A definability theorem for first order logic

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order formula. Our presentation is entirely selfcontained, and only requires familiarity with the most elementary properties of model theory

Short Time Existence for the Curve Diffusion Flow with a Contact Angle

We show short-time existence for curves driven by curve diffusion flow with a prescribed contact angle $\alpha \in (0, \pi)$: The evolving curve has free boundary points, which are supported on a line and it satisfies a no-flux condition. The initial data are suitable curves of class $W_2^{\gamma}$ with $\gamma \in (\tfrac{3}{2}, 2]$. For the proof the evolving curve is represented by a height function over a reference curve: The local well-posedness of the resulting quasilinear, parabolic, fourth-order PDE for the height function is proven with the help of contraction mapping principle. Difficulties arise due to the low regularity of the initial curve. To this end, we have to establish suitable product estimates in time weighted anisotropic $L_2$-Sobolev spaces of low regularity for proving that the non-linearities are well-defined and contractive for small times.Comment: 38 page

COST OF GOVERNMENT PROGRAMS IN AGRICULTURE

Public Economics,

First, do no harm

Not found

Characterization of mutations and loss of heterozygosity of p53 and K-\u3ci\u3eras\u3c/i\u3e2 in pancreatic cancer cell lines by immobilized polymerase chain reaction

Background The identification of known mutations in a cell population is important for clinical applications and basic cancer research. In this work an immobilized form of the polymerase chain reaction, referred to as polony technology, was used to detect mutations as well as gene deletions, resulting in loss of heterozygosity (LOH), in cancer cell lines. Specifically, the mutational hotspots in p53, namely codons 175, 245, 248, 249, 273, and 282, and K-ras2, codons 12, 13 and 61, were genotyped in the pancreatic cell line, Panc-1. In addition LOH analysis was also performed for these same two genes in Panc-1 by quantifying the relative gene copy number of p53 and K-ras2. Results Using polony technology, Panc-1 was determined to possess only one copy of p53, which possessed a mutation in codon 273, and two copies of K-ras2, one wildtype and one with a mutation in codon 12. To further demonstrate the general approach of this method, polonies were also used to detect K-ras2 mutations in the pancreatic cell lines, AsPc-1 and CAPAN-1. Conclusions In conclusion, we have developed an assay that can detect mutations in hotspots of p53 and K-ras2 as well as diagnose LOH in these same genes

Structural plasticity and associative memory in balanced neural networks with spike-time dependent inhibitory plasticity

Peer reviewe