The Disk Layout Problem

Imagine that we keep a daily log of the files that our computer reads from its hard disk. For most computer users the logs of one day compared to the next may be very similar. For example, opening up a commonly used program may require access to the same files in the same order every time that event occurs. We shall call such a sequence of files a trace. The essence of the problem therefore is: given a set of traces that are expected to be representative of common use, we must rearrange the files on the disk so that the performance is optimized. Programs called disk defragmenters use these simple principles to rearrange data records on a disk so that each file is contiguous, with no holes or few holes between data records. Some more sophisticated disk defragmenters also try to place related files near each other, usually based on simple static structure rather than a dynamic analysis of the accesses. We are interested in more dynamic defragmentation procedures. We first consider a 1D model of the disk. We then look at the results from an investigation of the 2D disk model followed by a discussion of caching strategies. Finally we list some of the complications that may need to be addressed in order to make the models more realistic

Fixing numbers for matroids

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have interpretations through permutation groups, and we make this connection explicit.Comment: This is a major revision of a previous versio

Higher Dimensional Lattice Chains and Delannoy Numbers

Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new proof of a recent result of Duichi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

Ein fall der tödlichen Zink-Phosphid Vergiftung

Opisan je slučaj otrovanja cinkovim fosfidom 32-godišnje pacijentice koja je nakon dva dana umrla. Klinička slika manifestirala se u prvom redu fokom i perifernom kardiovaskularnom insuficijencijom. Posljednjeg dana nastala je generalizirana anasarka.Es wird ein Fall von Zink-Phosphid-Vergiftung bei einer 32 Jahre alten Frau beschrieben, der nach zwei Tagen tödlich endete. Das klinische Bild hat sich in erster Reihe mit Schock und periferer kardiovaskulärer Insuffizienz manifestiert. Am letzten Tag hat sich im Laufe von 6 Stunden ein generalisiertes Anasarka gebildet

Maximum Difference Extreme Difference Method for Finding the Initial Basic Feasible Solution of Transportation Problems

A Transportation Problem can be modeled using Linear Programming to determine the best transportation schedule that will minimize the transportation cost. Solving a transportation problem requires finding the Initial Basic Feasible Solution (IBFS) before obtaining the optimal solution. We propose a new method for finding the IBFS called the Maximum Difference Extreme Difference Method (MDEDM) which yields an optimal or close to the optimal solution. We also investigate the computational time complexity of MDEDM, and show that it is O(mn)

Area, perimeter, height, and width of rectangle visibility graphs

A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width)

Counting lattice chains and Delannoy paths in higher dimensions

AbstractLattice chains and Delannoy paths represent two different ways to progress through a lattice. We use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in a lattice of arbitrary finite dimension. Specifically, fix nonnegative integers n1,…,nd, and let L denote the lattice of points (a1,…,ad)∈Zd that satisfy 0≤ai≤ni for 1≤i≤d. We prove that the number of chains in L is given by 2nd+1∑k=1kmax′∑i=1k(−1)i+kk−1i−1nd+k−1nd∏j=1d−1nj+i−1nj, where kmax′=n1+⋯+nd−1+1. We also show that the number of Delannoy paths in L equals ∑k=1kmax′∑i=1k(−1)i+k(k−1i−1)(nd+k−1nd)∏j=1d−1(nd+i−1nj). Setting ni=n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

Insulin-stimulated GLUT4 translocation requires the CAP-dependent activation of TC10

The stimulation of glucose uptake by insulin in muscle and adipose tissue requires translocation of the GLUT4 glucose transporter protein from intracellular storage sites to the cell surface(1-6). Although the cellular dynamics of GLUT4 vesicle trafficking are well described, the signalling pathways that link the insulin receptor to GLUT4 translocation remain poorly understood. Activation of phosphatidylinositol-3-OH kinase (PI(3)K) is required for this trafficking event, but it is not sufficient to produce GLUT4 translocation(7). We previously described a pathway involving the insulin-stimulated tyrosine phosphorylation of Cbl, which is recruited to the insulin receptor by the adapter protein CAP(8,9). On phosphorylation, Cbl is translocated to lipid rafts. Blocking this step completely inhibits the stimulation of GLUT4 translocation by insulin(10). Here we show that phosphorylated Cbl recruits the CrkII-C3G complex to lipid rafts, where C3G specifically activates the small GTP-binding protein TC10. This process is independent of PI(3)K, but requires the translocation of Cbl, Crk and C3G to the lipid raft. The activation of TC10 is essential for insulin-stimulated glucose uptake and GLUT4 translocation. The TC10 pathway functions in parallel with PI(3)K to stimulate fully GLUT4 translocation in response to insulin.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62864/1/410944a0.pd

Insulin Signaling in Microdomains of the Plasma Membrane

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73880/1/j.1600-0854.2003.00119.x.pd