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A directed graph is simple if each ordered pair of vertices is the head and tail of at most one edge; one loop may be present at each vertex. For each n ≥ 1, prove or disprove the following statement. Every simple directed graph with n vertices has two vertices with the same outdegree or two vertices with the same indegree.
(a) How many words of length 2 are there over the alphabet A = { 0; 1; 2; 3}?
(b) Construct the de Bruijn digraph D4,2 and use this digraph to nd an appropriate de Bruijn sequence.
(c) For b = 4 and n = 2, how many de Bruijn sequences can be formed?
Suppose [S, T] and [X, Y ] are two minimal cuts in a network N. Prove that both [S [X U T ∩ Y ] and [S ∩ X, T U Y ] are also minimal cuts in N.
Window variables are the variables measured during the constrained interval of an observation period which is accepted as the proxies for the information over the whole period. Fo
The type of longitudinal study in which the subjects receive different treatments on the various occasions. Random allocation is required to determine the order in which the treatm
Cohort study : An investigation in which the group of individuals (or the cohort) is identi?ed and followed prospectively, possibly for many years, and their subsequent medical his
The Null Hypothesis - H0: There is no first order autocorrelation The Alternative Hypothesis - H1: There is first order autocorrelation Durbin-Watson statistic = 1.98307
Quantalassay: The experiment in which the groups of subjects are exposed to the different doses of, generally, a drug, to which the particular number respond. Data from such type
Q1: The growth in bad debt expense for Aptara Pvt. Ltd. Company over the last 20 years is as follows. 1997 0.11 1998 0.09 1999 0.08 2000 0.08 2001 0.1 2002 0.11 2003 0.12 2004 0.1
Described by the leading proponent as 'the conscientious, explicit, and judicious uses of present best evidence in making the decisions about the care of individual patients, and
Multi dimensional unfolding is the form of multidimensional scaling applicable to both the rectangular proximity matrices where the rows and columns refer to the different sets of
Kaiser's rule is the rule frequently used in the principal components analysis for selecting the suitable the number of components. When the components are derived from correlati
Jelinski Moranda model is t he model of software reliability which supposes that failures occur according to the Poisson process with a rate decreasing as more faults are diagnos
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