Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Exploring Musical Diversity in the Collaborative Repertoire from 1880 through 1963

It is essential in musical performance not only to convey the unique language of the composers but also to approach each composition from the perspective of its style. During the 20th century, diverse musical idioms co-existed, sometimes mixing or fusing, yet retaining recognizable characteristics and thereby remaining distinctive. This dissertation explores myriad examples from Late Romanticism/Post- Romanticism, Naturalism, Neo-Classicism, Nationalism and Impressionism composed during this unusually rich period. In order to explore a broad range of collaborative repertoire and to deepen my knowledge of the styles and performance practices relating to these pieces, I studied and performed the repertoire with pianist Eunae Baik–Kim, clarinetist Jihoon Chang, and singers Joshua Brown and Young Joo Lee. The first program featured Post-Romantic, Neo-Classic and Impressionist two-piano works composed by Debussy, Rachmaninoff, and Stravinsky. Each of the three composers used their own distinctive harmonies, rhythms, melodic inventions, pedaling and figurations. In all of the works, both piano parts were densely interwoven, having equal importance. Lied and operatic aria was the focus of the second recital. Brahms’ Vier Ernste Gesänge Op. 121, Ravel’s Don Quichotte a Dulcineé and Italian, French and German operatic arias were the examples of Post-Romanticism and Nationalism. The representative composers were Verdi, Massenet, Korngold, Leoncavallo, Ravel and Wagner. Despite the fact that all of the repertoire was written in traditional musical forms, the composers’ unique voices mark each work as belonging to a particular genre. The third recital focused on Post-Romantic and Impressionistic music written for clarinet and piano: the Première Rhapsodie by Debussy, the Sonata by Poulenc and Brahms’ Sonata in F minor Op. 120, No. 1. These works, although profoundly different in style, share elements of simplicity, clarity and elegance as well as technical virtuosity, articulation and profound musical depth. The three recitals which comprise this dissertation project were performed at the University of Maryland Gildenhorn Recital Hall on February 27, 2010, October 25, 2010, and January 31, 2011. The recitals were recorded on compact disc and are archived within the Digital Repository at the University of Maryland (DRUM).