Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt{2}-1$. We show that the Poincar\'e-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisfies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon$, generalizing the results previously known for the golden number.Comment: 17 pages, 2 figure

Body Fluid Cytokine Levels in Mild Cognitive Impairment and Alzheimer’s Disease: a Comparative Overview

This article gives a comprehensive overview of cytokine and other inflammation associated protein levels in plasma, serum and cerebrospinal fluid (CSF) of patients with Alzheimer's disease (AD) and mild cognitive impairment (MCI). We reviewed 118 research articles published between 1989 and 2013 to compare the reported levels of 66 cytokines and other proteins related to regulation and signaling in inflammation in the blood or CSF obtained from MCI and AD patients. Several cytokines are evidently regulated in (neuro-) inflammatory processes associated with neurodegenerative disorders. Others do not display changes in the blood or CSF during disease progression. However, many reports on cytokine levels in MCI or AD are controversial or inconclusive, particularly those which provide data on frequently investigated cytokines like tumor necrosis factor alpha (TNF-α) or interleukin-6 (IL-6). The levels of several cytokines are possible indicators of neuroinflammation in AD. Some of them might increase steadily during disease progression or temporarily at the time of MCI to AD conversion. Furthermore, elevated body fluid cytokine levels may correlate with an increased risk of conversion from MCI to AD. Yet, research results are conflicting. To overcome interindividual variances and to obtain a more definite description of cytokine regulation and function in neurodegeneration, a high degree of methodical standardization and patients collective characterization, together with longitudinal sampling over years is essential

Mutational analysis of the β-subunit of yeast geranylgeranyl transferase I

The gene CAL1 (also known as CDC43 ) of Saccharomyces cerevisiae encodes the β subunit of geranylgeranyl transferase I (GGTase I), which modifies several small GTPases. Biochemical analyses of the mutant-enzymes encoded by cal1 , and cdc43-2 to cdc43-7 , expressed in bacteria, have hown that all of the mutant enzymes possess reduced activity, and that none shows temerature-sensitive enzymatic activities. Nonetheless, all of the cal1/cdc43 mutants show temperature-sensitive growth phenotypes. Increase in soluble pools of the small GTPases was observed in the yeast mutant cells at the restrictive temperature in vivo, suggesting that the yeast prenylation pathway itself is temperative sensitive. The cal-1 mutation, located most proximal to the C-terminus of the protein, differs from the other cdc43 mutations in several respects. An increase in soluble Rholp was observed in the cal-1 strain grown at the restrictive temperature. The temperature-sensitive phenotype of cal-1 is most efficiently suppressed by overproduction of Rholp. Overproduction of the other essential target, Cdc42p, in contrast, is deleterious in cal-1 cells, but not in other cdc43 mutants or the wild-type strains. The cdc43-5 mutant cells accumulate Cdc42p in soluble pools and cdc43-5 is suppressed by overproduction of Cdc42p. Thus, several phenotypic differences are observed among the cal1/cdc43 mutations, possibly due to alterations in substrate specificity caused by the mutations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42258/1/438-252-1-2-1_62520001.pd

A Duality for Involutive Bisemilattices

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation