【正文】 public facilities have signs in rooms used for public gatherings which state that it is unlawful for the rooms to be occupied by more than a specified number of people. Presumably, this number is based on the speed with which people in the room could be evacuated from the room39。s idea be made to work? Assuming that the grades given out are only (A,B,C,...)can the dean39。lack input capabilities for marking points in the picture before slicing。s notice would be appreciated. It would be ideal if the algorithm could also be used to make assignments for future meetings involving different levels of participation for each type of attendee. 1998 American MCM Problems Problem A MRI Scanners Introduction Industrial medical diagnostic machines known as Magic Resonance Imager (MRI) scan a threedimensional object such as a brain, and deliver their results in the form of a threedimensional array of pixel. Each pixel consists of one number indicating a color or a shade of gray that encodes a measure of water concentration in a small region of the scanned object at the location of the pixel .For instance,0 can picture high water concentration in black (ventricles, blood vessels),128 can picture a medium water concentration in gray(brain nuclei and gray matter),and 255 can picture a low water density in white (liquidrich white matter consisting of myelinated axons).Such MRI scanners also include facilities to picture on a screen any horizontal or vertical slice through the threedimensional array (slices are parallel to any of the three Cartesian coordinate axes ).Algorithms for picturing slices through oblique planes ,however ,are proprietary .Current algorithms are limited in terms of the angles and parameter options available 。s six senior officers. None of these officers are board members. Thus each senior officers will not be involved in the afternoon sessions and each of these sessions will consist of only four different discussion groups. The president of the corporation wants a list of boardmember assignment to discussion groups for each of the seven sessions. The assignments should achieve as much of a mix of the members as much as possible. The ideal assignment would have each board member in a discussion group the same number of times while minimizing mon membership of groups for the different sessions. The assignment should also satisfy the following criteria: the morning sessions ,no board member should be in the same senior officer39。s saythere are P=100 papers. A group of J judges is collected to acplish thejudging. Funding for the contest constains both the number of judges that canbe obtained and amount of time that they can judge. For eample if P=100, thenJ=8 is , each judge would read paper and rankorder them, but there are toomany papers for this. Instead, there will be a number of screening rounds inwhich each judge will read some number of papers and give them scores. Thensome selection scheme is used to reduce the number of papers under consideration: If the papers are rankordered, then the bottom 30% that eachjudge rankorders could be rejected. Alternatively, if the judges do not rankorder, but instead give them numerical score (say, from 1 to 100),then all papers below some cutoff level could be rejected. The new pool of papers is then passed back to the judges, and the process is repeated. A concern is then the total number of papers that judge reads must besubstantially less than P. The process is stopped when there are only W papersleft. There are the winners. Typically for P=100, W=3. Your task is to determine a selection scheme, using a bination of rankordering, numerical scoring, and other methods, by which the final Wpapers will include only papers from among the best 2W papers. (By best,we assume that there is an absolute rankordering to which all judges wouldagree.) For example, the top three papers. Among all such methods, the one thatrequired each judge to read the least number of papers is desired. Note the possibility of systematic bias in a numerical scoring scheme. For example, for a specific collection of papers, one judge could average 70points, while another could average 80 points. How would you scale your schemeto acmodate for changes in the contest parameters (P, J, and W)? 1997 American MCM Problems Problem A The Velociraptor Problem The velociraptor,Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter, and may have hunted in pairs or larger packs .Unfortunately, there is no way to observe its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached your team and asked for help in modeling the hunting behavior of the velociraptor. They hope to pare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals. The average adult velociraptor was 3 meters long with a hip height of meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast at speed of 60 km/hr for about 15 seconds. After the initial burst of speed ,the animal needed to stop and recover from a buildup of lactic acid in its muscles. Suppose that velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the Velociraptor. A biomachanical analysis of a fossilized Thescelosaurus indicates that it could run at a speed of about 50 km/hr. for long period of time. Part1 Assuming the velociraptor is a solitary hunter, design a mathematical model that describe a hunting strategy for a single velociraptor stalking and chasing a sin