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

Algorithms for Optimizing Search Schedules in a Polygon

In the area of motion planning, considerable work has been done on guarding problems, where "guards", modelled as points, must guard a polygonal space from "intruders". Different variants of this problem involve varying a number of factors. The guards performing the search may vary in terms of their number, their mobility, and their range of vision. The model of intruders may or may not allow them to move. The polygon being searched may have a specified starting point, a specified ending point, or neither of these. The typical question asked about one of these problems is whether or not certain polygons can be searched under a particular guarding paradigm defined by the types of guards and intruders. In this thesis, we focus on two cases of a chain of guards searching a room (polygon with a specific starting point) for mobile intruders. The intruders must never be allowed to escape through the door undetected. In the case of the two guard problem, the guards must start at the door point and move in opposite directions along the boundary of the polygon, never crossing the door point. At all times, the guards must be able to see each other. The search is complete once both guards occupy the same spot elsewhere on the polygon. In the case of a chain of three guards, consecutive guards in the chain must always be visible. Again, the search starts at the door point, and the outer guards of the chain must move from the door in opposite directions. These outer guards must always remain on the boundary of the polygon. The search is complete once the chain lies entirely on a portion of the polygon boundary not containing the door point. Determining whether a polygon can be searched is a problem in the area of visibility in polygons; further to that, our work is related to the area of planning algorithms. We look for ways to find optimal schedules that minimize the distance or time required to complete the search. This is done by finding shortest paths in visibility diagrams that indicate valid positions for the guards. In the case of the two-guard room search, we are able to find the shortest distance schedule and the quickest schedule. The shortest distance schedule is found in O(n^2) time by solving an L_1 shortest path problem among curved obstacles in two dimensions. The quickest search schedule is found in O(n^4) time by solving an L_infinity shortest path problem among curved obstacles in two dimensions. For the chain of three guards, a search schedule minimizing the total distance travelled by the outer guards is found in O(n^6) time by solving an L_1 shortest path problem among curved obstacles in two dimensions

Protective equipment applicable to a centralized cytostatic preparation unit

Occupational exposure to cytotoxic agents has been recognized as a potential danger to the health of handlers. However, collective and individual protection equipment has been developed for use by professionals. This article aims to identify and describe the protection equipment applicable to a centralized unit of cytostatics preparation, using a qualitative and quantitative descriptive analysis. A questionnaire survey yielded 83 responses, covering 18 centralized cytostatic preparation units. The results show some weaknesses detected in some institutions such as the absence of a shower and eyewash fountain, the lack of knowledge about the procedures manual, and the use of a surgical mask. However, the results point to awareness by the general manipulators regarding the use of some personal protective equipment. This study contributes to the investigation of the use of equipment for the protection of cytostatic manipulators at work in centralized cytostatic preparation units.The authors are grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support by national funds FCT/MCTES to UNIAG, under Project no. UIDB/04752/2020.info:eu-repo/semantics/publishedVersio

The rise of the sharing economy: estimating the impact of Airbnb on the hotel industry

Peer-to-peer markets, collectively known as the sharing economy, have emerged as alternative suppliers of goods and services traditionally provided by long-established industries. We explore the economic impact of the sharing economy on incumbent firms by studying the case of Airbnb, a prominent platform for short-term accommodations. We analyze Airbnb's entry into the state of Texas, and quantify its impact on the Texas hotel industry over the subsequent decade. We estimate that in Austin, where Airbnb supply is highest, the causal impact on hotel revenue is in the 8-10% range; moreover, the impact is non-uniform, with lower-priced hotels and those hotels not catering to business travelers being the most affected. The impact manifests itself primarily through less aggressive hotel room pricing, an impact that benefits all consumers, not just participants in the sharing economy. The price response is especially pronounced during periods of peak demand, such as SXSW, and is due to a differentiating feature of peer-to-peer platforms -- enabling instantaneous supply to scale to meet demand.Accepted manuscrip

Connectivity Constraints in Network Analysis

This dissertation establishes mathematical foundations of connectivity requirements arising in both abstract and geometric network analysis. Connectivity constraints are ubiquitous in network design and network analysis. Aside from the obvious applications in communication and transportation networks, they have also appeared in forest planning, political distracting, activity detection in video sequences and protein-protein interaction networks. Theoretically, connectivity constraints can be analyzed via polyhedral methods, in which we investigate the structure of (vertex)-connected subgraph polytope (CSP). One focus of this dissertation is on performing an extensive study of facets of CSP. We present the first systematic study of non-trivial facets of CSP. One advantage to study facets is that a facet-defining inequality is always among the tightest valid inequalities, so applying facet-defining inequalities when imposing connectivity constraints can guarantee good performance of the algorithm. We adopt lifting techniques to provide a framework to generate a wide class of facet-defining inequalities of CSP. We also derive the necessary and sufficient conditions when a vertex separator inequality, which plays a critical role in connectivity constraints, induces a facet of CSP. Another advantage to study facets is that CSP is uniquely determined by its facets, so full understanding of CSP's facets indicates full understanding of CSP itself. We are able to derive a full description of CSP for a wide class of graphs, including forest and several types of dense graphs, such as graphs with small independence number, s-plex with small s and s-defective cliques with small s. Furthermore, we investigate the relationship between lifting techniques, maximum weight connected subgraph problem and node-weight Steiner tree problem and study the computational complexity of generation of facet-defining inequalities. Another focus of this dissertation is to study connectivity in geometric network analysis. In geometric applications like wireless networks and communication networks, the concept of connectivity can be defined in various ways. In one case, connectivity is imposed by distance, which can be modeled by unit disk graphs (UDG). We create a polytime algorithm to identify large 2-clique in UDG; in another case when connectivity is based on visibility, we provide a generalization of the two-guard problem

Is there an app for that? A case study of the potentials and limitations of the participatory turn and networked publics for classical music audience engagement

The participatory turn, fuelled by discourses and rhetoric regarding social media, and in the aftermath of the dot.com crash of the early 2000s, enrols to some extent an idea of being able to deploy networks to achieve institutional aims. The arts and cultural sector in the UK, in the face of funding cuts, has been keen to engage with such ideas in order to demonstrate value for money; by improving the efficiency of their operations, improving their respective audience experience and ultimately increasing audience size and engagement. Drawing on a case study compiled via a collaborative research project with a UK-based symphony orchestra (UKSO) we interrogate the potentials of social media engagement for audience development work through participatory media and networked publics. We argue that the literature related to mobile phones and applications (‘apps’) has focused primarily on marketing for engagement where institutional contexts are concerned. In contrast, our analysis elucidates the broader potentials and limitations of social-media-enabled apps for audience development and engagement beyond a marketing paradigm. In the case of UKSO, it appears that the technologically deterministic discourses often associated with institutional enrolment of participatory media and networked publics may not necessarily apply due to classical music culture. More generally, this work raises the contradictory nature of networked publics and argues for increased critical engagement with the concept

Rising prevalence of BMI ≥40kg/m2: a high-demand epidemic needing better documentation

Whilst previously rare, some surveys indicate substantial increases in the population with body mass index (BMI) ≥40 kg/m2 since the 1980s. Clinicians report emerging care challenges for this population, often with high resource demands. Accurate prevalence data, gathered using reliable methods, are needed to inform health care practice, planning, and research. We searched digitally for English language sources with measured prevalence data on adult BMI ≥40 collected since 2010. The search strategy included sources identified from recent work by NCD‐RisC (2017), grey sources, a literature search to find current sources, and digital snowball searching. Eighteen countries, across five continents, reported BMI ≥40 prevalence data in surveys since 2010: 12% of eligible national surveys examined. Prevalence of BMI ≥40 ranged from 1.3% (Spain) to 7.7% (USA) for all adults, 0.7% (Serbia) to 5.6% (USA) for men, and 1.8% (Poland) to 9.7% (USA) for women. Limited trend data covering recent decades support significant growth of BMI ≥40 population. Methodological limitations include small samples and data collection methods likely to exclude people with very high BMIs. BMI ≥40 data are not routinely reported in international surveys. Lack of data impairs surveillance of population trends, understanding of causation, and societal provision for individuals living with higher weights

The Ithacan, 2003-01-30

https://digitalcommons.ithaca.edu/ithacan_2002-3/1016/thumbnail.jp

Vessel sanitation program operations manual 2000

U.S. Public Health Service, Centers for Disease Control and Prevention, National Center for Environmental Health.Cover title.Includes bibliographical references (p. 13.11-1-13.11-49)