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.

Historical logging, productivity, and structural characteristics of boreal coniferous forests in Norway

Abstract

A modified structural stress method for fatigue assessment of welded structures

Fatigue life assessment of weldedstructures is commonly based on the nominal stress method, but more flexible and accurate methods have been introduced. In general, the assessment accuracy is improved as more localized information about the weld is incorporated. The structural hot spot stress method includes the influence of macro geometric effects and structural discontinuities on the design stress but excludes the local features of the weld. In this thesis, the limitations of the structural hot spot stress method are discussed and a modified structural stress method with improved accuracy is developed and verified for selected welded details. The fatigue life of structures in the as-welded state consists mainly of crack growth from pre-existing cracks or defects. Crack growth rate depends on crack geometry and the stress state on the crack face plane. This means that the stress level and shape of the stress distribution in the assumed crack path governs thetotal fatigue life. In many structural details the stress distribution is similar and adequate fatigue life estimates can be obtained just by adjusting the stress level based on a single stress value, i.e., the structural hot spot stress. There are, however, cases for which the structural stress approach is less appropriate because the stress distribution differs significantly from the more common cases. Plate edge attachments and plates on elastic foundations are some examples of structures with this type of stress distribution. The importance of fillet weld size and weld load variation on the stress distribution is another central topic in this thesis. Structural hot spot stress determination is generally based on a procedure that involves extrapolation of plate surface stresses. Other possibilities for determining the structural hot spot stress is to extrapolate stresses through the thickness at the weld toe or to use Dong's method which includes through-thickness extrapolation at some distance from the weld toe. Both of these latter methods are less sensitive to the FE mesh used. Structural stress based on surface extrapolation is sensitive to the extrapolation points selected and to the FE mesh used near these points. Rules for proper meshing, however, are well defined and not difficult to apply. To improve the accuracy of the traditional structural hot spot stress, a multi-linear stress distribution is introduced. The magnitude of the weld toe stress after linearization is dependent on the weld size, weld load and plate thickness. Simple equations have been derived by comparing assessment results based on the local linear stress distribution and LEFM based calculations. The proposed method is called the modified structural stress method (MSHS) since the structural hot spot stress (SHS) value is corrected using information on weld size andweld load. The correction procedure is verified using fatigue test results found in the literature. Also, a test case was conducted comparing the proposed method with other local fatigue assessment methods.

Tandem-GMA Welding of Low Alloy Structural Steel

The Tandem-GMAW method is the latest development as the consequences of improvements in the welding methods. The twin-wire and then the Tandem-method with the separate power sources has got a remarkable place in the welding of many types of materials with different joint types. The biggest advantage of Tandem welding method is the flexibility of choosing both the electrodes of different types from each other according to the type of the parent material. This is possible because of the feasibility of setting the separate welding parameters for both the wires. In this thesis work the effect of the variation in three parameters on the weld bead in Tandem-GMA welding method is studied. Theses three parameters are the wire feed rate in the slave wire, the wire feed rate in the master wire and the voltage difference in both the wires. The results are then compared to study the behaviour of the weld bead with the change in these parameters.

Structural and optical properties of InAs/GaAs quantum structures

The goal of the thesis was to study fundamental structural and optical properties of InAs islands and In(Ga)As quantum rings. The research was carried out at the Department of Micro and Nanosciences of Helsinki University of Technology. A good surface quality can be essential for the potential applications in optoelectronic devices. For such device applications it is usually necessary to control size, density and arrangement of the islands. In order to study the dependence of the structural properties of the islands and the quantum rings on growth conditions, atomic force microscope was used. Obtained results reveal that the size and the density of the In(Ga)As quantum rings strongly depend on the growth temperature, the annealing time and the thickness of the partial capping layer. From obtained results it is possible to conclude that to get round shape islands and high density one has to use growth temperature of 500 ̊C. In the case of formation of In(Ga)As quantum rings the effect of mobility anisotropy is observed that so the shape of the rings is not symmetric. To exclude this effect it is preferable to use a higher annealing temperature of 570 ̊C. Optical properties were characterized by PL spectroscopy. PL emission was observed from buried InAs quantum dots and In(Ga)As quantum rings grown with different annealing time and temperature and covered with a various thickness of the partial capping layer.

On the effects of welding parameters on weld quality of plasma arc keyhole welding of structural steels

The possibility and the usefulness of applying plasma keyhole welding to structural steels with different compositions and material thicknesses, and in various welding positions has been examinated. Single pass butt welding with I groove in flat, horizontal vertical and vertical positions and root welding with V , Y and U grooves of thick plate material in flat position have been studied and the welds with high quality has been obtained. The technological conditions for successful welding are presented. The single and interactive effects of welding parameters on weld quality, especially on surface weld defects, geometrical form errors, internal defects and mechanical properties (strength, ductility, impact toughness, hardness and bendability) of weld joint, are presented. Welding parameter combinations providing the best quality welds are also presented.

Structural development of the harvester head saw unit

The main goal of the thesis was to further develop harvester head saw device to the Finnish forest machine manufacturer. The work was done from the basis of the manufacturer´s current production model and the earlier study from this same subject called: “Development of chain saw for harvester” Tero Kaatrasalo, 2004. The work was focused to improving the serviceability and reliability of the saw device, but design also included adding few beforehand determined new features into the saw unit. This was done to give some added value for the end customer. The work includes analysis of the earlier saw devices and ideations of the improvements for the structure.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

Structural studies on enzymes of biotechnological and biomedical interest

Structural studies of proteins aim at elucidating the atomic details of molecular interactions in biological processes of living organisms. These studies are particularly important in understanding structure, function and evolution of proteins and in defining their roles in complex biological settings. Furthermore, structural studies can be used for the development of novel properties in biomolecules of environmental, industrial and medical importance. X-ray crystallography is an invaluable tool to obtain accurate and precise information about the structure of proteins at the atomic level. Glutathione transferases (GSTs) are amongst the most versatile enzymes in nature. They are able to catalyze a wide variety of conjugation reactions between glutathione (GSH) and non-polar components containing an electrophilic carbon, nitrogen or sulphur atom. Plant GSTs from the Tau class (a poorly characterized class) play an important role in the detoxification of xenobiotics and stress tolerance. Structural studies were performed on a Tau class fluorodifen-inducible glutathione transferase from Glycine max (GmGSTU4-4) complexed with GSH (2.7 Å) and a product analogue Nb-GSH (1.7 Å). The three-dimensional structure of the GmGSTU4-4-GSH complex revealed that GSH binds in different conformations in the two subunits of the dimer: in an ionized form in one subunit and a non-ionized form in the second subunit. Only the ionized form of the substrate may lead to the formation of a catalytically competent complex. Structural comparison between the GSH and Nb-GSH bound complexes revealed significant differences with respect to the hydrogen-bonding, electrostatic interaction pattern, the upper part of -helix H4 and the C-terminus of the enzyme. These differences indicate an intrasubunit modulation between the G-and Hsites suggesting an induced-fit mechanism of xenobiotic substrate binding. A novel binding site on the surface of the enzyme was also revealed. Bacterial type-II L-asparaginases are used in the treatment of haematopoietic diseases such as acute lymphoblastic leukaemia (ALL) and lymphomas due to their ability to catalyze the conversion of L-asparagine to L-aspartate and ammonia. Escherichia coli and Erwinia chrysanthemi asparaginases are employed for the treatment of ALL for over 30 years. However, serious side-effects affecting the liver and pancreas have been observed due to the intrinsic glutaminase activity of the administered enzymes. Structural studies on Helicobacter pylori L-asparaginase (HpA) were carried out in an effort to discover novel L-asparaginases with potential chemotherapeutic utility in ALL treatment. Detailed analysis of the active site geometry revealed structurally significant differences between HpA and other Lasparaginases that may be important for the biological activities of the enzyme and could be further exploited in protein engineering efforts.

Dynamical and structural properties of dendrimer macromolecules

This work is devoted to the study of the dynamical and structural properties of dendrimers. Different approaches were used: analytical theory, computer simulation results and experimental NMR studies. The theory of the relaxation spectrum of dendrimer macromolecules was developed. Relaxation processes which are manifest in the local orientational mobility of dendrimer macromolecules were established and studied in detail. Theoretical results and conclusions were used for experimental studies of carbosilane dendimers.

The Structural Basis for inorganic Pyrophosphatase Catalysis and Regulation

Inorganic pyrophosphatases (PPases) are essential enzymes for every living cell. PPases provide the necessary thermodynamic pull for many biosynthetic reactions by hydrolyzing pyrophosphate. There are two types of PPases: integral membrane-bound and soluble enzymes. The latter type is divided into two non-homologous protein families, I and II. Family I PPases are present in all kingdoms of life, whereas family II PPases are only found in prokaryotes, including archae. Family I PPases, particularly that from Saccharomyces cerevisiae, are among the most extensively characterized phosphoryl transfer enzymes. In the present study, we have solved the structures of wild-type and seven active site variants of S. cerevisiae PPase bound to its natural metal cofactor, magnesium ion. These structures have facilitated derivation of the complete enzyme reaction scheme for PPase, fulfilling structures of all the reaction intermediates. The main focus in this study was on a novel subfamily of family II PPases (CBSPPase) containing a large insert formed by two CBS domains and a DRTGG domain within the catalytic domain. The CBS domain (named after cystathionine beta-synthase in which it was initially identified) usually occurs as tandem pairs with two or four copies in many proteins in all kingdoms of life. The structure formed by a pair of CBS domains is also known as a Bateman domain. CBS domains function as regulatory units, with adenylate ligands as the main effectors. The DRTGG domain (designated based on its most conserved residues) occurs less frequently and only in prokaryotes. Often, the domain co-exists with CBS domains, but its function remains unknown. The key objective of the current study was to explore the structural rearrangements in the CBS domains induced by regulatory adenylate ligands and their functional consequences. Two CBS-PPases were investigated, one from Clostridium perfringens (cpCBS-PPase) containing both CBS and DRTGG domains in its regulatory region and the other from Moorella thermoacetica (mt CBS-PPase) lacking the DRTGG domain. We additionally constructed a separate regulatory region of cpCBS-PPase (cpCBS). Both full-length enzymes and cpCBS formed homodimers. Two structures of the regulatory region of cpCBS-PPase complexed with the inhibitor, AMP, and activator, diadenosine tetraphosphate, were solved. The structures were significantly different, providing information on the structural pathway from bound adenylates to the interface between the regulatory and catalytic parts. To our knowledge, these are the first reported structures of a regulated CBS enzyme, which reveal large conformational changes upon regulator binding. The activator-bound structure was more open, consistent with the different thermostabilities of the activator- and inhibitor-bound forms of cpCBS-PPase. The results of the functional studies on wild-type and variant CBS-PPases provide support for inferences made on the basis of structural analyses. Moreover, these findings indicate that CBS-PPase activity is highly sensitive to adenine nucleotide distribution between AMP, ADP and ATP, and hence to the energy level of the cell. CBS-PPase activity is markedly inhibited at low energy levels, allowing PPi energy to be used for cell survival instead of being converted into heat.