How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP

We consider the 1-median problem with euclidean distances with uncertainty in the weights, expressed as possible changes within given bounds and a single budget constraint on the total cost of change. The upgrading (resp. downgrading) problem consists of minimizing (resp. maximizing) the optimal 1-median objective value over these weight changes. The upgrading problem is shown to belong to the family of continuous single facility location-allocation problems, whereas the downgrading problem reduces to a convex but highly non-differentiable optimization problem. Several structural properties of the optimal solution are proven for both problems, using novel planar partitions, the knapsack Voronoi diagrams, and lead to polynomial time solution algorithms.     

Algorithmic dimensionality reduction for molecular structure analysis

Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation--a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation.     

Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes

Methodology and Computing in Applied Probability - Let be X(t) = x ? μt + σBt ? Nt a Lévy process starting from x >?0, where μ ≥?0, σ...     

Solitary Waves to Assess the Internal Pressure and the Rubber Degradation of Tennis Balls

Experimental Mechanics - Rubber is a material present in many commodities, including tennis balls. The characteristics of tennis balls are specified by the International Tennis Federation and are...     

A locally convex version of Kadison’s representation theorem

Positivity - In this paper, we study the local ordered $$*$$ -vector spaces and their representations. We prove that each Archimedean local ordered $$*$$ -vector space, can be represented as a...     

On separation axioms and Ti-fuzzy continuity

We introduce and generalise concepts of T;-continuous functions in a fuzzy setting and study them in connection with the fuzzy continuity and fuzzy separation axioms. Some fuzzy topological properties are also investigated under such functions.