Higher Multiplicity in the One-Dimensional Allen-Cahn Action Functional

We prove the ¡-convergence of the Allen-Cahn action functional in the sharp-interface limit. In previous work, good lower bounds were developed under the assumption of single-multiplicity, but the bounds deteriorated in the case of higher-multiplicity interfaces. We develop improved bounds by working directly with the limiting energy measures

The sharp-interface limit of the action functional for Allen-Cahn in one space dimension

We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic srguments and numerical result heve suggested that the limiting action should“count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of \it{scaling}. In this paper, we prove that for $(d=1)$, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem

Neoplastic transformation of mouse C3H 10T1/2 and Syrian hamster embryo cells by heavy ions

C3H 10T1/2 mouse-embryo fibroblasts were used for transformation experiments to study the effectiveness of various heavy ions with energies up to 20 MeV/u and LET values from 170 to 16.000 keV/μm. The transformation frequency per unit absorbed dose decreased with increasing ionization density; at the highest values of LET we found a decrease even of the transformation efficiency per unit fluence. Uranium ions at energies of 5, 9, and 16.3 MeV/u did not induced any transformation. In additional studies piimary Syrian hamster embryo cells (SHE) were exposed to heavy ions in order to characterize cytological and molecular changes which may be correlated with neoplastic transformation. Growth behaviour, chromosomal status, tumorigenicity in nude mice, and expression of oncogenes of transformed cell lines were examined

Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a Cartan subalgebra. We prove that for a large class of groupoids $G$ with abelian isotropy---including all Deaconu--Renault groupoids associated to discrete abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of $k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for pointing out the error); v2 shows there is a conditional expectation onto $M$ iff the interior of the isotropy is closed. v3: Material (including some theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This version published in Integral Equations and Operator Theor

Alternative Mechanisms for Tn5 Transposition

Bacterial transposons are known to move to new genomic sites using either a replicative or a conservative mechanism. The behavior of transposon Tn5 is anomalous. In vitro studies indicate that it uses a conservative mechanism while in vivo results point to a replicative mechanism. To explain this anomaly, a model is presented in which the two mechanisms are not independent—as widely believed—but could represent alternate outcomes of a common transpositional pathway

Solution conformations of early intermediates in Mos1 transposition

DNA transposases facilitate genome rearrangements by moving DNA transposons around and between genomes by a cut-and-paste mechanism. DNA transposition proceeds in an ordered series of nucleoprotein complexes that coordinate pairing and cleavage of the transposon ends and integration of the cleaved ends at a new genomic site. Transposition is initiated by transposase recognition of the inverted repeat sequences marking each transposon end. Using a combination of solution scattering and biochemical techniques, we have determined the solution conformations and stoichiometries of DNA-free Mos1 transposase and of the transposase bound to a single transposon end. We show that Mos1 transposase is an elongated homodimer in the absence of DNA and that the N-terminal 55 residues, containing the first helix-turn-helix motif, are required for dimerization. This arrangement is remarkably different from the compact, crossed architecture of the dimer in the Mos1 paired-end complex (PEC). The transposase remains elongated when bound to a single-transposon end in a pre-cleavage complex, and the DNA is bound predominantly to one transposase monomer. We propose that a conformational change in the single-end complex, involving rotation of one half of the transposase along with binding of a second transposon end, could facilitate PEC assembly

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE

HER2/neu overexpression in the development of muscle-invasive transitional cell carcinoma of the bladder

The mortality from transitional cell carcinoma (TCC) of the urinary bladder increases significantly with the progression of superficial or locally invasive disease (pTa/pT1) to detrusor muscle-invasive disease (pT2+). The most common prognostic markers in clinical use are tumour stage and grade, which are subject to considerable intra- and interobserver variation. Polysomy 17 and HER2/neu gene amplification and protein overexpression have been associated with more advanced disease. Standardised techniques of fluorescence in situ hybridisation and immunohistochemistry, which are currently applied to other cancers with a view to offering anti-HER2/neu therapies, were applied to tumour pairs comprising pre- and postinvasive disease from 25 patients undergoing treatment for bladder cancer. In the preinvasive tumours, increased HER2/neu copy number was observed in 76% of cases and increased chromosome 17 copy number in 88% of cases, and in the postinvasive group these values were 92 and 96%, respectively (not significantly different P=0.09 and 0.07, respectively). HER2 gene amplification rates were 8% in both groups. Protein overexpression rates were 76 and 52%, respectively, in the pre- and postinvasive groups (P=0.06). These results suggest that HER2/neu abnormalities occur prior to and persist with the onset of muscle-invasive disease. Gene amplification is uncommon and other molecular mechanisms must account for the high rates of protein overexpression. Anti-HER2/neu therapy might be of use in the treatment of TCC

Alteration of gene expression profiles during mycoplasma-induced malignant cell transformation

BACKGROUND: Mycoplasmas are the smallest microorganisms capable of self-replication. Our previous studies show that some mycoplasmas are able to induce malignant transformation of host mammalian cells. This malignant transformation is a multistage process with the early infection, reversible and irreversible stages, and similar to human tumor development in nature. The purpose of this study is to explore mechanisms for this malignant transformation. METHODS: To better understand mechanisms for this unique process, we examined gene expression profiles of C3H cells at different stages of the mycoplasma-induced transformation using cDNA microarray technology. A total of 1185 genes involved in oncogenesis, apoptosis, cell growth, cell-cycle regulation, DNA repair, etc. were examined. Differences in the expression of these genes were compared and analyzed using the computer software AtlasImage. RESULTS: Among 1185 genes screened, 135 had aberrant expression at the early infection stage, 252 at the reversible stage and 184 at the irreversible stage. At the early infection stage, genes with increased expression (92 genes) were twice more than those with decreased expression (42 genes). The global gene expression at the reversible stage appeared to be more volatile than that at any other stages but still resembled the profile at the early infection stage. The expression profile at the irreversible stage shows a unique pattern of a wide range of expression levels and an increased number of expressing genes, especially the cancer-related genes. Oncogenes and tumor suppressors are a group of molecules that showed significant changes in expression during the transformation. The majority of these changes occurred in the reversible and irreversible stages. A prolonged infection by mycoplasmas lead to the expression of more cancer related genes at the irreversible stage. CONCLUSION: The results indicate that the expression profiles correspond with the phenotypic features of the cells in the mycoplasma induced transformation process. The early mycoplasma infection stage shares a common phenomenon with many other acute infections, genes with increased expression significantly outnumbering those with decreased expression. The reversible stage is a transition stage between benignancy and malignancy at the molecular level. Aberrant expression of oncogenes and tumor repressors plays a key role in mycoplasma-induced malignant transformation