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In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows (when pre-multiplying, to form PA) or columns (when post-multiplying, to form AP) of the matrix A.
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.
Transmission Control Protocol (TCP) uses a congestion control algorithm that includes various aspects of an additive increase/multiplicative decrease (AIMD) scheme, along with other schemes including slow start and congestion window (CWND), to achieve congestion avoidance. The TCP congestion-avoidance algorithm is the primary basis for congestion control in the Internet. Per the end-to-end principle, congestion control is largely a function of internet hosts, not the network itself.
Allocating tasks to machines in computing clusters is described. In an embodiment a set of tasks associated with a job are received at a scheduler. In an embodiment an index can be computed for each c
We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of intercontact times between mobile devices. Us
Collaborative ad-hoc dissemination of information has been proposed as an efficient means to disseminate information among devices in a wireless ad-hoc network. Devices help in forwarding the informat