On the cardinality of sumsets in torsion-free groups

Let $A, B$ be finite subsets of a torsion-free group $G$. We prove that for every positive integer $k$ there is a $c(k)$ such that if $|B|\ge c(k)$ then the inequality $|AB|\ge |A|+|B|+k$ holds unless a left translate of $A$ is contained in a cyclic subgroup. We obtain $c(k)<c_0k^{6}$ for arbitrary torsion-free groups, and $c(k)<c_0k^{3}$ for groups with the unique product property, where $c_0$ is an absolute constant. We give examples to show that $c(k)$ is at least quadratic in $k$

The number of conjugacy classes in pattern groups is not a polynomial function

A famous open problem due to Graham Higman asks if the number of conjugacy classes in the group of n x n unipotent upper triangular matrices over the q-element field can be expressed as a polynomial function of q for every fixed n. We consider the generalization of the problem for pattern groups and prove that for some pattern groups of nilpotency class two the number of conjugacy classes is not a polynomial function of q

Structural complexity at and around the Triassic–Jurassic GSSP at Kuhjoch, Northern Calcareous Alps, Austria

One of the key requirements for a Global Stratotype Section and Point (GSSP) is the absence of tectonic disturbance. The GSSP for the Triassic–Jurassic system boundary was recently defined at Kuhjoch, Northern Calcareous Alps, Austria. New field observations in the area of the Triassic–Jurassic boundary GSSP site demonstrate that the overturned, tight, and almost upright Karwendel syncline was formed at semibrittle deformation conditions, confirmed by axial planar foliation. Tight to isoclinal folds at various scales were related to a tectonic transport to the north. Brittle faulting occurred before and after folding as confirmed by tilt tests (the rotation of structural data by the average bedding). Foliation is ubiquitous in the incompetent units, including the Kendlbach Formation at the GSSP. A reverse fault (inferred to be formed as a normal fault before folding) crosscuts the GSSP sections, results in the partial tectonic omission of the Schattwald Beds, and thus makes it impossible to measure a complete and continuous stratigraphic section across the whole Kendlbach Formation. Based on these observations, the Kuhjoch sections do not fulfil the specific requirement for a GSSP regarding the absence of tectonic disturbances near boundary level.This study was supported by the Hungarian Scientific Research Fund (OTKA) Grant K72633. This paper benefited from the thorough reviews of Stephen Hesselbo and an anonymous reviewer. This is Cambridge Earth Sciences contribution number ESC.3793 and MTA-MTM-ELTE Paleo contribution number 228

On Mp-embedded primary subgroups of finite groups

A subgroup H of G is called Mp-embedded in G, if there exists a p-nilpotent subgroup B of G such that Hp ∈ Sylp(B) and B is Mp-supplemented in G. In this paper, we use Mp-embedded subgroups to study the structure of finite groups

Detailed clay mineralogy of the TriassicJurassic boundary section at Kendlbachgraben (Northern Calcareous Alps, Austria)

The Triassic-Jurassic boundary (TJB) is marked by one of the five largest Phanerozoic mass extinctions. To constrain existing models for TJB events, we obtained a stratigraphically highly resolved dataset from a marine section at Kendlbachgraben, Austria. The topmost Triassic Ko¨ssen Formation contains low to medium-charged smectite and vermiculite as alteration products of mafic-ultramafic minerals. The clay minerals in the boundary mudstone are kaolinite 5 illite + muscovite >> smectite > chlorite. Predominant kaolinite suggests humid climate and abundant terrigenous input. In the lowermost Jurassic, the clay mineral pattern changes to illite + muscovite >> kaolinite >> smectite, which reflects change to less humid and more moderate climate. The topmost Ko¨ssen Formation also contains clay spherules. Their composition, shape and size indicate that they are alteration products of airborne volcanic glass droplets solidified in the air, settled in the sea and altered rapidly with negligible transport in terrestrial or marine environments. Our data are consistent with sudden climatic change at the TJB, as a result of large-scale volcanic activity of the Central Atlantic Magmatic Province which produced distal airfall volcanic ash

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks.

BACKGROUND Signaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor. DESCRIPTION We developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org. CONCLUSIONS With SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks

ABSTRACT: BACKGROUND: Signaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor.Description: We developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org CONCLUSIONS: With SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses