The performance of DSVD was evaluated using simulated data encompassing the following 16 different types of structural variations (SVs): 1. Small insertions (of length l ∼ N (15, 3), where N (μ, σ) is a Normal distribution with mean μ and standard deviation σ.) 2. Small deletions (l ∼ N (15, 3)) 3. Deletions (l ∼ N (1000, 100)) 4. Inversions (l ∼ N (1000, 100)) 5. Tandem duplications (l ∼ N (10...

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

According to the central limit theorem (CLT ), the distribution function Fn of a normalized sum n(X1 + ... + Xn) of n independent random variables X1, ..., Xn , having a common distribution with mean zero and variance σ 2 > 0, converges to the distribution function Φσ of the normal distribution with mean zero and variance σ, as n → ∞. We will write Φ for Φ1 for the case σ = 1. The densities of ...

A quantum tube is essentially a tubular neighborhood about an immersed complete manifold in some Euclidean space. To be more precise, let Σ →֒ R, k ≥ 1, n = dim(Σ), be an isometric immersion, where Σ is a complete, noncompact, orientable manifold. Then consider the resulting normal bundle TΣ over Σ, and the submanifold F = {(x, ξ)|x ∈ Σ, |ξ < r} ⊂ TΣ for r small enough. The quantum tube is defin...

A measure of closeness among three or more means from normal populations was proposed by Ng (2000). The F-statistic was proposed to test the null hypothesis that this measure of closeness is greater than or equal to some prespecified δ (>0), against the alternative hypothesis that this measure of closeness is smaller than δ. The null distribution of the F-statistic at the boundary has a non-cen...

This paper supplements a previous by the author (Overgroups of subsystem subgroups in exceptional groups: 2 A 1 <mml:annotation encoding=...

Let Σ \Sigma be a finite collection of linear forms in alttext="double-struck K left-bracket ...

1.1 Z-scores versus one-sample T-tests If we knew the mean, µ , and standard deviation, σ , of the control "population", we could construct the "Z-score": σ µ p Z − = where p is the single patient score, and determine the probability of obtaining a Z-score this large from the "Z-distribution" (or "normal" or "Gaussian" distribution). In practice, Z-scores are often tested this way when the grou...

We discuss the Paris-Wilkie translation from bounded arithmetic proofs to bounded depth propositional proofs in both relativized and non-relativized forms. We describe normal forms for proofs in bounded arithmetic, and a definition of Σ -depth for PK-proofs that makes the translation from bounded arithmetic to propositional logic particularly transparent. Using this, we give new proofs of the w...

This note collects some facts, theorems in operator algebras and operator theory for fullfilling my understanding in my studying progress. Part I contains some fundamental notes which I collect from many textbooks and surveys. I will either try to provide some unclear details or solve some basic but important exercises. Other parts might include some parts in published articles which I try to f...