The TimeMachine for Inference on Stochastic Trees

The simulation of genealogical trees backwards in time, from observations up to the most recent common ancestor (MRCA), is hindered by the fact that, while approaching the root of the tree, coalescent events become rarer, with a corresponding increase in computation time. The recently proposed "Time Machine" tackles this issue by stopping the simulation of the tree before reaching the MRCA and correcting for the induced bias. We present a computationally efficient implementation of this approach that exploits multithreading

The Time Machine: A Simulation Approach for Stochastic Trees

In the following paper we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling (IS) and sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor (MRCA). However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this paper we propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface. The bias is investigated from a theoretical point of view. Results from simulation studies are also given to investigate the balance between loss of accuracy, saving in computing time and variance reduction.Comment: 22 Pages, 5 Figure

Intersystem soft handover for converged DVB-H and UMTS networks

Digital video broadcasting for handhelds (DVB-H) is the standard for broadcasting Internet Protocol (IP) data services to mobile portable devices. To provide interactive services for DVB-H, the Universal Mobile Telecommunications System (UMTS) can be used as a terrestrial interaction channel for the unidirectional DVB-H network. The converged DVB-H and UMTS network can be used to address the congestion problems due to the limited multimedia channel accesses of the UMTS network. In the converged network, intersystem soft handover between DVB-H and UMTS is needed for an optimum radio resource allocation, which reduces network operation cost while providing the required quality of service. This paper deals with the intersystem soft handover between DVB-H and UMTS in such a converged network. The converged network structure is presented. A novel soft handover scheme is proposed and evaluated. After considering the network operation cost, the performance tradeoff between the network quality of service and the network operation cost for the intersystem soft handover in the converged network is modeled using a stochastic tree and analyzed using a numerical simulation. The results show that the proposed algorithm is feasible and has the potential to be used for implementation in the real environment

Valuation of Multiple Exercise Options

Multiple exercise options may be considered as generalizations of American-style options as they provide the holder more than one exercise right. Examples of financial derivatives and real options with these properties have become more prevalent over the past decade and appear in sectors ranging from insurance to energy industries. Throughout the thesis particular attention is paid to swing options although we note that the methods described are equally applicable to other types of multiple exercise options. This thesis presents two novel methods for pricing multiple exercise option by simulation; the forest of stochastic trees and the forest of stochastic meshes. The proposed methods are of particular use in cases where there are potentially a large number (3 or more) of assets underlying the contract and/or if a number of risk factors are desirable for modelling the underlying price process. These valuation methods result in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. A confidence interval for the true option value is easily constructed. Examples confirm that the implementation of these methods is correct and consistent with the theoretical properties of the estimators. This thesis also explores in detail a number of methods meant to enhance the effectiveness of the proposed simulation methods. These include using high performance computing techniques which include both parallel computing techniques on CPU-clusters and General purpose Graphics Processing Units (GPGPU) that take advantage of relatively inexpensive processors. Additionally we explore bias-corrected estimators for the option values which attempt to estimate the bias introduced at each time step by the estimator and then subtract this result. These improvements are desirable due to the computationally intensive nature of both methods

Mathematical Methods in Composing Melodies

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals with the relationship between music and math. Contrary to previous investigations, the purpose of this thesis is to take something purely mathematical and make music from it. From the methods used, the music created from formulas for fractal music and chaotic unimodal quadratic maps created the most musically interesting melodies

Multiobjective simulation-based methodologies for medical decision making.

A variety of methodologies have been employed for decision making related to the treatment of diseases/injury. Decision trees are a functional way in which to examine problems under uncertainty by providing a method to analyze decisions under risk (Detsky, 1996, 97). However, conventional decision trees do not completely represent the real world since they cannot investigate problems that are cyclic in nature (Jaafari, 2003). The stochastic tree that developed Hazen during 1992-to-1996 is one of the most relevant methods and techniques related to decision analyses that append more incorporation for medical intervention related to recurring diseases/injuries. The approach combines features of continuous-time Markov chains with those of decision trees and that enable time to be modeled as a range where health state transitions can occur at any instant (Hazen 1992-to-96). It can also accommodate patients\u27 preferences regarding risk and quality of life. In this research we enhance Hazen\u27s stochastic tree by developing an analytical model, and we extend its capabilities more by developing multi-objective simulation based methodologists for medical decision making. First, with our enhancement on the Hazen\u27s stochastic tree, the model is improved by utilizing the Weibull Accelerated Failure Time model. This new technique will fill the gap between the experimental circumstances and the corresponding circumstances or conditions of standard/current treatment. Second, as simulation can be a final alternative for problems that are mathematically intractable for other techniques (Banks 1996), our multi-objective simulation based model for medical decision making extends the capabilities of Hazen stochastic tree. It adds more flexibility with the use of survival distributions for health states sojourn, and combines two sound theories: multi attribute utility (MAU) theory, and Ranking-Selection procedures. Indeed, our simulation model (considering patient\u27s profile/preferences and health states survival/quality/cost, QALY) presents an investigation of the use of simulation on the stochastic tree, with associated techniques related to ranking and selection, and multi-objectives decision analysis