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

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

Topological stability through tame retractions

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

Other Side of This Life : Death, Value, and Social Being in Thomas Pynchon's Fiction

This dissertation analyzes the interrelationship between death, the conditions of (wo)man s social being, and the notion of value as it emerges in the fiction of the American novelist Thomas Pynchon (1937 ). Pynchon s present work includes six novels V. (1963), The Crying of Lot 49 (1966), Gravity s Rainbow (1973), Vineland (1990), Mason & Dixon (1997), Against the Day (2006) and several short stories. Death constitues a central thematic in Pynchon s work, and it emerges through recurrent questions of mortality, suicide, mass destruction, sacrifice, afterlife, entropy, the relationship between the animate and the inanimate, and the limits of representation. In Pynchon, death is never a mere biological given (or event); it is always determined within a certain historical, cultural, and ideological context. Throughout his work, Pynchon questions the strict ontological separation of life and death by showing the relationship between this separation and social power. Conceptual divisions also reflect the relationship between society and its others, and death becomes that through which lines of social demarcation are articulated. Determined as a conceptual and social "other side", death in Pynchon forms a challenge to modern culture, and makes an unexpected return: the dead return to haunt the living, the inanimate and the animate fuse, and technoscientific attempts at overcoming and controlling death result in its re-emergence in mass destruction and ecological damage. The questioning of the ontological line also affects the structuration of Pynchon's prose, where the recurrent narrated and narrative desire to reach the limits of representation is openly associated with death. Textualized, death appears in Pynchon's writing as a sudden rupture within the textual functioning, when the "other side", that is, the bare materiality of the signifier is foregrounded. In this study, Pynchon s cultural criticism and his poetics come together, and I analyze the subversive role of death in his fiction through Jean Baudrillard s genealogy of the modern notion of death from L échange symbolique et la mort (1976). Baudrillard sees an intrinsic bond between the social repression of death in modernity and the emergence of modern political economy, and in his analysis economy and language appear as parallel systems for generating value (exchange value/ sign-value). For Baudrillard, the modern notion of death as negativity in relation to the positivity of life, and the fact that death cannot be given a proper meaning, betray an antagonistic relation between death and the notion of value. As a mode of negativity (that is, non-value), death becomes a moment of rupture in relation to value-based thinking in short, rationalism. Through this rupture emerges a form of thinking Baudrillard labels the symbolic, characterized by ambivalence and the subversion of conceptual opposites.

Le naturalisme finlandais : Une conception entropique du quotidien

Le naturalisme finlandais. Une conception entropique du quotidien. Finnish Naturalism. An Entropic Conception of Everyday Life. Nineteenth century naturalism was a strikingly international literary movement. After emerging in France in the 1870s, it spread all over Europe including young, small nations with a relatively recent literary tradition, such as Finland. This thesis surveys the role and influence of French naturalism on the Finnish literature of the 1880s and 1890s. On the basis of a selection of works of six Finnish authors (Juhani Aho, Minna Canth, Kauppis-Heikki, Teuvo Pakkala, Ina Lange and Karl August Tavaststjerna), the study establishes a view of the main features of Finnish naturalism in comparison with that of French authors, such as Zola, Maupassant and Flaubert. The study s methodological framework is genre theory: even though naturalist writers insisted on a transparent description of reality, naturalist texts are firmly rooted in general generic categories with definable relations and constants on which European novels impose variations. By means of two key concepts, entropy and everyday life , this thesis establishes the parameters of the naturalist genre. At the heart of the naturalist novel is a movement in the direction of disintegration and confusion, from order to disorder, from illusion to disillusion. This entropic vision is merged into the representation of everyday life, focusing on socially mediocre characters and discovering their miseries in all their banality and daily grayness. By using Mikhail Bakhtin s idea of literary genres as a means of understanding experience, this thesis suggests that everyday life is an ideological core of naturalist literature that determines not only its thematic but also generic distinctions: with relation to other genres, such as to Balzac s realism, naturalism appears primarily to be a banalization of everyday life. In idyllic genres, everyday life can be represented by means of sublimation, but a naturalist novel establishes a distressing, negative everyday life and thus strives to take a critical view of the modern society. Beside the central themes, the study surveys the generic blends in naturalism. The thesis analyzes how the coalition of naturalism and the melodramatic mode in the work of Minna Canth serves naturalisms ambition to discover the unconscious instincts underlying daily realities, and how the symbolic mode in the work of Juhani Aho duplicates the semantic level of the apparently insignificant, everyday naturalist details. The study compares the naturalist novel to the ideological novel (roman à these) and surveys the central dilemma of naturalism, the confrontation between the optimistic belief in social reform and the pessimistic theory of determinism. The thesis proposes that the naturalist novel s contribution to social reform lies in its shock effect. By means of representing the unpleasant truth the entropy of everyday life it aims to scandalize the reader and make him aware of the harsh realities that might apply also to him.

Liikkumisen ja kokemusten yhteys virtuaaliympäristöissä

The aim of this study was to build a model and analyze how users move in a virtual environment and to explore the experiential dimensions connected with different ways of moving. Due to the lack of previous research on this subject, this was an explorative study. This study also aimed to identify different ways how users move in virtual environments and the background variables connected to them. It was hypothesized that fluent movement in virtual environments is connected to high presence, skill and challenge assessments. Test participants (n = 68) were mostly highly educated young adults. A virtual environment was built using a CAVE -type virtual reality interface. The task was to search for objects that do not belong into a normal house. The participants movement in the virtual house was recorded on a computer. Movement was modelled using a cluster analysis of information entropy based movement measurements, acceleration, amount of stops and time spent being stationary. The experiential dimensions were measured using the EVEQ -questionnaire. We were able to identify four different ways of moving in virtual environments. In respect of background variables, the four groups differed only in the amount of weekly computer usage. However, fluent movement in virtual environments was connected to a high sense of presence. Furthermore, participants who moved fluently in the environment assessed their skills as being high and regarded the use of virtual environment as challenging. The results indicate that different ways of moving affects how people experience virtual environments. Consequently the participants assessment of their skills and level of challenge have an impact on the affective evaluation of the situation at hand. Entropy measures have not been previously applied when studying movement, and in addition the role of movement on the experiential dimensions of virtual environments is an unexplored subject. The movement analysis method introduced here is applicable to other research problems. Finally, this study expands on our knowledge of the special characteristics connected with the experiential dimensions of virtual environments.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

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

Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

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

Structure, function and intracellular dynamics of alphavirus replication complexes

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.

Studies on the assessment of the adequacy of anesthesia

Several hypnosis monitoring systems based on the processed electroencephalogram (EEG) have been developed for use during general anesthesia. The assessment of the analgesic component (antinociception) of general anesthesia is an emerging field of research. This study investigated the interaction of hypnosis and antinociception, the association of several physiological variables with the degree of intraoperative nociception, and aspects of EEG Bispectral Index Scale (BIS) monitoring during general anesthesia. In addition, EEG features and heart rate (HR) responses during desflurane and sevoflurane anesthesia were compared. A propofol bolus of 0.7 mg/kg was more effective than an alfentanil bolus of 0.5 mg in preventing the recurrence of movement responses during uterine dilatation and curettage (D C) after a propofol-alfentanil induction, combined with nitrous oxide (N2O). HR and several HR variability-, frontal electromyography (fEMG)-, pulse plethysmography (PPG)-, and EEG-derived variables were associated with surgery-induced movement responses. Movers were discriminated from non-movers mostly by the post-stimulus values per se or normalized with respect to the pre-stimulus values. In logistic regression analysis, the best classification performance was achieved with the combination of normalized fEMG power and HR during D C (overall accuracy 81%, sensitivity 53%, specificity 95%), and with the combination of normalized fEMG-related response entropy, electrocardiography (ECG) R-to-R interval (RRI), and PPG dicrotic notch amplitude during sevoflurane anesthesia (overall accuracy 96%, sensitivity 90%, specificity 100%). ECG electrode impedances after alcohol swab skin pretreatment alone were higher than impedances of designated EEG electrodes. The BIS values registered with ECG electrodes were higher than those registered simultaneously with EEG electrodes. No significant difference in the time to home-readiness after isoflurane-N2O or sevoflurane-N2O anesthesia was found, when the administration of the volatile agent was guided by BIS monitoring. All other early and intermediate recovery parameters were also similar. Transient epileptiform EEG activity was detected in eight of 15 sevoflurane patients during a rapid increase in the inspired volatile concentration, and in none of the 16 desflurane patients. The observed transient EEG changes did not adversely affect the recovery of the patients. Following the rapid increase in the inhaled desflurane concentration, HR increased transiently, reaching its maximum in two minutes. In the sevoflurane group, the increase was slower and more subtle. In conclusion, desflurane may be a safer volatile agent than sevoflurane in patients with a lowered seizure threshold. The tachycardia induced by a rapid increase in the inspired desflurane concentration may present a risk for patients with heart disease. Designated EEG electrodes may be superior to ECG electrodes in EEG BIS monitoring. When the administration of isoflurane or sevoflurane is adjusted to maintain BIS values at 50-60 in healthy ambulatory surgery patients, the speed and quality of recovery are similar after both isoflurane-N2O and sevoflurane-N2O anesthesia. When anesthesia is maintained by the inhalation of N2O and bolus doses of propofol and alfentanil in healthy unparalyzed patients, movement responses may be best avoided by ensuring a relatively deep hypnotic level with propofol. HR/RRI, fEMG, and PPG dicrotic notch amplitude are potential indicators of nociception during anesthesia, but their performance needs to be validated in future studies. Combining information from different sources may improve the discrimination of the level of nociception.

Measurements of adequacy of anesthesia and level of consciousness during surgery and intensive care

The adequacy of anesthesia has been studied since the introduction of balanced general anesthesia. Commercial monitors based on electroencephalographic (EEG) signal analysis have been available for monitoring the hypnotic component of anesthesia from the beginning of the 1990s. Monitors measuring the depth of anesthesia assess the cortical function of the brain, and have gained acceptance during surgical anesthesia with most of the anesthetic agents used. However, due to frequent artifacts, they are considered unsuitable for monitoring consciousness in intensive care patients. The assessment of analgesia is one of the cornerstones of general anesthesia. Prolonged surgical stress may lead to increased morbidity and delayed postoperative recovery. However, no validated monitoring method is currently available for evaluating analgesia during general anesthesia. Awareness during anesthesia is caused by an inadequate level of hypnosis. This rare but severe complication of general anesthesia may lead to marked emotional stress and possibly posttraumatic stress disorder. In the present series of studies, the incidence of awareness and recall during outpatient anesthesia was evaluated and compared with that of in inpatient anesthesia. A total of 1500 outpatients and 2343 inpatients underwent a structured interview. Clear intraoperative recollections were rare the incidence being 0.07% in outpatients and 0.13% in inpatients. No significant differences emerged between outpatients and inpatients. However, significantly smaller doses of sevoflurane were administered to outpatients with awareness than those without recollections (p<0.05). EEG artifacts in 16 brain-dead organ donors were evaluated during organ harvest surgery in a prospective, open, nonselective study. The source of the frontotemporal biosignals in brain-dead subjects was studied, and the resistance of bispectral index (BIS) and Entropy to the signal artifacts was compared. The hypothesis was that in brain-dead subjects, most of the biosignals recorded from the forehead would consist of artifacts. The original EEG was recorded and State Entropy (SE), Response Entropy (RE), and BIS were calculated and monitored during solid organ harvest. SE differed from zero (inactive EEG) in 28%, RE in 29%, and BIS in 68% of the total recording time (p<0.0001 for all). The median values during the operation were SE 0.0, RE 0.0, and BIS 3.0. In four of the 16 organ donors, EEG was not inactive, and unphysiologically distributed, nonreactive rhythmic theta activity was present in the original EEG signal. After the results from subjects with persistent residual EEG activity were excluded, SE, RE, and BIS differed from zero in 17%, 18%, and 62% of the recorded time, respectively (p<0.0001 for all). Due to various artifacts, the highest readings in all indices were recorded without neuromuscular blockade. The main sources of artifacts were electrocauterization, electromyography (EMG), 50-Hz artifact, handling of the donor, ballistocardiography, and electrocardiography. In a prospective, randomized study of 26 patients, the ability of Surgical Stress Index (SSI) to differentiate patients with two clinically different analgesic levels during shoulder surgery was evaluated. SSI values were lower in patients with an interscalene brachial plexus block than in patients without an additional plexus block. In all patients, anesthesia was maintained with desflurane, the concentration of which was targeted to maintain SE at 50. Increased blood pressure or heart rate (HR), movement, and coughing were considered signs of intraoperative nociception and treated with alfentanil. Photoplethysmographic waveforms were collected from the contralateral arm to the operated side, and SSI was calculated offline. Two minutes after skin incision, SSI was not increased in the brachial plexus block group and was lower (38 ± 13) than in the control group (58 ± 13, p<0.005). Among the controls, one minute prior to alfentanil administration, SSI value was higher than during periods of adequate antinociception, 59 ± 11 vs. 39 ± 12 (p<0.01). The total cumulative need for alfentanil was higher in controls (2.7 ± 1.2 mg) than in the brachial plexus block group (1.6 ± 0.5 mg, p=0.008). Tetanic stimulation to the ulnar region of the hand increased SSI significantly only among patients with a brachial plexus block not covering the site of stimulation. Prognostic value of EEG-derived indices was evaluated and compared with Transcranial Doppler Ultrasonography (TCD), serum neuron-specific enolase (NSE) and S-100B after cardiac arrest. Thirty patients resuscitated from out-of-hospital arrest and treated with induced mild hypothermia for 24 h were included. Original EEG signal was recorded, and burst suppression ratio (BSR), RE, SE, and wavelet subband entropy (WSE) were calculated. Neurological outcome during the six-month period after arrest was assessed with the Glasgow-Pittsburgh Cerebral Performance Categories (CPC). Twenty patients had a CPC of 1-2, one patient had a CPC of 3, and nine patients died (CPC 5). BSR, RE, and SE differed between good (CPC 1-2) and poor (CPC 3-5) outcome groups (p=0.011, p=0.011, p=0.008, respectively) during the first 24 h after arrest. WSE was borderline higher in the good outcome group between 24 and 48 h after arrest (p=0.050). All patients with status epilepticus died, and their WSE values were lower (p=0.022). S-100B was lower in the good outcome group upon arrival at the intensive care unit (p=0.010). After hypothermia treatment, NSE and S-100B values were lower (p=0.002 for both) in the good outcome group. The pulsatile index was also lower in the good outcome group (p=0.004). In conclusion, the incidence of awareness in outpatient anesthesia did not differ from that in inpatient anesthesia. Outpatients are not at increased risk for intraoperative awareness relative to inpatients undergoing general anesthesia. SE, RE, and BIS showed non-zero values that normally indicate cortical neuronal function, but were in these subjects mostly due to artifacts after clinical brain death diagnosis. Entropy was more resistant to artifacts than BIS. During general anesthesia and surgery, SSI values were lower in patients with interscalene brachial plexus block covering the sites of nociceptive stimuli. In detecting nociceptive stimuli, SSI performed better than HR, blood pressure, or RE. BSR, RE, and SE differed between the good and poor neurological outcome groups during the first 24 h after cardiac arrest, and they may be an aid in differentiating patients with good neurological outcomes from those with poor outcomes after out-of-hospital cardiac arrest.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

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

Search for single top quark production in pp̅ collisions at √s=1.96 TeV in the missing transverse energy plus jets topology

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.

Measurement of the Ratio σtt̅ /σZ/γ*→ll and Precise Extraction of the tt̅ Cross Section

We report a measurement of the ratio of the tt̅ to Z/γ* production cross sections in √s=1.96  TeV pp̅ collisions using data corresponding to an integrated luminosity of up to 4.6  fb-1, collected by the CDF II detector. The tt̅ cross section ratio is measured using two complementary methods, a b-jet tagging measurement and a topological approach. By multiplying the ratios by the well-known theoretical Z/γ*→ll cross section predicted by the standard model, the extracted tt̅ cross sections are effectively insensitive to the uncertainty on luminosity. A best linear unbiased estimate is used to combine both measurements with the result σtt̅ =7.70±0.52  pb, for a top-quark mass of 172.5  GeV/c2.

Measurement of the Ratio σtt̅ /σZ/γ*→ll and Precise Extraction of the tt̅ Cross Section

We report a measurement of the ratio of the tt̅ to Z/γ* production cross sections in √s=1.96  TeV pp̅ collisions using data corresponding to an integrated luminosity of up to 4.6  fb-1, collected by the CDF II detector. The tt̅ cross section ratio is measured using two complementary methods, a b-jet tagging measurement and a topological approach. By multiplying the ratios by the well-known theoretical Z/γ*→ll cross section predicted by the standard model, the extracted tt̅ cross sections are effectively insensitive to the uncertainty on luminosity. A best linear unbiased estimate is used to combine both measurements with the result σtt̅ =7.70±0.52  pb, for a top-quark mass of 172.5  GeV/c2.

Measurement of the Ratio σtt̅ /σZ/γ*→ll and Precise Extraction of the tt̅ Cross Section

We report a measurement of the ratio of the top-antitop to Z/gamma* production cross sections in sqrt(s) = 1.96 TeV proton-antiproton collisions using data corresponding to an integrated luminosity of up to 4.6 fb-1, collected by the CDF II detector. The top-antitop cross section ratio is measured using two complementary methods, a b-jet tagging measurement and a topological approach. By multiplying the ratios by the well-known theoretical Z/gamma*->ll cross section, the extracted top-antitop cross sections are effectively insensitive to the uncertainty on luminosity. A best linear unbiased estimate is used to combine both measurements with the result sigma_(top-antitop) = 7.70 +/- 0.52 pb, for a top-quark mass of 172.5 GeV/c^2.