scribe techniques for dissociating rat liver and isolating a high yield of viable hepatocytes for initiation of monolayer cultures representative of the hepatic parenchyma. The properties of hepatocyte cultures were studied and factors affecting their quality were examined. [The 5Cl~indicates that this paper and the three others in the series have been cited(individually or in some combination)...

We will look at MARKET CLEARING or MARKET EQUILIBRIUM prices. We will consider two models with linear utilities : FISHER model and ARROWDEBREU model. See [1] and chapter 5 of [2] for more details. Finally we see an application of the FISHER model to wireless networks. I have also used as reference the scribe notes for this same lecture when this course was taught by Prof. Hajiaghayi at Rutgers ...

We consider support for bandwidthdemanding applications such as video broadcasting using DHTs. We focus our investigations by considering the impact of heterogeneity in the outgoing bandwidth capabilities of nodes on Scribe, a representative and relatively mature DHT-based multicast protocol. We expose important issues that arise due to the mismatch between the ID space that underlies the DHT a...

As far as this author is aware this is the rst paper to de scribe the application of Progol to enantioseparations A scheme is pro posed for data mining a relational database of published enantiosepar ations using Progol The application of the scheme is described and a preliminary assessment of the usefulness of the resulting generalisations is made using their accuracy size ease of interpretati...

The first two sections are largely based on the first two lectures by Oded Regev, course ”Lattices in Computer Science, Fall 2004. The third part is somewhat based on the paper by Oded Regev and Daniele Micciancio Worst-case to Average-case Reductions based on Gaussian Measures, SIAM Journal on Computing 37(1) pp. 267-302, 2007. and to a larger extent on the paper by O. Goldreich, S. Goldwasser...

We begin with defining the ubiquitous concept of a vector space and several properties associated with them, as well as mathematical operations defined on them. The concept of a vector space is, in general, defined over an arbitrary field of scalars. However, we shall restrict ourselves to real vector spaces, i.e. those defined over the field of reals. Definition 2.1 (Vector Space). A real vect...

A group is a mathematical structure 〈G; ∗〉 consisting of a non-empty set G and a binary operation ∗ : G×G→ G and satisfying the following axioms: (A1) The operation ∗ is associative, i.e., for any x, y, z ∈ G, x ∗ (y ∗ z) = (x ∗ y) ∗ z. (A2) There exists a neutral element e for ∗, i.e., x ∗ e = e ∗ x = x for all x ∈ G. (A3) Every element x ∈ G has an inverse x̂, i.e., x ∗ x̂ = x̂ ∗ x = e. If ∗ is ...

Convolution as a Matrix/Vector multiplication Notice that (2) can be written as g = Y x where g is a column vector with elements gk = (x ∗ y)k, x is a column vector with elements xk, and Y is an NxN matrix. By examining (2), we can deduce that the elements of the first row of the matrix Y should be Y0,: = {y0, y−1, y−2, ..., y−(N−1)} Similarly, the second row should be Y1,: = {y1, y0, y−1, ...,...

A metric space, denoted by (X, d), is a set X with a real valued function d : X ×X → R (called a metric or a distance function) such that for every x, y, z ∈ X, 1. d(x, y) ≥ 0 with equality if and only if x = y, 2. d(x, y) = d(y, x), and 3. d(x, y) ≤ d(x, z) + d(y, z). We will restrict our attention to the case where both |X| and d are finite. The problem we are interested in is finding a way t...

Generally, in DNA sequence alignment, we have chosen the substitution matrix δ by assigning a match cost and a mismatch cost. With protein sequences, the situation is more complicated: in some situations, some amino acids are largely interchangeable, and in others, an exchange completely changes the structure and function of the resultant protein. In this sense, all mismatches are not created e...