21 resultados para Topological signatures
em Helda - Digital Repository of University of Helsinki
Resumo:
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.
Resumo:
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.
Resumo:
The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.
Resumo:
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.
Resumo:
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
Resumo:
Intracellular membrane alterations are hallmarks of positive-sense RNA (+RNA) virus replication. Strong evidence indicates that within these exotic compartments, viral replicase proteins engage in RNA genome replication and transcription. To date, fundamental questions such as the origin of altered membranes, mechanisms of membrane deformation and topological distribution and function of viral components, are still waiting for comprehensive answers. This study addressed some of the above mentioned questions for the membrane alterations induced during Semliki Forest virus (SFV) infection of mammalian cells. With the aid of electron and fluorescence microscopy coupled with radioactive labelling and immuno-cytochemistry techniques, our group and others showed that few hours after infection the four non structural proteins (nsP1-4) and newly synthesized RNAs of SFV colocalized in close proximity of small membrane invaginations, designated as spherules . These 50-70 nm structures were mainly detected in the perinuclear area, at the limiting membrane of modified endosomes and lysosomes, named CPV-I (cytopathic vacuoles type I). More rarely, spherules were also found at the plasma membrane (PM). In the first part of this study I present the first three-dimensional reconstruction of the CPV-I and the spherules, obtained by electron tomography after chemical or cryo-fixation. Different approaches for imaging these macromolecular assemblies to obtain better structure preservation and higher resolution are presented as unpublished data. This study provides insights into spherule organization and distribution of viral components. The results of this and other experiments presented in this thesis will challenge currently accepted models for virus replication complex formation and function. In a revisitation of our previous models, the second part of this work provides the first complete description of the biogenesis of the CPV-I. The results demonstrate that these virus-induced vacuoles, where hundreds of spherules accumulate at late stages during infection, represent the final phase of a journey initiated at the PM, which apparently serves as a platform for spherule formation. From the PM spherules were internalized by an endocytic event that required the activity of the class I PI3K, caveolin-1, cellular cholesterol and functional actin-myosin network. The resulting neutral endocytic carrier vesicle delivered the spherules to the membrane of pre-existing acidic endosomes via multiple fusion events. Microtubule based transport supported the vectorial transfer of these intermediates to the pericentriolar area where further fusions generated the CPV-I. A signal for spherule internalization was identified in one of the replicase proteins, nsP3. Infections of cells with viruses harbouring a deletion in a highly phosphorylated region of nsP3 did not result in the formation of CPV-Is. Instead, thousands of spherules remained at the PM throughout the infection cycle. Finally, the role of the replicase protein nsP2 during viral RNA replication and transcription was investigated. Three enzymatic activities, protease, NTPase and RNA-triphosphatase were studied with the aid of temperature sensitive mutants in vitro and, when possible, in vivo. The results highlighted the interplay of the different nsP2 functions during different steps of RNA replication and sub-genomic promoter regulation, and suggest that the protein could have different activities when participating in the replication complex or as a free enzyme.
Resumo:
This study addressed the large-scale molecular zoogeography in two brackish water bivalve molluscs, Macoma balthica and Cerastoderma glaucum, and genetic signatures of the postglacial colonization of Northern Europe by them. The traditional view poses that M. balthica in the Baltic, White and Barents seas (i.e. marginal seas) represent direct postglacial descendants of the adjacent Northeast Atlantic populations, but this has recently been challenged by observations of close genetic affinities between these marginal populations and those of the Northeast Pacific. The primary aim of the thesis was to verify, quantify and characterize the Pacific genetic contribution across North European populations of M. balthica and to resolve the phylogeographic histories of the two bivalve taxa in range-wide studies using information from mitochondrial DNA (mtDNA) and nuclear allozyme polymorphisms. The presence of recent Pacific genetic influence in M. balthica of the Baltic, White and Barents seas, along with an Atlantic element, was confirmed by mtDNA sequence data. On a broader temporal and geographical scale, altogether four independent trans-Arctic invasions of Macoma from the Pacific since the Miocene seem to have been involved in generating the current North Atlantic lineage diversity. The latest trans-Arctic invasion that affected the current Baltic, White and Barents Sea populations probably took place in the early post-glacial. The nuclear genetic compositions of these marginal sea populations are intermediate between those of pure Pacific and Atlantic subspecies. In the marginal sea populations of mixed ancestry (Barents, White and Northern Baltic seas), the Pacific and Atlantic components are now randomly associated in the genomes of individual clams, which indicates both pervasive historical interbreeding between the previously long-isolated lineages (subspecies), and current isolation of these populations from the adjacent pure Atlantic populations. These mixed populations can be characterized as self-supporting hybrid swarms, and they arguably represent the most extensive marine animal hybrid swarms so far documented. Each of the three swarms still has a distinct genetic composition, and the relative Pacific contributions vary from 30 to 90 % in local populations. This diversity highlights the potential of introgressive hybridization to rapidly give rise to new evolutionarily and ecologically significant units in the marine realm. In the south of the Danish straits and in the Southern Baltic Sea, a broad genetic transition zone links the pure North Sea subspecies M. balthica rubra to the inner Baltic hybrid swarm, which has about 60 % of Pacific contribution in its genome. This transition zone has no regular smooth clinal structure, but its populations show strong genotypic disequilibria typical of a hybrid zone maintained by the interplay of selection and gene flow by dispersing pelagic larvae. The structure of the genetic transition is partly in line with features of Baltic water circulation and salinity stratification, with greater penetration of Atlantic genes on the Baltic south coast and in deeper water populations. In all, the scenarios of historical isolation and secondary contact that arise from the phylogeographic studies of both Macoma and Cerastoderma shed light to the more general but enigmatic patterns seen in marine phylogeography, where deep genetic breaks are often seen in species with high dispersal potential.
Resumo:
In this thesis, the solar wind-magnetosphere-ionosphere coupling is studied observationally, with the main focus on the ionospheric currents in the auroral region. The thesis consists of five research articles and an introductory part that summarises the most important results reached in the articles and places them in a wider context within the field of space physics. Ionospheric measurements are provided by the International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer network, by the low-orbit CHAllenging Minisatellite Payload (CHAMP) satellite, by the European Incoherent SCATter (EISCAT) radar, and by the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite. Magnetospheric observations, on the other hand, are acquired from the four spacecraft of the Cluster mission, and solar wind observations from the Advanced Composition Explorer (ACE) and Wind spacecraft. Within the framework of this study, a new method for determining the ionospheric currents from low-orbit satellite-based magnetic field data is developed. In contrast to previous techniques, all three current density components can be determined on a matching spatial scale, and the validity of the necessary one-dimensionality approximation, and thus, the quality of the results, can be estimated directly from the data. The new method is applied to derive an empirical model for estimating the Hall-to-Pedersen conductance ratio from ground-based magnetic field data, and to investigate the statistical dependence of the large-scale ionospheric currents on solar wind and geomagnetic parameters. Equations describing the amount of field-aligned current in the auroral region, as well as the location of the auroral electrojets, as a function of these parameters are derived. Moreover, the mesoscale (10-1000 km) ionospheric equivalent currents related to two magnetotail plasma sheet phenomena, bursty bulk flows and flux ropes, are studied. Based on the analysis of 22 events, the typical equivalent current pattern related to bursty bulk flows is established. For the flux ropes, on the other hand, only two conjugate events are found. As the equivalent current patterns during these two events are not similar, it is suggested that the ionospheric signatures of a flux rope depend on the orientation and the length of the structure, but analysis of additional events is required to determine the possible ionospheric connection of flux ropes.
Resumo:
The superconducting (or cryogenic) gravimeter (SG) is based on the levitation of a superconducting sphere in a stable magnetic field created by current in superconducting coils. Depending on frequency, it is capable of detecting gravity variations as small as 10-11ms-2. For a single event, the detection threshold is higher, conservatively about 10-9 ms-2. Due to its high sensitivity and low drift rate, the SG is eminently suitable for the study of geodynamical phenomena through their gravity signatures. I present investigations of Earth dynamics with the superconducting gravimeter GWR T020 at Metsähovi from 1994 to 2005. The history and key technical details of the installation are given. The data processing methods and the development of the local tidal model at Metsähovi are presented. The T020 is a part of the worldwide GGP (Global Geodynamics Project) network, which consist of 20 working station. The data of the T020 and of other participating SGs are available to the scientific community. The SG T020 have used as a long-period seismometer to study microseismicity and the Earth s free oscillation. The annual variation, spectral distribution, amplitude and the sources of microseism at Metsähovi were presented. Free oscillations excited by three large earthquakes were analyzed: the spectra, attenuation and rotational splitting of the modes. The lowest modes of all different oscillation types are studied, i.e. the radial mode 0S0, the "football mode" 0S2, and the toroidal mode 0T2. The very low level (0.01 nms-1) incessant excitation of the Earth s free oscillation was detected with the T020. The recovery of global and regional variations in gravity with the SG requires the modelling of local gravity effects. The most important of them is hydrology. The variation in the groundwater level at Metsähovi as measured in a borehole in the fractured bedrock correlates significantly (0.79) with gravity. The influence of local precipitation, soil moisture and snow cover are detectable in the gravity record. The gravity effect of the variation in atmospheric mass and that of the non-tidal loading by the Baltic Sea were investigated together, as sea level and air pressure are correlated. Using Green s functions it was calculated that a 1 metre uniform layer of water in the Baltic Sea increases the gravity at Metsähovi by 31 nms-2 and the vertical deformation is -11 mm. The regression coefficient for sea level is 27 nms-2m-1, which is 87% of the uniform model. These studies are associated with temporal height variations using the GPS data of Metsähovi permanent station. Results of long time series at Metsähovi demonstrated high quality of data and correctly carried out offsets and drift corrections. The superconducting gravimeter T020 has been proved to be an eminent and versatile tool in studies of the Earth dynamics.
Resumo:
New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.
Resumo:
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.
Resumo:
Aneuploidy is among the most obvious differences between normal and cancer cells. However, mechanisms contributing to development and maintenance of aneuploid cell growth are diverse and incompletely understood. Functional genomics analyses have shown that aneuploidy in cancer cells is correlated with diffuse gene expression signatures and that aneuploidy can arise by a variety of mechanisms, including cytokinesis failures, DNA endoreplication and possibly through polyploid intermediate states. Here, we used a novel cell spot microarray technique to identify genes with a loss-of-function effect inducing polyploidy and/or allowing maintenance of polyploid cell growth of breast cancer cells. Integrative genomics profiling of candidate genes highlighted GINS2 as a potential oncogene frequently overexpressed in clinical breast cancers as well as in several other cancer types. Multivariate analysis indicated GINS2 to be an independent prognostic factor for breast cancer outcome (p = 0.001). Suppression of GINS2 expression effectively inhibited breast cancer cell growth and induced polyploidy. In addition, protein level detection of nuclear GINS2 accurately distinguished actively proliferating cancer cells suggesting potential use as an operational biomarker.
Resumo:
We report a search for single top quark production with the CDF II detector using 2.1 fb-1 of integrated luminosity of pbar p collisions at sqrt{s}=1.96 TeV. The data selected consist of events characterized by large energy imbalance in the transverse plane and hadronic jets, and no identified electrons and muons, so the sample is enriched in W -> tau nu decays. In order to suppress backgrounds, additional kinematic and topological requirements are imposed through a neural network, and at least one of the jets must be identified as a b-quark jet. We measure an excess of signal-like events in agreement with the standard model prediction, but inconsistent with a model without single top quark production by 2.1 standard deviations (sigma), with a median expected sensitivity of 1.4 sigma. Assuming a top quark mass of 175 GeV/c2 and ascribing the excess to single top quark production, the cross section is measured to be 4.9+2.5-2.2(stat+syst)pb, consistent with measurements performed in independent datasets and with the standard model prediction.