van der F Fons Sommen

On computing a longest path in a tree

The primary purpose of this note is to present an exercise in proof design. For us, such a design consists in isolating the relevant concepts for the problem at hand, introducing special-purpose notation for them that is geared to manipulation and to crisp formal specification, and then solving the problem in a demand-driven way, while onthe-fly extracting from the calculation additional theory useful for solving the problem proper. The problem chosen is demonstrating the correctness of an algorithm for computing the longest path in a tree. Given a finite tree with all edges having positive length, we wish to compute a longest path. This can be done using a procedure invented by Edsger W. Dijkstra around 1960, which is as follows. Build a physical model of the tree by connecting each pair of adjacent nodes by a piece of string of the given edge length. Now pick up the physical tree at an arbitrary node U , l t the contraption hang down, and determine a deepest node X. Then pick up the tree at X and determine a deepest node Y . The claim is that the path between X andY is a longest path in the tree. We have never seen a formal proof of this claim, and the purpose of this note is to provide one.

Supportive automatic annotation of early esophageal cancer using local gabor and color features

Over the past years High Definition (HD) endoscopy has become a crucial tool for the early detection of esophageal cancer. The high resolution offers specialist physicians high-quality visual information, enabling them to identify dysplastic tissue leading to Early Adenocarcinoma (EAC). The detection and removal of these early types of cancer drastically increases the survival chances of the patient. However, even for an experienced specialist it remains an arduous task to identify the patterns associated with early cancer. Therefore, a computer-aided detection system that supports the physician seems highly attractive. We present a novel algorithm for automatic detection of early cancerous tissue in HD endoscopic images. The algorithm computes local color- and texture features based on the original and on the Gabor-filtered image. We explore the spectral characteristics of the image regions that contain early cancer and we design appropriate filters based on this analysis. The features are classified by a trained Support Vector Machine (SVM) after which additional post-processing techniques are applied in order to annotate the image region containing early cancer. For 7 patients, we compare 32 annotations made by the algorithm with the corresponding delineations made by an expert gastroenterologist. Of 38 lesions indicated independently by the gastroenterologist, the system detects 36 of those lesions with a recall of 0.95 and a precision of 0.75.

Peterson's mutual exclusion algorithm revisited

This last technical chapter is not really about Peterson’s algorithm, although it may reinforce the beauty of that design. What this chapter really is about, is a serious and fundamental criticism that one may have of the method of multiprogramming proposed in this book. The method is invariably driven by the requirement of partial correctness, thereby largely neglecting the aspect of individual progress, or “liveness”. Of course, we do have some rules of thumb that prevent us from excluding progress beforehand, the most notable one being to choose the annotation and the induced guards as weak as possible. But how good is this? Is there a mathematical underpinning? The answer is simple: there isn’t!