K-Nearest Neighbor (KNN) is highly efficient classification algorithm due to its key features like: very easy to use, requires low training time, robust to noisy training data, easy to implement. However, it also has some shortcomings like high computational complexity, large memory requirement for large training datasets, curse of dimensionality and equal weights given to all attributes. Many ...

It is NP-hard to decide if a given pure strategy Nash equilibrium of a given three-player game in strategic form with integer payoffs is trembling hand perfect.

A graph is called t-perfect if its stable set polytope is fully described by non-negativity, edge and odd-cycle constraints. We characterise P5-free t-perfect graphs in terms of forbidden t-minors. Moreover, we show that P5-free t-perfect graphs can always be coloured with three colours, and that they can be recognised in polynomial time.

A mathematical model is presented in which a single mutation can affect multiple phenotypic characters, each of which is subject to stabilizing selection. A wide range of mutations is allowed, including ones that produce extremely small phenotypic changes. The analysis shows that, when three or more characters are affected by each mutation, a single optimal genetic sequence may become common. T...

A mixed hypergraph is a tripleH = (X, C,D), whereX is the vertex set and each of C, D is a family of subsets of X, the C-edges and D-edges, respectively. A proper k-coloring of H is an injective mapping c : X → {1, . . . , k} such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Maximum number of colors in a coloring using all the colo...

David Hume’s value theory—in particular, his theory of prudential value or self-interest—is rarely investigated in any depth. Though he makes a number of claims about what is in someone’s interest (including his discussion of the prudential value of the virtues in the second Enquiry1), there is very little material in Hume’s philosophic writing that yields a clear statement of his theory of wha...

our problem in this article is ibn miskawayh’s analysis of the nature of happiness, and its methodology is descriptive- analytic. ibn miskawayh considers happiness as “good” and “perfection” with respect to their holders; so, he establishes some inseparability between happiness, and good and perfection. ibn miskawayh has two definitions for the concept of good. he divides this conception into s...

In the development of a digital sculpture for a competition entry, a mathematical approach was investigated as a method to develop a variety of forms. This paper covers the initial inspiration for the sculpture, Georg Nees’s Gravel Stones, and then the series of approaches that were developed expanding the starting concept. Each step in the process is described including the decisions and alter...

The amount of research done by the MCMC community has been very impressive in the last two decades, as testified by this very volume. The power of MCMC has been demonstrated in countless instances in which more traditional numerical algorithms are helpless. However, one ubiquitous problem remains: the detection of convergence or lack thereof. Among the large number of procedures designed for de...

The ‘‘perfect’’ surgical scenario: You feel good, rested, and confident in the procedure you are about to perform. The patient is in good physical condition, is easy to communicate with, and seems to have a good understanding of what is required postoperatively. After the surgical procedure, you feel like everything worked out perfectly and you are confident that the patient will experience a g...