Hadwiger and Hajós conjectured that for every positive integer t, Kt+1-minor free graphs Kt+1-topological minor are properly t-colorable, respectively. Clustered coloring version of these two conjectures which only require monochromatic components to have bounded size has been extensively studied. In this paper we consider the clustered immersion-variant Hadwiger's Hajós' conjecture proposed by...

The problem of sequence and time-series segmentation has been discussed widely and it has been applied successfully in a variety of areas, including computational genomics, data analysis for scientific applications, and telecommunications. In many of these areas the sequences involved are multidimensional, and the goal of the segmentation is to discover sequence segments with small variability....

Defaults in a credit portfolio of many obligors or in an economy populated with firms tend to occur in waves. This may simply reflect their sharing of common risk factors and/or manifest their systemic linkages via credit chains. One popular approach to characterizing defaults in a large pool of obligors is the Poisson intensity model coupled with stochastic covariates. A constraining feature o...

The majority of vertebrate protocadherin (Pcdh) genes are clustered in a single genomic locus, and this remarkable genomic organization is highly conserved from teleosts to humans. These clustered Pcdhs are differentially expressed in individual neurons, they engage in homophilic trans-interactions as multimers and they are required for diverse neurodevelopmental processes, including neurite se...

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The paper introduces the reader to a new paradigm shift that is currently taking place in the data storage industry: the movement toward Clustered Storage architectures. Clustered Storage architectures are changing the rules of how data is stored and accessed. This paper discusses the trends that clearly define clustered storage architectures as the future of data storage, detail the requiremen...

We address the problem of constructing phylogenetic networks using two criteria: the number of cycles and the fit value of the network. Traditionally the fit value is the main objective for evaluating phylogenetic networks. However, a small number of cycles in a network is desired and pointed out in several publications. We propose a new phylogenetic network called CS-network and a method for c...

We present the latest advances of the multiscale approach to radiation damage caused by irradiation of a tissue with energetic ions and report the most recent advances in the calculations of complex DNA damage and the effects of thermal spikes on biomolecules. The multiscale approach aims to quantify the most important physical, chemical, and biological phenomena taking place during and followi...