Polyhedral geometry of Phylogenetic Rogue Taxa

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we construct polyhedral cones computationally which give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.Comment: In this version, we add quartet distances and fix Table 4

A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods

Topological tools for understanding complex systems

The behavior of complex systems is often influenced by their structure. In mathematics, the field of algebraic topology has been especially useful for characterizing mathematical structures. Topological data analysis (TDA) is a growing field in which methods from algebraic topology are applied to studying the structure of data. TDA has been used in a variety of applications, including biological data, granular materials, and demography. Social interactions are heavily informed by space and have complex structure due to patterns in the way humans arrange themselves geographically. Consequently, social applications can benefit from the application of TDA.In this dissertation, I develop topological methods for studying spatial networks and apply them to a wide variety of data sets. In particular, I study methods for building topological spaces (specifically, simplicial complexes) based on data. I present two novel simplicial-complex constructions, the adjacency complex and the level-set complex, for spatial data. I apply both constructions to random networks, cities, voting, and scientific images, gaining insights into the structure of these systems. I also propose a novel simplicial complex construction for studying patterns of neighborhood formation based on combining demographic and spatial data. I present case studies in neighborhood segregation for two U.S. cities. In addition to my topological research, I discuss two projects in the study of social systems using methods from network analysis. I present an extension to multilayer networks of the Hegselmann--Krause model for opinion dynamics and discuss preliminary findings on its convergence properties. I also present a framework for estimating homelessness underreporting in California Local Education agencies (LEAs)

Feasibility study of Preventing Snow Accumulations on Roofs using Airflows

This thesis is intended to contribute to research in cold climate engineering. Further it intends to provide a principle solution for structural and avalanche safety due to snowfall on roofs. We have conducted a feasibility study of preventing snow from accumulating on roofs using airflows. This includes empirical, numerical and experimental methods. Snow loads on roofs makes great impact on structural safety and is the cause of annual injuries due to snow removal. Studies have shown that incidents related to snow clearing activities occurs more frequent in winter seasons with heavy snowfall (Bylund, Johansson & Albertsson, 2016, p. 107). At the same time, several climate projections predict that the annual rainfall will increase significantly, along with increased global temperature. However, for several places in cold climate regions, the rise in temperature will not be enough for the rain to stay liquified. The consequences of increased snowfall can be severe, especially for lightweight structures or structures built according to outdated standards. Regardless of the climate changes, risks for humans associated with snow loads on roofs is present. To assess the risks for human and assets a PHA is conducted and supported by risk matrices and bow-tie method. The experiments are based on empiricism and CFD simulations of airflows. To generate airflows, a compressor was used as source and pneumatic hoses from Festo was applied. The falling snow seemed to behave as intended - to a certain extent - by the influence of airflows. Due to challenges related to the experiments, we were not able to efficiently prevent snow from accumulating at the surface. However, from the results and discussion it emerges potentials for achieving the purpose. If the design chosen in this study is applicable and how it can be improved is concluded in the last chapter, followed by suggestions for further work

Real-time rendering and simulation of trees and snow

Tree models created by an industry used package are exported and the structure extracted in order to procedurally regenerate the geometric mesh, addressing the limitations of the application's standard output. The structure, once extracted, is used to fully generate a high quality skeleton for the tree, individually representing each section in every branch to give the greatest achievable level of freedom of deformation and animation. Around the generated skeleton, a new geometric mesh is wrapped using a single, continuous surface resulting in the removal of intersection based render artefacts. Surface smoothing and enhanced detail is added to the model dynamically using the GPU enhanced tessellation engine. A real-time snow accumulation system is developed to generate snow cover on a dynamic, animated scene. Occlusion techniques are used to project snow accumulating faces and map exposed areas to applied accumulation maps in the form of dynamic textures. Accumulation maps are xed to applied surfaces, allowing moving objects to maintain accumulated snow cover. Mesh generation is performed dynamically during the rendering pass using surface o�setting and tessellation to enhance required detail

Acoustic sounding of snow water equivalent

An acoustic frequency-swept wave was investigated as a means for determining Snow Water Equivalent (SWE) in cold wind-swept prairie and sub-alpine environments. Building on previous research conducted by investigators who have examined the propagation of sound in snow, digital signal processing was used to determine acoustic pressure wave reflection coefficients at the interfaces between 'layers' indicative of changes in acoustic impedance. Using an iterative approach involving boundary conditions at the interfaces, the depth-integrated SWE was determined using the Berryman equation from porous media physics. Apparatuses used to send and receive sound waves were designed and deployed during the winter season at field sites situated near the city of Saskatoon, Saskatchewan, and in Yoho National Park, British Columbia. Data collected by gravimetric sampling was used as comparison for the SWE values determined by acoustic sounding. The results are encouraging and suggest that this procedure is similar in accuracy to SWE data collected using gravimetric sampling. Further research is required to determine the applicability of this technique for snow situated at other geographic locations

Epäilyttävien pankkitapahtumien tunnistaminen oppivien tilastollisten menetelmien avulla

In this thesis the aim was to find a more efficient way for detecting suspicious transactions from banking data. The chosen approach was to utilize outlier detection methods. The methods were first chosen based on a theoretical review but then narrowed down to those that have stable implementations in Python. The banking transaction data was then preprocessed and fed to the methods. For clustering methods we reviewed the running time and the CH index and for outlier detection the comparison was made from running time and visual exploration of the results. Finally it was found that GMM and iForest were the best performing methods. They were able to perform outlier detection on the large datasets in just minutes and should scale to a dataset of any size. They also have existing implementations in SKlearn and could be implemented as a part of a detection system.Tämän diplomityön tavoitteena oli löytää tehokkaampi tapa tunnistaa poikkeavia pankkitapahtumia. Läthökohdaksi valittiin poikkeamien tunnistusmenetelmät. Alustavat menetelmät valittiin teoreettisen tarkastelun pohjalta, mutta näistä karsittiin pois ne, joilla ei ollut vakaata toteutusta Pythonissa. Pankkitapahtumatiedot esikäsiteltiin ja syötettiin metodeille, jonka jälkeen eri metodien tuloksia tarkasteltiin. Ryhmittely menetelmien osalta tarkasteltiin ajoaikaa ja CH-indeksiä. Poikkeamien tunnistuksessa tarkasteltiin ajoaikaa ja tuloksia käytiin läpi visualisointien avulla. Työssä löydettiin kaksi hyvin toimivaa menetelmää: GMM ja iForest. Ne pystyivät suorittamaan poikkeamien tunnistusta suurille tietomäärille vain minuuteissa ja niiden pitäisi skaalautua minkä kokoiseen tietomäärään vain. Niistä on myöskin olemassa olevat toteutukset SKlearnissa, joten ne voitaisiin toteuttaa osaksi tunnistusjärjestelmää