857 research outputs found

    Empty Squares in Arbitrary Orientation Among Points

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    This paper studies empty squares in arbitrary orientation among a set PP of nn points in the plane. We prove that the number of empty squares with four contact pairs is between Ω(n)\Omega(n) and O(n2)O(n^2), and that these bounds are tight, provided PP is in a certain general position. A contact pair of a square is a pair of a point pPp\in P and a side \ell of the square with pp\in \ell. The upper bound O(n2)O(n^2) also applies to the number of empty squares with four contact points, while we construct a point set among which there is no square of four contact points. These combinatorial results are based on new observations on the LL_\infty Voronoi diagram with the axes rotated and its close connection to empty squares in arbitrary orientation. We then present an algorithm that maintains a combinatorial structure of the LL_\infty Voronoi diagram of PP, while the axes of the plane continuously rotates by 9090 degrees, and simultaneously reports all empty squares with four contact pairs among PP in an output-sensitive way within O(slogn)O(s\log n) time and O(n)O(n) space, where ss denotes the number of reported squares. Several new algorithmic results are also obtained: a largest empty square among PP and a square annulus of minimum width or minimum area that encloses PP over all orientations can be computed in worst-case O(n2logn)O(n^2 \log n) time.Comment: 39 pages, 11 figure

    The Reverse Kakeya Problem

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    Inscribing or Circumscribing a Histogon to a Convex Polygon

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    We consider two optimization problems of approximating a convex polygon, one by a largest inscribed histogon and the other by a smallest circumscribed histogon. An axis-aligned histogon is an axis-aligned rectilinear polygon such that every horizontal edge has an integer length. A histogon of orientation ? is a copy of an axis-aligned histogon rotated by ? in counterclockwise direction. The goal is to find a largest inscribed histogon and a smallest circumscribed histogon over all orientations in [0,?). Depending on whether the horizontal width of a histogon is predetermined or not, we consider several different versions of the problem and present exact algorithms. These optimization problems belong to shape analysis, classification, and simplification, and they have applications in various cost-optimization problems

    Kalman Filter Sensor Fusion for Mecanum Wheeled Automated Guided Vehicle Localization

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    The Mecanum automated guided vehicle (AGV), which can move in any direction by using a special wheel structure with a LIMwheel and a diagonally positioned roller, holds considerable promise for the field of industrial electronics. A conventional method for Mecanum AGV localization has certain limitations, such as slip phenomena, because there are variations in the surface of the road and ground friction. Therefore, precise localization is a very important issue for the inevitable slip phenomenon situation. So a sensor fusion technique is developed to cope with this drawback by using the Kalman filter. ENCODER and StarGazer were used for sensor fusion. StarGazer is a position sensor for an image recognition device and always generates some errors due to the limitations of the image recognition device. ENCODER has also errors accumulating over time. On the other hand, there are no moving errors. In this study, we developed a Mecanum AGV prototype system and showed by simulation that we can eliminate the disadvantages of each sensor. We obtained the precise localization of the Mecanum AGV in a slip phenomenon situation via sensor fusion using a Kalman filter

    Kalman Filter Sensor Fusion for Mecanum Wheeled Automated Guided Vehicle Localization

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    The Mecanum automated guided vehicle (AGV), which can move in any direction by using a special wheel structure with a LIM-wheel and a diagonally positioned roller, holds considerable promise for the field of industrial electronics. A conventional method for Mecanum AGV localization has certain limitations, such as slip phenomena, because there are variations in the surface of the road and ground friction. Therefore, precise localization is a very important issue for the inevitable slip phenomenon situation. So a sensor fusion technique is developed to cope with this drawback by using the Kalman filter. ENCODER and StarGazer were used for sensor fusion. StarGazer is a position sensor for an image recognition device and always generates some errors due to the limitations of the image recognition device. ENCODER has also errors accumulating over time. On the other hand, there are no moving errors. In this study, we developed a Mecanum AGV prototype system and showed by simulation that we can eliminate the disadvantages of each sensor. We obtained the precise localization of the Mecanum AGV in a slip phenomenon situation via sensor fusion using a Kalman filter

    Successful Hemostasis with Recombinant Activated Factor VII in a Patient with Massive Hepatic Subcapsular Hematoma

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    Recombinant activated coagulation factor VII (rFVIIa) is known to be effective in the management of acquired deficiencies of factor VII and platelet function defects. But recently, rFVIIa has been successfully used to treat ongoing bleeding in disseminated intravascular coagulopathy (DIC) condition. The patient reported here was suspected to be suffering from toxic hepatitis on admission. After percutaneous liver biopsy, bleeding occurred and did not stop even after right hepatic artery embolization. The patient developed a severe hemorrhage that resulted in hypovolemic shock, hemoperitoneum, and a massive subcapsular hematoma. The patient then developed DIC due to massive transfusion, as well as acute liver necrosis. The patient was given 400 μg/kg of rFVIIa. Recombinant factor VIIa was administered in an attempt to control the bleeding. This stabilized the hemoglobin levels of the patient. The patient gradually recovered in 4 months. In conclusion, this case suggests that rFVIIa can be successfully used for the hemostasis of uncontrolled bleeding in DIC
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