Church-Rosser Systems, Codes with Bounded Synchronization Delay and Local Rees Extensions

What is the common link, if there is any, between Church-Rosser systems, prefix codes with bounded synchronization delay, and local Rees extensions? The first obvious answer is that each of these notions relates to topics of interest for WORDS: Church-Rosser systems are certain rewriting systems over words, codes are given by sets of words which form a basis of a free submonoid in the free monoid of all words (over a given alphabet) and local Rees extensions provide structural insight into regular languages over words. So, it seems to be a legitimate title for an extended abstract presented at the conference WORDS 2017. However, this work is more ambitious, it outlines some less obvious but much more interesting link between these topics. This link is based on a structure theory of finite monoids with varieties of groups and the concept of local divisors playing a prominent role. Parts of this work appeared in a similar form in conference proceedings where proofs and further material can be found.Comment: Extended abstract of an invited talk given at WORDS 201

Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos correcte

HAG1 and SWI3A/B control of male germ line development in P. patens suggests conservation of epigenetic reproductive control across land plants

Bryophytes as models to study the male germ line: loss-of-function mutants of epigenetic regulators HAG1 and SWI3a/b demonstrate conserved function in sexual reproduction

Reverse Engineering Time Discrete Finite Dynamical Systems: A Feasible Undertaking?

With the advent of high-throughput profiling methods, interest in reverse engineering the structure and dynamics of biochemical networks is high. Recently an algorithm for reverse engineering of biochemical networks was developed by Laubenbacher and Stigler. It is a top-down approach using time discrete dynamical systems. One of its key steps includes the choice of a term order, a technicality imposed by the use of Gröbner-bases calculations. The aim of this paper is to identify minimal requirements on data sets to be used with this algorithm and to characterize optimal data sets. We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display. Furthermore, we identified optimal data sets, which we characterized using a geometric property called “general position”. Moreover, we developed a constructive method to generate optimal data sets, provided a codimensional condition is fulfilled. In addition, we present a generalization of their algorithm that does not depend on the choice of a term order. For this method we derived a formula for the probability of finding the correct model, provided the data set used is optimal. We analyzed the asymptotic behavior of the probability formula for a growing number of variables n (i.e. interacting chemicals). Unfortunately, this formula converges to zero as fast as , where and . Therefore, even if an optimal data set is used and the restrictions in using term orders are overcome, the reverse engineering problem remains unfeasible, unless prodigious amounts of data are available. Such large data sets are experimentally impossible to generate with today's technologies

Topological wave functions and heat equations

It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise: (i) we give a new, purely holomorphic version of the holomorphic anomaly equations, clarifying their relation to the heat equation satisfied by the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian symmetric tube domain $G/K$, we show that the general solution of the anomaly equations is a matrix element \IP{\Psi | g | \Omega} of the Schr\"odinger-Weil representation of a Heisenberg extension of $G$, between an arbitrary state $\bra{\Psi}$ and a particular vacuum state $\ket{\Omega}$. Based on these results, we speculate on the existence of a one-parameter generalization of the usual topological amplitude, which in symmetric cases transforms in the smallest unitary representation of the duality group $G'$ in three dimensions, and on its relations to hypermultiplet couplings, nonabelian Donaldson-Thomas theory and black hole degeneracies.Comment: 50 pages; v2: small typos fixed, references added; v3: cosmetic changes, published version; v4: typos fixed, small clarification adde

Reference ranges for Doppler indices of umbilical and fetal middle cerebral arteries and cerebroplacental ratio: systematic review.

OBJECTIVE: To assess studies reporting reference ranges for umbilical artery (UA) and fetal middle cerebral artery (MCA) Doppler indices and cerebroplacental ratio (CPR), using a set of predefined methodological quality criteria for study design, statistical analysis and reporting methods. METHODS: This was a systematic review of observational studies in which the primary aim was to create reference ranges for UA and MCA Doppler indices and CPR in fetuses of singleton gestations. A search for relevant articles was performed in MEDLINE, EMBASE, CINAHL, Web of Science (from inception to 31 December 2016) and references of the retrieved articles. Two authors independently selected studies, assessed the risk of bias and extracted the data. Studies were scored against a predefined set of independently agreed methodological criteria and an overall quality score was assigned to each study. Linear multiple regression analysis assessing the association between quality scores and study characteristics was performed. RESULTS: Thirty-eight studies met the inclusion criteria. The highest potential for bias was noted in the following fields: 'ultrasound quality control measures', in which only two studies demonstrated a comprehensive quality-control strategy; 'number of measurements taken for each Doppler variable', which was apparent in only three studies; 'sonographer experience', in which no study on CPR reported clearly the experience or training of the sonographers, while only three studies on UA Doppler and four on MCA Doppler did; and 'blinding of measurements', in which only one study, on UA Doppler, reported that sonographers were blinded to the measurement recorded during the examination. Sample size estimations were present in only seven studies. No predictors of quality were found on multiple regression analysis. Reference ranges varied significantly with important clinical implications for what is considered normal or abnormal, even when restricting the analysis to the highest scoring studies. CONCLUSIONS: There is considerable methodological heterogeneity in studies reporting reference ranges for UA and MCA Doppler indices and CPR, and the resulting references have important implications for clinical practice. There is a need for the standardization of methodologies for Doppler velocimetry and for the development of reference standards, which can be correctly interpreted and applied in clinical practice. We propose a set of recommendations for this purpose. Copyright © 2018 ISUOG. Published by John Wiley & Sons Ltd

PEATmoss (Physcomitrella Expression Atlas Tool): a unified gene expression atlas for the model plant Physcomitrella patens

Abstract Physcomitrella patens is a bryophyte model plant that is often used to study plant evolution and development. Its resources are of great importance for comparative genomics and evo-devo approaches. However, expression data from Physcomitrella patens were so far generated using different gene annotation versions and three different platforms: CombiMatrix and NimbleGen expression microarrays and RNA sequencing. The currently available P. patens expression data are distributed across three tools with different visualization methods to access the data. Here, we introduce an interactive expression atlas, Physcomitrella Expression Atlas Tool (PEATmoss), that unifies publicly available expression data for P. patens and provides multiple visualization methods to query the data in a single web-based tool. Moreover, PEATmoss includes 35 expression experiments not previously available in any other expression atlas. To facilitate gene expression queries across different gene annotation versions, and to access P. patens annotations and related resources, a lookup database and web tool linked to PEATmoss was implemented. PEATmoss can be accessed at https://peatmoss.online.uni-marburg.d