermodal phase, the triangulation of containers or carriers is a process that is sought to minimize cost by saving a possible transport leg. In this paper, we discuss an optimal triangulation process of containers carried by trucks in an intermodal transport network. We are addressing a specific triangulation process for the trucks engaged in import drops or export pickups of containers such that they can be effectively reused for the next export pickups or import drops in locations within a neighbourhood. We propose a mathematical model to address this problem in the framework of minimum cost network flows. Further, we introduce a heuristic method using the successive shortest path algorithm for the proposed model. The model is analyzed using data from current shipping network...
Acta Applicandae Mathematicae, 2010
In this paper we propose a method of using nonlinear generalization of Singular Value Decompositi... more 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 abo...
An end-to-end supply chain operation for inland logistics requires coordination and planning amon... more An end-to-end supply chain operation for inland logistics requires coordination and planning among various operations of import pickups, export delivery and empty container positioning for reuse and evacuations of unused containers through the ports. A major business goal of all these operations focuses on reducing the transport costs by utilizing maximum network capacity across active modes of hinterland transport. Designing an efficient network, ensuring that customer commitments are met with timely delivery of containers, is a complex and challenging task. In this paper, we explore optimization opportunities for an inland network with a heavy and unbalanced container traffic flow through its ports. We propose techniques for the strategic placement of empty resources, for optimal allocation at depots-terminals in the presence of time constraints. The novelties of our method include (i) strategic relocation of the resources to high demand areas, maximizing the resource utilization,...
IACR Cryptol. ePrint Arch., 2005
This paper discusses cryptography based on the property of chaotic synchronization. Specifically,... more This paper discusses cryptography based on the property of chaotic synchronization. Specifically, it is about Round III of such a cryptographic method. Round I showed the feasibility of using chaotic synchronization for cryptography. Round II consisted of a method to counter attack. This paper is Round III and shows how to counter the counter attacks. First, we show numerical evidence that synchronization is possible between two Lorenz systems if one system sends information about x0 at a slower rate. The second system evolves on its own, except that when it receives a signal from the first system, it replaces its own value of y0 by the received x0. We have found that the two systems eventually synchronize, but often after a long time. Therefore, we have devised a technique to speed-up this synchronization. Once this is done, it is possible for the authorized receiver (with the possession of the initial super-key) to keep synchronizing with slowly sampled inputs, whereas the known m...
Singular Value Decomposition can be considered as an effective method for Signal Processing/espec... more Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to nonlinear ARMA method for fitting a nonlinear equation to the data.
Synchronization of two identical chaotic systems which starts with different initial conditions, ... more 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].
Citeseer
This paper discusses cryptography based on the property of chaotic synchronization. Specifically,... more This paper discusses cryptography based on the property of chaotic synchronization. Specifically, it is about Round III of such a cryptographic method. Round I showed the feasibility of using chaotic synchronization for cryptography. Round II consisted of a method to counter attack. This paper is Round III and shows how to counter the counter attacks. First, we show numerical evidence that synchronization is possible between two Lorenz systems if one system sends information about x0 at a slower rate. The second system evolves on its own, except that when it receives a signal from the first system, it replaces its own value of y0 by the received x0. We have found that the two systems eventually synchronize, but often after a long time. Therefore, we have devised a technique to speed-up this synchronization. Once this is done, it is possible for the authorized receiver (with the possession of the initial super-key) to keep synchronizing with slowly sampled inputs, whereas the known methods of Round II do not help an eavesdropper.
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper demonstrates an application of nonlinear SVD to identify parameters when the signal is generated by a nonlinear transformation. Examples of maps (Logistic map and Henon map) and flows (Van der Pol oscillator and Duffing oscillator) are used to illustrate the method of nonlinear SVD to identify parameters. The paper presents the recovery of parameters in the following scenarios: (i) data generated by maps and flows, (ii) comparison of the method for both noisy and noise-free data, (iii) surrogate data analysis for both the noisy and noise-free cases. The paper includes two applications of the method: (i) Mathematical Modeling and (ii) Chaotic Cryptanalysis.
Abstract—Synchronization of two identical chaotic systems which starts with different initial con... more 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]
Lecture Notes in Computer Science
Acta Applicandae Mathematicae, Feb 6, 2010
Acta Applicandae Mathematicae, Jan 23, 2010
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper demonstrates an application of nonlinear SVD to identify parameters when the signal is generated by a nonlinear transformation. Examples of maps (Logistic map and Henon map) and flows (Van der Pol oscillator and Duffing oscillator) are used to illustrate the method of nonlinear SVD to identify parameters. The paper presents the recovery of parameters in the following scenarios: (i) data generated by maps and flows, (ii) comparison of the method for both noisy and noise-free data, (iii) surrogate data analysis for both the noisy and noise-free cases. The paper includes two applications of the method: (i) Mathematical Modeling and (ii) Chaotic Cryptanalysis.
arXiv: Chaotic Dynamics, 2017
The paper introduces a novel topological method for prediction and modeling for a nonlinear time-... more The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few overlapping recurrence neighborhoods. The inherent redundancy structure of the delay embedding procedure and the property of recurrence are used to reduce the computational load, which is inevitable in nonlinear analysis. The modeling and prediction possibilities of the model are demonstrated using (i) a numerical data generated by a dynamical system: the Duffing oscillator and (ii) a real--life data: Electrocardiogram ECG data of a healthy human. A potential application of the proposed model is demonstrated for a multivariate cardiovascular data set that exhibits the property of recurrence. Real--time monitoring of cardiovascular signals are essential in clinical research and corruption of data are very common. It is a challenging task for a mod...
Modeling a system based on time series is a complicated problem in general, especially when the t... more 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 h...
2019 Fifteenth International Conference on Information Processing (ICINPRO), 2019
Management of containers and carriers in a supply chain that spreads across different intermodal ... more Management of containers and carriers in a supply chain that spreads across different intermodal legs of ocean, land, river, rail and air transport is a challenging task in the shipping industry. During the intermodal phase, the triangulation of containers or carriers is a process that is sought to minimize cost by saving a possible transport leg. In this paper, we discuss an optimal triangulation process of containers carried by trucks in an intermodal transport network. We are addressing a specific triangulation process for the trucks engaged in import drops or export pickups of containers such that they can be effectively reused for the next export pickups or import drops in locations within a neighbourhood. We propose a mathematical model to address this problem in the framework of minimum cost network flows. Further, we introduce a heuristic method using the successive shortest path algorithm for the proposed model. The model is analyzed using data from current shipping network...
Acta Applicandae Mathematicae, 2010
In this paper we propose a method of using nonlinear generalization of Singular Value Decompositi... more 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 abo...
An end-to-end supply chain operation for inland logistics requires coordination and planning amon... more An end-to-end supply chain operation for inland logistics requires coordination and planning among various operations of import pickups, export delivery and empty container positioning for reuse and evacuations of unused containers through the ports. A major business goal of all these operations focuses on reducing the transport costs by utilizing maximum network capacity across active modes of hinterland transport. Designing an efficient network, ensuring that customer commitments are met with timely delivery of containers, is a complex and challenging task. In this paper, we explore optimization opportunities for an inland network with a heavy and unbalanced container traffic flow through its ports. We propose techniques for the strategic placement of empty resources, for optimal allocation at depots-terminals in the presence of time constraints. The novelties of our method include (i) strategic relocation of the resources to high demand areas, maximizing the resource utilization,...
IACR Cryptol. ePrint Arch., 2005
This paper discusses cryptography based on the property of chaotic synchronization. Specifically,... more This paper discusses cryptography based on the property of chaotic synchronization. Specifically, it is about Round III of such a cryptographic method. Round I showed the feasibility of using chaotic synchronization for cryptography. Round II consisted of a method to counter attack. This paper is Round III and shows how to counter the counter attacks. First, we show numerical evidence that synchronization is possible between two Lorenz systems if one system sends information about x0 at a slower rate. The second system evolves on its own, except that when it receives a signal from the first system, it replaces its own value of y0 by the received x0. We have found that the two systems eventually synchronize, but often after a long time. Therefore, we have devised a technique to speed-up this synchronization. Once this is done, it is possible for the authorized receiver (with the possession of the initial super-key) to keep synchronizing with slowly sampled inputs, whereas the known m...
Singular Value Decomposition can be considered as an effective method for Signal Processing/espec... more Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to nonlinear ARMA method for fitting a nonlinear equation to the data.
Synchronization of two identical chaotic systems which starts with different initial conditions, ... more 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].
Citeseer
This paper discusses cryptography based on the property of chaotic synchronization. Specifically,... more This paper discusses cryptography based on the property of chaotic synchronization. Specifically, it is about Round III of such a cryptographic method. Round I showed the feasibility of using chaotic synchronization for cryptography. Round II consisted of a method to counter attack. This paper is Round III and shows how to counter the counter attacks. First, we show numerical evidence that synchronization is possible between two Lorenz systems if one system sends information about x0 at a slower rate. The second system evolves on its own, except that when it receives a signal from the first system, it replaces its own value of y0 by the received x0. We have found that the two systems eventually synchronize, but often after a long time. Therefore, we have devised a technique to speed-up this synchronization. Once this is done, it is possible for the authorized receiver (with the possession of the initial super-key) to keep synchronizing with slowly sampled inputs, whereas the known methods of Round II do not help an eavesdropper.
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper demonstrates an application of nonlinear SVD to identify parameters when the signal is generated by a nonlinear transformation. Examples of maps (Logistic map and Henon map) and flows (Van der Pol oscillator and Duffing oscillator) are used to illustrate the method of nonlinear SVD to identify parameters. The paper presents the recovery of parameters in the following scenarios: (i) data generated by maps and flows, (ii) comparison of the method for both noisy and noise-free data, (iii) surrogate data analysis for both the noisy and noise-free cases. The paper includes two applications of the method: (i) Mathematical Modeling and (ii) Chaotic Cryptanalysis.
Abstract—Synchronization of two identical chaotic systems which starts with different initial con... more 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]
Lecture Notes in Computer Science
Acta Applicandae Mathematicae, Feb 6, 2010