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.

CONSERVATIVE AND PROGFESSIVE ASPECTS OF THE SONATA FROM LATE BEETHOVEN TO PROKOFIEV

The term 'sonata' arose in the early seventeenth-century Baroque period and was originally used to distinguish instrumental (sonata) music from vocal music. Later. the sonata style, as a reliable yet flexible compositional framework, was extensively shaped and utilized throughout the Classical period. Subsequently, in the Romantic period, freer creative, individualistic. and expressive musical elements began to be preferred by composers in their use of harmonj., tone color, form, and rhythm. However, even during the revolutionary Romantic period in music. the compositions which did not have a pre-defined format (character pieces, etc) were often comfortably framed and limited within the recognizable boundaries provided by the Classical sonata style. The sonata format, when used as a tool in musical composition, provides logical boundaries that may serve to organize any unexpected emotional expressions on the part of the composer. Yet the sonata framework is also flexible enough to allow freedom of expression. In the Romantic period and beyond, composers had relied, some more than others, upon the sonata's adaptable blend of stability and flexibility. In my opinion, it is more persuasive to express oneself musically within the framework of an established musical style. Thus, I have chosen my dissertation topic as the performance of six pieces incorporating elements of the reliable and flexible sonata style. The sonata of each composer that I have selected clearly demonstrates a tension between logic and emotion expressed within the sonata framework. However, the compositions can be divided interestingly into two groups, such as 'conservative' and 'progressive' group. The 'conservative' group consists of composers who seemed to strive for greater freedom of self-expression within the constraints of the traditional sonata form. On the other hand, the 'progressive' group consists of composers who seemed more to rely upon the sonata form to rein in and add stability to their highly individual and emotional musical ideas. It is my hope that this project will provide a stimulating viewpoint from which to consider the evolution and utilization of the sonata style especially as it is applied to the composition and performance of these six diverse and interesting pieces.

LUCIANO BERIO’S NATURALE: A STORY COMBINING FOLK MUSIC AND ART MUSIC

The study of a score by a serious performer is a fundamental step in the process of arriving at a knowledgeable and deeply informed approach to performing a piece of music. In order to obtain this knowledge numerous aspects of the score must be taken into consideration. It is the intent of this dissertation to gather and analyze the information concerning Naturale, a work written by Luciano Berio in 1985 for viola, percussion and recorded voice, based on Sicilian folk songs. All the aspects surrounding Naturale’s existence are taken into consideration in this study. First, it is important to reflect on Berio’s compositional style and traits, the manner in which he relates his works one to another, what he sees in folk music and his own personal desire to intertwine art music and folk music. For Berio Naturale is not an isolated venture into the realm of mixing folk music and his own avant-garde style; it is instead one of many works resulting from his long-standing relationship with folk music. Another essential aspect in this case is the study of Sicilian folk music itself, and the sources used by Berio to find the songs by which he was inspired. The work is examined section by section with figures showing both excerpts of Naturale as well as the original songs with their translations. An analysis containing harmonic, thematic and formal aspects of the score was developed in order to arrive at a better understanding of the structure and pacing of the piece. For this research the author went to Italy to conduct an interview with Maestro Aldo Bennici, the Sicilian violist for whom Naturale was composed. This interview helped in the discovery of two more songs used by Berio that have not to this point been identified in any other document. Bennici’s outstanding testimony portrayed the expressive character of this music and the evocative imagery behind this score. I hope to bring this knowledge to other performers, that they may fully understand and appreciate the unique beauty and power of Berio’s Naturale.