Structural and Computational Existence Results for Multidimensional Subshifts

Symbolic dynamics is a branch of mathematics that studies the structure of infinite sequences of symbols, or in the multidimensional case, infinite grids of symbols. Classes of such sequences and grids defined by collections of forbidden patterns are called subshifts, and subshifts of finite type are defined by finitely many forbidden patterns. The simplest examples of multidimensional subshifts are sets of Wang tilings, infinite arrangements of square tiles with colored edges, where adjacent edges must have the same color. Multidimensional symbolic dynamics has strong connections to computability theory, since most of the basic properties of subshifts cannot be recognized by computer programs, but are instead characterized by some higher-level notion of computability. This dissertation focuses on the structure of multidimensional subshifts, and the ways in which it relates to their computational properties. In the first part, we study the subpattern posets and Cantor-Bendixson ranks of countable subshifts of finite type, which can be seen as measures of their structural complexity. We show, by explicitly constructing subshifts with the desired properties, that both notions are essentially restricted only by computability conditions. In the second part of the dissertation, we study different methods of defining (classes of ) multidimensional subshifts, and how they relate to each other and existing methods. We present definitions that use monadic second-order logic, a more restricted kind of logical quantification called quantifier extension, and multi-headed finite state machines. Two of the definitions give rise to hierarchies of subshift classes, which are a priori infinite, but which we show to collapse into finitely many levels. The quantifier extension provides insight to the somewhat mysterious class of multidimensional sofic subshifts, since we prove a characterization for the class of subshifts that can extend a sofic subshift into a nonsofic one.

Securin, Cdc20 and Cdc27 in predicting the outcome of human breast cancer

Deregulated proliferation has been recognized among the most important factors promoting breast cancer development and progression. The aim of the project is to gain understanding of the role of specific cell cycle regulators of metaphase-anaphase transition and evaluate their potential in breast cancer prognostication and treatment decisions. Metaphase-anaphase transition is triggered by activation of anaphase promoting complex (APC) which is activated by a cascade of regulatory proteins, among them securin, Cdc20 and Cdc27. These proteins promote the metaphase–anaphase transition and participate in the timely separation of the chromatids. This study is based on a patient material of approximately 600 breast cancer patients and up to 22 years of follow-up. As the main observation, based on DNA cytometric and immunohistochemical methods, securin, Cdc20 and Cdc27 protein expressions were associated with abnormal DNA content and outcome of breast cancer. In the studied patient material, high securin expression alone and in combination with Cdc20 and Cdc27 predicted up to 9.8-fold odds for aneuploid DNA content in human breast cancer. In Kaplan–Meier analyses, high expression of securin systematically indicated decrease in breast cancer survival as compared to low expression cases. The adverse effect of high securin expression was further strengthened by combining it with Cdc20 or Cdc27 expressions, resulting in up to 6.8-fold risk of breast cancer death. High securin and Cdc20 expression was also associated with triple-negative breast cancer type with high statistical significance. Securin, Cdc20 or Cdc27 have not previously been investigated in a clinically relevant large breast cancer patient material or in association with DNA ploidy. The present findings suggest that the studied proteins may serve as potential biomarkers for identification of aggressive course of disease and unfavourable outcome of human breast cancer, and that they may provide a future research aim for understanding abnormal proliferation in malignant disease.

Continuous Counter-current Solvent Extraction of Magnesium and Calcium from Lithium-rich Brine

Solvent extraction of calcium and magnesium impurities from a lithium-rich brine (Ca ~ 2,000 ppm, Mg ~ 50 ppm, Li ~ 30,000 ppm) was investigated using a continuous counter-current solvent extraction mixer-settler set-up. The literature review includes a general review about resources, demands and production methods of Li followed by basics of solvent extraction. Experimental section includes batch experiments for investigation of pH isotherms of three extractants; D2EHPA, Versatic 10 and LIX 984 with concentrations of 0.52, 0.53 and 0.50 M in kerosene respectively. Based on pH isotherms LIX 984 showed no affinity for solvent extraction of Mg and Ca at pH ≤ 8 while D2EHPA and Versatic 10 were effective in extraction of Ca and Mg. Based on constructed pH isotherms, loading isotherms of D2EHPA (at pH 3.5 and 3.9) and Versatic 10 (at pH 7 and 8) were further investigated. Furthermore based on McCabe-Thiele method, two extraction stages and one stripping stage (using HCl acid with concentration of 2 M for Versatic 10 and 3 M for D2EHPA) was practiced in continuous runs. Merits of Versatic 10 in comparison to D2EHPA are higher selectivity for Ca and Mg, faster phase disengagement, no detrimental change in viscosity due to shear amount of metal extraction and lower acidity in stripping. On the other hand D2EHPA has less aqueous solubility and is capable of removing Mg and Ca simultaneously even at higher Ca loading (A/O in continuous runs > 1). In general, shorter residence time (~ 2 min), lower temperature (~23 °C), lower pH values (6.5-7.0 for Versatic 10 and 3.5-3.7 for D2EHPA) and a moderately low A/O value (< 1:1) would cause removal of 100% of Ca and nearly 100% of Mg while keeping Li loss less than 4%, much lower than the conventional precipitation in which 20% of Li is lost.

Monolithic zirconium dioxide as a full contour restorative material: With special emphasis on the optical and mechanical properties

Full contour monolithic zirconia restorations have shown an increased popularity in the dental field over the recent years, owing to its mechanical and acceptable optical properties. However, many features of the restoration are yet to be researched and supported by clinical studies to confirm its place among the other indirect restorative materials This series of in vitro studies aimed at evaluating and comparing the optical and mechanical properties, light cure irradiance, and cement polymerization of multiple monolithic zirconia material at variable thicknesses, environments, treatments, and stabilization. Five different monolithic zirconia materials, four of which were partially stabilized and one fully stabilized were investigated. The optical properties in terms of surface gloss, translucency parameter, and contrast ratio were determined via a reflection spectrophotometer at variable thicknesses, coloring, sintering method, and after immersion in an acidic environment. Light cure irradiance and radiant exposure were quantified through the specimens at variable thicknesses and the degree of conversion of two dual-cure cements was determined via Fourier Transform Infrared spectroscopy. Bi-axial flexural strength was evaluated to compare between the partially and fully stabilized zirconia prepared using different coloring and sintering methods. Surface characterization was performed using a scanning electron microscope and a spinning disk confocal microscope. The surface gloss and translucency of the zirconia investigated were brand and thickness dependent with the translucency values decreasing as the thickness increased. Staining decreased the translucency of the zirconia and enhanced surface gloss as well as the flexural strength of the fully stabilized zirconia but had no effect on partially stabilized zirconia. Immersion in a corrosive acid increased surface gloss and decreased the translucency of some zirconia brands. Zirconia thickness was inversely related to the amount of light irradiance, radiant exposure, and degree of monomer conversion. Type of sintering furnace had no effect on the optical and mechanical properties of zirconia. Monolithic zirconia maybe classified as a semi-translucent material that is well influenced by the thickness, limiting its use in the esthetic zones. Conventional acid-base reaction, autopolymerizing and dual-cure cements are recommended for its cementation. Its desirable mechanical properties give it a high potential as a restoration for posterior teeth. However, close monitoring with controlled clinical studies must be determined before any definite clinical recommendations can be drawn.

Phenolic compounds and antioxidant activity of blueberry cultivars grown in Brazil

The aim of this study was to evaluate the content of the phenolic compounds and anthocyanins and the antioxidant activity of blueberry (Vaccinium sp.) cultivars grown in Brazil. The Folin-Ciocalteau method was applied in order to quantify the phenolic compounds and ABTS, DPPH, FRAP, and β-carotene/linoleic acid methods were applied in order to evaluated antioxidant activity. The phenolic compounds content ranged from 274.48 to 694.60 mg GAE.100 g-1 of fresh weight (FW). Anthocyanins content ranged from 40.62 to 378.31 mg.100 g-1 FW for Bluecrop and Tifblue cultivars, respectively. Antioxidant activities assessed by ABTS, DPPH and FRAP methods presented significant differences among the studied cultivars ranging from 1238.48 to 2445.96, 1014.24 to 2055.06 and 699.78 to 1740.25 µmol TEAC.100 g-1 FW, respectively. The results confirm the blueberry as a source of phenolic compounds with high antioxidant activity and also show that there are different levels of concentrations of phenolic compounds and antioxidant activity according to the cultivar and production location.