QSpace Community: Queen's UniversityInformationQueen's UniversityInformationhttp://hdl.handle.net/1974/62015-09-04T12:31:03Z2015-09-04T12:31:03ZDistributed Online Optimization on time-varying networksAkbari Varnousfaderani, Mohammad Jrhttp://hdl.handle.net/1974/135512015-09-02T05:19:08Z2015-09-01T04:00:00ZTitle: Distributed Online Optimization on time-varying networks
Authors: Akbari Varnousfaderani, Mohammad Jr
Abstract: This thesis introduces two classes of discrete-time distributed online optimization algorithms, with a group of agents which communicate over a network. At each time, a private convex objective function is revealed to each agent. In the next time step, each agent updates its state using its own objective function and the information gathered from its immediate in-neighbours at that time. We design algorithms distributed over the network topologies, which guarantee that the individual regret, the diﬀerence between the network cost incurred by the agent’s states estimation and the cost incurred by the best ﬁxed choice, grows only sublinearly. One algorithm is based on gradient-ﬂow, which provably works for a sequence of time-varying uniformly strongly connected graphs. The other one is based on Alternating Direction Method of Multipliers, which works on ﬁxed undirected graphs and gives an explicit
regret bound in terms of the size of the network. We implement the proposed algorithms on a sensor network and the results demonstrate the good performance for both algorithms.
Description: Thesis (Master, Mathematics & Statistics) -- Queen's University, 2015-08-31 09:59:41.2612015-09-01T04:00:00ZCurves of low genus on surfaces and applications to Diophantine problemsGarcia, Nataliahttp://hdl.handle.net/1974/135452015-09-01T05:04:05Z2015-08-31T04:00:00ZTitle: Curves of low genus on surfaces and applications to Diophantine problems
Authors: Garcia, Natalia
Abstract: We describe in detail a technique due to Vojta for finding the explicit set of curves of low genus on certain algebraic surfaces of general type, and refine some of its aspects. We then provide applications of this method to three Diophantine problems.
We prove under the Bombieri-Lang Conjecture that there are finitely many non-trivial sequences of integers of length 11 whose squares have constant second differences, and we prove unconditionally the analogous result for function fields of characteristic zero.
We prove under the Bombieri-Lang Conjecture that there are finitely many integer sequences of length 8 whose k-th powers have second differences equal to 2, we give an unconditional result for function fields of characteristic zero. Moreover, this gives new examples of surfaces having no curves of genus 0 or 1.
The third application is related to the surface parametrizing perfect cuboids. We give some new properties about their curves of genus 0 or 1 and we give new bounds for the degree of curves in this surface, in terms of their genus.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2015-08-28 10:03:04.0562015-08-31T04:00:00ZPrediction and Filtering of Stationary Processes: Yaglom’s Method and Minimax FilteringMascher, Philipphttp://hdl.handle.net/1974/134932015-08-13T05:26:39Z2015-08-11T04:00:00ZTitle: Prediction and Filtering of Stationary Processes: Yaglom’s Method and Minimax Filtering
Authors: Mascher, Philipp
Abstract: The aim of this work is to give a basic introduction to the theory of stationary stochastic processes, particularly to the somewhat specialized problem of prediction and filtering of such processes. Kolmogorov was the first to make
a contribution to its solution using involved mathematical theory. In the years following the publication of Wiener’s famous book, the theory gained considerable popularity from the applied sciences, particularly radio engineering. In this work, we shall present Yaglom’s method to solving the problems considered in Wiener’s book. This alternative approach is entirely based on rather basic facts from Hilbert space theory and the theory of complex variables. As it turns out, the theory of filtering of stationary processes heavily relies on spectral properties of the processes. In particular, Yaglom’s approach assumes complete knowledge of the spectral densities. In this work, however, we shall not be concerned with the problem of estimating such quantities based on a finite sample. Instead, in order to account for uncertainty as frequently encountered in practice, we shall discuss the problem of minimax filtering which has emerged from the practical need of allowing for incomplete knowledge about spectral properties.2015-08-11T04:00:00ZOptimality of Walrand-Varaiya Type Policies and Approximation Results for Zero-Delay Coding of Markov SourcesWood, RICHARDhttp://hdl.handle.net/1974/134572015-07-29T05:14:11Z2015-07-28T04:00:00ZTitle: Optimality of Walrand-Varaiya Type Policies and Approximation Results for Zero-Delay Coding of Markov Sources
Authors: Wood, RICHARD
Abstract: Optimal zero-delay coding of a finite state Markov source through quantization is considered. Building on previous literature, the existence and structure of optimal policies are studied using a stochastic control problem formulation. In the literature, the optimality of deterministic Markov coding policies (or Walrand-Varaiya type policies) for infinite horizon problems has been established. This work expands on this result for systems with finite source alphabets, proving the optimality of de- terministic and stationary Markov coding policies for the infinite horizon setup. In addition, the ε-optimality of finite memory quantizers is established and the depen- dence between the memory length and ε is quantified. An algorithm to find the optimal policy for the finite time horizon problem is presented. Numerical results produced using this algorithm are shown.
Description: Thesis (Master, Mathematics & Statistics) -- Queen's University, 2015-07-27 15:57:18.6672015-07-28T04:00:00Z