contrary to majority of islamic jurists, those who believe in singularity of reality and a certain rule in disagreement cases, in opinion of some of the scholars, the truth and the rule is plural and all of the jurist(modjtahedin) are just. imam mohammad ghazzali is one of these scholars. in his opinion, the theory of proscription (takteah) is incorrect and contradictory. with the exception of ...

We present a very simple explicit technique to generate a large family of point configurations with neighborly Delaunay triangulations. This proves that there are superexponentially many combinatorially distinct neighborly d-polytopes with n vertices that admit realizations inscribed on the sphere. These are the first examples of inscribable neighborly polytopes that are not cyclic polytopes, a...

In this paper, we demonstrate that simple fuzzy rule-based classification systems with high interpretability are obtained through multiobjective genetic rule selection. In our approach, first a prespecified number of candidate fuzzy rules are extracted from numerical data in a heuristic manner using rule evaluation criteria. Then multiobjective genetic rule selection is applied to the extracted...

Local rules theory describes virus capsid self-assembly in terms of simple local binding preferences of discrete subunit conformations. The theory offered a parsimonious explanation for the complexity and regularity of virus capsids that resolved several inconsistencies between experimental observations and prior theories. Simultaneously, it provided a valuable practical abstraction for simulat...

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f -, hand γ-vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h-vectors and γ-vectors involving descent statistics. This includes a combinatorial interpret...

Estimating the number of vertices of a convex polytope defined by a system of linear inequalities is crucial for bounding the run-time of exact generation methods. It is not easy to achieve a good estimator, since this problem belongs to the #P complexity class. In this paper we present two randomized algorithms for estimating the number of vertices in polytopes. The first is based on the well-...