Asymmetric coloring games on incomparability graphs

Consider the following game on a graph $G$: Alice and Bob take turns coloring the vertices of $G$ properly from a fixed set of colors; Alice wins when the entire graph has been colored, while Bob wins when some uncolored vertices have been left. The game chromatic number of $G$ is the minimum number of colors that allows Alice to win the game. The game Grundy number of $G$ is defined similarly except that the players color the vertices according to the first-fit rule and they only decide on the order in which it is applied. The $(a,b)$-game chromatic and Grundy numbers are defined likewise except that Alice colors $a$ vertices and Bob colors $b$ vertices in each round. We study the behavior of these parameters for incomparability graphs of posets with bounded width. We conjecture a complete characterization of the pairs $(a,b)$ for which the $(a,b)$-game chromatic and Grundy numbers are bounded in terms of the width of the poset; we prove that it gives a necessary condition and provide some evidence for its sufficiency. We also show that the game chromatic number is not bounded in terms of the Grundy number, which answers a question of Havet and Zhu

Coloring triangle-free rectangle overlap graphs with O(log⁡log⁡n)O(\log\log n) colors

Recently, it was proved that triangle-free intersection graphs of $n$ line segments in the plane can have chromatic number as large as $\Theta(\log\log n)$. Essentially the same construction produces $\Theta(\log\log n)$-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected sets in $\mathbb{R}^2$ closed under horizontal scaling, vertical scaling, and translation, except for axis-parallel rectangles. We show that this construction is asymptotically optimal for intersection graphs of boundaries of axis-parallel rectangles, which can be alternatively described as overlap graphs of axis-parallel rectangles. That is, we prove that triangle-free rectangle overlap graphs have chromatic number $O(\log\log n)$, improving on the previous bound of $O(\log n)$. To this end, we exploit a relationship between off-line coloring of rectangle overlap graphs and on-line coloring of interval overlap graphs. Our coloring method decomposes the graph into a bounded number of subgraphs with a tree-like structure that "encodes" strategies of the adversary in the on-line coloring problem. Then, these subgraphs are colored with $O(\log\log n)$ colors using a combination of techniques from on-line algorithms (first-fit) and data structure design (heavy-light decomposition).Comment: Minor revisio

Miłosz i Andrzejewski — trudny dialog

The article brings an attempt at a reconstruction of a dialogue of both writers on the basis of correspondence and literary works. In spite of the author’s introductory remarks, correspondence documents were used to a minimal degree, whereas more attention was paid to the image of Andrzejewski in The Captive Mind, ideological evolution of the Ashes and diamonds author’s as well as his biography.The article brings an attempt at a reconstruction of a dialogue of both writers on the basis of correspondence and literary works. In spite of the author’s introductory remarks, correspondence documents were used to a minimal degree, whereas more attention was paid to the image of Andrzejewski in The Captive Mind, ideological evolution of the Ashes and diamonds author’s as well as his biography

A survey on learning from imbalanced data streams: taxonomy, challenges, empirical study, and reproducible experimental framework

Class imbalance poses new challenges when it comes to classifying data streams. Many algorithms recently proposed in the literature tackle this problem using a variety of data-level, algorithm-level, and ensemble approaches. However, there is a lack of standardized and agreed-upon procedures on how to evaluate these algorithms. This work presents a taxonomy of algorithms for imbalanced data streams and proposes a standardized, exhaustive, and informative experimental testbed to evaluate algorithms in a collection of diverse and challenging imbalanced data stream scenarios. The experimental study evaluates 24 state-of-the-art data streams algorithms on 515 imbalanced data streams that combine static and dynamic class imbalance ratios, instance-level difficulties, concept drift, real-world and semi-synthetic datasets in binary and multi-class scenarios. This leads to the largest experimental study conducted so far in the data stream mining domain. We discuss the advantages and disadvantages of state-of-the-art classifiers in each of these scenarios and we provide general recommendations to end-users for selecting the best algorithms for imbalanced data streams. Additionally, we formulate open challenges and future directions for this domain. Our experimental testbed is fully reproducible and easy to extend with new methods. This way we propose the first standardized approach to conducting experiments in imbalanced data streams that can be used by other researchers to create trustworthy and fair evaluation of newly proposed methods. Our experimental framework can be downloaded from https://github.com/canoalberto/imbalanced-streams

Where Have the Litigants Gone?

The recognition of coral species based on underwater texture images pose a significant difficulty for machine learning algorithms, due to the three following challenges embedded in the nature of this data: 1) datasets do not include information about the global structure of the coral; 2) several species of coral have very similar characteristics; and 3) defining the spatial borders between classes is difficult as many corals tend to appear together in groups. For this reason, the classification of coral species has always required an aid from a domain expert. The objective of this paper is to develop an accurate classification model for coral texture images. Current datasets contain a large number of imbalanced classes, while the images are subject to inter-class variation. We have analyzed 1) several Convolutional Neural Network (CNN) architectures, 2) data augmentation techniques and 3) transfer learning. We have achieved the state-of-the art accuracies using different variations of ResNet on the two current coral texture datasets, EILAT and RSMAS.Comment: 22 pages, 10 figure