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

DoOP: Databases of Orthologous Promoters, collections of clusters of orthologous upstream sequences from chordates and plants

DoOP (http://doop.abc.hu/) is a database of eukaryotic promoter sequences (upstream regions) aiming to facilitate the recognition of regulatory sites conserved between species. The annotated first exons of human and Arabidopsis thaliana genes were used as queries in BLAST searches to collect the most closely related orthologous first exon sequences from Chordata and Viridiplantae species. Up to 3000 bp DNA segments upstream from these first exons constitute the clusters in the chordate and plant sections of the Database of Orthologous Promoters. Release 1.0 of DoOP contains 21 061 chordate clusters from 284 different species and 7548 plant clusters from 269 different species. The database can be used to find and retrieve promoter sequences of a given gene from various species and it is also suitable to see the most trivial conserved sequence blocks in the orthologous upstream regions. Users can search DoOP with either sequence or text (annotation) to find promoter clusters of various genes. In addition to the sequence data, the positions of the conserved sequence blocks derived from multiple alignments, the positions of repetitive elements and the positions of transcription start sites known from the Eukaryotic Promoter Database (EPD) can be viewed graphically

40Ar/39Ar ages of the sill complex of the Karoo large igneous province: implications for the Pliensbachian-Toarcian climate change.

Reliable geochronological results gathered so far (n = 76) have considerably constrained the timing of the emplacement of the Karoo large igneous province (LIP). Yet strikingly missing from this dating effortis the huge southern sill complex cropping out in the >0.6 x 10(6) km2 Main Karoo sedimentary basin. We present 16 new 40Ar/39Ar analyses carried out on fresh plagioclase and biotite separates from 15 sill samples collected along a N-S trend in the eastern part of the basin. The results show a large range of plateau and miniplateau ages (176.2 +- 1.3 to 183.8 +- 2.4 Ma), with most dates suggesting a -3 Ma (181-184 Ma) duration for the main sill events. The available age database allows correlation of the Karoo LIP emplacement with the Pliensbachian-Toarcian second-order biotic extinction, the global warming, and the Toarcian anoxic event (provided that adequate calibration between the 40K and 238U decay constant ismade). The mass extinction and the isotopic excursions recorded at the base of the Toarcian appear to be synchronous with both the increase of magma emission of the Karoo LIP and the emplacement of the sills.The CO2 and SO2 derived from both volcanic emissions as well as carbon-rich sedimentary layers intrudedby sills might be the main culprits of the Pliensbachian-Toarcian climate perturbations. We propose that the relatively low eruption rate of the Karoo LIP is one of the main reasons explaining why its impact on thebiosphere is relatively low contrary to, e.g., the CAMP (Triassic-Jurassic) and Siberia (Permo-Triassic) LIPs

Identification of hypertensive patients with dominant affective temperaments might improve the psychopathological and cardiovascular risk stratification: a pilot, case-control study.

BACKGROUND: Although mood disorders and cardiovascular diseases have widely studied psychosomatic connections, data concerning the influence of the psychopathologically important affective temperaments in hypertension are scarce. To define a possibly higher cardiovascular risk subpopulation we investigated in well-treated hypertensive patients with dominant affective temperaments (DOM) and in well-treated hypertensive patients without dominant temperaments the level of depression and anxiety, arterial stiffness and serum Brain-derived Neurotrophic Factor (seBDNF). METHODS: 175 hypertensive patients, free of the history of psychiatric diseases, completed the TEMPS-A, Beck Depression Inventory and Hamilton Anxiety Scale questionnaires in two primary care practices. Of those 175 patients, 24 DOM patients and 24 hypertensive controls (matched in age, sex and the presence of diabetes) were selected for measurements of arterial stiffness and seBDNF level. RESULTS: Beck and Hamilton scores in DOM patients were higher compared with controls. Pulse wave velocity and augmentation index did not differ between the groups while in the DOM patients decreased brachial systolic and diastolic and central diastolic blood pressures were found compared with controls. SeBDNF was lower in the DOM group than in the controls (22.4 +/- 7.2 vs. 27.3 +/- 7.8 ng/mL, p < 0.05). CONCLUSIONS: Although similar arterial stiffness parameters were found in DOM patients, their increased depression and anxiety scores, the decreased brachial and central diastolic blood pressures as well as the decreased seBDNF might refer to their higher vulnerability regarding the development not only of major mood disorders, but also of cardiovascular complications. These data suggest that the evaluation of affective temperaments should get more attention both with regard to psychopathology and cardiovascular health management

Evolution of the Toarcian (Early Jurassic) carbon-cycle and global climatic controls on local sedimentary processes (Cardigan Bay Basin, UK)

The late Early Jurassic Toarcian Stage represents the warmest interval of the Jurassic Period, with an abrupt rise in global temperatures of up to ∼7 °C in mid-latitudes at the onset of the early Toarcian Oceanic Anoxic Event (T-OAE; ∼183 Ma). The T-OAE, which has been extensively studied in marine and continental successions from both hemispheres, was marked by the widespread expansion of anoxic and euxinic waters, geographically extensive deposition of organic-rich black shales, and climatic and environmental perturbations. Climatic and environmental processes following the T-OAE are, however, poorly known, largely due to a lack of study of stratigraphically well-constrained and complete sedimentary archives. Here, we present integrated geochemical and physical proxy data (high-resolution carbon-isotope data (δ13C), bulk and molecular organic geochemistry, inorganic petrology, mineral characterisation, and major- and trace-element concentrations) from the biostratigraphically complete and expanded entire Toarcian succession in the Llanbedr (Mochras Farm) Borehole, Cardigan Bay Basin, Wales, UK. With these data, we (1) construct the first high-resolution biostratigraphically calibrated chemostratigraphic reference record for nearly the complete Toarcian Stage, (2) establish palaeoceanographic and depositional conditions in the Cardigan Bay Basin, (3) show that the T-OAE in the hemipelagic Cardigan Bay Basin was marked by the occurrence of gravity-flow deposits that were likely linked to globally enhanced sediment fluxes to continental margins and deeper marine (shelf) basins, and (4) explore how early Toarcian (tenuicostatum and serpentinum zones) siderite formation in the Cardigan Bay Basin may have been linked to low global oceanic sulphate concentrations and elevated supply of iron (Fe) from the hinterland, in response to climatically induced changes in hydrological cycling, global weathering rates and large-scale sulphide and evaporite deposition

First record of Rhabdoceras suessi (Ammonoidea, Late Triassic) from the Transylvanian Triassic Series of the Eastern Carpathians (Romania) and a review of its biochronology, paleobiogeography and paleoecology

Abstract The occurrence of the heteromorphic ammonoid Rhabdoceras suessi Hauer, 1860, is recorded for the first time in the Upper Triassic limestone of the Timon-Ciungi olistolith in the Rarău Syncline, Eastern Carpathians. A single specimen of Rhabdoceras suessi co-occurs with Monotis (Monotis) salinaria that constrains its occurrence here to the Upper Norian (Sevatian 1). It is the only known heteromorphic ammonoid in the Upper Triassic of the Romanian Carpathians. Rhabdoceras suessi is a cosmopolitan species widely recorded in low and mid-paleolatitude faunas. It ranges from the Late Norian to the Rhaetian and is suitable for high-resolution worldwide correlations only when it co-occurs with shorter-ranging choristoceratids, monotid bivalves, or the hydrozoan Heterastridium. Formerly considered as the index fossil for the Upper Norian (Sevatian) Suessi Zone, by the latest 1970s this species lost its key biochronologic status among Late Triassic ammonoids, and it generated a controversy in the 1980s concerning the status of the Rhaetian stage. New stratigraphic data from North America and Europe in the subsequent decades resulted in a revised ammonoid biostratigraphy for the uppermost Triassic, the Rhaetian being reinstalled as the topmost stage in the current standard timescale of the Triassic. The geographic distribution of Rhabdoceras is compiled from published worldwide records, and its paleobiogeography and paleoecology are discussed