Engineering Art Galleries

The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive experiment. Furthermore, we show what core algorithmic ingredients have led to recent successes

Algorithms for Art Gallery Illumination

We consider a variant of the Art Gallery Problem, where a polygonal region is to be covered with light sources, with light fading over distance. We describe two practical algorithms, one based on a discrete approximation, and another based on nonlinear programming by means of simplex partitioning strategies. For the case where the light positions are given, we describe a fully polynomial-time approximation scheme. For both algorithms we present an experimental evaluation

The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure

Engineering Art Galleries

The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive experiment. Furthermore, we show what core algorithmic ingredients have led to recent successes

Adaptation of eye and hand movements to target displacements of different size

Previous work has documented that the direction of eye and hand movements can be adaptively modified using the double-step paradigm. Here we report that both motor systems adapt not only to small direction steps (5° gaze angle) but also to large ones (28° gaze angle). However, the magnitude of adaptation did not increase with step size, and the relative magnitude of adaptation therefore decreased from 67% with small steps to 15% with large steps. This decreasing efficiency of adaptation may reflect the participation of directionally selective neural circuits in double-step adaptation

Comparison of Effects of Ivabradine versus Carvedilol in Murine Model with the Coxsackievirus B3-Induced Viral Myocarditis

BACKGROUND: Elevated heart rate is associated with increased cardiovascular morbidity. The selective I(f) current inhibitor ivabradine reduces heart rate without affecting cardiac contractility, and has been shown to be cardioprotective in the failing heart. Ivabradine also exerts some of its beneficial effects by decreasing cardiac proinflammatory cytokines and inhibiting peroxidants and collagen accumulation in atherosclerosis or congestive heart failure. However, the effects of ivabradine in the setting of acute viral myocarditis and on the cytokines, oxidative stress and cardiomyocyte apoptosis have not been investigated. METHODOLOGY/PRINCIPAL FINDINGS: The study was designed to compare the effects of ivabradine and carvedilol in acute viral myocarditis. In a coxsackievirus B3 murine myocarditis model (Balb/c), effects of ivabradine and carvedilol (a nonselective β-adrenoceptor antagonist) on myocardial histopathological changes, cardiac function, plasma noradrenaline, cytokine levels, cardiomyocyte apoptosis, malondialdehyde and superoxide dismutase contents were studied. Both ivabradine and carvedilol similarly and significantly reduced heart rate, attenuated myocardial lesions and improved the impairment of left ventricular function. In addition, ivabradine treatment as well as carvedilol treatment showed significant effects on altered myocardial cytokines with a decrease in the amount of plasma noradrenaline. The increased myocardial MCP-1, IL-6, and TNF-α. in the infected mice was significantly attenuated in the ivabradine treatment group. Only carvedilol had significant anti-oxidative and anti-apoptoic effects in coxsackievirus B3-infected mice. CONCLUSIONS/SIGNIFICANCE: These results show that the protective effects of heart rate reduction with ivabradine and carvedilol observed in the acute phase of coxsackievirus B3 murine myocarditis may be due not only to the heart rate reduction itself but also to the downregulation of inflammatory cytokines