We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. ... more We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or enemies (negative links). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link. This model generalizes DeGroot model to account for negative links: when two enemies interact, their opinions go in opposite directions. We provide conditions for convergence and divergence in expectation, in mean-square, and in almost sure sense, and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph. We establish a no-survivor theorem, stating that the difference in opinions of any two nodes diverges whenever ...
Recent studies from social, biological, and engineering network systems have drawn attention to t... more Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes...
Abstract—Two approximate techniques for analyzing the window size distribution of TCP flows shari... more Abstract—Two approximate techniques for analyzing the window size distribution of TCP flows sharing a RED-like bottleneck queue are pre-sented. Both methods presented first use a fixed point algorithm to ob-tain the mean window sizes of the flows, and the mean queue length in the bottleneck buffer. The simpler of the two methods then uses the ‘square root formula ’ for TCP; the other method is more complicated. More of-ten than not, the simpler method is slightly more accurate; this is proba-bly due to the fact that window sizes of the different flows are negatively correlated. Keywords—TCP, multiple, distribution, RED, queues. I.
In this paper we address the problem of multi-agent optimization for convex functions expressible... more In this paper we address the problem of multi-agent optimization for convex functions expressible as sums of convex functions. Each agent has access to only one function in the sum and can use only local information to update its current estimate of the optimal solution. We consider two consensus-based iterative algorithms, based on a combination between a consensus step and a subgradient decent update. The main difference between the two algorithms is the order in which the consensus-step and the subgradient descent update are performed. We show that updating first the current estimate in the direction of a subgradient and then executing the consensus step ensures better performance than executing the steps in reversed order. In support of our analytical results, we give some numerical simulations of the algorithms as well.
In this paper, we consider the binary hypothesis testing problem with two observers. There are tw... more In this paper, we consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations are collected by two observers. The observations are statistically related to the true state of nature. Given the observations, the objective of both observers is to find out what is the true state of nature. We present four different approaches to address the problem. In the first (centralized) approach, the observations collected by both observers are sent to a central coordinator where hypothesis testing is performed. In the second approach, each observer performs hypothesis testing based on locally collected observations. Then they exchange binary information to arrive at a consensus. In the third approach, each observer constructs an aggregated probability space based on the observations collected by it and the decision it receives from the alternate observer and performs hypothesis testing in the new probability space. In th...
In this paper we address the problem of providing full connectivity in large (wide area) ad hoc n... more In this paper we address the problem of providing full connectivity in large (wide area) ad hoc networks by placing advantaged nodes like UAVs (as relay nodes) in appropriate places. We provide a formulation where we can treat the connectivity problem as a clustering problem with a summation-form distortion function. We then adapt the Deterministic Annealing clustering algorithm to our formulation and using that we find the minimum number of UAVs required to provide connectivity and their locations. Furthermore, we describe enhancements that can be used to extend the basic connectivity problem to support notions of reliable connectivity that can lead to improved network performance. We establish the validity of our algorithm and compare its performance with optimal (exhaustive search) as well as non-opitmal (hard clustering) algorithms. We show that our algorithm is nearoptimal both for the basic connectivity problem as well as extended notions of connectivity.
In this paper, we address the multicast routing problem for mobile ad hoc networks (MANETs). We p... more In this paper, we address the multicast routing problem for mobile ad hoc networks (MANETs). We present the Source Grouped Flooding approach to achieve multicast in MANETs. In this protocol, each source creates a flooding group consisting of nodes connecting the source to the multicast members. The nodes in the flooding group are recruited based on hop count distance constraints obtained during a request-reply phase. The flooding group though robust may result in redundant data transmissions. We also propose a probabilisticdata forwarding mechanism to achieve efficient data dissemination. The protocol aims to achieve the robustness of flooding and data distribution efficiency of tree based protocols. Simulation resul ts verify performance.
In this work, we describe a novel non-repudiation mechanism for an authentication protocol based ... more In this work, we describe a novel non-repudiation mechanism for an authentication protocol based on the extended TESLA certificate construct. With the non-repudiation mechanism, the authentication protocol is ideally suited for source authentication of low-powered nodes that participate in group communication in hybrid satellite/wireless networks. Security is a necessary parameter in hybrid wireless networks (consisting of groups of terrestrial wireless nodes interconnected by a satellite overlay) if the communication between a pair of nodes, or amongst a group of nodes, is to be protected from unauthorized The focus of our research work is on user authentication and message integrity protocols, which are required to enable communications and ensure that messages between communicating nodes are correctly delivered. This is a non-trivial problem in group communication, where authentication has been traditionally done using asymmetric cryptographic techniques such as public key certif...
We present a graphical tool for the calculation of treewidth, a metric on the parametric structur... more We present a graphical tool for the calculation of treewidth, a metric on the parametric structure of a system that is intimately tied to the complexity of system analysis. For many graphically describable systems, such as systems of parametric equations, as in a SysML Parametric Diagram, or Bayesian networks or even mind maps and writing term papers, analysis of the system is exponential in treewidth and linear in system size. A tool facilitating comprehensive analysis can serve to bring competitive advantage to a systems engineering workflow by reducing costly unanticipated behaviors. Furthermore, a byproduct of computing treewidth is a framework for enumerating computationally compatible distributed algorithms. In this paper, we pose this NP-complete problem from the perspective of finding satisficing solutions, exposing choices that can influence the complexity of the resulting system to the designer. A designer can contribute two important things to the structure of the system:...
Packet level forward error correction (FEC) coding has been widely accepted as an efficient way o... more Packet level forward error correction (FEC) coding has been widely accepted as an efficient way of reducing the number of retransmissions and recovering from packet losses for reliable multicast in satellite networks. While there has been a significant effort in defining packet level FEC schemes that detail the structure, organization and delivery of the encoding packets, little attention has been given to how the physical channel, channel coding, and the downlink power budget affect the design space of these schemes in the context of a satellite network architecture. In this paper, we take a step in this direction, and define the points of interaction between various components and build a simulation environment. Using this simulation setup, we provide design suggestions for integrating FEC coding into reliable multicast transport protocols.
Despite intensive efforts towards modeling of smart grids we do not have todate a methodology and... more Despite intensive efforts towards modeling of smart grids we do not have todate a methodology and associated tools that allow easy and modular creation of accurate models of smart grids at various space-time scales and which are expandable. Furthermore, the testbeds that exist do not link easily to tradeoff and decision making tools for design and operation. Finally, and this is the weakest component of the overall modeling and synthesis and performance evaluation environment we do not have a rigorous representation of requirements and metrics that can be easily linked to such modeling environments for the purpose of testing and validation of requirements and performance metrics. In this paper and presentation we will present our ongoing methodology and framework for developing integrated modeling hubs for smart grids that can accommodate heterogeneous physical and cyber components, at various spatial and temporal scales. The hub utilizes a modern and rigorous model-based systems en...
The present thesis develops a framework for Health Care Management Systems using modern Model-Bas... more The present thesis develops a framework for Health Care Management Systems using modern Model-Based Systems Engineering methodologies and applies it to Diabetes Mellitus. The desired architecture of such systems is described. Tests and interventions, including Health Care IT, used for Diabetes 2 diagnosis and treatment, are described and modeled. A Controlled Markov Chain model for the progression of Diabetes Mellitus with three states, three diagnostic tests, ten interventions, three patient types, is developed. Evaluation metrics for healthcare quality and associated costs are developed. Using these metrics and disease models, two methods for tradeoff analysis between healthcare quality and costs are developed and analyzed. One is an exhaustive Monte Carlo simulation and the other utilizes multi-criteria optimization with full state information. The latter obtains similar results as the former at a fraction of the time. Practical examples illustrate the powerful capabilities of the framework. Future research directions and extensions are described.
This paper demonstrates that it is possible to model attacks with a low number of states and clas... more This paper demonstrates that it is possible to model attacks with a low number of states and classify them using Hidden Markov Models with very low False Alarm rate and very few False Negatives. We also show that the models developed can be used for both detection and classification. We put emphasis on detection and classification of network intrusions and attacks using Hidden Markov Models and training on anomalous sequences. We test several algorithms, apply different rules for classification and evaluate the relative performance of these. Several of the attack examples presented exploit buffer overflow vulnerabilities, due to availability of data for such attacks. We emphasize that the purpose of our algorithms is not only the detection and classification of buffer overflows; they are designed for detecting and classifying a broad range of attacks.
This paper presents a mathematical technique for computing the stationary distribution of Markov ... more This paper presents a mathematical technique for computing the stationary distribution of Markov processes that evolve deterministically between arbitrarily distributed ‘failure events’. The key innovation in this paper is the use of a state-dependent time re-scaling technique, such that the re-scaled process can be described by a Poisson-interrupted stochastic differential equation. This technique is first applied to compute the stationary window distribution of a TCP flow performing idealized classical congestion avoidance under variable, but state-dependent, packet loss, and subsequently, to study the distribution of a TCP flow performing generalized congestion avoidance. We show how the stochastic differential equation can be solved by a rapidly convergent numerical technique to obtain the stationary distribution in the re-scaled (subjective) time, and present the re-scalings needed to eventually obtain the distribution of the original Markov process. We demonstrate how this ana...
Research supported by the Army Research Office under MURI award W911NF-08-1-0238 and by the Natio... more Research supported by the Army Research Office under MURI award W911NF-08-1-0238 and by the National Science Foundation under grant CNS1018346.
We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. ... more We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or enemies (negative links). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link. This model generalizes DeGroot model to account for negative links: when two enemies interact, their opinions go in opposite directions. We provide conditions for convergence and divergence in expectation, in mean-square, and in almost sure sense, and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph. We establish a no-survivor theorem, stating that the difference in opinions of any two nodes diverges whenever ...
Recent studies from social, biological, and engineering network systems have drawn attention to t... more Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes...
Abstract—Two approximate techniques for analyzing the window size distribution of TCP flows shari... more Abstract—Two approximate techniques for analyzing the window size distribution of TCP flows sharing a RED-like bottleneck queue are pre-sented. Both methods presented first use a fixed point algorithm to ob-tain the mean window sizes of the flows, and the mean queue length in the bottleneck buffer. The simpler of the two methods then uses the ‘square root formula ’ for TCP; the other method is more complicated. More of-ten than not, the simpler method is slightly more accurate; this is proba-bly due to the fact that window sizes of the different flows are negatively correlated. Keywords—TCP, multiple, distribution, RED, queues. I.
In this paper we address the problem of multi-agent optimization for convex functions expressible... more In this paper we address the problem of multi-agent optimization for convex functions expressible as sums of convex functions. Each agent has access to only one function in the sum and can use only local information to update its current estimate of the optimal solution. We consider two consensus-based iterative algorithms, based on a combination between a consensus step and a subgradient decent update. The main difference between the two algorithms is the order in which the consensus-step and the subgradient descent update are performed. We show that updating first the current estimate in the direction of a subgradient and then executing the consensus step ensures better performance than executing the steps in reversed order. In support of our analytical results, we give some numerical simulations of the algorithms as well.
In this paper, we consider the binary hypothesis testing problem with two observers. There are tw... more In this paper, we consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations are collected by two observers. The observations are statistically related to the true state of nature. Given the observations, the objective of both observers is to find out what is the true state of nature. We present four different approaches to address the problem. In the first (centralized) approach, the observations collected by both observers are sent to a central coordinator where hypothesis testing is performed. In the second approach, each observer performs hypothesis testing based on locally collected observations. Then they exchange binary information to arrive at a consensus. In the third approach, each observer constructs an aggregated probability space based on the observations collected by it and the decision it receives from the alternate observer and performs hypothesis testing in the new probability space. In th...
In this paper we address the problem of providing full connectivity in large (wide area) ad hoc n... more In this paper we address the problem of providing full connectivity in large (wide area) ad hoc networks by placing advantaged nodes like UAVs (as relay nodes) in appropriate places. We provide a formulation where we can treat the connectivity problem as a clustering problem with a summation-form distortion function. We then adapt the Deterministic Annealing clustering algorithm to our formulation and using that we find the minimum number of UAVs required to provide connectivity and their locations. Furthermore, we describe enhancements that can be used to extend the basic connectivity problem to support notions of reliable connectivity that can lead to improved network performance. We establish the validity of our algorithm and compare its performance with optimal (exhaustive search) as well as non-opitmal (hard clustering) algorithms. We show that our algorithm is nearoptimal both for the basic connectivity problem as well as extended notions of connectivity.
In this paper, we address the multicast routing problem for mobile ad hoc networks (MANETs). We p... more In this paper, we address the multicast routing problem for mobile ad hoc networks (MANETs). We present the Source Grouped Flooding approach to achieve multicast in MANETs. In this protocol, each source creates a flooding group consisting of nodes connecting the source to the multicast members. The nodes in the flooding group are recruited based on hop count distance constraints obtained during a request-reply phase. The flooding group though robust may result in redundant data transmissions. We also propose a probabilisticdata forwarding mechanism to achieve efficient data dissemination. The protocol aims to achieve the robustness of flooding and data distribution efficiency of tree based protocols. Simulation resul ts verify performance.
In this work, we describe a novel non-repudiation mechanism for an authentication protocol based ... more In this work, we describe a novel non-repudiation mechanism for an authentication protocol based on the extended TESLA certificate construct. With the non-repudiation mechanism, the authentication protocol is ideally suited for source authentication of low-powered nodes that participate in group communication in hybrid satellite/wireless networks. Security is a necessary parameter in hybrid wireless networks (consisting of groups of terrestrial wireless nodes interconnected by a satellite overlay) if the communication between a pair of nodes, or amongst a group of nodes, is to be protected from unauthorized The focus of our research work is on user authentication and message integrity protocols, which are required to enable communications and ensure that messages between communicating nodes are correctly delivered. This is a non-trivial problem in group communication, where authentication has been traditionally done using asymmetric cryptographic techniques such as public key certif...
We present a graphical tool for the calculation of treewidth, a metric on the parametric structur... more We present a graphical tool for the calculation of treewidth, a metric on the parametric structure of a system that is intimately tied to the complexity of system analysis. For many graphically describable systems, such as systems of parametric equations, as in a SysML Parametric Diagram, or Bayesian networks or even mind maps and writing term papers, analysis of the system is exponential in treewidth and linear in system size. A tool facilitating comprehensive analysis can serve to bring competitive advantage to a systems engineering workflow by reducing costly unanticipated behaviors. Furthermore, a byproduct of computing treewidth is a framework for enumerating computationally compatible distributed algorithms. In this paper, we pose this NP-complete problem from the perspective of finding satisficing solutions, exposing choices that can influence the complexity of the resulting system to the designer. A designer can contribute two important things to the structure of the system:...
Packet level forward error correction (FEC) coding has been widely accepted as an efficient way o... more Packet level forward error correction (FEC) coding has been widely accepted as an efficient way of reducing the number of retransmissions and recovering from packet losses for reliable multicast in satellite networks. While there has been a significant effort in defining packet level FEC schemes that detail the structure, organization and delivery of the encoding packets, little attention has been given to how the physical channel, channel coding, and the downlink power budget affect the design space of these schemes in the context of a satellite network architecture. In this paper, we take a step in this direction, and define the points of interaction between various components and build a simulation environment. Using this simulation setup, we provide design suggestions for integrating FEC coding into reliable multicast transport protocols.
Despite intensive efforts towards modeling of smart grids we do not have todate a methodology and... more Despite intensive efforts towards modeling of smart grids we do not have todate a methodology and associated tools that allow easy and modular creation of accurate models of smart grids at various space-time scales and which are expandable. Furthermore, the testbeds that exist do not link easily to tradeoff and decision making tools for design and operation. Finally, and this is the weakest component of the overall modeling and synthesis and performance evaluation environment we do not have a rigorous representation of requirements and metrics that can be easily linked to such modeling environments for the purpose of testing and validation of requirements and performance metrics. In this paper and presentation we will present our ongoing methodology and framework for developing integrated modeling hubs for smart grids that can accommodate heterogeneous physical and cyber components, at various spatial and temporal scales. The hub utilizes a modern and rigorous model-based systems en...
The present thesis develops a framework for Health Care Management Systems using modern Model-Bas... more The present thesis develops a framework for Health Care Management Systems using modern Model-Based Systems Engineering methodologies and applies it to Diabetes Mellitus. The desired architecture of such systems is described. Tests and interventions, including Health Care IT, used for Diabetes 2 diagnosis and treatment, are described and modeled. A Controlled Markov Chain model for the progression of Diabetes Mellitus with three states, three diagnostic tests, ten interventions, three patient types, is developed. Evaluation metrics for healthcare quality and associated costs are developed. Using these metrics and disease models, two methods for tradeoff analysis between healthcare quality and costs are developed and analyzed. One is an exhaustive Monte Carlo simulation and the other utilizes multi-criteria optimization with full state information. The latter obtains similar results as the former at a fraction of the time. Practical examples illustrate the powerful capabilities of the framework. Future research directions and extensions are described.
This paper demonstrates that it is possible to model attacks with a low number of states and clas... more This paper demonstrates that it is possible to model attacks with a low number of states and classify them using Hidden Markov Models with very low False Alarm rate and very few False Negatives. We also show that the models developed can be used for both detection and classification. We put emphasis on detection and classification of network intrusions and attacks using Hidden Markov Models and training on anomalous sequences. We test several algorithms, apply different rules for classification and evaluate the relative performance of these. Several of the attack examples presented exploit buffer overflow vulnerabilities, due to availability of data for such attacks. We emphasize that the purpose of our algorithms is not only the detection and classification of buffer overflows; they are designed for detecting and classifying a broad range of attacks.
This paper presents a mathematical technique for computing the stationary distribution of Markov ... more This paper presents a mathematical technique for computing the stationary distribution of Markov processes that evolve deterministically between arbitrarily distributed ‘failure events’. The key innovation in this paper is the use of a state-dependent time re-scaling technique, such that the re-scaled process can be described by a Poisson-interrupted stochastic differential equation. This technique is first applied to compute the stationary window distribution of a TCP flow performing idealized classical congestion avoidance under variable, but state-dependent, packet loss, and subsequently, to study the distribution of a TCP flow performing generalized congestion avoidance. We show how the stochastic differential equation can be solved by a rapidly convergent numerical technique to obtain the stationary distribution in the re-scaled (subjective) time, and present the re-scalings needed to eventually obtain the distribution of the original Markov process. We demonstrate how this ana...
Research supported by the Army Research Office under MURI award W911NF-08-1-0238 and by the Natio... more Research supported by the Army Research Office under MURI award W911NF-08-1-0238 and by the National Science Foundation under grant CNS1018346.
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