Data envelopment analysis which is a nonparametric technique for evaluating relative efficiency of the decision making units with multiple inputs and outputs, has been a very popular method among researchers. While this nonparametric technique is popular, it has some drawbacks such as lack of discrimination in efficient units and weights dispersion .The present study, which is a model based on ...

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2ΛQCD). This approach allows simulations to be performed at much lighter quark masses than possible with conventio...

For data sampled from an arbitrary density on a manifold embedded in Euclidean space, we introduce the Continuous k-Nearest Neighbors (CkNN) graph construction. We prove that CkNN is the unique unweighted construction that is consistent with the underlying manifold topology in the limit of large data, for compact Riemannian manifolds and a large class of non-compact manifolds. In contrast to pe...

This paper lays the foundations of an approach to applying Gromov’s ideas on quantitative topology to topological data analysis. We introduce the “contiguity complex”, a simplicial complex of maps between simplicial complexes defined in terms of the combinatorial notion of contiguity. We generalize the Simplicial Approximation Theorem to show that the contiguity complex approximates the homotop...

This thesis presents a novel computational framework that allows for a robust extraction and quantification of the Morse-Smale complex of a scalar field given on a 2or 3dimensional manifold. The proposed framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency of the computed complex. Using a graph theoretical formulation of this theory, we present an a...

Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for observations that are persistence diagrams are limited. Specifically, there is a need for tests that can assess the strength of evidence against a claim that tw...

This paper gives a detailed overview of the problem of missing data in parametric and nonparametric regression. Theoretical basics, properties as well as simulation results may help the reader to get familiar with the common problem of incomplete data sets. Of course, not all occurences can be discussed so this paper could be seen as an introduction to missing data within regression analysis an...

Given a finite set in a metric space, the topological analysis generalizes hierarchical clustering using a 1-parameter family of homology groups to quantify connectivity in all dimensions. Going beyond Euclidean distance and really beyond metrics, we show that the tools of topological data analysis also apply when we measure distance with Bregman divergences. While these divergences violate two...