Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz Domains

For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in particular with Neumann boundary conditions are Hoelder continuous for sufficiently $L^p$-regular right-hand sides. From this we deduce that the parabolic problem with Robin or Wentzell-Robin boundary conditions are well-posed on $\mathrm{C}(\bar{\Omega})$.Comment: 18 page

A Method for Reasoning about other Agents\u27 Beliefs from Observations

Traditional work in belief revision deals with the question of what an agent should believe upon receiving new information. We will give an overview about what can be concluded about an agent based on an observation of its belief revision behaviour. The observation contains partial information about the revision inputs received by the agent and its beliefs upon receiving them. We will sketch a method for reasoning about past and future beliefs of the agent and predicting which inputs it accepts and rejects. The focus of this talk will be on different degrees of incompleteness of the observation and variants of the general question we are able to deal with

Loss of expression of the tumor suppressor CEACAM1 links different hereditary colorectal carcinoma sub-types to the genesis of sporadic colorectal carcinoma

According to their carcinogenesis, colorectal cancer (CRC) subtypes show distinct molecular parameters. Hereditary non-polypous colorectal cancer (HNPCC) is the most common inherited CRC characterized by clinical criteria and confirmed microsatellite instability (MSI). Interestingly, a recently identified subtype, familial colorectal cancer type X (FCC-X), shows the same clinical criteria but microsatellite stability (MSS). CEACAM1 is a known tumor suppressor that regulates apoptosis in colon cells, and its loss is one of the most frequent events in early tumorigenesis of CRC. Therefore its loss may characterize precursor colon cells prior to neoplastic transformation. We analyzed tumor specimens of HNPCC and FCC-X patients in order to investigate whether there is a loss of CEACAM1 expression analogous to sporadic CRC and whether the expression of CEACAM1 would distinguish between these tumor entities. No differences in CEACAM1 expression were noted between HNPPC (n = 38) and FCC-X (n = 30) tumors. CEACAM1 was reduced in near-identical frequencies in 36/38 (95%) HNPCC and 29/30 (97%) FCC-X. This is the first report to demonstrate the loss of CEACAM1 expression in hereditary CRC. There was no difference between HNPCC and FCC-X. The frequency of expression loss was comparable to sporadic CRC, indicating that loss of CEACAM1 is an early event in colorectal tumorigenesis linking the genesis of sporadic and hereditary CRC