Hadwiger Number and the Cartesian Product of Graphs

The Hadwiger number eta(G) of a graph G is the largest integer n for which the complete graph K-n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, eta(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G square H of graphs. As the main result of this paper, we prove that eta(G(1) square G(2)) >= h root 1 (1 - o(1)) for any two graphs G(1) and G(2) with eta(G(1)) = h and eta(G(2)) = l. We show that the above lower bound is asymptotically best possible when h >= l. This asymptotically settles a question of Z. Miller (1978). As consequences of our main result, we show the following: 1. Let G be a connected graph. Let G = G(1) square G(2) square ... square G(k) be the ( unique) prime factorization of G. Then G satisfies Hadwiger's conjecture if k >= 2 log log chi(G) + c', where c' is a constant. This improves the 2 log chi(G) + 3 bound in [2] 2. Let G(1) and G(2) be two graphs such that chi(G1) >= chi(G2) >= clog(1.5)(chi(G(1))), where c is a constant. Then G1 square G2 satisfies Hadwiger's conjecture. 3. Hadwiger's conjecture is true for G(d) (Cartesian product of G taken d times) for every graph G and every d >= 2. This settles a question by Chandran and Sivadasan [2]. ( They had shown that the Hadiwger's conjecture is true for G(d) if d >= 3).

Mitochondrial helicase Twinkle in mtDNA copy number regulation and a late-onset disease model

Mitochondrial diseases are caused by disturbances of the energy metabolism. The disorders range from severe childhood neurological diseases to muscle diseases of adults. Recently, mitochondrial dysfunction has also been found in Parkinson s disease, diabetes, certain types of cancer and premature aging. Mitochondria are the power plants of the cell but they also participate in the regulation of cell growth, signaling and cell death. Mitochondria have their own genetic material, mtDNA, which contains the genetic instructions for cellular respiration. Single cell may host thousands of mitochondria and several mtDNA molecules may reside inside single mitochondrion. All proteins needed for mtDNA maintenance are, however, encoded by the nuclear genome, and therefore, mutations of the corresponding genes can also cause mitochondrial disease. We have here studied the function of mitochondrial helicase Twinkle. Our research group has previously identified nuclear Twinkle gene mutations underlying an inherited adult-onset disorder, progressive external ophthalmoplegia (PEO). Characteristic for the PEO disease is the accumulation of multiple mtDNA deletions in tissues such as the muscle and brain. In this study, we have shown that Twinkle helicase is essential for mtDNA maintenance and that it is capable of regulating mtDNA copy number. Our results support the role of Twinkle as the mtDNA replication helicase. No cure is available for mitochondrial disease. Good disease models are needed for studies of the cause of disease and its progression and for treatment trials. Such disease model, which replicates the key features of the PEO disease, has been generated in this study. The model allows for careful inspection of how Twinkle mutations lead to mtDNA deletions and further causes the PEO disease. This model will be utilized in a range of studies addressing the delay of the disease onset and progression and in subsequent treatment trials. In conclusion, in this thesis fundamental knowledge of the function of the mitochondrial helicase Twinkle was gained. In addition, the first model for adult-onset mitochondrial disease was generated.

Aerosol size distribution and its connection to cloud droplet number concentration

In order to predict the current state and future development of Earth s climate, detailed information on atmospheric aerosols and aerosol-cloud-interactions is required. Furthermore, these interactions need to be expressed in such a way that they can be represented in large-scale climate models. The largest uncertainties in the estimate of radiative forcing on the present day climate are related to the direct and indirect effects of aerosol. In this work aerosol properties were studied at Pallas and Utö in Finland, and at Mount Waliguan in Western China. Approximately two years of data from each site were analyzed. In addition to this, data from two intensive measurement campaigns at Pallas were used. The measurements at Mount Waliguan were the first long term aerosol particle number concentration and size distribution measurements conducted in this region. They revealed that the number concentration of aerosol particles at Mount Waliguan were much higher than those measured at similar altitudes in other parts of the world. The particles were concentrated in the Aitken size range indicating that they were produced within a couple of days prior to reaching the site, rather than being transported over thousands of kilometers. Aerosol partitioning between cloud droplets and cloud interstitial particles was studied at Pallas during the two measurement campaigns, First Pallas Cloud Experiment (First PaCE) and Second Pallas Cloud Experiment (Second PaCE). The method of using two differential mobility particle sizers (DMPS) to calculate the number concentration of activated particles was found to agree well with direct measurements of cloud droplet. Several parameters important in cloud droplet activation were found to depend strongly on the air mass history. The effects of these parameters partially cancelled out each other. Aerosol number-to-volume concentration ratio was studied at all three sites using data sets with long time-series. The ratio was found to vary more than in earlier studies, but less than either aerosol particle number concentration or volume concentration alone. Both air mass dependency and seasonal pattern were found at Pallas and Utö, but only seasonal pattern at Mount Waliguan. The number-to-volume concentration ratio was found to follow the seasonal temperature pattern well at all three sites. A new parameterization for partitioning between cloud droplets and cloud interstitial particles was developed. The parameterization uses aerosol particle number-to-volume concentration ratio and aerosol particle volume concentration as the only information on the aerosol number and size distribution. The new parameterization is computationally more efficient than the more detailed parameterizations currently in use, but the accuracy of the new parameterization was slightly lower. The new parameterization was also compared to directly observed cloud droplet number concentration data, and a good agreement was found.

Patient doses in ct, dental cone beam ct and projection radiography in Finland, with emphasis on paediatric patients

Diagnostic radiology represents the largest man-made contribution to population radiation doses in Europe. To be able to keep the diagnostic benefit versus radiation risk ratio as high as possible, it is important to understand the quantitative relationship between the patient radiation dose and the various factors which affect the dose, such as the scan parameters, scan mode, and patient size. Paediatric patients have a higher probability for late radiation effects, since longer life expectancy is combined with the higher radiation sensitivity of the developing organs. The experience with particular paediatric examinations may be very limited and paediatric acquisition protocols may not be optimised. The purpose of this thesis was to enhance and compare different dosimetric protocols, to promote the establishment of the paediatric diagnostic reference levels (DRLs), and to provide new data on patient doses for optimisation purposes in computed tomography (with new applications for dental imaging) and in paediatric radiography. Large variations in radiation exposure in paediatric skull, sinus, chest, pelvic and abdominal radiography examinations were discovered in patient dose surveys. There were variations between different hospitals and examination rooms, between different sized patients, and between imaging techniques; emphasising the need for harmonisation of the examination protocols. For computed tomography, a correction coefficient, which takes individual patient size into account in patient dosimetry, was created. The presented patient size correction method can be used for both adult and paediatric purposes. Dental cone beam CT scanners provided adequate image quality for dentomaxillofacial examinations while delivering considerably smaller effective doses to patient compared to the multi slice CT. However, large dose differences between cone beam CT scanners were not explained by differences in image quality, which indicated the lack of optimisation. For paediatric radiography, a graphical method was created for setting the diagnostic reference levels in chest examinations, and the DRLs were given as a function of patient projection thickness. Paediatric DRLs were also given for sinus radiography. The detailed information about the patient data, exposure parameters and procedures provided tools for reducing the patient doses in paediatric radiography. The mean tissue doses presented for paediatric radiography enabled future risk assessments to be done. The calculated effective doses can be used for comparing different diagnostic procedures, as well as for comparing the use of similar technologies and procedures in different hospitals and countries.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.

The EU and Institutional Twinning in Morocco - An inquiry into the motives of cooperation through discourse ethics

This study examines Institutional Twinning in Morocco as a case of EU cooperation through the pragmatic, ethical and moral logics of reason in Jürgen Habermas’s discourse ethics. As a former accession tool, Twinning was introduced in 2004 for legal approximation in the context of the European Neighborhood Policy. Twinning is a unique instrument in development cooperation from a legal perspective. With its long historical and cultural ties to Europe, Morocco presents an interesting case study of this new form of cooperation. We will analyse motives behind the Twinning projects on illegal immigration, environment legislation and customs reform. As Twinning is a new policy instrument within the ENP context, there is relatively little preceding research, which, in itself, constitutes a reason to inquire into the subject. While introducing useful categories, the approaches discussing “normative power Europe” do not offer methodological tools precise enough to analyse the motives of the Twinning cooperation from a broad ethical standpoint. Helene Sjursen as well as Esther Barbé and Elisabeth Johansson-Nogués have elaborated on Jürgen Habermas’ discourse ethics in determining the extent of altruism in the ENP in general. Situating the analysis in the process-oriented framework of Critical Theory, discourse ethics provides the methodological framework for our research. The case studies reveal that the context in which they operate affects the pragmatic, ethical and moral aspirations of the actors. The utilitarian notion of profit maximization is quite pronounced both in terms of the number of Twinning projects in the economic sphere and the pragmatic logics of reason instrumental to security and trade-related issues. The historical background as well internal processes, however, contribute to defining areas of mutual interest to the actors as well as the motives Morocco and the EU sometimes described as the external projection of internal values. Through its different aspects, Twinning cooperation portrays the functioning of the pragmatic, ethical and moral logics of reason in international relations.

MECHANISMS AND EFFECTS OF MITOCHONDRIAL DNA INSTABILITY AND COPY NUMBER MANIPULATION

Defects in mitochondrial DNA (mtDNA) maintenance cause a range of human diseases, including autosomal dominant progressive external ophthalmoplegia (adPEO). This study aimed to clarify the molecular background of adPEO. We discovered that deoxynucleoside triphosphate (dNTP) metabolism plays a crucial in mtDNA maintenance and were thus prompted to search for therapeutic strategies based on the modulation of cellular dNTP pools or mtDNA copy number. Human mtDNA is a 16.6 kb circular molecule present in hundreds to thousands of copies per cell. mtDNA is compacted into nucleoprotein clusters called nucleoids. mtDNA maintenance diseases result from defects in nuclear encoded proteins that maintain the mtDNA. These syndromes typically afflict highly differentiated, post-mitotic tissues such as muscle and nerve, but virtually any organ can be affected. adPEO is a disease where mtDNA molecules with large-scale deletions accumulate in patients tissues, particularly in skeletal muscle. Mutations in five nuclear genes, encoding the proteins ANT1, Twinkle, POLG, POLG2 and OPA1, have previously been shown to cause adPEO. Here, we studied a large North American pedigree with adPEO, and identified a novel heterozygous mutation in the gene RRM2B, which encodes the p53R2 subunit of the enzyme ribonucleotide reductase (RNR). RNR is the rate-limiting enzyme in dNTP biosynthesis, and is required both for nuclear and mitochondrial DNA replication. The mutation results in the expression of a truncated form of p53R2, which is likely to compete with the wild-type allele. A change in enzyme function leads to defective mtDNA replication due to altered dNTP pools. Therefore, RRM2B is a novel adPEO disease gene. The importance of adequate dNTP pools and RNR function for mtDNA maintenance has been established in many organisms. In yeast, induction of RNR has previously been shown to increase mtDNA copy number, and to rescue the phenotype caused by mutations in the yeast mtDNA polymerase. To further study the role of RNR in mammalian mtDNA maintenance, we used mice that broadly overexpress the RNR subunits Rrm1, Rrm2 or p53R2. Active RNR is a heterotetramer consisting of two large subunits (Rrm1) and two small subunits (either Rrm2 or p53R2). We also created bitransgenic mice that overexpress Rrm1 together with either Rrm2 or p53R2. In contrast to the previous findings in yeast, bitransgenic RNR overexpression led to mtDNA depletion in mouse skeletal muscle, without mtDNA deletions or point mutations. The mtDNA depletion was associated with imbalanced dNTP pools. Furthermore, the mRNA expression levels of Rrm1 and p53R2 were found to correlate with mtDNA copy number in two independent mouse models, suggesting nuclear-mitochondrial cross talk with regard to mtDNA copy number. We conclude that tight regulation of RNR is needed to prevent harmful alterations in the dNTP pool balance, which can lead to disordered mtDNA maintenance. Increasing the copy number of wild-type mtDNA has been suggested as a strategy for treating PEO and other mitochondrial diseases. Only two proteins are known to cause a robust increase in mtDNA copy number when overexpressed in mice; the mitochondrial transcription factor A (TFAM), and the mitochondrial replicative helicase Twinkle. We studied the mechanisms by which Twinkle and TFAM elevate mtDNA levels, and showed that Twinkle specifically implements mtDNA synthesis. Furthermore, both Twinkle and TFAM were found to increase mtDNA content per nucleoid. Increased mtDNA content in mouse tissues correlated with an age-related accumulation of mtDNA deletions, depletion of mitochondrial transcripts, and progressive respiratory dysfunction. Simultaneous overexpression of Twinkle and TFAM led to a further increase in the mtDNA content of nucleoids, and aggravated the respiratory deficiency. These results suggested that high mtDNA levels have detrimental long-term effects in mice. These data have to be considered when developing and evaluating treatment strategies for elevating mtDNA copy number.

A cost effective pipelined divider for double precision floating point number

he growth of high-performance application in computer graphics, signal processing and scientific computing is a key driver for high performance, fixed latency; pipelined floating point dividers. Solutions available in the literature use large lookup table for double precision floating point operations.In this paper, we propose a cost effective, fixed latency pipelined divider using modified Taylor-series expansion for double precision floating point operations. We reduce chip area by using a smaller lookup table. We show that the latency of the proposed divider is 49.4 times the latency of a full-adder. The proposed divider reduces chip area by about 81% than the pipelined divider in [9] which is based on modified Taylor-series.

An Estimator Algorithm For Learning Automata With Changing Number Of Actions

In many problems of decision making under uncertainty the system has to acquire knowledge of its environment and learn the optimal decision through its experience. Such problems may also involve the system having to arrive at the globally optimal decision, when at each instant only a subset of the entire set of possible alternatives is available. These problems can be successfully modelled and analysed by learning automata. In this paper an estimator learning algorithm, which maintains estimates of the reward characteristics of the random environment, is presented for an automaton with changing number of actions. A learning automaton using the new scheme is shown to be e-optimal. The simulation results demonstrate the fast convergence properties of the new algorithm. The results of this study can be extended to the design of other types of estimator algorithms with good convergence properties.

New phase unwrapping strategy for rapid and dense 3D data acquisition in structured light approach

Sinusoidal structured light projection (SSLP) technique, specifically-phase stepping method, is in widespread use to obtain accurate, dense 3-D data. But, if the object under investigation possesses surface discontinuities, phase unwrapping (an intermediate step in SSLP) stage mandatorily require several additional images, of the object with projected fringes (of different spatial frequencies), as input to generate a reliable 3D shape. On the other hand, Color-coded structured light projection (CSLP) technique is known to require a single image as in put, but generates sparse 3D data. Thus we propose the use of CSLP in conjunction with SSLP to obtain dense 3D data with minimum number of images as input. This approach is shown to be significantly faster and reliable than temporal phase unwrapping procedure that uses a complete exponential sequence. For example, if a measurement with the accuracy obtained by interrogating the object with 32 fringes in the projected pattern is carried out with both the methods, new strategy proposed requires only 5 frames as compared to 24 frames required by the later method.

Design of crosspoint-irredundant PLAs using minimal number of control inputs

The problem of determining a minimal number of control inputs for converting a programmable logic array (PLA) with undetectable faults to crosspoint-irredundant PLA for testing has been formulated as a nonstandard set covering problem. By representing subsets of sets as cubes, this problem has been reformulated as familiar problems. It is noted that this result has significance because a crosspoint-irredundant PLA can be converted to a completely testable PLA in a straightforward fashion, thus achieving very good fault coverage and easy testability.

Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.