INTRODUCTION Hardness is one of the basic properties of dental materials, specially composite resins which is relevant to their polymerization. The aim of this study was to evaluate the effect of light curing distance and the color of clear Mylar strips on surface hardness of Silorane-based (SCR) and Methacrylate-based composite resins (MCR). MATERIALS AND METHODS 40 samples of MCRs (Filtek Z...

It becomes a great challenge in the research area of metaheuristics to predict the hardness of combinatorial optimization problem instances for a given algorithm. In this study, we focus on the hardness of the traveling salesman problem (TSP) for 2-opt. In the existing literature, two approaches are available to measure the hardness of TSP instances for 2-opt based on the single objective: the ...

A measurement system is capable if it produces measurements with uncertainties small enough for demonstration of compliance with product specifications. To establish the capability of a system for Rock-well C scale hardness, one must assess measurement uncertainty and, when hardness is only an indicator, quantify the relation between hardness and the product property of real interest. The uncer...

Ever since the invention of Genetic Algorithms (GAs), researchers have put a lot of efforts into understanding what makes a function or problem instance hard for GAs to optimize. Many measures have been proposed to distinguish socalled GA-hard from GA-easy problems. None of these, however, has yet achieved the goal of being a reliable predictive GA-hardness measure. In this paper, we first pres...

We study the natural problem of estimating the expansion of subsets of vertices on one side of a bipartite graph. More precisely, given a bipartite graph G(U, V,E) and a parameter β, the goal is to find a subset V ′ ⊆ V containing β fraction of the vertices of V which minimizes the size of N(V ′), the neighborhood of V ′. This problem, which we call Bipartite Expansion, is a special case of sub...

We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE, ...) using an arbitrary function that is hard for C. This construction reveals an equivalence between the problem of proving lower b...

We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone errorcorrecting codes, and show that hardness amplification for NP is essentially equivalent to constructing efficiently locally encodable and locally list-decodable monotone codes. The previous hardness amplification resul...

The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one of the main research objectives in the context...