Neural network design for switching network control

A neural network is a highly interconnected set of simple processors. The many connections allow information to travel rapidly through the network, and due to their simplicity, many processors in one network are feasible. Together these properties imply that we can build efficient massively parallel machines using neural networks. The primary problem is how do we specify the interconnections in a neural network. The various approaches developed so far such as outer product, learning algorithm, or energy function suffer from the following deficiencies: long training/ specification times; not guaranteed to work on all inputs; requires full connectivity.

Alternatively we discuss methods of using the topology and constraints of the problems themselves to design the topology and connections of the neural solution. We define several useful circuits-generalizations of the Winner-Take-All circuitthat allows us to incorporate constraints using feedback in a controlled manner. These circuits are proven to be stable, and to only converge on valid states. We use the Hopfield electronic model since this is close to an actual implementation. We also discuss methods for incorporating these circuits into larger systems, neural and nonneural. By exploiting regularities in our definition, we can construct efficient networks. To demonstrate the methods, we look to three problems from communications. We first discuss two applications to problems from circuit switching; finding routes in large multistage switches, and the call rearrangement problem. These show both, how we can use many neurons to build massively parallel machines, and how the Winner-Take-All circuits can simplify our designs.

Next we develop a solution to the contention arbitration problem of high-speed packet switches. We define a useful class of switching networks and then design a neural network to solve the contention arbitration problem for this class. Various aspects of the neural network/switch system are analyzed to measure the queueing performance of this method. Using the basic design, a feasible architecture for a large (1024-input) ATM packet switch is presented. Using the massive parallelism of neural networks, we can consider algorithms that were previously computationally unattainable. These now viable algorithms lead us to new perspectives on switch design.

Role of feedback and dynamics in a gene regulatory network

Cells exhibit a diverse repertoire of dynamic behaviors. These dynamic functions are implemented by circuits of interacting biomolecules. Although these regulatory networks function deterministically by executing specific programs in response to extracellular signals, molecular interactions are inherently governed by stochastic fluctuations. This molecular noise can manifest as cell-to-cell phenotypic heterogeneity in a well-mixed environment. Single-cell variability may seem like a design flaw but the coexistence of diverse phenotypes in an isogenic population of cells can also serve a biological function by increasing the probability of survival of individual cells upon an abrupt change in environmental conditions. Decades of extensive molecular and biochemical characterization have revealed the connectivity and mechanisms that constitute regulatory networks. We are now confronted with the challenge of integrating this information to link the structure of these circuits to systems-level properties such as cellular decision making. To investigate cellular decision-making, we used the well studied galactose gene-regulatory network in \textit{Saccharomyces cerevisiae}. We analyzed the mechanism and dynamics of the coexistence of two stable on and off states for pathway activity. We demonstrate that this bimodality in the pathway activity originates from two positive feedback loops that trigger bistability in the network. By measuring the dynamics of single-cells in a mixed sugar environment, we observe that the bimodality in gene expression is a transient phenomenon. Our experiments indicate that early pathway activation in a cohort of cells prior to galactose metabolism can accelerate galactose consumption and provide a transient increase in growth rate. Together these results provide important insights into strategies implemented by cells that may have been evolutionary advantageous in competitive environments.

An integrated design approach to power systems : from power flows to electricity markets

Power system is at the brink of change. Engineering needs, economic forces and environmental factors are the main drivers of this change. The vision is to build a smart electrical grid and a smarter market mechanism around it to fulfill mandates on clean energy. Looking at engineering and economic issues in isolation is no longer an option today; it needs an integrated design approach. In this thesis, I shall revisit some of the classical questions on the engineering operation of power systems that deals with the nonconvexity of power flow equations. Then I shall explore some issues of the interaction of these power flow equations on the electricity markets to address the fundamental issue of market power in a deregulated market environment. Finally, motivated by the emergence of new storage technologies, I present an interesting result on the investment decision problem of placing storage over a power network. The goal of this study is to demonstrate that modern optimization and game theory can provide unique insights into this complex system. Some of the ideas carry over to applications beyond power systems.

Information-theoretic Studies and Capacity Bounds: Group Network Codes and Energy Harvesting Communication Systems

Network information theory and channels with memory are two important but difficult frontiers of information theory. In this two-parted dissertation, we study these two areas, each comprising one part. For the first area we study the so-called entropy vectors via finite group theory, and the network codes constructed from finite groups. In particular, we identify the smallest finite group that violates the Ingleton inequality, an inequality respected by all linear network codes, but not satisfied by all entropy vectors. Based on the analysis of this group we generalize it to several families of Ingleton-violating groups, which may be used to design good network codes. Regarding that aspect, we study the network codes constructed with finite groups, and especially show that linear network codes are embedded in the group network codes constructed with these Ingleton-violating families. Furthermore, such codes are strictly more powerful than linear network codes, as they are able to violate the Ingleton inequality while linear network codes cannot. For the second area, we study the impact of memory to the channel capacity through a novel communication system: the energy harvesting channel. Different from traditional communication systems, the transmitter of an energy harvesting channel is powered by an exogenous energy harvesting device and a finite-sized battery. As a consequence, each time the system can only transmit a symbol whose energy consumption is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is random, instantaneous, and has memory. Furthermore, naturally, the energy harvesting process is observed causally at the transmitter, but no such information is provided to the receiver. Both of these features pose great challenges for the analysis of the channel capacity. In this work we use techniques from channels with side information, and finite state channels, to obtain lower and upper bounds of the energy harvesting channel. In particular, we study the stationarity and ergodicity conditions of a surrogate channel to compute and optimize the achievable rates for the original channel. In addition, for practical code design of the system we study the pairwise error probabilities of the input sequences.