Iterative-deepening heuristic search for optimal and semi-optimal resource allocation

It is demonstrated that when iterative-deepening A asterisk (IDA asterisk) is applied to one type of resource allocation problem, it uses far less storage than A asterisk, but opens far more nodes and thus has unacceptable time complexity. This is shown to be due, at least in part, to the low-valued effective branching factor that is a characteristic of problems with real-valued cost functions. The semi-optimal, epsilon-admissible IDA asterisk sub epsilon search algorithm that the authors described was shown to open fewer nodes than both A asterisk and IDA asterisk with storage complexity proportional to the depth of the search tree

Using the distribution of cells by dimension in a cylindrical algebraic decomposition

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather, the distribution is inherent to the cylindrical structure and determined mostly by the number of variables. This insight is then combined with an algorithm that produces only full-dimensional cells to give an accurate method of predicting the number of cells in a complete CAD. Since constructing only full-dimensional cells is relatively inexpensive (involving no costly algebraic number calculations) this leads to heuristics for helping with various questions of problem formulation for CAD, such as choosing an optimal variable ordering. Our experiments demonstrate that this approach can be highly effective.Comment: 8 page

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Albert Einstein's 1916 Review Article on General Relativity

The first comprehensive overview of the final version of the general theory of relativity was published by Einstein in 1916 after several expositions of preliminary versions and latest revisions of the theory in November 1915. A historical account of this review paper is given, of its prehistory, including a discussion of Einstein's collaboration with Marcel Grossmann, and of its immediate reception.Comment: 27 pages, 1 jpg imag

Automated multigravity assist trajectory planning with a modified ant colony algorithm

The paper presents an approach to transcribe a multigravity assist trajectory design problem into an integrated planning and scheduling problem. A modified Ant Colony Optimization (ACO) algorithm is then used to generate optimal plans corresponding to optimal sequences of gravity assists and deep space manoeuvers to reach a given destination. The modified Ant Colony Algorithm is based on a hybridization between standard ACO paradigms and a tabu-based heuristic. The scheduling algorithm is integrated into the trajectory model to provide a fast time-allocation of the events along the trajectory. The approach demonstrated to be very effective on a number of real trajectory design problems