This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for ...

Lesions located in the bilateral posterior incisural space are difficult to treat due to limited exposure. The classical approaches to this area are limited for lesions located bilaterally and especially when the lesion extends also below the tentorium as it may occur with meningiomas. Kawashima et al. reported, in anatomic studies, a new occipital transtentorial approach: the occipital bi-tran...

This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of mini...

The new ternary phase Ba(5)In(4)Bi(5) was synthesized by direct reaction of the corresponding elements at high temperature. It crystallizes in a noncentrosymmetric space group and represents a new structure type (tetragonal, P4nc with a=10.620(2) and c=9.009(2) A, Z=2). The structure is built of interconnected heteroatomic clusters of In(4)Bi(5), square pyramids with In(4)-bases and four exo-bo...

We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bi-vector, a two-form and an inverse metric. Lifting the topological sector of this action to three dimensions produces several Wess-Zumino like terms which encode the bi-vector generalization of the Courant bracket. This bracket may be familiar to physicists throu...

Several recent papers have shown how to approximate the difference ∑i |ai−bi| or ∑ |ai−bi| between two functions, when the function values ai and bi are given in a data stream, and their order is chosen by an adversary. These algorithms use little space (much less than would be needed to store the entire stream) and little time to process each item in the stream. They approximate with small rel...

Introduction. This paper deals with locales and their spaces of points in intuitionistic analysis or, if you like, in (Grothendieck) toposes. One of the important aspects of the problem whether a certain locale has enough points is that it is directly related to the (constructive) completeness of a geometric theory. A useful exposition of this relationship may be found in [1], and we will assum...

We first introduce two functions on finitely additive probability spaces that behave well under products: discrepancy, which measures how close one space comes to extending another, and bi-discrepancy, which is a pseudo-metric on the collection of all spaces on a given set, and a metric on the collection of complete spaces. We then apply these to show that the Loeb space of the internal product...

We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with (N,+,×) if and only if the space of non-maximal prime ideals of A is nonempty and connected in the Zariski topology and the nilradical of A has a nontrivial annihilator in Z. Notably, by constructing a nontrivial...