Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Evolutionary recruitment of flexible Esrp-dependent splicing programs into diverse embryonic morphogenetic processes

Epithelial-mesenchymal interactions are crucial for the development of numerous animal structures. Thus, unraveling how molecular tools are recruited in different lineages to control interplays between these tissues is key to understanding morphogenetic evolution. Here, we study Esrp genes, which regulate extensive splicing programs and are essential for mammalian organogenesis. We find that Esrp homologs have been independently recruited for the development of multiple structures across deuterostomes. Although Esrp is involved in a wide variety of ontogenetic processes, our results suggest ancient roles in non-neural ectoderm and regulating specific mesenchymal-to-epithelial transitions in deuterostome ancestors. However, consistent with the extensive rewiring of Esrp-dependent splicing programs between phyla, most developmental defects observed in vertebrate mutants are related to other types of morphogenetic processes. This is likely connected to the origin of an event in Fgfr, which was recruited as an Esrp target in stem chordates and subsequently co- opted into the development of many novel traits in vertebrates

Computing Expected Differential Probability of (Truncated) Differentials and Expected Linear Potential of (Multidimensional) Linear Hulls in SPN Block Ciphers

In this paper we introduce new algorithms that, based only on the independent round keys assumption, allow to practically compute the exact expected differential probability of (truncated) differentials and the expected linear potential of (multidimensional) linear hulls. That is, we can compute the exact sum of the probability or the potential of all characteristics that follow a given activity pattern. We apply our algorithms to various recent SPN ciphers and discuss the results

Parsimonious Higher-Order Hidden Markov Models for Improved Array-CGH Analysis with Applications to Arabidopsis thaliana

Array-based comparative genomic hybridization (Array-CGH) is an important technology in molecular biology for the detection of DNA copy number polymorphisms between closely related genomes. Hidden Markov Models (HMMs) are popular tools for the analysis of Array-CGH data, but current methods are only based on first-order HMMs having constrained abilities to model spatial dependencies between measurements of closely adjacent chromosomal regions. Here, we develop parsimonious higher-order HMMs enabling the interpolation between a mixture model ignoring spatial dependencies and a higher-order HMM exhaustively modeling spatial dependencies. We apply parsimonious higher-order HMMs to the analysis of Array-CGH data of the accessions C24 and Col-0 of the model plant Arabidopsis thaliana. We compare these models against first-order HMMs and other existing methods using a reference of known deletions and sequence deviations. We find that parsimonious higher-order HMMs clearly improve the identification of these polymorphisms. Moreover, we perform a functional analysis of identified polymorphisms revealing novel details of genomic differences between C24 and Col-0. Additional model evaluations are done on widely considered Array-CGH data of human cell lines indicating that parsimonious HMMs are also well-suited for the analysis of non-plant specific data. All these results indicate that parsimonious higher-order HMMs are useful for Array-CGH analyses. An implementation of parsimonious higher-order HMMs is available as part of the open source Java library Jstacs (www.jstacs.de/index.php/PHHMM)