Online Correlation Clustering

We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is revealed, so that for each u we are told whether v is similar to u. The algorithm can create a new cluster for v and merge existing clusters. When the objective is to minimize disagreements between the clustering and the input, we prove that a natural greedy algorithm is O(n)-competitive, and this is optimal. When the objective is to maximize agreements between the clustering and the input, we prove that the greedy algorithm is .5-competitive; that no online algorithm can be better than .834-competitive; we prove that it is possible to get better than 1/2, by exhibiting a randomized algorithm with competitive ratio .5+c for a small positive fixed constant c.Comment: 12 pages, 1 figur

Applets and Groupwork in Intro. Electromagnetism

Three introductory electromagnetism conference sections were given groupwork, applets, or nothing in class before each exam, and the resulting exam grades were compared. To correct for differences between tests and between sections, each section was given groupwork, applets, and control in different orders. Each group performed within 3 points of the control, within the statistical margin of error. A different set of students was given applets and groupwork the next term and interviewed about the experience

Discrete Wigner Function Formulation of Qubits

This project investigates the discrete Wigner function for systems of qubits following Wootters\u27s recent work. The general formalism is developed for n qubits and applied to systems of one and two qubits. Among the applications considered are: implementation of rotations and gates on 1- and 2-qubit systems and state reconstruction through quantum tomography. We discover that crossing two 1-qubit DWFs to form one 2-qubit DWF requires the use of different quantum nets. We also investigate reduction of the 2-qubit DWF

Parallel Graph Algorithms in Constant Adaptive Rounds: Theory meets Practice

We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only $O(n^\epsilon)$ space per machine, where $0 < \epsilon < 1$. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distriubted computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines

Peripheral Oedema - Institute of Chiropodists and Podiatrists March AGM 2010

In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many others. We apply our method to derive general concentration inequalities for polynomials of independent random variables. We show that our method implies concentration inequalities for some previously open problems, e.g. permanent of random symmetric matrices. We show that our concentration inequality is stronger than the wellknownconcentration inequalityduetoKimandVu[29]. The main advantage of our method in comparison with the existing ones is a wide range of random variables we can handle and bounds for previously intractable regimes of high degree polynomials and small expectations. On the negative side we show that even for boolean random variables each term in our concentration inequality is tight