Flat Surfaces

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type singularities. Such flat surfaces are naturally organized into families which appear to be isomorphic to the moduli spaces of holomorphic one-forms. One can obtain much information about the geometry and dynamics of an individual flat surface by studying both its orbit under the Teichmuller geodesic flow and under the linear group action. In particular, the Teichmuller geodesic flow plays the role of a time acceleration machine (renormalization procedure) which allows to study the asymptotic behavior of interval exchange transformations and of surface foliations. This long survey is an attempt to present some selected ideas, concepts and facts in Teichmuller dynamics in a playful way.Comment: (152 pages; 51 figures) Based on the lectures given by the author at the Les Houches School "Number Theory and Physics" in March of 2003 and at the workshop on dynamical systems in ICTP, Trieste, in July 2004. See "Frontiers in Number Theory, Physics and Geometry. Volume 1: On random matrices, zeta functions and dynamical systems'', P.Cartier; B.Julia; P.Moussa; P.Vanhove (Editors), Springer-Verlag (2006) for the entire collection (including, in particular, the complementary lectures of J.-C. Yoccoz). For a short version see the paper "Geodesics on Flat Surfaces", arXiv.math.GT/060939

Athermal Phonon Sensors in Searches for Light Dark Matter

In recent years, theoretical and experimental interest in dark matter (DM) candidates have shifted focus from primarily Weakly-Interacting Massive Particles (WIMPs) to an entire suite of candidates with masses from the zeV-scale to the PeV-scale to 30 solar masses. One particular recent development has been searches for light dark matter (LDM), which is typically defined as candidates with masses in the range of keV to GeV. In searches for LDM, eV-scale and below detector thresholds are needed to detect the small amount of kinetic energy that is imparted to nuclei in a recoil. One such detector technology that can be applied to LDM searches is that of Transition-Edge Sensors (TESs). Operated at cryogenic temperatures, these sensors can achieve the required thresholds, depending on the optimization of the design. In this thesis, I will motivate the evidence for DM and the various DM candidates beyond the WIMP. I will then detail the basics of TES characterization, expand and apply the concepts to an athermal phonon sensor--based Cryogenic PhotoDetector (CPD), and use this detector to carry out a search for LDM at the surface. The resulting exclusion analysis provides the most stringent limits in DM-nucleon scattering cross section (comparing to contemporary searches) for a cryogenic detector for masses from 93 to 140 MeV, showing the promise of athermal phonon sensors in future LDM searches. Furthermore, unknown excess background signals are observed in this LDM search, for which I rule out various possible sources and motivate stress-related microfractures as an intriguing explanation. Finally, I will shortly discuss the outlook of future searches for LDM for various detection channels beyond nuclear recoils.Comment: 243 pages, Ph.D. Thesis in Physics at UC Berkele

Cutting sequences on Bouw-Moeller surfaces : an S-adic characterization.

Résumé. On considère un codage symbolique des géodésiques sur une famille de surfaces de Veech (surfaces de translation riches en symétries affines) récemment découverte par Bouw et Möller. Ces surfaces, comme l’a remarqué Hooper, peuvent être réalisées en coupant et collant une collection de polygones semi-réguliers. Dans cet article, on caractérise l’ensemble des suites symboliques (“suites de coupage”) qui correspondent au codage de trajectoires linéaires, à l’aide de la suite des côtés des polygones croisés. On donne une caractérisation complète de l’adhérence de l’ensemble des suites de coupage, dans l’esprit de la caractérisation classique des suites sturmiennes et de la récente caractérisation par Smillie-Ulcigrai des suites de coupage des trajectoires linéaires dans les polygones réguliers. La caractérisation est donnée en termes d’un système fini de substitutions (connu aussi sous le nom de présentation S-adique), réglé par une transformation unidimensionnelle qui ressemble à l’algorithme de fraction continue. Comme dans le cas sturmien et dans celui des polygones réguliers, la caractérisation est basée sur la renormalisation et sur la définition d’un opérateur combinatoire de dérivation approprié. Une des nouveautés est que la dérivation se fait en deux étapes, sans utiliser directement les éléments du groupe de Veech, mais en utilisant un difféomorphisme affine qui envoie une surface de Bouw-Möller vers sa surface “duale”, qui est dans le même disque de Teichmüller. Un outil technique utilisé est la présentation des surfaces de Bouw-Möller par les diagrammes de Hooper. ABSTRACT. We consider a symbolic coding for geodesics on the family of Veech surfaces (translation surfaces rich with affine symmetries) recently discovered by Bouw and Möller. These surfaces, as noticed by Hooper, can be realized by cutting and pasting a collection of semi-regular polygons. We characterize the set of symbolic sequences (cutting sequences) that arise by coding linear trajectories by the sequence of polygon sides crossed. We provide a full characterization for the closure of the set of cutting sequences, in the spirit of the classical characterization of Sturmian sequences and the recent characterization of Smillie-Ulcigrai of cutting sequences of linear trajectories on regular polygons. The characterization is in terms of a system of finitely many substitutions (also known as an S-adic presentation), governed by a one-dimensional continued fraction-like map. As in the Sturmian and regular polygon case, the characterization is based on renormalization and the definition of a suitable combinatorial derivation operator. One of the novelties is that derivation is done in two steps, without directly using Veech group elements, but by exploiting an affine diffeomorphism that maps a Bouw- Möller surface to the dual Bouw-Möller surface in the same Teichmüller disk. As a technical tool, we crucially exploit the presentation of Bouw-Möller surfaces via Hooper diagrams

Multiple Instance Learning: A Survey of Problem Characteristics and Applications

Multiple instance learning (MIL) is a form of weakly supervised learning where training instances are arranged in sets, called bags, and a label is provided for the entire bag. This formulation is gaining interest because it naturally fits various problems and allows to leverage weakly labeled data. Consequently, it has been used in diverse application fields such as computer vision and document classification. However, learning from bags raises important challenges that are unique to MIL. This paper provides a comprehensive survey of the characteristics which define and differentiate the types of MIL problems. Until now, these problem characteristics have not been formally identified and described. As a result, the variations in performance of MIL algorithms from one data set to another are difficult to explain. In this paper, MIL problem characteristics are grouped into four broad categories: the composition of the bags, the types of data distribution, the ambiguity of instance labels, and the task to be performed. Methods specialized to address each category are reviewed. Then, the extent to which these characteristics manifest themselves in key MIL application areas are described. Finally, experiments are conducted to compare the performance of 16 state-of-the-art MIL methods on selected problem characteristics. This paper provides insight on how the problem characteristics affect MIL algorithms, recommendations for future benchmarking and promising avenues for research

Characterizing Families of Cuts That Can Be Represented by Axis-Parallel Rectangles

A drawing of a family of cuts of a graph is an augmented drawing of the graph such that every cut is represented by a simple closed curve and vice versa. We show tha

The most recent (682-792 C.E.) volcanic eruption in the Jombolok lava field, East Sayan, Central Asia triggered exodus of Mongolian pre-Chinggis Khaan tribes (778-786 C.E.)

International audienceThis study presents new data on one of the most recent (historical) volcanic eruptions in Central Asia. The Jombolok lava field located in the East Sayan Mountains (Southern Siberia) was formed during Late Pleistocene and Holocene times. At least four phases of volcanic activity have been identified and evidences associated with the last phase have been found in the upper reaches of the Khi-Gol valley and in the Oka-Jombolok basin. The volcanic activity is represented by young basaltic lava located among older lavas. Live and dead trees have been sampled in the young lava field. Nine fragments of wood have been found embedded in lavas of the latest eruption. Dendrochronological analysis, radiocarbon dating and the analysis of historical chronicles have shown that the latest eruption occurred during the period 682-792 A.D. The volcanic activity possibly triggered the migration of Mongolian tribes out of the locality known in historical chronicles as Ergune-Kun towards the Onon River, which, 400 years later, became the place of birth and rise of Chinggis Khaan