Deterministically and Sudoku-Deterministically Recognizable Picture Languages

The recognizable 2-dimensional languages are a robust class with many characterizations, comparable to the regular languages in the 1-dimensional case. One characterization is by tiling systems. The corresponding word problem is NP-complete. Therefore, notions of determinism for tiling systems were suggested. For the notion which was called "deterministically recognizable" it was open since 1998 whether it implies recognizability. By showing that acyclicity of grid graphs is recognizable we answer this question positively. In contrast to that, we show that non-recognizable languages can be accepted by a generalization of this tiling system determinism which we call sudoku-determinism. Its word problem, however, is still in linear time. We show that Sudoku-determinism even contains the set of 2-dimensional languages which can be recognized by 4-way alternating automata

The atnext/atprevious hierarchy on the starfree languages

The temporal logic operators atnext and atprevious are alternatives for the operators until and since. P atnext Q has the meaning: at the next position in the future where Q holds it holds P. We define an asymmetric but natural notion of depth for the expressions of this linear temporal logic. The sequence of classes at_n of languages expressible via such depth-n expressions gives a parametrization of the starfree regular languages which we call the atnext/atprevious hierarchy, or simply at hierarchy. It turns out that the at hierarchy equals the hierarchy given by the n-fold weakly iterated block product of DA. It is shown that the at hierarchy is situated properly between the until/since and the dot-depth hierarchy

Searching paths of constant bandwidth

As a generalization of paths, the notion of paths of bandwidth w is introduced. We show that, for a given constant w >= 1, the corresponding search problem for such a path of length k in a given graph is NP-complete and fixed-parameter tractable in the parameter k, like this is known for the special case w=1, the LONGEST PATH problem. We state the FPT algorithm in terms of a guess and check protocol which uses witnesses of size polynomial in the parameter

Exponential Multiplication Schemes

We present an idea to describe a polynomial with 2^n distinct integer zeros by an n-tuple of integers via a scheme of n recurring equations. We call such an n-tuple an exponential multiplication scheme of size n. Exponential multiplication schemes of size 1,2,3, and 4 are presented. Under the assumption that fast exponential multiplication scheme generators exist we suggest a fast randomized heuristic for the factorization problem

Segment-based Visual Cryptography

A version of Visual Cryptography is presented which is not pixel-based but segment-based. It is used to encrypt messages consisting of symbols which can be represented by a segment display. For example, the decimal digits 0,...,9 can be represented by the well-known seven-segment display. The advantage of the segment-based encryption is that it may be easier to adjust the secret images and that the symbols are potentially easier to recognize for the human eye, especially in a transparency-on-screen szenario

CARBON FIBER REINFORCED POLYMER - THE FABRIC OF THE FUTURE?

This Article is about chances for carbon fiber reinforced polymers, following shortened CFRP, concerning its efficient, powerful, ecosensitive, sustainably and new technical inventions in several areas. It discusses this innovative new material concerning previous history, its production, its pros and cons and new possibilities, as well as the recycling in all its perspectives. Also, biodegradable alternatives of CFRP, like green composites and biocomposites are discussed

The dot-depth and the polynomial hierarchy correspond on the delta levels

It is well-known that the Sigma_k- and Pi_k-levels of the dot-depth hierarchy and the polynomial hierarchy correspond via leaf languages. In this paper this correspondence will be extended to the Delta_k-levels of these hierarchies: Leaf^P(Delta_k^L) = Delta_k^p

Epidemiology and recurrence rates of Clostridium difficile infections in Germany: a secondary data analysis

Clostridium difficile infection (CDI) is the most common cause of health-care-associated infectious diarrhea. Recurrence rates are as high as 20–30% after standard treatment with metronidazole or vancomycin, and appear to be reduced for patients treated with fidaxomicin. According to the literature, the risk of CDI recurrence increases after the second relapse to 30–65%. Accurate data for Germany are not yet available. Methods: Based on the research database of arvato health analytics (Munich, Germany), a secondary data analysis for the incidence, treatment characteristics and course of CDI was performed. The database included high granular accounting information of about 1.46 million medically insured patients covering the period 2006–2013, being representative for Germany. The analysis was based on new-onset CDI in 2012 in patients which either received outpatient antibiotic therapy for CDI or were hospitalized. Results: The ICD-10 coded incidence of CDI in 2012 was 83 cases per 100,000 population