21 resultados para TOPOLOGICAL INDEXES

em Helda - Digital Repository of University of Helsinki


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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.

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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.

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A large fraction of an XML document typically consists of text data. The XPath query language allows text search via the equal, contains, and starts-with predicates. Such predicates can be efficiently implemented using a compressed self-index of the document's text nodes. Most queries, however, contain some parts querying the text of the document, plus some parts querying the tree structure. It is therefore a challenge to choose an appropriate evaluation order for a given query, which optimally leverages the execution speeds of the text and tree indexes. Here the SXSI system is introduced. It stores the tree structure of an XML document using a bit array of opening and closing brackets plus a sequence of labels, and stores the text nodes of the document using a global compressed self-index. On top of these indexes sits an XPath query engine that is based on tree automata. The engine uses fast counting queries of the text index in order to dynamically determine whether to evaluate top-down or bottom-up with respect to the tree structure. The resulting system has several advantages over existing systems: (1) on pure tree queries (without text search) such as the XPathMark queries, the SXSI system performs on par or better than the fastest known systems MonetDB and Qizx, (2) on queries that use text search, SXSI outperforms the existing systems by 1-3 orders of magnitude (depending on the size of the result set), and (3) with respect to memory consumption, SXSI outperforms all other systems for counting-only queries.

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Atherosclerosis is the main underlying pathology of coronary heart disease. Coronary heart disease is a serious health problem in Finland, and it is the leading cause of morbidity and mortality in industrialized countries. Psychological stress correlates with coronary heart disease events – myocardial infarction and sudden death, which are the most common clinical syndromes of atherosclerotic narrowing of arteries. The present series of studies examines the interaction between stress and endothelial function in relation to atherosclerosis. The study also aims to give new information on the mechanisms through which stress has its effect on atherosclerosis progression, focusing on possible relations between psychological stress and the functioning of the endothelium. Our project is based on data from one of the largest national epidemiological studies, the Cardiovascular Risk in Young Finns study, which has monitored the development of risk factors for coronary heart disease in 3596 young adults since 1980. The present study combines experimental stress research with epidemiology and uses an advanced method for examining atherosclerosis development in healthy subjects (intima-media thickness ultrasound measurement). The physiological parameters used were heart rate, respiratory sinus arrhythmia and pre-ejection period. Chronic stress was assessed by vital exhaustion. The ultrasound measurements that served as the indexes of preclinical atherosclerosis were carotid intima-media thickness, brachial flow-mediated dilatation and carotid artery compliance. The effects of cardiovascular risk factors found to be important were taken into account: serum cholesterols level, triglyceride level, serum insulin level and systolic and diastolic blood pressure. There were 69, 1596, 81 and 1721 participants in studies I-IV, respectively. The results showed that both chronic and acute stress may exert an effect on atherosclerosis in subjects with impaired endothelial responses. The findings are consistent with the idea that risk factors are more harmful if the endothelium is not working properly. Chronic stress was found to be a risk if it has resulted in ineffective cardiac stress reactivity or delayed recovery. Men were shown to be at increased risk for atherosclerotic progression in early life, which suggests men’s decreased stress coping ability in relation to stressful psychosocial coronary risk factors. Autonomic imbalance may be the common mechanism of the stress influence on atherosclerosis development. The results of the present study contain background information for the identification the first stages of atherosclerosis, and they may be useful for preventive medicine programs for young adults and could help to improve cardiovascular health in Finland as well as in other countries.

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The present study examines how the landscape of the rural immigrant colony of New Finland (Saskatchewan, Canada) has reflected the Finnish origins of the about 350 settlers and their descendants, their changing ideologies, values, sense of collectiveness and the meanings of the Finnish roots. The study also reveals the reasons and power structures behind the ethnic expressions. Researched time period runs from the beginning of the settlement in 1888 to the turn of the millennium. The research concentrates on buildings, cemeteries, personal names and place names which contain strong visual and symbolic messages and are all important constituents of mundane landscapes. For example, the studied personal names are important identity-political indexes telling about the value of the Finnish nationalism, community spirit, dual Finnish-Canadian identities and also the process of assimilation which, for example, had differences between genders. The study is based on empirical field research, and iconographical and textual interpretations supported by classifications and comparative analyses. Several interviews and literature were essential means of understanding the changing political contexts which influenced the Finnish settlement and its multiple landscape representations. Five historical landscape periods were identified in New Finland. During these periods the meanings and representations of Finnish identity changed along with national and international politics and local power structures. For example, during the Second World War Canada discouraged representations of Finnish culture because Finland and Canada were enemies. But Canada s multicultural policy in the 1980s led to several material and symbolic representations indicating the Finnish settlement after a period of assimilation and deinstitutionalization. The study shows how these representations were indications of the politics of a (selective) memory. Especially Finnish language, cultural traditions and the Evangelical-Lutheran values of the pioneers, which have been passed down to new generations, are highly valued part of the Finnish heritage. Also the work of the pioneers and their participation in the building of Saskatchewan is an important collective narrative. The selectiveness of a memory created the landscape of forgetting which includes deliberately forgotten parts of the history. For example, the occasional disputes between the congregations are something that has been ignored. The results show how the different landscape elements can open up a useful perspective to diaspora colonies or other communities also by providing information which otherwise would be indistinguishable. In this case, for example, two cemeteries close together were a sign of religious distributions among the early settlers.

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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.

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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.

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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.

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Background. Cardiovascular disease (CVD) remains the most serious threat to life and health in industrialized countries. Atherosclerosis is the main underlying pathology associated with CVD, in particular coronary artery disease (CAD), ischaemic stroke, and peripheral arterial disease. Risk factors play an important role in initiating and accelerating the complex process of atherosclerosis. Most studies of risk factors have focused on the presence or absence of clinically defined CVD. Less is known about the determinants of the severity and extent of atherosclerosis in symptomatic patients. Aims. To clarify the association between coronary and carotid artery atherosclerosis, and to study the determinants associated with these abnormalities with special regard to novel cardiovascular risk factors. Subjects and methods. Quantitative coronary angiography (QCA) and B-mode ultrasound were used to assess coronary and carotid artery atherosclerosis in 108 patients with clinically suspected CAD referred for elective coronary angiography. To evaluate anatomic severity and extent of CAD, several QCA parameters were incorporated into indexes. These measurements reflected CAD severity, extent, and overall atheroma burden and were calculated for the entire coronary tree and separately for different coronary segments (i.e., left main, proximal, mid, and distal segments). Maximum and mean intima-media thickness (IMT) values of carotid arteries were measured and expressed as mean aggregate values. Furthermore, the study design included extensive fasting blood samples, oral glucose tolerance test, and an oral fat-load test to be performed in each participant. Results. Maximum and mean IMT values were significantly correlated with CAD severity, extent, and atheroma burden. There was heterogeneity in associations between IMT and CAD indexes according to anatomical location of CAD. Maximum and mean IMT values, respectively, were correlated with QCA indexes for mid and distal segments but not with the proximal segments of coronary vessels. The values of paraoxonase-1 (PON1) activity and concentration, respectively, were lower in subjects with significant CAD and there was a significant relationship between PON1 activity and concentration and coronary atherosclerosis assessed by QCA. PON1 activity was a significant determinant of severity of CAD independently of HDL cholesterol. Neither PON1 activity nor concentration was associated with carotid IMT. The concentration of triglycerides (TGs), triglyceride-rich lipoproteins (TRLs), oxidized LDL (oxLDL), and the cholesterol content of remnant lipoprotein particle (RLP-C) were significantly increased at 6 hours after intake of an oral fatty meal as compared with fasting values. The mean peak size of LDL remained unchanged 6 hours after the test meal. The correlations between total TGs, TRLs, and RLP-C in fasting and postprandial state were highly significant. RLP-C correlated with oxLDL both in fasting and in fed state and inversely with LDL size. In multivariate analysis oxLDL was a determinant of severity and extent of CAD. Neither total TGs, TRLs, oxLDL, nor LDL size were linked to carotid atherosclerosis. Insulin resistance (IR) was associated with an increased severity and extent of coronary atherosclerosis and seemed to be a stronger predictor of coronary atherosclerosis in the distal parts of the coronary tree than in the proximal and mid parts. In the multivariate analysis IR was a significant predictor of the severity of CAD. IR did not correlate with carotid IMT. Maximum and mean carotid IMT were higher in patients with the apoE4 phenotype compared with subjects with the apoE3 phenotype. Likewise, patients with the apoE4 phenotype had a more severe and extensive CAD than individuals with the apoE3 phenotype. Conclusions. 1) There is an association between carotid IMT and the severity and extent of CAD. Carotid IMT seems to be a weaker predictor of coronary atherosclerosis in the proximal parts of the coronary tree than in the mid and distal parts. 2) PON1 activity has an important role in the pathogenesis of coronary atherosclerosis. More importantly, the study illustrates how the protective role of HDL could be modulated by its components such that equivalent serum concentrations of HDL cholesterol may not equate with an equivalent, potential protective capacity. 3) RLP-C in the fasting state is a good marker of postprandial TRLs. Circulating oxLDL increases in CAD patients postprandially. The highly significant positive correlation between postprandial TRLs and postprandial oxLDL suggests that the postprandial state creates oxidative stress. Our findings emphasize the fundamental role of LDL oxidation in the development of atherosclerosis even after inclusion of conventional CAD risk factors. 4) Disturbances in glucose metabolism are crucial in the pathogenesis of coronary atherosclerosis. In fact, subjects with IR are comparable with diabetic subjects in terms of severity and extent of CAD. 5) ApoE polymorphism is involved in the susceptibility to both carotid and coronary atherosclerosis.

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Intensive care is to be provided to patients benefiting from it, in an ethical, efficient, effective and cost-effective manner. This implies a long-term qualitative and quantitative analysis of intensive care procedures and related resources. The study population consists of 2709 patients treated in the general intensive care unit (ICU) of Helsinki University Hospital. Study sectors investigate intensive care patients mortality, quality of life (QOL), Quality-Adjusted Life-Years (QALY units) and factors related to severity of illness, length of stay (LOS), patient s age, evaluation period as well as experiences and memories connected with the ICU episode. In addition, the study examines the qualities of two QOL measures, the RAND 36 Item Health Survey 1.0 (RAND-36) and the 5 Item EuroQol-5D (EQ-5D) and assesses the correlation of the test results. Patients treated in 1995 responded to the RAND-36 questionnaire in 1996. All patients, treated from 1995-2000, received a QOL questionnaires in 2001, when 1 7 years had lapsed from the intensive treatment. Response rate was 79.5 %. Main Results 1) Of the patients who died within the first year (n = 1047) 66 % died during the intensive care period or within the following month. The non-survivors were more aged than the surviving patients, had generally a higher than average APACHE II and SOFA score depicting the severity of illness, their ICU LOS was longer and hospital stay shorter than of the surviving patients (p < 0.001). Mortality of patients receiving conservative treatment was higher than of those receiving surgical treatment. Patients replying to the QOL survey in 2001 (n = 1099) had recovered well: 97 % of those lived at home. More than half considered their QOL as good or extremely good, 40 % as satisfactory and 7 % as bad. All QOL indexes of those of working-age were considerably lower (p < 0.001) than comparable figures of the age- and gender-adjusted Finnish population. The 5-year monitoring period made evident that mental recovery was slower than physical recovery. 2) The results of RAND-36 and EQ-5D correlated well (p < 0.01). The RAND-36 profile measure distinguished more clearly between the different categories of QOL and their levels. EQ-5D measured well the patient groups general QOL and the sum index was used to calculate QALY units. 3) QALY units were calculated by multiplying the time the patient survived after ICU stay or expected life-years by the EQ-5D sum index. Aging automatically lowers the number of QALY units. Patients under the age of 65 receiving conservative treatment benefited from treatment to a greater extent measured in QALY units than their peers receiving surgical treatment, but in the age group 65 and over patients with surgical treatment received higher QALY ratings than recipients of conservative treatment. 4) The intensive care experience and QOL ratings were connected. The QOL indices were statistically highest for those recipients with memories of intensive care as a positive experience, albeit their illness requiring intensive care treatment was less serious than average. No statistically significant differences were found in the QOL indices of those with negative memories, no memories or those who did not express the quality of their experiences.

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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.

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A repetitive sequence collection is one where portions of a base sequence of length n are repeated many times with small variations, forming a collection of total length N. Examples of such collections are version control data and genome sequences of individuals, where the differences can be expressed by lists of basic edit operations. Flexible and efficient data analysis on a such typically huge collection is plausible using suffix trees. However, suffix tree occupies O(N log N) bits, which very soon inhibits in-memory analyses. Recent advances in full-text self-indexing reduce the space of suffix tree to O(N log σ) bits, where σ is the alphabet size. In practice, the space reduction is more than 10-fold, for example on suffix tree of Human Genome. However, this reduction factor remains constant when more sequences are added to the collection. We develop a new family of self-indexes suited for the repetitive sequence collection setting. Their expected space requirement depends only on the length n of the base sequence and the number s of variations in its repeated copies. That is, the space reduction factor is no longer constant, but depends on N / n. We believe the structures developed in this work will provide a fundamental basis for storage and retrieval of individual genomes as they become available due to rapid progress in the sequencing technologies.

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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.