High-throughput determination of structural phase diagram and constituent phases using GRENDEL

After [15], [31], [19], [8], [25], [5], minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push-relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

Throughout history, scientists and engineers have relied on the slow and serendipitous trial-and-error process for discovering and developing new materials. In contrast, an emerging theme in modern materials science is the notion of intelligent design of materials. Pioneered by the pharmaceutical industry and adapted for the purposes of materials science and engineering, the combinatorial approach represents a watershed in the process of accelerated discovery, development and optimization of materials. To survey large compositional landscapes rapidly, thousands of compositionally varying samples may be synthesized, processed and screened in a single experiment. Recent developments have been aided by innovative rapid characterization tools, and by advanced materials synthesis techniques such as laser molecular beam epitaxy which can be used to perform parallel-processed design and control of materials down to the atomic scale. Here we review the fast-growing field of combinatorial materials science, with an emphasis on inorganic functional materials.