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

k-Spectra of weakly-c-Balanced Words

A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered factors of a given word w, called here $k$-spectrum and denoted \ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w) for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e., words over a two-letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has $c$-more occurrences than the other. In particular, we consider the question which cardinalities n= |\ScatFact_k(w)| are obtainable, for a positive integer $k$, when $w$ is either a strictly balanced binary word of length $2k$, or a $c$-balanced binary word of length $2k-c$. We also consider the problem of reconstructing words from their $k$-spectra

Collinear Microstrip Patch Antenna

The paper presents a brief overview of the development of so called collinear types of antenna arrays. A new type of this structure in microstrip technology is further introduced. The principle of the antenna operation is explained via surface current distribution of excited modes. Such distribution is reached via geometrical perturbation of a radiating element by slots introduced in such a way that they e liminate radiation from even half current wavelengths . The initial design and optimization of the prototype operating in RFID band (869 MHz) has been performed in planar simulator Zeland IE3D. A prototype has been realized and measured. The reached results show that the presented antenna has directional character as it can be expected due to the proposed technology and the presence of a planar ground plane

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

Air-sea interaction in the tropical Pacific Ocean

Charts of 3-month sea surface temperature (SST) anomalies in the eastern tropical Pacific Ocean were produced for the period 1949 to 1970. The anomalies along the United States and South American west coasts and in the eastern tropical Pacific appeared to be oscillating in phase during this period. Similarly, the satellite-derived cloudiness for each of four quadrants of the Pacific Ocean (130 deg E to 100 deg W, 30 deg N to 25 deg S) appeared to be oscillating in phase. In addition, a global tropical cloudiness oscillation from 30 deg N to 30 deg S was noted from 1965 to 1970, by using monthly satellite television nephanalyses. The SST anomalies were found to have a good degree of correlation both positive and negative with the following monthly geophysical parameters: (1) satellite-derived cloudiness, (2) strength of the North and South Pacific semipermanent anticyclones, (3) tropical Pacific island rainfall, and (4) Darwin surface pressure. Several strong direct local and crossequatorial relationships were noted. In particular, the high degree of correlation between the tropical island rainfall and the SST anomalies (r = +0.93) permitted the derivation of SST's for the tropical Pacific back to 1905. The close occurrence of cold tropical SST and North Pacific 700-mb positive height anomalies with central United States drought conditions was noted

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

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