Static waves in corporate space : characterizing oscillating trading patterns in New York stock exchange

Various researches in the field of econophysics has shown that fluid flow have analogous phenomena in financial market behavior, the typical parallelism being delivered between energy in fluids and information on markets. However, the geometry of the manifold on which market dynamics act out their dynamics (corporate space) is not yet known. In this thesis, utilizing a Seven year time series of prices of stocks used to compute S&P500 index on the New York Stock Exchange, we have created local chart to the corporate space with the goal of finding standing waves and other soliton like patterns in the behavior of stock price deviations from the S&P500 index. By first calculating the correlation matrix of normalized stock price deviations from the S&P500 index, we have performed a local singular value decomposition over a set of four different time windows as guides to the nature of patterns that may emerge. I turns out that in almost all cases, each singular vector is essentially determined by relatively small set of companies with big positive or negative weights on that singular vector. Over particular time windows, sometimes these weights are strongly correlated with at least one industrial sector and certain sectors are more prone to fast dynamics whereas others have longer standing waves.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

Convenience of scallops in plate structures

In this thesis was performed comprehensive study about the convenience of scallops in plate structures. A literature review was performed and lack of knowledge was fulfilled with fatigue tests performed in the laboratory of Steel Structures at the Lappeenranta University of Technology and with finite element method. The aim of this thesis was to produce design guidance for the use of scallops for different structural details and different loading conditions. An additional aim was to include more precise instructions for scallop design to produce good fatigue resistance and appropriate manufacturing quality. The literature review was performed searching bridge engineering and maritime standards and design guides and studies from scientific databases and reference lists from the literature of this field. Fatigue tests were used to research the effect of using scallops or not using scallops to fatigue strength of bracket specimen. Tests were performed on three specimens with different scallop radii and to five specimens without scallops with different weld penetration depths. Finite element method using solid elements, symmetry and submodels was used to determine stress concentration factors for I-beams with scallops. Stresses were defined with hot spot stress method. Choosing to use a scallop or not in the structure is affected by many factors, such as structural and loading conditions and manufacturability. As a rule of thumb, scallops should be avoided because those cause stress concentration points to the structure and take a lot of time to manufacture. When scallops are not used, good quality welding should be provided and full weld penetration is recommended to be used in load carrying corner weld areas. In some cases, it is advisable to use scallops. In that case, circular scallops are recommended to be used and radius should be chosen from fatigue strength or manufacturing point of view.