Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Voter Participation in the 1998 Bundestag Elections: A Theoretical Modification and Empirical Application of Downs’ Theory of Voter Participation

This article seeks to contribute to the illumination of the so-called 'paradox of voting' using the German Bundestag elections of 1998 as an empirical case. Downs' model of voter participation will be extended to include elements of the theory of subjective expected utility (SEU). This will allow a theoretical and empirical exploration of the crucial mechanisms of individual voters' decisions to participate, or abstain from voting, in the German general election of 1998. It will be argued that the infinitely low probability of an individual citizen's vote to decide the election outcome will not necessarily reduce the probability of electoral participation. The empirical analysis is largely based on data from the ALLBUS 1998. It confirms the predictions derived from SEU theory. The voters' expected benefits and their subjective expectation to be able to influence government policy by voting are the crucial mechanisms to explain participation. By contrast, the explanatory contribution of perceived information and opportunity costs is low.

A Restriction-Centered Theory of Reasoning and Computation to materialize a Web 3.0

Researchers suggest that personalization on the Semantic Web adds up to a Web 3.0 eventually. In this Web, personalized agents process and thus generate the biggest share of information rather than humans. In the sense of emergent semantics, which supplements traditional formal semantics of the Semantic Web, this is well conceivable. An emergent Semantic Web underlying fuzzy grassroots ontology can be accomplished through inducing knowledge from users' common parlance in mutual Web 2.0 interactions [1]. These ontologies can also be matched against existing Semantic Web ontologies, to create comprehensive top-level ontologies. On the Web, if augmented with information in the form of restrictions andassociated reliability (Z-numbers) [2], this collection of fuzzy ontologies constitutes an important basis for an implementation of Zadeh's restriction-centered theory of reasoning and computation (RRC) [3]. By considering real world's fuzziness, RRC differs from traditional approaches because it can handle restrictions described in natural language. A restriction is an answer to a question of the value of a variable such as the duration of an appointment. In addition to mathematically well-defined answers, RRC can likewise deal with unprecisiated answers as "about one hour." Inspired by mental functions, it constitutes an important basis to leverage present-day Web efforts to a natural Web 3.0. Based on natural language information, RRC may be accomplished with Z-number calculation to achieve a personalized Web reasoning and computation. Finally, through Web agents' understanding of natural language, they can react to humans more intuitively and thus generate and process information.

White matter in aphasia: a historical review of the Dejerines' studies

The Objective was to describe the contributions of Joseph Jules Dejerine and his wife Augusta Dejerine-Klumpke to our understanding of cerebral association fiber tracts and language processing. The Dejerines (and not Constantin von Monakow) were the first to describe the superior longitudinal fasciculus/arcuate fasciculus (SLF/AF) as an association fiber tract uniting Broca's area, Wernicke's area, and a visual image center in the angular gyrus of a left hemispheric language zone. They were also the first to attribute language-related functions to the fasciculi occipito-frontalis (FOF) and the inferior longitudinal fasciculus (ILF) after describing aphasia patients with degeneration of the SLF/AF, ILF, uncinate fasciculus (UF), and FOF. These fasciculi belong to a functional network known as the Dejerines' language zone, which exceeds the borders of the classically defined cortical language centers. The Dejerines provided the first descriptions of the anatomical pillars of present-day language models (such as the SLF/AF). Their anatomical descriptions of fasciculi in aphasia patients provided a foundation for our modern concept of the dorsal and ventral streams in language processing.

Quantitative Myocardial Contrast Echocardiography during Pharmacological Stress for Diagnosis of Coronary Artery Disease: A Systematic Review and Meta-analysis of Diagnostic Accuracy Studies

AIMS: We conducted a meta-analysis to evaluate the accuracy of quantitative stress myocardial contrast echocardiography (MCE) in coronary artery disease (CAD). METHODS AND RESULTS: Database search was performed through January 2008. We included studies evaluating accuracy of quantitative stress MCE for detection of CAD compared with coronary angiography or single-photon emission computed tomography (SPECT) and measuring reserve parameters of A, beta, and Abeta. Data from studies were verified and supplemented by the authors of each study. Using random effects meta-analysis, we estimated weighted mean difference (WMD), likelihood ratios (LRs), diagnostic odds ratios (DORs), and summary area under curve (AUC), all with 95% confidence interval (CI). Of 1443 studies, 13 including 627 patients (age range, 38-75 years) and comparing MCE with angiography (n = 10), SPECT (n = 1), or both (n = 2) were eligible. WMD (95% CI) were significantly less in CAD group than no-CAD group: 0.12 (0.06-0.18) (P < 0.001), 1.38 (1.28-1.52) (P < 0.001), and 1.47 (1.18-1.76) (P < 0.001) for A, beta, and Abeta reserves, respectively. Pooled LRs for positive test were 1.33 (1.13-1.57), 3.76 (2.43-5.80), and 3.64 (2.87-4.78) and LRs for negative test were 0.68 (0.55-0.83), 0.30 (0.24-0.38), and 0.27 (0.22-0.34) for A, beta, and Abeta reserves, respectively. Pooled DORs were 2.09 (1.42-3.07), 15.11 (7.90-28.91), and 14.73 (9.61-22.57) and AUCs were 0.637 (0.594-0.677), 0.851 (0.828-0.872), and 0.859 (0.842-0.750) for A, beta, and Abeta reserves, respectively. CONCLUSION: Evidence supports the use of quantitative MCE as a non-invasive test for detection of CAD. Standardizing MCE quantification analysis and adherence to reporting standards for diagnostic tests could enhance the quality of evidence in this field.

IN.PACT Amphirion paclitaxel eluting balloon versus standard percutaneous transluminal angioplasty for infrapopliteal revascularization of critical limb ischemia: rationale and protocol for an ongoing randomized controlled trial

BACKGROUND The effectiveness and durability of endovascular revascularization therapies for chronic critical limb ischemia (CLI) are challenged by the extensive burden of infrapopliteal arterial disease and lesion-related characteristics (e.g., severe calcification, chronic total occlusions), which frequently result in poor clinical outcomes. While infrapopliteal vessel patency directly affects pain relief and wound healing, sustained patency and extravascular care both contribute to the ultimate "patient-centric" outcomes of functional limb preservation, mobility and quality of life (QoL). METHODS/DESIGN IN.PACT DEEP is a 2:1 randomized controlled trial designed to assess the efficacy and safety of infrapopliteal arterial revascularization between the IN.PACT Amphirion™ paclitaxel drug-eluting balloon (IA-DEB) and standard balloon angioplasty (PTA) in patients with Rutherford Class 4-5-6 CLI. DISCUSSION This multicenter trial has enrolled 358 patients at 13 European centers with independent angiographic core lab adjudication of the primary efficacy endpoint of target lesion late luminal loss (LLL) and clinically driven target lesion revascularization (TLR) in major amputation-free surviving patients through 12-months. An independent wound core lab will evaluate all ischemic wounds to assess the extent of healing and time to healing at 1, 6, and 12 months. A QoL questionnaire including a pain scale will assess changes from baseline scores through 12 months. A Clinical Events Committee and Data Safety Monitoring Board will adjudicate the composite primary safety endpoints of all-cause death, major amputation, and clinically driven TLR at 6 months and other trial endpoints and supervise patient safety throughout the study. All patients will be followed for 5 years. A literature review is presented of the current status of endovascular treatment of CLI with drug-eluting balloon and standard PTA. The rationale and design of the IN.PACT DEEP Trial are discussed. IN.PACT DEEP is a milestone, prospective, randomized, robust, independent core lab-adjudicated CLI trial that will evaluate the role of a new infrapopliteal revascularization technology, the IA-DEB, compared to PTA. It will assess the overall impact on infrapopliteal artery patency, limb salvage, wound healing, pain control, QoL, and patient mobility. The 1-year results of the adjudicated co-primary and secondary endpoints will be available in 2014. TRIAL REGISTRATION NCT00941733

A Normative Theory of Forgetting: Lessons from the Fruit Fly

Recent experiments revealed that the fruit fly Drosophila melanogaster has a dedicated mechanism for forgetting: blocking the G-protein Rac leads to slower and activating Rac to faster forgetting. This active form of forgetting lacks a satisfactory functional explanation. We investigated optimal decision making for an agent adapting to a stochastic environment where a stimulus may switch between being indicative of reward or punishment. Like Drosophila, an optimal agent shows forgetting with a rate that is linked to the time scale of changes in the environment. Moreover, to reduce the odds of missing future reward, an optimal agent may trade the risk of immediate pain for information gain and thus forget faster after aversive conditioning. A simple neuronal network reproduces these features. Our theory shows that forgetting in Drosophila appears as an optimal adaptive behavior in a changing environment. This is in line with the view that forgetting is adaptive rather than a consequence of limitations of the memory system.

Plant-plant interactions, environmental gradients and plant diversity: A global synthesis of community-level studies

Previous syntheses on the effects of environmental conditions on the outcome of plant-plant interactions summarize results from pairwise studies. However, the upscaling to the community-level of such studies is problematic because of the existence of multiple species assemblages and species-specific responses to both the environmental conditions and the presence of neighbors. We conducted the first global synthesis of community-level studies from harsh environments, which included data from 71 alpine and 137 dryland communities to: (i) test how important are facilitative interactions as a driver of community structure, (ii) evaluate whether we can predict the frequency of positive plant-plant interactions across differing environmental conditions and habitats, and (iii) assess whether thresholds in the response of plant-plant interactions to environmental gradients exists between ``moderate'' and ``extreme'' environments. We also used those community-level studies performed across gradients of at least three points to evaluate how the average environmental conditions, the length of the gradient studied, and the number of points sampled across such gradient affect the form and strength of the facilitation-environmental conditions relationship. Over 25% of the species present were more spatially associated to nurse plants than expected by chance in both alpine and chyland areas, illustrating the high importance of positive plant-plant interactions for the maintenance of plant diversity in these environments. Facilitative interactions were more frequent, and more related to environmental conditions, in alpine than in dryland areas, perhaps because drylands are generally characterized by a larger variety of environmental stress factors and plant functional traits. The frequency of facilitative interactions in alpine communities peaked at 1000 mm of annual rainfall, and globally decreased with elevation. The frequency of positive interactions in dtyland communities decreased globally with water scarcity or temperature annual range. Positive facilitation-drought stress relationships are more likely in shorter regional gradients, but these relationships are obscured in regions with a greater species turnover or with complex environmental gradients. By showing the different climatic drivers and behaviors of plant-plant interactions in dryland and alpine areas, our results will improve predictions regarding the effect of facilitation on the assembly of plant communities and their response to changes in environmental conditions.

Constraints on the effective fluid theory of stationary branes

We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian containing the information about the elastic dynamics of the brane embedding as well as the hydrodynamics of the effective fluid living on the brane. The Lagrangian is corrected order-by-order in a derivative expansion, where we take into account the dipole moment of the brane which encompasses finite-thickness corrections, including transverse spin. We describe how to extract the thermodynamics from the Lagrangian and we obtain constraints on the higher-derivative terms with one and two derivatives. These constraints follow by comparing the brane thermodynamics with the conserved currents associated with background Killing vector fields. In particular, we fix uniquely the one- and two-derivative terms describing the coupling of the transverse spin to the background space-time. Finally, we apply our formalism to two blackfold examples, the black tori and charged black rings and compare the latter to a numerically generated solution.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.