Guarding and Searching Polyhedra

Guarding and searching problems have been of fundamental interest since the early years of Computational Geometry. Both are well-developed areas of research and have been thoroughly studied in planar polygonal settings. In this thesis we tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra. We solve the Art Gallery Problem with reflex edge guards in orthogonal polyhedra having reflex edges in just two directions: generalizing a classic theorem by O'Rourke, we prove that r/2 + 1 reflex edge guards are sufficient and occasionally necessary, where r is the number of reflex edges. We also show how to compute guard locations in O(n log n) time. Then we investigate the Art Gallery Problem with mutually parallel edge guards in orthogonal polyhedra with e edges, showing that 11e/72 edge guards are always sufficient and can be found in linear time, improving upon the previous state of the art, which was e/6. We also give tight inequalities relating e with the number of reflex edges r, obtaining an upper bound on the guard number of 7r/12 + 1. We further study the Art Gallery Problem with edge guards in polyhedra having faces oriented in just four directions, obtaining a lower bound of e/6 - 1 edge guards and an upper bound of (e+r)/6 edge guards. All the previously mentioned results hold for polyhedra of any genus. Additionally, several guard types and guarding modes are discussed, namely open and closed edge guards, and orthogonal and non-orthogonal guarding. Next, we model the Searchlight Scheduling Problem, the problem of searching a given polyhedron by suitably turning some half-planes around their axes, in order to catch an evasive intruder. After discussing several generalizations of classic theorems, we study the problem of efficiently placing guards in a given polyhedron, in order to make it searchable. For general polyhedra, we give an upper bound of r^2 on the number of guards, which reduces to r for orthogonal polyhedra. Then we prove that it is strongly NP-hard to decide if a given polyhedron is entirely searchable by a given set of guards. We further prove that, even under the assumption that an orthogonal polyhedron is searchable, approximating the minimum search time within a small-enough constant factor to the optimum is still strongly NP-hard. Finally, we show that deciding if a specific region of an orthogonal polyhedron is searchable is strongly PSPACE-hard. By further improving our construction, we show that the same problem is strongly PSPACE-complete even for planar orthogonal polygons. Our last results are especially meaningful because no similar hardness theorems for 2-dimensional scenarios were previously known

An art museum for Manila in the Philippines

Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1958.ACCOMPANYING drawings held by MIT Museum.Includes bibliographical references (leaf 37).Bruce Gemmill.M.Arch

Method and madness at the Isabella Stewart Gardner museum

The Isabella Stewart Gardner museum in Boston, Massachusetts is unique in history and design. Originating as a privately held collection, the Gardner Museum reflects its namesake’s eccentricities and stands in stark contrast to the backdrop of contemporary Boston. Although much has been written about the individual masterpieces held within the Gardner collection and there are numerous biographies of “Mrs. Jack,” as Gardner was sometimes called, little work has been done to investigate the museum in light of contemporary research in museology and the practices of collecting and display. Understanding collecting and curating as modes of knowledge production, this study seeks to discover the types of knowledge produced by and within the Gardner Museum. Because the museum highlights forms of knowledge other than that associated with textual criticism, I focus on the affective and historical material transfers at work in museum practice. As such, this study offers an opportunity to explore the nature of a performance-based method or orientation to scholarship. I both make use of and question “performative writing” as a mode of presentation, so that what emerges is an understanding of a method that, like the Gardner Museum, seeks to discover ways of knowing beyond (but not in lieu of) processes of representation and signification. In a sense then, performance methodology becomes both an object of study and my method. In bringing the Isabella Stewart Gardner Museum into relationship with the disciplinary problem of performative writing, I have conceived of my research and writing practices as processes of collecting and curating

Public Health Rep

19314498PMCnul

Facility location and related problems

PRINTAUSGABE IN HAUPTBIBLIOTHEK NICHT EINGELANGT! -- Bei Standortoptimierungsproblemen geht es um eine strategisch günstige Auswahl von Orten unter den Gesichtspunkten des Nutzens und der Aufwände, die mit den Standort-entscheidungen einhergehen. Beispielsweise können in der Planung die lageabhängigen Betriebskosten und die Errichtungskosten gegeneinander aufgewogen werden. Der zentrale Beitrag der vorliegenden Arbeit sind zwei Erweiterungen von Standortproblemen die durch einen Überblick klassischer Modelle eingefasst werden. Die eine Erweiterung behandelt ein dynamisches Warehouse-Location Problem in einem stochastischen Umfeld: Während mehrerer Perioden können Standorte geöffnet und geschlossen werden. Ziel ist die Minimierung der erwarteten Kosten die sich aus Betriebskosten, Produktionskosten, Transportkosten, Lagerhaltungskosten und Strafkosten bei Fehlmengen zusammensetzen. Ein exaktes und ein heuristisches Lösungsverfahren werden vorgestellt. Die zweite Erweiterung kann man als doppeltes Set-Cover Problem verstehen. Es sollen Kunden mit zwei Dienstleistungen bedient werden, die an Zentren gebunden sind. Jeder Kunde muss von mindestens einem Zentrum eines jeden Dienstleistungstyps erreichbar sein. Gleichzeitig ist darauf zu achten, dass die Anzahl verwendeter Zentren beschränkt ist und dass die Zentren höchstens einer Dienstleistung zugeordnet sind. Es werden verschiedene Anwendungen vorgestellt, und durch Einschränkungen wird versucht die Grenze zwischen Problemen mit polynomiellem Aufwand und NP-schweren Problemen zu ziehen. Im Rahmen einer bioinformatischen Anwendung wird eine Ant-Colony Metaheuristik eingesetzt.Facility location treats the problem of choosing locations while respecting effort and utility. E.g.: we can think of balancing the maintenance and setup costs for a facility. The central contribution of this work are two extensions of classical location models that get enclosed into the presentation of standard facility location models. One of the extensions is a dynamic warehouse location problem in a stochastic environment. Within a planning horizon of given number of periods we are able to open and close facilities and the aim is to minimize the expected costs. The costs consist of operating costs, production costs, inventory costs and penalty costs for shortages. We present an exact method and a heuristic approach. The second extension can be regarded as a double Set Cover Problem. We have to maintain two services by allocating corresponding sites and each customer has to be reachable by at least one of the centers and each service type. Simultaneously we have to respect that the number of used locations is limited, while no location is assigned to two services. We present different applications and by restricting the problem we draw the line between polynomially solvable problems and intractable ones. In the context of an application in bio-informatics we develop an ACO heuristic

A history of ornamental buildings and structures in Scotland's gardens and designed landscapes: from the 12th century to 1840

This thesis offers a history of ornamental garden buildings in Scotland. It is based on a comprehensive inventory of the country's garden structures, compiled from primary sources, secondary sources and site visits. The thesis is divided into an introduction and six chapters. The introduction outlines past research into the subject of garden buildings generally and those in Scotland particularly, and sets out the need for historical revision. The first two chapters treat of the period between the 12th century and the Restoration, and focus upon the architecture and iconography of ornamental structures at Linlithgow Palace, Pinkie House and Dundas Castle. The third chapter examines developments up to the Union of Parliaments and evaluates the oeuvre and influence of Sir William Bruce. The fourth chapter covers the period up to the last Jacobite rebellion and draws attention to the role of garden buildings in focusing views upon ruined towers and `sublime' natural features. It is suggested that such features were emblematic of Scotland's lost nationhood. The fifth chapter analyses mid -18th- century garden buildings and is structured around John Dalrymple's contemporary text, An Essay on Landscape Gardening, which, it is suggested, articulated commonly -held Scottish attitudes to landscape design. The style and distribution of garden buildings are offered as evidence in support of this assertion. Attention is also drawn to the allegorical significance of the Hermitage at Dunkeld. The final chapter chronicles the demise in popularity of garden buildings in the years between 1780 and 1840, and looks at those most commonly built during this time - the tower and the mausoleum. The thesis concludes that the study of garden buildings in their proper context can contribute appreciably to our understanding of Scotland's intellectual, architectural and garden history

For The Boys in Blue : The Art Galleries of the Sanitary Fairs

Beginning in 1863 and continuing until 1865, the Sanitary Fairs held in Northern cities, to raise money for Union soldiers were the most significant fundraisers of the Civil War. The fairs combined the local with the global, and enticed visitors with relics of the colonial past, interesting artifacts of Native American culture, souvenirs from far away lands, and fascinating technological inventions. For the majority of the fairs however, the art exhibitions were without doubt the most significant, complex and politically charged exhibits, and they are the focus of this paper. Visitors to the art galleries were attracted by their educational mission and their ability to elevate the psyche of visitors above the serious tribulations of the war. The national faith in Manifest Destiny and Divine Providence was strongly evidenced in the art galleries by the many paintings that celebrated the exceptionality of American nature, the setting of America\u27s greatest historical accomplishments, which were also acknowledged by many works of depicting events from colonial history. From Chicago to Cleveland and Cincinnati, St. Louis, Philadelphia, New York and Boston, artists and collectors generously lent works, allowing audiences a retrospective of American art of the first half of the nineteenth century. The art galleries showcased the works of younger and lesser-known American artists, including women, when other venues for their promotion were entirely lacking. Furthermore, the art galleries gave audiences the opportunity to compare the relative merits of American versus European art. Their remarkable attendance records indicated the desire of the public to have access to public art collections and ultimately led to the creation of American museums at the last quarter of the nineteenth century