The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

Intersection over Union (IoU) is the most popular evaluation metric used in the object detection benchmarks. However, there is a gap between optimizing the commonly used distance losses for regressing the parameters of a bounding box and maximizing this metric value. The optimal objective for a metric is the metric itself. In the case of axis-aligned 2D bounding boxes, it can be shown that IoU can be directly used as a regression loss. However, IoU has a plateau making it infeasible to optimize in the case of non-overlapping bounding boxes. In this paper, we address the this weakness by introducing a generalized version of IoU as both a new loss and a new metric. By incorporating this generalized IoU ( GIoU) as a loss into the state-of-the art object detection frameworks, we show a consistent improvement on their performance using both the standard, IoU based, and new, GIoU based, performance measures on popular object detection benchmarks such as PASCAL VOC and MS COCO.

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Generalized Intersection Over Union: A Metric and a Loss for Bounding Box Regression

Computational geometry

Survey: Graph clustering

A note on the triangle inequality for the Jaccard distance

Automatic and interactive data analysis is instrumental in making use of increasing amounts of complex data. Owing to novel sensor modalities, analysis of data generated in professional team sport leagues such as soccer, baseball, and basketball has recently become of concern, with potentially high commercial and research interest. The analysis of team ball games can serve many goals, e.g., in coaching to understand effects of strategies and tactics, or to derive insights improving performance. Also, it is often decisive to trainers and analysts to understand why a certain movement of a player or groups of players happened, and what the respective influencing factors are. We consider team sport as group movement including collaboration and competition of individuals following specific rule sets. Analyzing team sports is a challenging problem as it involves joint understanding of heterogeneous data perspectives, including high-dimensional, video, and movement data, as well as considering team behavior and rules (constraints) given in the particular team sport. We identify important components of team sport data, exemplified by the soccer case, and explain how to analyze team sport data in general. We identify challenges arising when facing these data sets and we propose a multi-facet view and analysis including pattern detection, context-aware analysis, and visual explanation. We also present applicable methods and technologies covering the heterogeneous aspects in team sport data.

How to make sense of team sport data: From acquisition to data modeling and research aspects

Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.

In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of n OR functions of positive literals, we present a polynomial time algorithm. For finding an attractor of period 2 of a BN consisting of n AND/OR functions of literals, we present an O(1.985^n) time algorithm. For finding an attractor of a fixed period of a BN consisting of n nested canalyzing functions and having constant treewidth w, we present an O(n^{2p(w+1)} poly(n)) time algorithm.

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Finding a Periodic Attractor of a Boolean Network

We introduce the boolean hierarchy of k-partitions over NP for k > 3 as a generalization of the boolean hierarchy of sets (i.e., 2-partitions) over NP. Whereas the structure of the latter hierarchy is rather simple the structure of the boolean hierarchy of k-partitions over NP for k > 3 turns out to be much more complicated. We establish the Embedding Conjecture which enables us to get a complete idea of this structure. This conjecture is supported by several partial results.

Sven Kosub

Papers

A note on the triangle inequality for the Jaccard distance

How to make sense of team sport data: From acquisition to data modeling and research aspects

A note on the triangle inequality for the Jaccard distance

Finding a Periodic Attractor of a Boolean Network

The boolean hierarchy of NP-partitions