The study of cancer is multidisciplin-ary, bringing together physicians fromall subspecialties and scientists from ex-tremely diverse backgrounds. In thisera, no one can claim expertise in all ofthese fields. However, the need to un-derstand cancer at a basic level requiresa specific and in-depth awareness ofmany disciplines, and this presents achallenge to the modern physician/scientist. Introduction to [...]
A Linear Algebra Approach to the Vector Space Model
This is an improved (revised and updated) version of a fast track tutorial on vector space calculations. The tutorialcovers term-document and term-query matrices, matrix transposition, dot products, and cosine similarities.A modern linear algebra approach, based on reaction equations, is used. The virtues of this approach aredescribed in http://www.miislita.com/information-retrieval-tutorial/association-scalar-clusters-tutorial-1.pdf. Keywords: term vector calculations, cosine similarities, term-document, [...]
Maple Tutorial Part 2: Linear Algebra with Maple
At the beginning of each worksheet, it is best to restart Maple: > restart;Then, you should load Linear Algebra package using the following command:> with(Linear Algebra):To define a matrix, type> A:=Matrix([[1,2,3],[3,4,5],[6,7,8]]); :=A ???????????? 1 2 33 4 56 7 8 > B:=Matrix([[1.2,3.4,7.5],[1.8,4.9,6.3]]); :=B ???????? 1.2 3.4 7.51.8 4.9 6.3 To define a vector, type> v:=Vector([1,2,3]); [...]
Linear Algebra- Tutorial Sheet 3
1. The Hilbert matrix Hn is defined as the n × n matrix whose (i, j)th entry is1i + j ? 1for i, j = 1,…,n. Obtain H?1 3 by the Gauss Jordan Method.2. Find the inverse of the matrix ????? 1 3 ?22 5 ?70 1 ?4 ????? using elementary row operations.3. Compute the [...]
Linear Algebra – Tutorial Sheet 1
1. Let A and B be symmetric matrices of the same size. Show that AB is a symmetricmatrix if and only if AB = BA.2. The trace of a square matrix A = (aij) is defined as the sum of its diagonalelements, that is, trA := ?i aii. Prove that if A, B are square [...]
Tutorial 4 Numerical Linear Algebra
This tutorial is devoted to discussion of the computational methods used in numerical linearalgebra. Topics discussed include, matrix multiplication, matrix transformations, numericalmethods for solving systems of linear equations, the linear least squares, orthogonality, singularvalue decomposition, the matrix eigenvalue problem, and computations with sparse matrices. 4.1MATLAB functions used in Tutorial 4 The following MATLAB functions will [...]
A Bayesian Perspective
Bayesian Methods The philosophy within statistics known as Bayesian inference has a very long history, but has only relatively recently been used explicitly in image processing in astronomy. It is distinguished from the perhaps more familiar classical statistical ideas by using prior information about the images being studied.Image restoration in astronomy involves considering the image [...]
Astronomy Magazine
Imaging Sciences Laboratory Focuses on Maximum Scientific Return The traditional icon of astronomy is Galileo, spending his time squinting through the eyepiece of his telescope and jotting down sketches of what he saw. Today, in contrast, astronomers use sensitive instruments attached to telescopes, analyze the light from the objects being observed, and output the data [...]
5 RED PLANET and QUEST
RED PLANET – Mars Mars, the red planet, is the world on which next we will walk. The Martian day is a comfortable 24-and-a-half hours. But the rest is strange – planet-wide dust storms,overnight temperatures below minus 100 degrees Celsius and a daytime high just above freezing. Mars has the biggest volcano in the Solar [...]
Mercury – Astronomy for Kids
Mercury – the Winged Messenger Tiny Mercury is the smallest planet in our solar system. As a matter of fact, there are two moons in the solar system that are larger than this planet! Jupiter’s moon Ganymede and Saturn’s moon Titan are both larger than the closest planet to the Sun.In addition, the surface temperature [...]