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).

Maan magneettikentän dipolimallin toimivuus inklinaatiojakauman perusteella

The magnetic field of the Earth is 99 % of the internal origin and generated in the outer liquid core by the dynamo principle. In the 19th century, Carl Friedrich Gauss proved that the field can be described by a sum of spherical harmonic terms. Presently, this theory is the basis of e.g. IGRF models (International Geomagnetic Reference Field), which are the most accurate description available for the geomagnetic field. In average, dipole forms 3/4 and non-dipolar terms 1/4 of the instantaneous field, but the temporal mean of the field is assumed to be a pure geocentric axial dipolar field. The validity of this GAD (Geocentric Axial Dipole) hypothesis has been estimated by using several methods. In this work, the testing rests on the frequency dependence of inclination with respect to latitude. Each combination of dipole (GAD), quadrupole (G2) and octupole (G3) produces a distinct inclination distribution. These theoretical distributions have been compared with those calculated from empirical observations from different continents, and last, from the entire globe. Only data from Precambrian rocks (over 542 million years old) has been used in this work. The basic assumption is that during the long-term course of drifting continents, the globe is sampled adequately. There were 2823 observations altogether in the paleomagnetic database of the University of Helsinki. The effect of the quality of observations, as well as the age and rocktype, has been tested. For comparison between theoretical and empirical distributions, chi-square testing has been applied. In addition, spatiotemporal binning has effectively been used to remove the errors caused by multiple observations. The modelling from igneous rock data tells that the average magnetic field of the Earth is best described by a combination of a geocentric dipole and a very weak octupole (less than 10 % of GAD). Filtering and binning gave distributions a more GAD-like appearance, but deviation from GAD increased as a function of the age of rocks. The distribution calculated from so called keypoles, the most reliable determinations, behaves almost like GAD, having a zero quadrupole and an octupole 1 % of GAD. In no earlier study, past-400-Ma rocks have given a result so close to GAD, but low inclinations have been prominent especially in the sedimentary data. Despite these results, a greater deal of high-quality data and a proof of the long-term randomness of the Earth's continental motions are needed to make sure the dipole model holds true.

On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

Rot bilong mipela

In my master's thesis I explore the political significance of logging in Papua New Guinea (PNG). In commercial logging the post-colonial state of PNG, its local communities, transnational companies and non-governmental organizations come interestingly together. The central research questions are what forms of political awareness and mobilization does commercial logging bring up in the small scale communities and how – if at all – does logging change the relationship between these communities and the state of PNG. The thesis is based on three months of ethnographic fieldwork conducted in 2007 in a village located in the East New Britain province of PNG. The village, inhabited mainly by the Mengen people, was an interesting case, because logging operations had been conducted in the area with the permission of the people, while on the other hand some villagers had formed a conservation association of their own. Parliamentary elections were also held in PNG during the time of my fieldwork. During my stay in the village I took part in the village life and conducted interviews. In addition to this, much of my material is based on informal discussions with people. On my way to and from the village I also interviewed several Papua New Guinean NGO-workers in the national and provincial capitals. In my thesis I show that environmental conservation in the village is part of a larger attempt to protect local autonomy, culture and the environment, i.e. it is a ”localistic” movement. Locals supporting conservation, as well as those supporting logging, take actively part in national parliamentary as well as local level politics. In my thesis I have attempted to unpack the notion of ”local” by examining internal power relations of the community and describing various lines of thought and opinions that base on local cultural values. Along with this, commercial logging seems also to elicit the role of the state in two-fold way in East New Britain. On the one hand, the government seeks to use logging roads built by logging companies as the basis of its own national infrastructure, even though the company roads are often of manifestably poor quality and short-lived. On the other hand, problems caused by logging, such as land disputes, create a need among local communities for the state and its services. Central themes in my thesis are the local values invested in the environment, as well as the ways in which the locals produce their environment both conceptually as well as physically. As subsistence farmers the locals depend economically on the condition of their environment. However, the value of the environment goes beyond economical questions. For example, the environment holds proof of the history of the community. Conversely, also the state and companies attempt to conceptualize, modify and administer the environment. This is done through processes such as mapping and road building, both crucial political questions in East New Britain. Here the anthropological discussion about space and place, as well as political geography are central. The diverse ways of conceptualizing the environment, as well as logging, cause often disputes about the ownership of land areas. Because of this I discuss local ways of holding the land communally, as well as PNG's land legislation and ways of dispute management. Land tenure and disputes are political questions that the locals have to deal with and in some cases these questions also create a need for the judiciary system of the state. The disputes affect also political activity, which I discuss at some length in my thesis as well. Interestingly, the locals, regardless of their political views and affiliations, establish transnational connections ranging from NGOs to government departments and multinational companies.

Developing Peer-To-Peer Web Applications

As the virtual world grows more complex, finding a standard way for storing data becomes increasingly important. Ideally, each data item would be brought into the computer system only once. References for data items need to be cryptographically verifiable, so the data can maintain its identity while being passed around. This way there will be only one copy of the users family photo album, while the user can use multiple tools to show or manipulate the album. Copies of users data could be stored on some of his family members computer, some of his computers, but also at some online services which he uses. When all actors operate over one replicated copy of the data, the system automatically avoids a single point of failure. Thus the data will not disappear with one computer breaking, or one service provider going out of business. One shared copy also makes it possible to delete a piece of data from all systems at once, on users request. In our research we tried to find a model that would make data manageable to users, and make it possible to have the same data stored at various locations. We studied three systems, Persona, Freenet, and GNUnet, that suggest different models for protecting user data. The main application areas of the systems studied include securing online social networks, providing anonymous web, and preventing censorship in file-sharing. Each of the systems studied store user data on machines belonging to third parties. The systems differ in measures they take to protect their users from data loss, forged information, censorship, and being monitored. All of the systems use cryptography to secure names used for the content, and to protect the data from outsiders. Based on the gained knowledge, we built a prototype platform called Peerscape, which stores user data in a synchronized, protected database. Data items themselves are protected with cryptography against forgery, but not encrypted as the focus has been disseminating the data directly among family and friends instead of letting third parties store the information. We turned the synchronizing database into peer-to-peer web by revealing its contents through an integrated http server. The REST-like http API supports development of applications in javascript. To evaluate the platform’s suitability for application development we wrote some simple applications, including a public chat room, bittorrent site, and a flower growing game. During our early tests we came to the conclusion that using the platform for simple applications works well. As web standards develop further, writing applications for the platform should become easier. Any system this complex will have its problems, and we are not expecting our platform to replace the existing web, but are fairly impressed with the results and consider our work important from the perspective of managing user data.

Trishanku, a novel regulator of cell-type stability and morphogenesis in Dictyostelium discoideum

We have identified a novel gene, trishanku (triA), by random insertional mutagenesis of Dictyostelium discoideum. TriA is a Broad complex Tramtrack bric-a-brac domain-containing protein that is expressed strongly during the late G2 phase of cell cycle and in presumptive spore (prespore (psp)) cells. Disrupting triA destabilizes cell fate and reduces aggregate size; the fruiting body has a thick stalk, a lowered spore: stalk ratio, a sub-terminal spore mass and small, rounded spores. These changes revert when the wild-type triA gene is re-expressed under a constitutive or a psp-specific promoter. By using short- and long-lived reporter proteins, we show that in triA(-) slugs the prestalk (pst)/psp proportion is normal, but that there is inappropriate transdifferentiation between the two cell types. During culmination, regardless of their current fate, all cells with a history of pst gene expression contribute to the stalk, which could account for the altered cell-type proportion in the mutant.

Characterization of human symptomatic rotavirus isolates MP409 and MP480 having ‘long’ RNA electropherotype and subgroup I specificity, highly related to the P6[1],G8 type bovine rotavirus A5, from Mysore, India

In an epidemiological study of symptomatic human rotaviruses in Mysore, India during 1993 and 1994, isolates MP409 and MP480 were isolated from two children suffering from severe, acute dehydrating diarrhea. Both isolates exhibited 'long' RNA pattern and subgroup I specificity suggesting the likelihood of their animal origin. Both isolates did not react with monoclonal antibodies (MAbs) specific for serotypes G1 to G6 as well as CIO. To determine the genetic origin of these isolates, complete nucleotide sequences of genes encoding the outer capsid proteins VP4 and VP7, nonstructural proteins NSP1 and NSP3 and viral enterotoxin protein NSP4 from MP409 and partial sequences of genes from MP480 were determined. Comparison of the 5' and 3' terminal sequences of 250 nucleotides revealed complete identity of the gene sequences in both strains suggesting that MP409 and MP480 are two different isolates of a single strain. Comparison of the nucleotide and deduced amino acid sequences of VP4, VP7, NSP1 and NSP3 of MP409 with published sequences of strains belonging to different serotypes revealed that both outer capsid proteins VP4 and VP7 and NSP1 are highly related to the respective proteins from the P6[1], G8 type bovine rotavirus A5 isolated from a calf with diarrhoea in Thailand and that the NSP3 is highly homologous to that of bovine rotaviruses. The NSP 1 protein showed greatest sequence identity with NSP4s belonging to the KUN genetic group to which NSP4s from human G2 type strains and bovine rotaviruses belong. MP409 and MP480 likely signify interspecies transmission of P6[1], G8 type strains from cattle to humans and represent the first P6[1] type rotaviruses isolated in humans. These and our previous studies on the asymptomatic neonatal strain I321 are of evolutionary and epidemiological significance in the context of close association of majority of the Indian population with cattle.

Association between molecular variation in the phosphoglucose isomerase (Pgi) locus and migration propensity in the Glanville fritillary butterfly

Habitat fragmentation produces patches of suitable habitat surrounded by unfavourable matrix habitat. A species may persist in such a fragmented landscape in an equilibrium between the extinctions and recolonizations of local populations, thus forming a metapopulation. Migration between local populations is necessary for the long-term persistence of a metapopulation. The Glanville fritillary butterfly (Melitaea cinxia) forms a metapopulation in the Åland islands in Finland. There is migration between the populations, the extent of which is affected by several environmental factors and variation in the phenotype of individual butterflies. Different allelic forms of the glycolytic enzyme phosphoglucose isomerase (Pgi) has been identified as a possible genetic factor influencing flight performance and migration rate in this species. The frequency of a certain Pgi allele, Pgi-f, follows the same pattern in relation to population age and connectivity as migration propensity. Furthermore, variation in flight metabolic performance, which is likely to affect migration propensity, has been linked to genetic variation in Pgi or a closely linked locus. The aim of this study was to investigate the association between Pgi genotype and the migration propensity in the Glanville fritillary both at the individual and population levels using a statistical modelling approach. A mark-release-recapture (MRR) study was conducted in a habitat patch network of M. cinxia in Åland to collect data on the movements of individual butterflies. Larval samples from the study area were also collected for population level examinations. Each butterfly and larva was genotyped at the Pgi locus. The MRR data was parameterised with two mathematical models of migration: the Virtual Migration Model (VM) and the spatially explicit diffusion model. VM model predicted and observed numbers of emigrants from populations with high and low frequencies of Pgi-f were compared. Posterior predictive data sets were simulated based on the parameters of the diffusion model. Lack-of-fit of observed values to the model predicted values of several descriptors of movements were detected, and the effect of Pgi genotype on the deviations was assessed by randomizations including the genotype information. This study revealed a possible difference in the effect of Pgi genotype on migration propensity between the two sexes in the Glanville fritillary. The females with and males without the Pgi-f allele moved more between habitat patches, which is probably related to differences in the function of flight in the two sexes. Females may use their high flight capacity to migrate between habitat patches to find suitable oviposition sites, whereas males may use it to acquire mates by keeping a territory and fighting off other intruding males, possibly causing them to emigrate. The results were consistent across different movement descriptors and at the individual and population levels. The effect of Pgi is likely to be dependent on the structure of the landscape and the prevailing environmental conditions.

QCD with dynamical Wilson fermions. II

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

Structural features of B-DNA dodecamer crystal structures: Influence of crystal packing versus base sequence

We have analyzed the set of inter and intra base pair parameters for each dinucleotide step in single crystal structures of dodecamers, solved at high and medium resolution and all crystallized in P2(1)2(1)2(1) space group. The objective was to identify whether all the structures which have either the Drew-Dickerson (DD) sequence d[CGCGAATTCGCG] with some base modification or related sequence (non-DD), would display the same sequence dependent structural variability about its palindromic sequence, despite the molecule being bent at one end because of similar crystal lattice packing effect. Most of the local doublet parameters for base pairs steps G2-C3 and G10-C11 positions, symmetrically situated about the lateral twofold, were significantly correlated between themselves. In non-DD sequences, significant correlations between these positional parameters were absent. The different range of local step parameter values at each sequence position contributed to the gross feature of smooth helix axis bending in all structures. The base pair parameters in some of the positions, for medium resolution DD sequence, were quite unlike the high-resolution set and encompassed a higher range of values. Twist and slide are the two main parameters that show wider conformational range for the middle region of non-DD sequence structures in comparison to DD sequence structures. On the contrary, the minor and major groove features bear good resemblance between DD and non-DD sequence crystal structure datasets. The sugar-phosphate backbone torsion angles are similar in all structures, in sharp contrast to base pair parameter variation for high and low resolution DD and non-DD sequence structures, consisting of unusual (epsilon =g(-), xi =t) B-II conformation at the 10(th) position of the dodecamer sequence. Thus examining DD and non-DD sequence structures packed in the same crystal lattice arrangement, we infer that inter and intra base pair parameters are as symmetrically equivalent in its value as the symmetry related step for the palindromic DD sequence about lateral two-fold axis. This feature would lead us to agree with the conclusion that DNA conformation is not substantially affected by end-to-end or lateral inter-molecular interaction due to crystal lattice packing effect. Non-DD sequence structures acquire step parameter values which reflect the altered sequence at each of the dodecamer sequence position in the orthorhombic lattice while showing similar gross features of DD sequence structures

1H NMR Study of Molecular Motions and Phase Transitions in Methyl Ammonium Hexabromo Selenate [(CH3NH3)2SeBr6]

The temperature dependence of 1H spin-lattice relaxation time, T1, and that of the second moment, M2, are analysed in the temperature range 390 K to 77 K. A plot of T1 vs inverse temperature shows three phase transitions at 250 K, 167 K and 111 K. At 167 K, T1 displays a large jump while it shows changes in slope at 250 K and 111 K. In the high temperature phase (> 167 K), the correlated motion of CH3 and NH3 groups is found to cause the relaxation while their uncorrelated motion takes over in the low temperature phases (< 167 K). The unusual T1 behaviour in phase II (250 K-167 K) is ascribed to the small angle torsion of the cation. A constant M2 value of ∼ 9.7 G2, throughout the range of temperature studied, indicates the presence of reorientation of CH3 and NH3 groups.

Perturbative corrections for staggered four-fermion operators

We present results for one-loop matching coefficients between continuum four-fermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark fines, and ''penguin'' diagrams containing quark loops. For the former we use Landau-gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KKBAR mixing and K --> pipi decays with all corrections of O(g2) included. We also discuss the mixing of DELTAS = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.

Diperoxovanadate can substitute for H(2)O(2) at much lower concentration in inducing features of premature cellular senescence in mouse fibroblasts (NIH3T3)

Stress induced premature senescence (SIPS) in mammalian cells is an accelerated ageing response and experimentally obtained on treatment of cells with high concentrations of H(2)O(2), albeit at sub-lethal doses, because H(2)O(2) gets depleted by abundant cellular catalase. In the present study diperoxovanadate (DPV) was used as it is known to be stable at physiological pH, to be catalase-resistant and to substitute for H(2)O(2) in its activities at concentrations order of magnitudes lower. On treating NIH3T3 cells with DPV, SIPS-like morphology was observed along with an immediate response of rounding of the cells by disruption of actin cytoskeleton and transient G2/M arrest. DPV could bring about growth arrest and senescence associated features at 25 mu M dose, which were not seen with similar doses of either H(2)O(2) or vanadate. A minimal dose of 150 mu M of H(2)O(2) was required to induce similar affects as 25 mu M DPV. Increase in senescent associated markers such as p21, HMGA2 and PAI-1 was more prominent in DPV treated cells compared to similar dose of H(2)O(2). DPV-treated cells showed marked relocalization of Cyclin D1 from nucleus to cytoplasm. These results indicate that DPV, stable inorganic peroxide, is more efficient in inducing SIPS at lower concentrations compared to H(2)O(2). (C) 2011 Elsevier Ireland Ltd. All rights reserved.