On the Number of Unbordered Factors

We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length

Ringtail Disorder observed in Cotton Rats (Sigmodon hispidus)

This is the first description of ringtail syndrome in cotton rats (Sigmodon hispidus). The disorder was sporadically observed in a laboratory reared breeding colony. Incidence of tail lesions decreased after standardization of environmental humidityin the laboratory animal facility

Unambiguous 1-Uniform Morphisms

A morphism h is unambiguous with respect to a word w if there is no other morphism g that maps w to the same image as h. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform morphism, i.e., a morphism that maps every letter in the word to an image of length 1.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Natural history of Arabidopsis thaliana and oomycete symbioses

Molecular ecology of plant–microbe interactions has immediate significance for filling a gap in knowledge between the laboratory discipline of molecular biology and the largely theoretical discipline of evolutionary ecology. Somewhere in between lies conservation biology, aimed at protection of habitats and the diversity of species housed within them. A seemingly insignificant wildflower called Arabidopsis thaliana has an important contribution to make in this endeavour. It has already transformed botanical research with deepening understanding of molecular processes within the species and across the Plant Kingdom; and has begun to revolutionize plant breeding by providing an invaluable catalogue of gene sequences that can be used to design the most precise molecular markers attainable for marker-assisted selection of valued traits. This review describes how A. thaliana and two of its natural biotrophic parasites could be seminal as a model for exploring the biogeography and molecular ecology of plant–microbe interactions, and specifically, for testing hypotheses proposed from the geographic mosaic theory of co-evolution

The molecular basis of host specialization in bean pathovars of Pseudomonas syringae

Biotrophic phytopathogens are typically limited to their adapted host range. In recent decades, investigations have teased apart the general molecular basis of intraspecific variation for innate immunity of plants, typically involving receptor proteins that enable perception of pathogen-associated molecular patterns or avirulence elicitors from the pathogen as triggers for defense induction. However, general consensus concerning evolutionary and molecular factors that alter host range across closely related phytopathogen isolates has been more elusive. Here, through genome comparisons and genetic manipulations, we investigate the underlying mechanisms that structure host range across closely related strains of Pseudomonas syringae isolated from different legume hosts. Although type III secretionindependent virulence factors are conserved across these three strains, we find that the presence of two genes encoding type III effectors (hopC1 and hopM1) and the absence of another (avrB2) potentially contribute to host range differences between pathovars glycinea and phaseolicola. These findings reinforce the idea that a complex genetic basis underlies host range evolution in plant pathogens. This complexity is present even in host–microbe interactions featuring relatively little divergence among both hosts and their adapted pathogens

On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

SSGAN: Secure Steganography Based on Generative Adversarial Networks

In this paper, a novel strategy of Secure Steganograpy based on Generative Adversarial Networks is proposed to generate suitable and secure covers for steganography. The proposed architecture has one generative network, and two discriminative networks. The generative network mainly evaluates the visual quality of the generated images for steganography, and the discriminative networks are utilized to assess their suitableness for information hiding. Different from the existing work which adopts Deep Convolutional Generative Adversarial Networks, we utilize another form of generative adversarial networks. By using this new form of generative adversarial networks, significant improvements are made on the convergence speed, the training stability and the image quality. Furthermore, a sophisticated steganalysis network is reconstructed for the discriminative network, and the network can better evaluate the performance of the generated images. Numerous experiments are conducted on the publicly available datasets to demonstrate the effectiveness and robustness of the proposed method

A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Restricted ambiguity of erasing morphisms

A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism of strongly restricted ambiguity. Furthermore, we demonstrate that there are strings for which the set of unambiguous morphisms, depending on the size of the target alphabet of these morphisms, is empty, finite or infinite. Finally, we show that the problem of the existence of unambiguous erasing morphisms is equivalent to some basic decision problems for nonerasing multi-pattern languages

Covering Problems for Partial Words and for Indeterminate Strings

We consider the problem of computing a shortest solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding position. We also consider covering partial words, which are a special case of indeterminate strings where each non-solid symbol is a don't care symbol. We prove that indeterminate string covering problem and partial word covering problem are NP-complete for binary alphabet and show that both problems are fixed-parameter tractable with respect to $k$, the number of non-solid symbols. For the indeterminate string covering problem we obtain a $2^{O(k \log k)} + n k^{O(1)}$-time algorithm. For the partial word covering problem we obtain a $2^{O(\sqrt{k}\log k)} + nk^{O(1)}$-time algorithm. We prove that, unless the Exponential Time Hypothesis is false, no $2^{o(\sqrt{k})} n^{O(1)}$-time solution exists for either problem, which shows that our algorithm for this case is close to optimal. We also present an algorithm for both problems which is feasible in practice.Comment: full version (simplified and corrected); preliminary version appeared at ISAAC 2014; 14 pages, 4 figure