A construction of bent functions from plateaued functions

In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analysed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent function with some additional properties that enable the construction of strongly regular graphs are constructed, and explicit expressions for bent functions with maximal degree are presented

c-Met overexpression in inflammatory breast carcinomas: automated quantification on tissue microarrays

Inflammatory breast carcinoma (IBC) is a rare but aggressive tumour associated with poor outcome owing to early metastases. Increased expression of c-Met protein correlates with reduced survival and high metastatic risk in human cancers including breast carcinomas and is targetable by specific drugs, that could potentially improve the prognosis. In the present study, we compared c-Met expression in IBC (n=41) and non-IBC (n=480) immunohistochemically (Ventana Benchmark autostainer) in two tissue microarrays (TMA) along with PI3K and E-cadherin. The results were quantified through an automated image analysis device (SAMBA Technologies). We observed that (i) c-Met was significantly overexpressed in IBC as compared with non-IBC (P<0.001), (ii) PI3K was overexpressed (P<0.001) in IBC, suggesting that the overexpressed c-Met is functionally active at least through the PI3K signal transduction pathway; and (iii) E-cadherin was paradoxically also overexpressed in IBC. We concluded that overexpressed c-Met in IBC constitutes a potential target for specific therapy for the management of patients with poor-outcome tumours such as IBC. Automated image analysis of TMA proved to be a valuable tool for high-throughput immunohistochemical quantification of the expression of intratumorous protein markers

Constructive Relationships Between Algebraic Thickness and Normality

We study the relationship between two measures of Boolean functions; \emph{algebraic thickness} and \emph{normality}. For a function $f$, the algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero coefficients in the unique GF(2) polynomial representing $f$, and the normality is the largest dimension of an affine subspace on which $f$ is constant. We show that for $0 < \epsilon<2$, any function with algebraic thickness $n^{3-\epsilon}$ is constant on some affine subspace of dimension $\Omega\left(n^{\frac{\epsilon}{2}}\right)$. Furthermore, we give an algorithm for finding such a subspace. We show that this is at most a factor of $\Theta(\sqrt{n})$ from the best guaranteed, and when restricted to the technique used, is at most a factor of $\Theta(\sqrt{\log n})$ from the best guaranteed. We also show that a concrete function, majority, has algebraic thickness $\Omega\left(2^{n^{1/6}}\right)$.Comment: Final version published in FCT'201

Evaluation of the Water Film Weber Number in Glaze Icing Scaling

Icing scaling tests were performed in the NASA Glenn Icing Research Tunnel to evaluate a new scaling method, developed and proposed by Feo for glaze icing, in which the scale liquid water content and velocity were found by matching reference and scale values of the nondimensional water-film thickness expression and the film Weber number. For comparison purpose, tests were also conducted using the constant We(sub L) method for velocity scaling. The reference tests used a full-span, fiberglass, 91.4-cm-chord NACA 0012 model with velocities of 76 and 100 knot and MVD sizes of 150 and 195 microns. Scale-to-reference model size ratio was 1:2.6. All tests were made at 0deg AOA. Results will be presented for stagnation point freezing fractions of 0.3 and 0.5