LECTURE: Correlation Analysis.

Lecture 13 : Correlation Decay : Independence Polynomial

Lecture Notes on Geometric Analysis

§0 Introduction §1 First and Second Variational Formulas for Area §2 Bishop Comparison Theorem §3 Bochner-Weitzenböck Formulas §4 Laplacian Comparison Theorem §5 Poincaré Inequality and the First Eigenvalue §6 Gradient Estimate and Harnack Inequality §7 Mean Value Inequality §8 Reilly’s Formula and Applications §9 Isoperimetric Inequalities and Sobolev Inequalities §10 Lower Bounds of Isoperime...

Lecture Notes in Functional Analysis

1.1. Introducton to Banach Spaces Definition 1.1. Let X be a K–vector space. A functional p ∶ X → [0,+∞) is called a seminorm, if (a) p(λx) = ∣λ∣p(x), ∀λ ∈ K, x ∈X, (b) p(x + y) ≤ p(x) + p(y), ∀x, y ∈X. Definition 1.2. Let p be a seminorm such that p(x) = 0 ⇒ x = 0. Then, p is a norm (denoted by ∥ ⋅ ∥). Definition 1.3. A pair (X, ∥ ⋅ ∥) is called a normed linear space. Lemma 1.4. Each normed sp...

Lecture Notes in Real Analysis

Lecture 10 Linkage Analysis February

Although the title of this lecture is “linkage analysis” it is going to be mostly about computing probabilities. Linkage analysis can be performed for a variety of species. We will concentrate on the case where the individuals in the pedigree are humans. Human pedigrees present some unique problems in that the data is often incomplete. In particular some individuals may be unobserved, or the tr...