Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.

Could machine learning improve the prediction of pelvic nodal status of prostate cancer patients? Preliminary results of a pilot study.

We tested and compared performances of Roach formula, Partin tables and of three Machine Learning (ML) based algorithms based on decision trees in identifying N+ prostate cancer (PC). 1,555 cN0 and 50 cN+ PC were analyzed. Results were also verified on an independent population of 204 operated cN0 patients, with a known pN status (187 pN0, 17 pN1 patients). ML performed better, also when tested on the surgical population, with accuracy, specificity, and sensitivity ranging between 48-86%, 35-91%, and 17-79%, respectively. ML potentially allows better prediction of the nodal status of PC, potentially allowing a better tailoring of pelvic irradiation.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Knapsack sets for cryptography

The basic goal of this study is to extend old and propose new ways to generate knapsack sets suitable for use in public key cryptography. The knapsack problem and its cryptographic use are reviewed in the introductory chapter. Terminology is based on common cryptographic vocabulary. For example, solving the knapsack problem (which is here a subset sum problem) is termed decipherment. Chapter 1 also reviews the most famous knapsack cryptosystem, the Merkle Hellman system. It is based on a superincreasing knapsack and uses modular multiplication as a trapdoor transformation. The insecurity caused by these two properties exemplifies the two general categories of attacks against knapsack systems. These categories provide the motivation for Chapters 2 and 4. Chapter 2 discusses the density of a knapsack and the dangers of having a low density. Chapter 3 interrupts for a while the more abstract treatment by showing examples of small injective knapsacks and extrapolating conjectures on some characteristics of knapsacks of larger size, especially their density and number. The most common trapdoor technique, modular multiplication, is likely to cause insecurity, but as argued in Chapter 4, it is difficult to find any other simple trapdoor techniques. This discussion also provides a basis for the introduction of various categories of non injectivity in Chapter 5. Besides general ideas of non injectivity of knapsack systems, Chapter 5 introduces and evaluates several ways to construct such systems, most notably the "exceptional blocks" in superincreasing knapsacks and the usage of "too small" a modulus in the modular multiplication as a trapdoor technique. The author believes that non injectivity is the most promising direction for development of knapsack cryptosystema. Chapter 6 modifies two well known knapsack schemes, the Merkle Hellman multiplicative trapdoor knapsack and the Graham Shamir knapsack. The main interest is in aspects other than non injectivity, although that is also exploited. In the end of the chapter, constructions proposed by Desmedt et. al. are presented to serve as a comparison for the developments of the subsequent three chapters. Chapter 7 provides a general framework for the iterative construction of injective knapsacks from smaller knapsacks, together with a simple example, the "three elements" system. In Chapters 8 and 9 the general framework is put into practice in two different ways. Modularly injective small knapsacks are used in Chapter 9 to construct a large knapsack, which is called the congruential knapsack. The addends of a subset sum can be found by decrementing the sum iteratively by using each of the small knapsacks and their moduli in turn. The construction is also generalized to the non injective case, which can lead to especially good results in the density, without complicating the deciphering process too much. Chapter 9 presents three related ways to realize the general framework of Chapter 7. The main idea is to join iteratively small knapsacks, each element of which would satisfy the superincreasing condition. As a whole, none of these systems need become superincreasing, though the development of density is not better than that. The new knapsack systems are injective but they can be deciphered with the same searching method as the non injective knapsacks with the "exceptional blocks" in Chapter 5. The final Chapter 10 first reviews the Chor Rivest knapsack system, which has withstood all cryptanalytic attacks. A couple of modifications to the use of this system are presented in order to further increase the security or make the construction easier. The latter goal is attempted by reducing the size of the Chor Rivest knapsack embedded in the modified system. '

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface - a low-degree surface approximation - is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure

A Comparative Study of Desktop, Fishtank, and Cave Systems for the Exploration of Volume Rendered Confocal Data Sets

We present a participant study that compares biological data exploration tasks using volume renderings of laser confocal microscopy data across three environments that vary in level of immersion: a desktop, fishtank, and cave system. For the tasks, data, and visualization approach used in our study, we found that subjects qualitatively preferred and quantitatively performed better in the cave compared with the fishtank and desktop. Subjects performed real-world biological data analysis tasks that emphasized understanding spatial relationships including characterizing the general features in a volume, identifying colocated features, and reporting geometric relationships such as whether clusters of cells were coplanar. After analyzing data in each environment, subjects were asked to choose which environment they wanted to analyze additional data sets in - subjects uniformly selected the cave environment.

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

Numbers and sets

In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.

Prediction of free-stall occupancy rate in dairycattle barns through fuzzy sets

The goal of this study was to develop a fuzzy model to predict the occupancy rate of free-stalls facilities of dairy cattle, aiding to optimize the design of projects. The following input variables were defined for the development of the fuzzy system: dry bulb temperature (Tdb, °C), wet bulb temperature (Twb, °C) and black globe temperature (Tbg, °C). Based on the input variables, the fuzzy system predicts the occupancy rate (OR, %) of dairy cattle in free-stall barns. For the model validation, data collecting were conducted on the facilities of the Intensive System of Milk Production (SIPL), in the Dairy Cattle National Research Center (CNPGL) of Embrapa. The OR values, estimated by the fuzzy system, presented values of average standard deviation of 3.93%, indicating low rate of errors in the simulation. Simulated and measured results were statistically equal (P>0.05, t Test). After validating the proposed model, the average percentage of correct answers for the simulated data was 89.7%. Therefore, the fuzzy system developed for the occupancy rate prediction of free-stalls facilities for dairy cattle allowed a realistic prediction of stalls occupancy rate, allowing the planning and design of free-stall barns.

Forecasting financial weather - can we foresee market sentiment? Quantitative analysis of nodal prices in the New Zealand Electricity Spot Market

Time series of hourly electricity spot prices have peculiar properties. Electricity is by its nature difficult to store and has to be available on demand. There are many reasons for wanting to understand correlations in price movements, e.g. risk management purposes. The entire analysis carried out in this thesis has been applied to the New Zealand nodal electricity prices: offer prices (from 29 May 2002 to 31 March 2009) and final prices (from 1 January 1999 to 31 March 2009). In this paper, such natural factors as location of the node and generation type in the node that effects the correlation between nodal prices have been reviewed. It was noticed that the geographical factor affects the correlation between nodes more than others. Therefore, the visualisation of correlated nodes was done. However, for the offer prices the clear separation of correlated and not correlated nodes was not obtained. Finally, it was concluded that location factor most strongly affects correlation of electricity nodal prices; problems in visualisation probably associated with power losses when the power is transmitted over long distance.