Interval non-edge-colorable bipartite graphs and multigraphs

An edge-coloring of a graph $G$ with colors $1,...,t$ is called an interval $t$-coloring if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. In 1991 Erd\H{o}s constructed a bipartite graph with 27 vertices and maximum degree 13 which has no interval coloring. Erd\H{o}s's counterexample is the smallest (in a sense of maximum degree) known bipartite graph which is not interval colorable. On the other hand, in 1992 Hansen showed that all bipartite graphs with maximum degree at most 3 have an interval coloring. In this paper we give some methods for constructing of interval non-edge-colorable bipartite graphs. In particular, by these methods, we construct three bipartite graphs which have no interval coloring, contain 20,19,21 vertices and have maximum degree 11,12,13, respectively. This partially answers a question that arose in [T.R. Jensen, B. Toft, Graph coloring problems, Wiley Interscience Series in Discrete Mathematics and Optimization, 1995, p. 204]. We also consider similar problems for bipartite multigraphs.Comment: 18 pages, 7 figure

Constructions of skew-tolerant and skew-detecting codes

The paradigm of skew-tolerant parallel asynchronous communication was introduced by Blaum and Bruck (see ibid., vol. 39, 1993) along with constructions for codes that can tolerate or detect skew. Some of these constructions were improved by Khachatrian (1991). In this paper these constructions are improved upon further, and the authors prove that the new constructions are, in a certain sense, optimal

On q-ary codes correcting all unidirectional errors of a limited magnitude

We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of unidirectional errors of level l. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a component smaller than the transmitted one. Moreover, the absolute value of the difference between a transmitted component and its received version is at most l. We introduce and study q-ary codes capable of correcting all unidirectional errors of level l. Lower and upper bounds for the maximal size of those codes are presented. We also study codes for this aim that are defined by a single equation on the codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting binary asymmetric errors). We finally consider the problem of detecting all unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian Academy of Sciences, special issue dedicated to Rom Varshamo

Identifying and Disentangling Spurious Features in Pretrained Image Representations

Neural networks employ spurious correlations in their predictions, resulting in decreased performance when these correlations do not hold. Recent works suggest fixing pretrained representations and training a classification head that does not use spurious features. We investigate how spurious features are represented in pretrained representations and explore strategies for removing information about spurious features. Considering the Waterbirds dataset and a few pretrained representations, we find that even with full knowledge of spurious features, their removal is not straightforward due to entangled representation. To address this, we propose a linear autoencoder training method to separate the representation into core, spurious, and other features. We propose two effective spurious feature removal approaches that are applied to the encoding and significantly improve classification performance measured by worst group accuracy

Effect of halogen substitution on the enthalpies of solvation and hydrogen bonding of organic solutes in chlorobenzene and 1,2-dichlorobenzene derived using multi-parameter correlations

Article on the effect of halogen substitution on the enthalpies of solvation and hydrogen bonding of organic solutes in chlorobenzene and 1,2-dichlorobenzene derived using multi-parameter correlations

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd