Modeling and inference of multisubject fMRI data

Functional magnetic resonance imaging (fMRI) is a rapidly growing technique for studying the brain in action. Since its creation [1], [2], cognitive scientists have been using fMRI to understand how we remember, manipulate, and act on information in our environment. Working with magnetic resonance physicists, statisticians, and engineers, these scientists are pushing the frontiers of knowledge of how the human brain works. The design and analysis of single-subject fMRI studies has been well described. For example, [3], chapters 10 and 11 of [4], and chapters 11 and 14 of [5] all give accessible overviews of fMRI methods for one subject. In contrast, while the appropriate manner to analyze a group of subjects has been the topic of several recent papers, we do not feel it has been covered well in introductory texts and review papers. Therefore, in this article, we bring together old and new work on so-called group modeling of fMRI data using a consistent notation to make the methods more accessible and comparable

Drawing graphs for cartographic applications

Graph Drawing is a relatively young area that combines elements of graph theory, algorithms, (computational) geometry and (computational) topology. Research in this field concentrates on developing algorithms for drawing graphs while satisfying certain aesthetic criteria. These criteria are often expressed in properties like edge complexity, number of edge crossings, angular resolutions, shapes of faces or graph symmetries and in general aim at creating a drawing of a graph that conveys the information to the reader in the best possible way. Graph drawing has applications in a wide variety of areas which include cartography, VLSI design and information visualization. In this thesis we consider several graph drawing problems. The first problem we address is rectilinear cartogram construction. A cartogram, also known as value-by-area map, is a technique used by cartographers to visualize statistical data over a set of geographical regions like countries, states or counties. The regions of a cartogram are deformed such that the area of a region corresponds to a particular geographic variable. The shapes of the regions depend on the type of cartogram. We consider rectilinear cartograms of constant complexity, that is cartograms where each region is a rectilinear polygon with a constant number of vertices. Whether a cartogram is good is determined by how closely the cartogram resembles the original map and how precisely the area of its regions describe the associated values. The cartographic error is defined for each region as jAc¡Asj=As, where Ac is the area of the region in the cartogram and As is the specified area of that region, given by the geographic variable to be shown. In this thesis we consider the construction of rectilinear cartograms that have correct adjacencies of the regions and zero cartographic error. We show that any plane triangulated graph admits a rectilinear cartogram where every region has at most 40 vertices which can be constructed in O(nlogn) time. We also present experimental results that show that in practice the algorithm works significantly better than suggested by the complexity bounds. In our experiments on real-world data we were always able to construct a cartogram where the average number of vertices per region does not exceed five. Since a rectangle has four vertices, this means that most of the regions of our rectilinear car tograms are in fact rectangles. Moreover, the maximum number vertices of each region in these cartograms never exceeded ten. The second problem we address in this thesis concerns cased drawings of graphs. The vertices of a drawing are commonly marked with a disk, but differentiating between vertices and edge crossings in a dense graph can still be difficult. Edge casing is a wellknown method—used, for example, in electrical drawings, when depicting knots, and, more generally, in information visualization—to alleviate this problem and to improve the readability of a drawing. A cased drawing orders the edges of each crossing and interrupts the lower edge in an appropriate neighborhood of the crossing. One can also envision that every edge is encased in a strip of the background color and that the casing of the upper edge covers the lower edge at the crossing. If there are no application-specific restrictions that dictate the order of the edges at each crossing, then we can in principle choose freely how to arrange them. However, certain orders will lead to a more readable drawing than others. In this thesis we formulate aesthetic criteria for a cased drawing as optimization problems and solve these problems. For most of the problems we present either a polynomial time algorithm or demonstrate that the problem is NP-hard. Finally we consider a combinatorial question in computational topology concerning three types of objects: closed curves in the plane, surfaces immersed in the plane, and surfaces embedded in space. In particular, we study casings of closed curves in the plane to decide whether these curves can be embedded as the boundaries of certain special surfaces. We show that it is NP-complete to determine whether an immersed disk is the projection of a surface embedded in space, or whether a curve is the boundary of an immersed surface in the plane that is not constrained to be a disk. However, when a casing is supplied with a self-intersecting curve, describing which component of the curve lies above and which below at each crossing, we can determine in time linear in the number of crossings whether the cased curve forms the projected boundary of a surface in space. As a related result, we show that an immersed surface with a single boundary curve that crosses itself n times has at most 2n=2 combinatorially distinct spatial embeddings and we discuss the existence of fixed-parameter tractable algorithms for related problems

Elliptic fibrations associated with the Einstein spacetimes

Given a conformally nonflat Einstein spacetime we define a fibration $P$ over it. The fibres of this fibration are elliptic curves (2-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched cover of the bundle of null direction over the spacetime and is equipped with six linearly independent 1-forms which satisfy certain relatively simple system of equations.Comment: 15 pages, Late

Is Acupuncture Effective in the Prophylaxis of Recurrent Urinary Tract Infections in Adult Women?

OBJECTIVE: The objective of this selective EBM review is to determine whether or not acupuncture is effective in the prophylaxis of recurrent urinary infections in adult women. STUDY DESIGN: Systematic review of three English language primary studies, published between 1998 and 2003. DATA SOURCES: Three randomized, controlled trials published after 1996, comparing acupuncture to placebo in the prophylaxis of urinary tract infections were obtained using EBSCOhost and PubMed. OUTCOMES MEASURED: All three studies measured incidence or absence of urinary tract infections, as defined by distal urinary symptoms and/or bacteriuria of ≥ 105 cfu/ml. RESULTS: Three randomized, controlled studies found that acupuncture treatment significantly decreased the incidence of urinary tract infections as compared to no treatment. Alraek et al 2003 additionally showed that Kidney qi/yang xu acupuncture was significantly more effective in UTI prophylaxis than Spleen yang/qui xu acupuncture and Liver qui stagnation. CONCLUSIONS: Data suggests that acupuncture therapy, specifically for Kidney qi/yang xu, is effective in the prophylaxis of recurrent urinary tract infections in adult women, as evidenced by statistically significant reductions in the incidence of UTIs, as well as low NNT. Acupuncture may be considered as an option for UTI prophylaxis prior to long-term antibiotic therapy. However, further research is needed to determine the mechanism by which acupuncture affects the pathogenesis of UTIs, as well as the cost effectiveness of these acupuncture treatments

The breeding biology of the Acadian Flycatcher

http://deepblue.lib.umich.edu/bitstream/2027.42/56369/1/MP125.pd

Notes on Euclidean Wilson loops and Riemann Theta functions

The AdS/CFT correspondence relates Wilson loops in N=4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 space. Using known mathematical results for such minimal area surfaces we describe an infinite parameter family of analytic solutions for closed Wilson loops. The solutions are given in terms of Riemann theta functions and the validity of the equations of motion is proven based on the trisecant identity. The world-sheet has the topology of a disk and the renormalized area is written as a finite, one-dimensional contour integral over the world-sheet boundary. An example is discussed in detail with plots of the corresponding surfaces. Further, for each Wilson loops we explicitly construct a one parameter family of deformations that preserve the area. The parameter is the so called spectral parameter. Finally, for genus three we find a map between these Wilson loops and closed curves inside the Riemann surface.Comment: 35 pages, 7 figures, pdflatex. V2: References added. Typos corrected. Some points clarifie

Virasoro constraints and the Chern classes of the Hodge bundle

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth simply-connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on the compactification of M_{g,n}. In particular, we show that the Virasoro conjecture for CP^2 implies the numerical part of Faber's conjecture on the tautological Chow ring of M_g.Comment: 12 pages, latex2

2D-Shape Analysis Using Conformal Mapping

The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates a metric space of shapes, whose mathematical structure is inherently relevant to the classification task. One intriguing metric space comes from using conformal mappings of 2D shapes into each other, via the theory of Teichmüller spaces. In this space every simple closed curve in the plane (a “shape”) is represented by a ‘fingerprint’ which is a diffeomorphism of the unit circle to itself (a differentiable and invertible, periodic function). More precisely, every shape defines to a unique equivalence class of such diffeomorphisms up to right multiplication by a Möbius map. The fingerprint does not change if the shape is varied by translations and scaling and any such equivalence class comes from some shape. This coset space, equipped with the infinitesimal Weil-Petersson (WP) Riemannian norm is a metric space. In this space, the shortest path between each two shapes is unique, and is given by a geodesic connecting them. Their distance from each other is given by integrating the WP-norm along that geodesic. In this paper we concentrate on solving the “welding” problem of “sewing” together conformally the interior and exterior of the unit circle, glued on the unit circle by a given diffeomorphism, to obtain the unique 2D shape associated with this diffeomorphism. This will allow us to go back and forth between 2D shapes and their representing diffeomorphisms in this “space of shapes”. We then present an efficient method for computing the unique shortest path, the geodesic of shape morphing between each two end-point shapes. The group of diffeomorphisms of S^1 acts as a group of isometries on the space of shapes and we show how this can be used to define shape transformations, like for instance ‘adding a protruding limb’ to any shape.Mathematic