Methods explained - Business Structure Database

Sums of Squares Methods Explained: Part I

Let p(~x) ∈ R[~x] be SOS in t real polynomial squares. Then, p(~x) must have even degree. Let deg(p(~x)) = 2k. Then, ∃q1, . . . , qt ∈ R[~x] s.t. deg(qi(~x)) ≤ k and p(~x) = ∑t i=1 q 2 i (~x). A key observation is that we can now exactly characterise the finitely many possible power-products that could occur in each qi(~x). Definition 1.1. Let Λn(d) = {α = 〈α1, . . . , αn〉 ∈ Nn | α1 + . . .+ αn...

Construction of crystal structure prototype database: methods and applications.

Crystal structure prototype data have become a useful source of information for materials discovery in the fields of crystallography, chemistry, physics, and materials science. This work reports the development of a robust and efficient method for assessing the similarity of structures on the basis of their interatomic distances. Using this method, we proposed a simple and unambiguous definitio...

Market structure explained by pairwise interactions

Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here we give empirical evidence, by making as few assumptions as possible, that the market microstructure capturing almost all of the available information in the data of stock markets does not involve higher order than pairwise interactions. We give an economic i...

Business Forecasting Methods

An organization needs to develop a forecasting system involving several approaches to predicting uncertain events. Such forecasting systems require the development of expertise in identifying forecasting problems, applying a range of forecasting methods, selecting appropriate methods for each problem, and evaluating and refining forecasting methods over time. It is also important to have strong...

Explained Bioinformatics explained : RNA secondary structure partition function , calculation and use