For a certain class of Z²-actions, we provide a proof of a conjecture that the ratio of the Perron eigenvalues of the transfer matrices of the free boundary restrictions converge to the entropy of that action. Also, a novel method for computing the entropy of Z²-actions is conjectured.
In this thesis, I present the variational database management system, a formal framework and its implementation for representing variation in relational databases and managing variational information needs. A variational database is intended to support any kind of variation in a database. Specific kinds of variation in databases have already been...
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately...
This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
Advances in sensor technology are greatly expanding the range of quantities that can be measured while simultaneously reducing the cost. However, deployed sensors drift out of calibration and fail, so every sensor network requires quality control procedures to promptly detect these failures. To address these problems, we propose a two-level...
Multi-relation aggregation queries process the join operator before computing the aggregation function. This join is arguably the most costly operation since traditional join algorithms spend majority of their time trying to join the parts of the relations that do not generate any output tuples. This causes slow response times with...
Relational binary operators, such as join, are arguably the most costly and frequently used operations in relational data systems. In many join algorithms, the majority of the process time is spent on scanning and attempting to join the parts of the relations that do not satisfy the join condition and...
In this work, we study network coding technique, its relation to random matrices, and their applications to communication systems. The dissertation consists of three main contributions. First, we propose efficient algorithms for data synchronization via a broadcast channel using random network coding. Second, we study the resiliency of network coding...
Anomaly detection aims at detecting the points that appear different than the majority of the data, such that they are suspected to be generated from a different distribution. Anomaly detectors have been applied in many different fields, such as detecting fraudulent behaviors in bank transaction, finding broken sensors in a...
We present a method for decentralized, multi-robot exploration in adverse environments where communication is minimal. A key conceptual feature of our method is enabling implicit coordination between robots by training a Convolutional Neural Network (CNN) as a heuristic for planning using Monte Carlo Tree Search (MCTS). Our method consists of...