In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...

Binomial trees have been used extensively for broadcasting in clusters of workstations. In the case of heterogeneous nondedicated clusters and grid environments, the broadcasting occurs over a heterogeneous network, and the performance obtained by the broadcast algorithm will depend on the organization of the nodes onto the binomial tree. The organization of the nodes should take into account t...

Clinicians need to predict the number of involved nodes in breast cancer patients in order to ascertain severity, prognosis, and design subsequent treatment. The distribution of involved nodes often displays over-dispersion-a larger variability than expected. Until now, the negative binomial model has been used to describe this distribution assuming that over-dispersion is only due to unobserve...

The triangular array of binomial coefficients, or Pascal’s triangle, is formed by starting with an apex of 1. Every row of Pascal’s triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal to the number of ways the line-graph can be constructed when starting with this node and adding ...

San Fermı́n is a system for aggregating large amounts of data from the nodes of large-scale distributed systems. Each San Fermı́n node individually computes the aggregated result by swapping data with other nodes to dynamically create its own binomial tree. Nodes that fall behind abort their trees, thereby reducing overhead. Having each node create its own binomial tree makes San Fermı́n highly re...

Most multicast algorithms proposed in the literature assume an arbitrarily long message being communicated as a single packet. Modern networks typically limit the size of the largest packet, and long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the comm...

It is a common belief that the standard binomial algorithm of Cox-Ross-Rubinstein (CRR) cannot be used to deal with barrier options with multiple or time-varying boundaries. We propose an extension of the CRR model to evaluate options with exponential boundaries. The essence of the extended binomial model relies upon the construction of a binomial tree for the underlying asset price dynamics, c...

Embedding is of great importance in the applications of parallel computing. Every parallel application has its intrinsic communication pattern. The communication pattern graph is mapped onto the topology of multiprocessor structures so that the corresponding application can be executed. To increase the reliability of parallel applications, fault-tolerant embedding is necessary. In this paper, w...

Modern networks typically limit the size of the largest packet for efficient communication. Thus, long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the communication protocol. This paper presents a concept of smart network interface support for packetiz...