Molecular structure of a cyclic tetrapeptide disulfide. A novel 310 helical conformation with an S-S bridge

The crystal structure of the cyclic peptide disulfide Boc-Cys-Pro-Aib-Cys-NHMe has been determined by X-ray diffraction. The peptide crystallizes in the space group P212121, with A = 8.646(1), B = 18.462(2), C = 19.678(3)Å and Z = 4. The molecules adopt a highly folded compact conformation, stabilized by two intramolecular 4→ 1 hydrogen bonds between the Cys (1) and Pro (2) CO groups and the Cys (4) and methylamide NH groups, respectively. The backbone conformational angles for the peptide lie very close to those expected for a 310 helix. The S-S bridge adopts a right handed twist with a dihedral angle of 82°. The structure illustrates the role of stereochemically constrained residues, in generating novel peptide conformations. Aib, α-aminoisobutyric acid; Z, benzyloxycarbonyl; Boc, t-butyloxycarbonyl; OMe, methyl ester; OBz, benzyl ester; NHMe, N-methylamide; Tosyl, p-toluenesulfonyl.

Spinorial relativistic rotator: The transformation from quasi-Newtonian to Minkowski coordinates

There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies.

Northern challanges for profitable production of quality naked oat

Naked oat (Avena sativa f.sp. nuda L.) is the highest quality cereal in northern growing conditions. However the cultivation area of naked oat is remarkably small. Major challenges for naked oat production are to observe its nakedness. The caryopsis of naked oat is sensitive to mechanical damage at harvest, especially at high grain moisture content. The greater the grain moisture content of naked oat at harvest, the more loses of germination capacity was caused by threshing. For producing high quality naked oat seed, it is recommended that harvesting be done at as low grain moisture content as possible. However, if this is not possible, better germination can be ensure with gentle harvest by reducing the cylinder speed. In spite of conventional oat s excellent fat and amino acid composition in animal feed use, as far as nutritional value is concerned, the total energy yield of oat is weaker than other cereals because of the hulls. Also with naked oat the dehulling is not complete, while hull content on different cultivars mostly varied between one to six percent. In addition to genotype, environmental conditions markedly control the expression of nakedness. Thresher settings had only limited effects on hull content. The function of hulls is to protect the groat, but this was confirmed only for Finnish, small grain, cultivar Lisbeth. The oat kernel is generally covered with fine silky hairs termed trichomes. The trichomes of naked oat are partly lost during threshing and handling of grains. Trichomes can cause itchiness in those handling the grains and also accumulate and form fine dust and can block-up machinery. The cultivars differed considerably in pubescence. Some thresher settings, including increased cylinder speed, slightly increased grain polishing such that grains had some areas completely free of trichomes. Adjusting thresher settings was generally not an efficient means of solving the problems associated with naked oat trichomes. The main differences in cultivation costs between naked and conventional oat lie in the amount of seeds required and the drying costs. The main differences affecting the economic result lie in market prices, yield level and feed value. The results indicate that naked oat is financially more profitable than conventional oat, when the crop is sold at a specific price at all yield levels and when the crop is used as feed at highest yield level. At lower yield levels, conventional oat is, in spite of its lower feed value, the more profitable option for feed use. Dehulled oat did not achieve the same economic result as naked oat, as the cost of dehulling, including the hull waste, was considerable. According to this study naked oat can be cultivated successfully under northern conditions, when taking into consideration the soft, naked grain through cultivation chain.

Validity of a self-report recall tool for estimating sedentary behaviour in adults

BACKGROUND Sedentary behavior is continuing to emerge as an important target for health promotion. The purpose of this study was to determine the validity of a self-report use of time recall tool, the Multimedia Activity Recall for Children and Adults (MARCA) in estimating time spent sitting/lying, compared with a device-based measure. METHODS Fifty-eight participants (48% female, [mean±standard deviation] 28±7.4 years of age, 23.9±3.05 kg/m2) wore an activPAL device for 24-h and the following day completed the MARCA. Pearson correlation coefficients (r) were used to analyse convergent validity of the adult MARCA compared with activPAL estimates of total sitting/lying time. Agreement was examined using Bland-Altman plots. RESULTS According to activPAL estimates, participants spent 10.4 hr/day [standard deviation (SD)=2.06] sitting or lying down while awake. The correlation between MARCA and activPAL estimates of total sit/lie time was r=0.77 (95% confidence interval = 0.64-0.86; p<0.001). Bland-Altman analyses revealed a mean bias of +0.59 hr/day with moderately wide limits of agreement (-2.35 hours to +3.53 hr/day). CONCLUSIONS This study found a moderate to strong agreement between the adult MARCA and the activPAL, suggesting that the MARCA is an appropriate tool for the measurement of time spent sitting or lying down in an adult population.

Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow.

Syntheses and Self-Assembling Characteristics of Amphiphilic Star Diblock Copolymers

Uusien polymeeripohjaisten teknologioiden ja materiaalien myötä räätälöityjen polymeerien tarve on kasvanut. Viime vuosituhannen lopussa kehitetyt kontrolloidut polymerointimenetelmät ovat avanneet uusia mahdollisuuksia paitsi monimutkaisten polymeerien synteesiin, myös itsejärjestyvyyteen perustuvien funktionaalisten nanorakenteiden suunnitteluun ja valmistukseen. Nämä voivat jäljitellä luonnossa esiintyviä rakenteita, joita muodostavat esimerkiksi lipidit ja proteiinit. Itsejärjestyvät molekyylit ovat usein amfifiilisiä eli ne koostuvat hydrofiilisistä ja hydrofobisista osista ja polymeereissä nämä osat voivat olla omina lohkoinaan, jolloin puhutaan amfifiilisistä lohko- tai blokkikopolymeereistä. Riippuen järjestyneiden rakenteiden koostumuksesta ja muodosta, amfifiilisiä blokkikopolymeerejä on tutkittu tai jo käytetty nanoteknologiassa, elastomeereissä, voiteluaineissa, pinta-aktiivisina aineina, lääkkeenannostelussa, maaleissa, sekä elektroniikka-, kosmetiikka- ja elintarviketeollisuudessa. Tavallisimmin käytetyt amfifiiliset blokkikopolymeerit ovat olleet lineaarisia, mutta viime aikoina tutkimus on suuntautunut kohti monimutkaisempia rakenteita. Tällaisia ovat esimerkiksi tähtipolymeerit. Tähtimäisissä polymeereissä miselleille tyypillinen ydin-kuori-rakenne säilyy hyvin alhaisissakin polymeerikonsentraatioissa, koska polymeeriketjut ovat kiinni toisissaan yhdessä pisteessä. Siten ne ovat erityisen kiinnostavia tutkimuskohteita erilaisten hydrofobisten orgaanisten yhdisteiden sitomiseksi ja vapauttamiseksi. Tässä työssä on tarkasteltu amfifiilisten tähtipolymeerien itsejärjestymistä vesiliuoksissa sekä kokeellisesti ja tietokonesimulaatioin. Työ koostuu kahdesta osasta: tähtipolymeerien synteesistä makrosyklisillä initiaattoreilla ja amfifiilisten tähtimäisten blokkikopolymeerien ominaisuuksien tutkimisesta.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

Let X be a topological space and K the real algebra of the reals, the complex numbers, the quaternions, or the octonions. The functions form X to K form an algebra T(X,K) with pointwise addition and multiplication. We study first-order definability of the constant function set N' corresponding to the set of the naturals in certain subalgebras of T(X,K). In the vocabulary the symbols Constant, +, *, 0', and 1' are used, where Constant denotes the predicate defining the constants, and 0' and 1' denote the constant functions with values 0 and 1 respectively. The most important result is the following. Let X be a topological space, K the real algebra of the reals, the compelex numbers, the quaternions, or the octonions, and R a subalgebra of the algebra of all functions from X to K containing all constants. Then N' is definable in , if at least one of the following conditions is true. (1) The algebra R is a subalgebra of the algebra of all continuous functions containing a piecewise open mapping from X to K. (2) The space X is sigma-compact, and R is a subalgebra of the algebra of all continuous functions containing a function whose range contains a nonempty open set of K. (3) The algebra K is the set of reals or the complex numbers, and R contains a piecewise open mapping from X to K and does not contain an everywhere unbounded function. (4) The algebra R contains a piecewise open mapping from X to the set of the reals and function whose range contains a nonempty open subset of K. Furthermore R does not contain an everywhere unbounded function.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Algorithms for 13C metabolic flux analysis

The metabolism of an organism consists of a network of biochemical reactions that transform small molecules, or metabolites, into others in order to produce energy and building blocks for essential macromolecules. The goal of metabolic flux analysis is to uncover the rates, or the fluxes, of those biochemical reactions. In a steady state, the sum of the fluxes that produce an internal metabolite is equal to the sum of the fluxes that consume the same molecule. Thus the steady state imposes linear balance constraints to the fluxes. In general, the balance constraints imposed by the steady state are not sufficient to uncover all the fluxes of a metabolic network. The fluxes through cycles and alternative pathways between the same source and target metabolites remain unknown. More information about the fluxes can be obtained from isotopic labelling experiments, where a cell population is fed with labelled nutrients, such as glucose that contains 13C atoms. Labels are then transferred by biochemical reactions to other metabolites. The relative abundances of different labelling patterns in internal metabolites depend on the fluxes of pathways producing them. Thus, the relative abundances of different labelling patterns contain information about the fluxes that cannot be uncovered from the balance constraints derived from the steady state. The field of research that estimates the fluxes utilizing the measured constraints to the relative abundances of different labelling patterns induced by 13C labelled nutrients is called 13C metabolic flux analysis. There exist two approaches of 13C metabolic flux analysis. In the optimization approach, a non-linear optimization task, where candidate fluxes are iteratively generated until they fit to the measured abundances of different labelling patterns, is constructed. In the direct approach, linear balance constraints given by the steady state are augmented with linear constraints derived from the abundances of different labelling patterns of metabolites. Thus, mathematically involved non-linear optimization methods that can get stuck to the local optima can be avoided. On the other hand, the direct approach may require more measurement data than the optimization approach to obtain the same flux information. Furthermore, the optimization framework can easily be applied regardless of the labelling measurement technology and with all network topologies. In this thesis we present a formal computational framework for direct 13C metabolic flux analysis. The aim of our study is to construct as many linear constraints to the fluxes from the 13C labelling measurements using only computational methods that avoid non-linear techniques and are independent from the type of measurement data, the labelling of external nutrients and the topology of the metabolic network. The presented framework is the first representative of the direct approach for 13C metabolic flux analysis that is free from restricting assumptions made about these parameters.In our framework, measurement data is first propagated from the measured metabolites to other metabolites. The propagation is facilitated by the flow analysis of metabolite fragments in the network. Then new linear constraints to the fluxes are derived from the propagated data by applying the techniques of linear algebra.Based on the results of the fragment flow analysis, we also present an experiment planning method that selects sets of metabolites whose relative abundances of different labelling patterns are most useful for 13C metabolic flux analysis. Furthermore, we give computational tools to process raw 13C labelling data produced by tandem mass spectrometry to a form suitable for 13C metabolic flux analysis.