On a problem of A. Weil

A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant is complete, i.e. the geodesic lamination can be recovered from the invariant. The continuous part of the invariant has geometric meaning of a slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations

Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete list of antisymmetric eigenfunctions of integral equation in terms of Kleinian membranes is given.Comment: 33 pages, 13 figures. This paper is an extended version of CV/061173

Prefrontal cortex activation and young driver behaviour: a fNIRS study

Road traffic accidents consistently show a significant over-representation for young, novice and particularly male drivers. This research examines the prefrontal cortex activation of young drivers and the changes in activation associated with manipulations of mental workload and inhibitory control. It also considers the explanation that a lack of prefrontal cortex maturation is a contributing factor to the higher accident risk in this young driver population. The prefrontal cortex is associated with a number of factors including mental workload and inhibitory control, both of which are also related to road traffic accidents. This experiment used functional near infrared spectroscopy to measure prefrontal cortex activity during five simulated driving tasks: one following task and four overtaking tasks at varying traffic densities which aimed to dissociate workload and inhibitory control. Age, experience and gender were controlled for throughout the experiment. The results showed that younger drivers had reduced prefrontal cortex activity compared to older drivers. When both mental workload and inhibitory control increased prefrontal cortex activity also increased, however when inhibitory control alone increased there were no changes in activity. Along with an increase in activity during overtaking manoeuvres, these results suggest that prefrontal cortex activation is more indicative of workload in the current task. There were no differences in the number of overtakes completed by younger and older drivers but males overtook significantly more than females. We conclude that prefrontal cortex activity is associated with the mental workload required for overtaking. We additionally suggest that the reduced activation in younger drivers may be related to a lack of prefrontal maturation which could contribute to the increased crash risk seen in this population

The Effect of Insecticide Synergists on the Response of Scabies Mites to Pyrethroid Acaricides

Synergists are commonly used in combination with pesticides to suppress metabolism-based resistance and increase the efficacy of the agents. They are also useful as tools for laboratory investigation of specific resistance mechanisms based on their ability to inhibit specific metabolic pathways. To determine the role of metabolic degradation as a mechanism for acaricide resistance in human scabies, PBO (piperonyl butoxide), DEF (S,S,S-tributyl phosphorotrithioate) and DEM (diethyl maleate) were used with permethrin as synergists in a bioassay of mite killing. A statistically significant difference in survival time of permethrin-resistant Sarcoptes scabiei variety canis was noted when any of the three synergists were used in combination with permethrin compared to survival time of mites exposed to permethrin alone (p<0.0001). These results indicate the potential utility of synergists in reversing tolerance to pyrethroid-based acaricides (i.e. the addition of synergists to permethrin-containing topical acaricide cream commonly used to treat scabies). To further verify specific metabolic pathways being inhibited by these synergists, enzyme assays were developed to measure esterase, glutathione S-transferase (GST) and cytochrome P450 monooxygenase activity in scabies mites. Results of in vitro enzyme inhibition experiments showed lower levels of esterase activity with DEF; lower levels of GST activity with DEM and lower levels of cytochrome monooxygenase activity with PBO. These findings indicate a metabolic mechanism as mediating pyrethroid resistance in scabies mites

Transparency and Trust in Human-AI-Interaction: The Role of Model-Agnostic Explanations in Computer Vision-Based Decision Support

Computer Vision, and hence Artificial Intelligence-based extraction of information from images, has increasingly received attention over the last years, for instance in medical diagnostics. While the algorithms' complexity is a reason for their increased performance, it also leads to the "black box" problem, consequently decreasing trust towards AI. In this regard, "Explainable Artificial Intelligence" (XAI) allows to open that black box and to improve the degree of AI transparency. In this paper, we first discuss the theoretical impact of explainability on trust towards AI, followed by showcasing how the usage of XAI in a health-related setting can look like. More specifically, we show how XAI can be applied to understand why Computer Vision, based on deep learning, did or did not detect a disease (malaria) on image data (thin blood smear slide images). Furthermore, we investigate, how XAI can be used to compare the detection strategy of two different deep learning models often used for Computer Vision: Convolutional Neural Network and Multi-Layer Perceptron. Our empirical results show that i) the AI sometimes used questionable or irrelevant data features of an image to detect malaria (even if correctly predicted), and ii) that there may be significant discrepancies in how different deep learning models explain the same prediction. Our theoretical discussion highlights that XAI can support trust in Computer Vision systems, and AI systems in general, especially through an increased understandability and predictability

An extension result for maps admitting and algebraic addition theorem

We prove that if an analytic map : U [flecha] Cn, where U [incluye] C [elevado a ] n is an open neighborhood of the origin, admits an algebraic addition theorem then, there exists a meromorphic map g : C [elevado a]n [flecha] C [elevado a]n admitting an algebraic addition theorem such that each coordinate function of f is algebraic over C(g) on U (this was proved by K. Weierstrass for n = 1). Furthermore, g admits a rational addition theorem

Asymmetry, sex differences and age-related changes in the white matter in the healthy elderly: a tract-based study

<p>Abstract</p> <p>Background</p> <p>Hemispherical asymmetry, sex differences and age-related changes have been reported for the human brain. Meanwhile it was still unclear the presence of the asymmetry or sex differences in the human brain occurred whether as a normal development or as consequences of any pathological changes. The aim of this study was to investigate hemispherical asymmetry, sex differences and age-related changes by using a tract-based analysis in the nerve bundles.</p> <p>Methods</p> <p>40 healthy elderly subjects underwent magnetic resonance diffusion tensor imaging, and we calculated fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values along the major white matter bundles.</p> <p>Results</p> <p>We identified hemispherical asymmetry in the ADC values for the cingulate fasciculus in the total subject set and in males, and a sex difference in the FA values for the right uncinate fasciculus. For age-related changes, we demonstrated a significant increase in ADC values with advancing age in the right cingulum, left temporal white matter, and a significant decrease in FA values in the right superior longitudinal fasciculus.</p> <p>Conclusion</p> <p>In this study, we found hemispherical asymmetry, sex differences and age-related changes in particular regions of the white matter in the healthy elderly. Our results suggest considering these differences can be important in imaging studies.</p

Accessory parameters for Liouville theory on the torus

We give an implicit equation for the accessory parameter on the torus which is the necessary and sufficient condition to obtain the monodromy of the conformal factor. It is shown that the perturbative series for the accessory parameter in the coupling constant converges in a finite disk and give a rigorous lower bound for the radius of convergence. We work out explicitly the perturbative result to second order in the coupling for the accessory parameter and to third order for the one-point function. Modular invariance is discussed and exploited. At the non perturbative level it is shown that the accessory parameter is a continuous function of the coupling in the whole physical region and that it is analytic except at most a finite number of points. We also prove that the accessory parameter as a function of the modulus of the torus is continuous and real-analytic except at most for a zero measure set. Three soluble cases in which the solution can be expressed in terms of hypergeometric functions are explicitly treated.Comment: 30 pages, LaTex; typos corrected, discussion of eq.(74) improve

Some geometric invariants from resolutions of Hilbert modules

The model theory of Sz.-Nagy and Foias for contractions was reformulated in [15, chapter 3]. The existence of a unique minimal unitary dilation amounts to the exis-tence of a Silov resolution for contractive Hilbert modulesM over the disc algebra A(D) along with the fact that any two minimal Silov resolutions are isomorphic