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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.
Probit analysis is the technique most commonly employed in the bioassay, specifically toxicological experiments where the group of animals is subjected to known levels of a toxin
Log-linear models is the models for count data in which the logarithm of expected value of a count variable is modelled as the linear function of parameters; the latter represent
Confidence interval : A range of the values, calculated from the sample observations which is believed, with the particular probability, to posses the true parameter value. A 95% c
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
Demographic data: Age: continuous variable Gender: categorical variable with males coded 1, females coded 2. Relationship status: categorical variable 1 to 5. Rational
This is the branch of mathematics which deals with the theory of contests between two or more players under the specified sets of rules. The subject supposes a statistical aspect w
Multi-hit model is the model for a toxic response which results from the random occurrence of one or the more fundamental biological events. A response is supposed to be induced o
hello I have a dataset including both categorical & numerical variable for market segmentation.how can i cluster them via k-means in matlab? thank you
How has quantitative analysis changed the current scenario in the management world today?
The biggest and smallest variate values among the sample of observations. Significant in various regions, for instance flood levels of the river, speed of wind and snowfall.
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