Proof. This theorem is a corollary of the (much more general) Kruskal-Katona theorem. The Kruskal-Katona theorem has a very hands-on proof, based on iteratively modifying the graph. We will see a linear-algebraic proof. Let A be the n×n adjacency matrix of G (Auv = 1 if vertex u is adjacent to vertex v, and Auv = 0 otherwise). Note that A is symmetric. It turns out that e and t are both fundame...

Calculating the statistical linear response of turbulent dynamical systems to the change in external forcing is a problem of wide contemporary interest. Here the authors apply linear regression models with memory, AR(p) models, to approximate this statistical linear response by directly fitting the autocorrelations of the underlying turbulent dynamical system without further computational exper...

Mutual information (MI) is a robust nonparametric statistical approach for identifying associations between genotypes and gene expression levels. Using the data of Problem 1 provided for the Genetic Analysis Workshop 15, we first compared a quantitative MI (Tsalenko et al. 2006 J Bioinform Comput Biol 4:259-4) with the standard analysis of variance (ANOVA) and the nonparametric Kruskal-Wallis (...

OBJECTIVE The time of contact between the product and enamel surface is important in ensuring the efficacy of fluoride varnishes. Thus, some alternatives could avoid fluoride loss to saliva and improve the anticariogenic action of the product. This study evaluated the effect of an experimental coat on the anticariogenic action of fluoride varnishes. MATERIAL AND METHODS Enamel bovine blocks w...

Kemampuan kuantitatif dibutuhkan calon guru biologi dalam memahami fenomena biologis. Hal pertama yang perlu dilakukan menyelesaikan masalah ini adalah perlunya eksplorasi kondisi kecemasan matematika biologi. Penelitian bertujuan mengeksplorasi tingkat dan perbedaannya berdasarkan gender angkatan masuk kuliah. Data dikumpulkan dengan menggunakan kuisioner AMAS (Abbreviated Math Anxiety Scale)....