Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Hyperbolic type metrics and distortion of quasiconformal map pings

This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.

Ultrafine grinding of FGD and phosphogypsum with an attrition bead mill and a jet mill : optimisation and modelling of grinding and mill comparison

Fine powders of minerals are used commonly in the paper and paint industry, and for ceramics. Research for utilizing of different waste materials in these applications is environmentally important. In this work, the ultrafine grinding of two waste gypsum materials, namely FGD (Flue Gas Desulphurisation) gypsum and phosphogypsum from a phosphoric acid plant, with the attrition bead mill and with the jet mill has been studied. The ' objective of this research was to test the suitability of the attrition bead mill and of the jet mill to produce gypsum powders with a particle size of a few microns. The grinding conditions were optimised by studying the influences of different operational grinding parameters on the grinding rate and on the energy consumption of the process in order to achieve a product fineness such as that required in the paper industry with as low energy consumption as possible. Based on experimental results, the most influential parameters in the attrition grinding were found to be the bead size, the stirrer type, and the stirring speed. The best conditions, based on the product fineness and specific energy consumption of grinding, for the attrition grinding process is to grind the material with small grinding beads and a high rotational speed of the stirrer. Also, by using some suitable grinding additive, a finer product is achieved with a lower energy consumption. In jet mill grinding the most influential parameters were the feed rate, the volumetric flow rate of the grinding air, and the height of the internal classification tube. The optimised condition for the jet is to grind with a small feed rate and with a large rate of volumetric flow rate of grinding air when the inside tube is low. The finer product with a larger rate of production was achieved with the attrition bead mill than with the jet mill, thus the attrition grinding is better for the ultrafine grinding of gypsum than the jet grinding. Finally the suitability of the population balance model for simulation of grinding processes has been studied with different S , B , and C functions. A new S function for the modelling of an attrition mill and a new C function for the modelling of a jet mill were developed. The suitability of the selected models with the developed grinding functions was tested by curve fitting the particle size distributions of the grinding products and then comparing the fitted size distributions to the measured particle sizes. According to the simulation results, the models are suitable for the estimation and simulation of the studied grinding processes.

Regulation of Spermatogenesis: Differentiation of GFP-labeled Stem Cells and the Function of Cytoplasmic Bridges

During spermatogenesis, different genes are expressed in a strictly coordinated fashion providing an excellent model to study cell differentiation. Recent identification of testis specific genes and the development of green fluorescence protein (GFP) transgene technology and an in vivo system for studying the differentiation of transplanted male germ cells in infertile testis has opened new possibilities for studying the male germ cell differentiation at molecular level. We have employed these techniques in combination with transillumination based stage recognition (Parvinen and Vanha-Perttula, 1972) and squash preparation techniques (Parvinen and Hecht, 1981) to study the regulation of male germ cell differentiation. By using transgenic mice expressing enhanced-(E)GFP as a marker we have studied the expression and hormonal regulation of beta-actin and acrosin proteins in the developmentally different living male germ cells. Beta-actin was demonstrated in all male germ cells, whereas acrosin was expressed only in late meiotic and in postmeiotic cells. Follicle stimulating hormone stimulated b-actin-EGFP expression at stages I-VI and enhanced the formation of microtubules in spermatids and this way reduced the size of the acrosomic system. When EGFP expressing spermatogonial stem cells were transplanted into infertile mouse testis differentiation and the synchronized development of male germ cells could be observed during six months observation time. Each colony developed independently and maintained typical stage-dependent cell associations. Furthermore, if more than two colonies were fused, each of them was adjusted to one stage and synchronized. By studying living spermatids we were able to demonstrate novel functions for Golgi complex and chromatoid body in material sharing between neighbor spermatids. Immunosytochemical analyses revealed a transport of haploid cell specific proteins in spermatids (TRA54 and Shippo1) and through the intercellular bridges (TRA54). Cytoskeleton inhibitor (nocodazole) demonstrated the importance of microtubules in material sharing between spermatids and in preserving the integrity of the chromatoid body. Golgi complex inhibitor, brefeldin A, revealed the great importance of Golgi complex i) in acrosomic system formation ii) TRA54 translation and in iii) granule trafficking between spermatids.

Functions for estimating stem diameter and tree age using tree height, crown width and existing stand database information

Abstract

On the differential evolution algorithm and its appliation to training radial basis function networks

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

New kernel functions and learning methods for text and data mining

Recent advances in machine learning methods enable increasingly the automatic construction of various types of computer assisted methods that have been difficult or laborious to program by human experts. The tasks for which this kind of tools are needed arise in many areas, here especially in the fields of bioinformatics and natural language processing. The machine learning methods may not work satisfactorily if they are not appropriately tailored to the task in question. However, their learning performance can often be improved by taking advantage of deeper insight of the application domain or the learning problem at hand. This thesis considers developing kernel-based learning algorithms incorporating this kind of prior knowledge of the task in question in an advantageous way. Moreover, computationally efficient algorithms for training the learning machines for specific tasks are presented. In the context of kernel-based learning methods, the incorporation of prior knowledge is often done by designing appropriate kernel functions. Another well-known way is to develop cost functions that fit to the task under consideration. For disambiguation tasks in natural language, we develop kernel functions that take account of the positional information and the mutual similarities of words. It is shown that the use of this information significantly improves the disambiguation performance of the learning machine. Further, we design a new cost function that is better suitable for the task of information retrieval and for more general ranking problems than the cost functions designed for regression and classification. We also consider other applications of the kernel-based learning algorithms such as text categorization, and pattern recognition in differential display. We develop computationally efficient algorithms for training the considered learning machines with the proposed kernel functions. We also design a fast cross-validation algorithm for regularized least-squares type of learning algorithm. Further, an efficient version of the regularized least-squares algorithm that can be used together with the new cost function for preference learning and ranking tasks is proposed. In summary, we demonstrate that the incorporation of prior knowledge is possible and beneficial, and novel advanced kernels and cost functions can be used in algorithms efficiently.

Role and Function of c-Jun Protein Complex in Cancer Cell Behavior

Transcription factors play a crucial role in the regulation of cell behavior by modulating gene expression profiles. Previous studies have described a dual role for the AP-1 family transcription factor c-Jun in the regulation of cellular fate. In various cell types weak and transient activations of c-Jun N-terminal kinase (JNK) and c-Jun appear to contribute to proliferation and survival, whereas strong and prolonged activation of JNK and c-Jun result in apoptosis. These opposite roles played by c-Jun are cell type specific and the molecular mechanisms defining these antonymous c-Jun-mediated responses remain incompletely understood. c-Jun activity in transformed cells is regulated by signalling cascades downstream of oncoproteins such as Ras and Raf. In addition, the pro-proliferative role and the survival promoting function for c-Jun has been described in various cancer models. Furthermore, c-Jun was described to be overexpressed in different cancer types. However, the molecular mechanisms by which c-Jun exerts these oncogenic functions are not all clearly established. Therefore it is of primary interest to further identify molecular mechanisms and functions for c-Jun in cancer. Regulation of gene expression is tightly dependent on accurate protein-protein interactions. Therefore, co-factors for c-Jun may define the functions for c-Jun in cancer. Identification of protein-protein interactions promoting cancer may provide novel possibilities for cancer treatment. In this study, we show that DNA topoisomerase I (TopoI) is a transcriptional co-factor for c-Jun. Moreover, c-Jun and TopoI together promote expression of epidermal growth factor receptor (EGFR) in cancer cells. We also show that the clinically used TopoI inhibitor topotecan reduces EGFR expression. Importantly, the effect of TopoI on EGFR transcription was shown to depend on c-Jun as Jun-/- cells or cells treated with JNK inhibitor SP600125 are resistant to topotecan treatment both in regulation of EGFR expression and cell proliferation. Moreover, c-Jun regulates the nucleolar localization and the function of the ribonucleic acid (RNA) helicase DDX21, a previously identified member of c-Jun protein complex. In addition, c-Jun stimulates rRNA processing by supporting DDX21 rRNA binding. Finally, this study characterizes a DDX21 dependent expression of cyclin dependent kinase (Cdk) 6, a correlation of DDX21 expression with prostate cancer progression and a substrate binding dependency of DDX21 nucleolar localization in prostate cancer cells. Taken together, the results of this study validate the c-Jun-TopoI interaction and precise the c-Jun-DDX21 interaction. Moreover, these results show the importance for protein-protein interaction in the regulation of their cellular functions in cancer cell behavior. Finally, the results presented here disclose new exciting therapeutic opportunities for cancer treatment.

NADPH-Dependent Thioredoxin System In Regulation of Chloroplast Functions

Photosynthesis, the process in which carbon dioxide is converted into sugars using the energy of sunlight, is vital for heterotrophic life on Earth. In plants, photosynthesis takes place in specific organelles called chloroplasts. During chloroplast biogenesis, light is a prerequisite for the development of functional photosynthetic structures. In addition to photosynthesis, a number of other metabolic processes such as nitrogen assimilation, the biosynthesis of fatty acids, amino acids, vitamins, and hormones are localized to plant chloroplasts. The biosynthetic pathways in chloroplasts are tightly regulated, and especially the reduction/oxidation (redox) signals play important roles in controlling many developmental and metabolic processes in chloroplasts. Thioredoxins are universal regulatory proteins that mediate redox signals in chloroplasts. They are able to modify the structure and function of their target proteins by reduction of disulfide bonds. Oxidized thioredoxins are restored via the action of thioredoxin reductases. Two thioredoxin reductase systems exist in plant chloroplasts, the NADPHdependent thioredoxin reductase C (NTRC) and ferredoxin-thioredoxin reductase (FTR). The ferredoxin-thioredoxin system that is linked to photosynthetic light reactions is involved in light-activation of chloroplast proteins. NADPH can be produced via both the photosynthetic electron transfer reactions in light, and in darkness via the pentose phosphate pathway. These different pathways of NADPH production enable the regulation of diverse metabolic pathways in chloroplasts by the NADPH-dependent thioredoxin system. In this thesis, the role of NADPH-dependent thioredoxin system in the redox-control of chloroplast development and metabolism was studied by characterization of Arabidopsis thaliana T-DNA insertion lines of NTRC gene (ntrc) and by identification of chloroplast proteins regulated by NTRC. The ntrc plants showed the strongest visible phenotypes when grown under short 8-h photoperiod. This indicates that i) chloroplast NADPH-dependent thioredoxin system is non-redundant to ferredoxinthioredoxin system and that ii) NTRC particularly controls the chloroplast processes that are easily imbalanced in daily light/dark rhythms with short day and long night. I identified four processes and the redox-regulated proteins therein that are potentially regulated by NTRC; i) chloroplast development, ii) starch biosynthesis, iii) aromatic amino acid biosynthesis and iv) detoxification of H₂O₂. Such regulation can be achieved directly by modulating the redox state of intramolecular or intermolecular disulfide bridges of enzymes, or by protecting enzymes from oxidation in conjunction with 2-cysteine peroxiredoxins. This thesis work also demonstrated that the enzymatic antioxidant systems in chloroplasts, ascorbate peroxidases, superoxide dismutase and NTRC-dependent 2-cysteine peroxiredoxins are tightly linked up to prevent the detrimental accumulation of reactive oxygen species in plants.

Orthogonal function method in modelling paper web quality variation

This work is devoted to the analysis of signal variation of the Cross-Direction and Machine-Direction measurements from paper web. The data that we possess comes from the real paper machine. Goal of the work is to reconstruct the basis weight structure of the paper and to predict its behaviour to the future. The resulting synthetic data is needed for simulation of paper web. The main idea that we used for describing the basis weight variation in the Cross-Direction is Empirical Orthogonal Functions (EOF) algorithm, which is closely related to Principal Component Analysis (PCA) method. Signal forecasting in time is based on Time-Series analysis. Two principal mathematical procedures that we used in the work are Autoregressive-Moving Average (ARMA) modelling and Ornstein–Uhlenbeck (OU) process.

Creating possibilities for collective creativity : Brokerage Functions in Practice-Based Innovation

In the network era, creative achievements like innovations are more and more often created in interaction among different actors. The complexity of today‘s problems transcends the individual human mind, requiring not only individual but also collective creativity. In collective creativity, it is impossible to trace the source of new ideas to an individual. Instead, creative activity emerges from the collaboration and contribution of many individuals, thereby blurring the contribution of specific individuals in creating ideas. Collective creativity is often associated with diversity of knowledge, skills, experiences and perspectives. Collaboration between diverse actors thus triggers creativity and gives possibilities for collective creativity. This dissertation investigates collective creativity in the context of practice-based innovation. Practice-based innovation processes are triggered by problem setting in a practical context and conducted in non-linear processes utilising scientific and practical knowledge production and creation in cross-disciplinary innovation networks. In these networks diversity or distances between innovation actors are essential. Innovation potential may be found in exploiting different kinds of distances. This dissertation presents different kinds of distances, such as cognitive, functional and organisational which could be considered as sources of creativity and thus innovation. However, formation and functioning of these kinds of innovation networks can be problematic. Distances between innovating actors may be so great that a special interpretation function is needed – that is, brokerage. This dissertation defines factors that enhance collective creativity in practice-based innovation and especially in the fuzzy front end phase of innovation processes. The first objective of this dissertation is to study individual and collective creativity at the employee level and identify those factors that support individual and collective creativity in the organisation. The second objective is to study how organisations use external knowledge to support collective creativity in their innovation processes in open multi-actor innovation. The third objective is to define how brokerage functions create possibilities for collective creativity especially in the context of practice-based innovation. The research objectives have been studied through five substudies using a case-study strategy. Each substudy highlights various aspects of creativity and collective creativity. The empirical data consist of materials from innovation projects arranged in the Lahti region, Finland, or materials from the development of innovation methods in the Lahti region. The Lahti region has been chosen as the research context because the innovation policy of the region emphasises especially the promotion of practice-based innovations. The results of this dissertation indicate that all possibilities of collective creativity are not utilised in internal operations of organisations. The dissertation introduces several factors that could support collective creativity in organisations. However, creativity as a social construct is understood and experienced differently in different organisations, and these differences should be taken into account when supporting creativity in organisations. The increasing complexity of most potential innovations requires collaborative creative efforts that often exceed the boundaries of the organisation and call for the involvement of external expertise. In practice-based innovation different distances are considered as sources of creativity. This dissertation gives practical implications on how it is possible to exploit different kinds of distances knowingly. It underlines especially the importance of brokerage functions in open, practice-based innovation in order to create possibilities for collective creativity. As a contribution of this dissertation, a model of brokerage functions in practice-based innovation is formulated. According to the model, the results and success of brokerage functions are based on the context of brokerage as well as the roles, tasks, skills and capabilities of brokers. The brokerage functions in practice-based innovation are also possible to divide into social and cognitive brokerage.

The Structure and Function of αI Domains in Collagen Receptor and Leukocyte Integrins

Integrins are heterodimeric, signaling transmembrane adhesion receptors that connect the intracellular actin microfilaments to the extracellular matrix composed of collagens and other matrix molecules. Bidirectional signaling is mediated via drastic conformational changes in integrins. These changes also occur in the integrin αI domains, which are responsible for ligand binding by collagen receptor and leukocyte specific integrins. Like intact integrins, soluble αI domains exist in the closed, low affinity form and in the open, high affinity form, and so it is possible to use isolated αI domains to study the factors and mechanisms involved in integrin activation/deactivation. Integrins are found in all mammalian tissues and cells, where they play crucial roles in growth, migration, defense mechanisms and apoptosis. Integrins are involved in many human diseases, such as inflammatory, cardiovascular and metastatic diseases, and so plenty of effort has been invested into developing integrin specific drugs. Humans have 24 different integrins, four of which are collagen receptor (α1β1, α2β1, α10β1, α11β1) and five leukocyte specific integrins (αLβ2, αMβ2, αXβ2, αDβ2, αEβ7). These two integrin groups are quite unselective having both primary and secondary ligands. This work presents the first systematic studies performed on these integrin groups to find out how integrin activation affects ligand binding and selectivity. These kinds of studies are important not only for understanding the partially overlapping functions of integrins, but also for drug development. In general, our results indicated that selectivity in ligand recognition is greatly reduced upon integrin activation. Interestingly, in some cases the ligand binding properties of integrins have been shown to be cell type specific. The reason for this is not known, but our observations suggest that cell types with a higher integrin activation state have lower ligand selectivity, and vice versa. Furthermore, we solved the three-dimensional structure for the activated form of the collagen receptor α1I domain. This structure revealed a novel intermediate conformation not previously seen with any other integrin αI domain. This is the first 3D structure for an activated collagen receptor αI domain without ligand. Based on the differences between the open and closed conformation of the αI domain we set structural criteria for a search for effective collagen receptor drugs. By docking a large number of molecules into the closed conformation of the α2I domain we discovered two polyketides, which best fulfilled the set structural criteria, and by cell adhesion studies we showed them to be specific inhibitors of the collagen receptor integrins.

Training executive functions in the laboratory and in real life : cognitive consequences of computer-based exercises and bilingualism

The question of the trainability of executive functions and the impact of such training on related cognitive skills has stirred considerable research interest. Despite a number of studies investigating this, the question has not yet been solved. The general aim of this thesis was to investigate two very different types of training of executive functions: laboratory-based computerized training (Studies I-III) and realworld training through bilingualism (Studies IV-V). Bilingualism as a kind of training of executive functions is based on the idea that managing two languages requires executive resources, and previous studies have suggested a bilingual advantage in executive functions. Three executive functions were studied in the present thesis: updating of working memory (WM) contents, inhibition of irrelevant information, and shifting between tasks and mental sets. Studies I-III investigated the effects of computer-based training of WM updating (Study I), inhibition (Study II), and set shifting (Study III) in healthy young adults. All studies showed increased performance on the trained task. More importantly, improvement on an untrained task tapping the trained executive function (near transfer) was seen in Study I and II. None of the three studies showed improvement on untrained tasks tapping some other cognitive function (far transfer) as a result of training. Study I also used PET to investigate the effects of WM updating training on a neurotransmitter closely linked to WM, namely dopamine. The PET results revealed increased striatal dopamine release during WM updating performance as a result of training. Study IV investigated the ability to inhibit task-irrelevant stimuli in bilinguals and monolinguals by using a dichotic listening task. The results showed that the bilinguals exceeded the monolinguals in inhibiting task-irrelevant information. Study V introduced a new, complementary research approach to study the bilingual executive advantage and its underlying mechanisms. To circumvent the methodological problems related to natural groups design, this approach focuses only on bilinguals and examines whether individual differences in bilingual behavior correlate with executive task performances. Using measures that tap the three above-entioned executive functions, the results suggested that more frequent language switching was associated with better set shifting skills, and earlier acquisition of the second language was related to better inhibition skills. In conclusion, the present behavioral results showed that computer-based training of executive functions can improve performance on the trained task and on closely related tasks, but does not yield a more general improvement of cognitive skills. Moreover, the functional neuroimaging results reveal that WM training modulates striatal dopaminergic function, speaking for training-induced neural plasticity in this important neurotransmitter system. With regard to bilingualism, the results provide further support to the idea that bilingualism can enhance executive functions. In addition, the new complementary research approach proposed here provides some clues as to which aspects of everyday bilingual behavior may be related to the advantage in executive functions in bilingual individuals.

How can we agree on some product agnostic repository function fundamentals?

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014