Algorithms for scheduling without preemptions

University of Technology Sydney. Faculty of Science.This thesis is concerned with algorithms for scheduling without preemptions and it contributes to research as follows. The new area of research, which has gained attention only in the last 15 years, is concerned with flow shop models where the storage requirement varies from job to job and a job occupies the storage continuously from the start of its first operation till the completion of its last operation. This thesis contributes to research by developing a new approach of constructing feasible solutions for such flow shop problems with job-dependent storage. This approach utilises Lagrangian relaxation and decomposition - the techniques that have never been used before for such flow shop problems. In this thesis, several Lagrangian relaxation and decomposition-based heuristics are developed for $NP$-hard flow-shop problems with job-dependent storage and the effectiveness of these heuristics is demonstrated by the results of computational experiments. In this thesis, a new discrete optimisation procedure is introduced. This optimisation procedure can be viewed as an alternative exact method to a branch and bound algorithm for a class of discrete optimisation problems with certain properties. This class includes several NP-hard scheduling problems. This discrete optimisation procedure is an iterative algorithm, that searches for a feasible solution with the objective value of the current lower bound or determines that such a solution does not exist. Various methods of how this search can be carried out are investigated, and these methods are compared computationally in application to a scheduling problem. The worst-case analysis of a polynomial-time approximation algorithm for a maximum lateness scheduling problem with parallel identical machines, arbitrary processing times and arbitrary precedence constraints is provided. The algorithm is a modification of the Brucker-Garey-Johnson algorithm originally developed as an exact algorithm for the case of the problem with unit execution time tasks and precedence constraints represented by an in-tree. For the case when the largest processing time does not exceed the number of machines, a worst-case performance guarantee which is tight for arbitrary large instances of the considered maximum lateness problem has been obtained. It is shown that, if the largest processing time is greater than the number of machines, then the worst-case performance guarantee for the list algorithm, obtained by Hall and Shmoys, is tight

Coordination of Cell Proliferation and Cell Fate Determination by CES-1 Snail

<div><p>The coordination of cell proliferation and cell fate determination is critical during development but the mechanisms through which this is accomplished are unclear. We present evidence that the Snail-related transcription factor CES-1 of <i>Caenorhabditis elegans</i> coordinates these processes in a specific cell lineage. CES-1 can cause loss of cell polarity in the NSM neuroblast. By repressing the transcription of the BH3-only gene <i>egl-1</i>, CES-1 can also suppress apoptosis in the daughters of the NSM neuroblasts. We now demonstrate that CES-1 also affects cell cycle progression in this lineage. Specifically, we found that CES-1 can repress the transcription of the <i>cdc-25.2</i> gene, which encodes a Cdc25-like phosphatase, thereby enhancing the block in NSM neuroblast division caused by the partial loss of <i>cya-1</i>, which encodes Cyclin A. Our results indicate that CDC-25.2 and CYA-1 control specific cell divisions and that the over-expression of the <i>ces-1</i> gene leads to incorrect regulation of this functional ‘module’. Finally, we provide evidence that <i>dnj-11</i> MIDA1 not only regulate CES-1 activity in the context of cell polarity and apoptosis but also in the context of cell cycle progression. In mammals, the over-expression of Snail-related genes has been implicated in tumorigenesis. Our findings support the notion that the oncogenic potential of Snail-related transcription factors lies in their capability to, simultaneously, affect cell cycle progression, cell polarity and apoptosis and, hence, the coordination of cell proliferation and cell fate determination.</p></div

<i>ces-1(n703</i>gf<i>)</i>; <i>cya-1(bc416)</i> causes temperature-sensitive embryonic lethality.

<p>(A) The percentages of embryonic lethality at 15°C and 25°C. The numbers above the bars represent the percentage of embryonic lethality. For each genotype, around 1000 embryos were scored. DIC images of embryos arrested during the elongation stage of embryogenesis (B, D, E) or during the first larval stage (L1) (C) when grown at 25°C are shown. White arrows point to abnormalities in the hypodermis. All strains analyzed were homozygous for <i>bcIs66</i>. RNAi was performed by injection.</p

<i>ces-1(n703</i>gf<i>)</i>; <i>cya-1(bc416)</i> blocks cell divisions in the ABarp, C and E lineages.

<p>All strains analyzed were homozygous for <i>bcIs66</i>. Lineage analyses were performed for two (wild-type, <i>+/+</i>), three (<i>ces-1(n703</i>gf<i>); cya-1(bc416)</i>) and three (<i>cdc-25.2(RNAi)</i>) embryos raised at 25°C. The ABarp, C and E lineages are shown. Vertical axis indicates approximate time in min after the 1^st round of embryonic division, in which P0 divides into AB and P1. In the case of <i>ces-1(n703</i>gf<i>); cya-1(bc416)</i>, cell division defects observed in three out of three embryos are depicted in red, defects found in two out of three embryos are depicted in blue, and defects found in one out of three embryos are depicted in orange. In the case of <i>cdc-25.2(RNAi)</i>, RNAi was carried out by injection. Since there is some variability of the RNAi effect, the lineage shown here was derived from the embryo with the strongest phenotype (cell division defects observed in this embryo are depicted in green), and the lineages from the other two <i>cdc-25.2(RNAi)</i> embryos are shown in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003884#pgen.1003884.s006" target="_blank">Figure S6</a>. The severe cell division defects in the ABarp, C and E lineages were seen in all three <i>cdc-25.2(RNAi)</i> embryos. The cell death in the ABarp lineage is labeled with the cross. The defects in the C lineage and ABarp lineage result in a defect in the formation of the hypodermis (the mitoses that generate hyp7, hyp5, hyp11, H0, H1, H2, V1, V2, V4, and V6 fail to occur).</p

<i>ces-1(n703</i>gf<i>); cya-1(bc416)</i> affects the number of ‘NSM-like’ cells.

<p><i>ces-1(n703</i>gf<i>); cya-1(bc416)</i> affects the number of ‘NSM-like’ cells.</p

<i>ces-1</i> Snail represents a functional link between cell cycle progression, cell polarity and apoptosis in the NSM lineage.

<p>Genetic model of <i>ces-1</i> Snail functions in the NSM neuroblast (top), the NSM and the NSM sister cell (bottom). In the NSM neuroblast, <i>ces-1</i> function is negatively regulated by the genes <i>dnj-11</i> MIDA1 and <i>ces-2</i> bZIP. <i>ces-1</i> affects cell cycle progression in the NSM neuroblast by negatively regulating <i>cdc-25.2</i> Cdc25. <i>ces-1</i> also affects the polarity of the NSM neuroblast. However, to date, it is unclear through what mechanism. After the asymmetric division of the NSM neuroblast, the level of <i>ces-1</i> activity is high in the larger NSM (left) and low in the smaller NSM sister cell (right). The activity of <i>ces-1</i> in the NSM is sufficient to block the function of <i>hlh-2/3</i> bHLH, thereby resulting in a level of <i>egl-1</i> BH3-only activity that is too low to induce apoptosis. Conversely, in the NSM sister cell, the activity of <i>ces-1</i> is not sufficient to block the function of <i>hlh-2/3</i>, thereby resulting in a level of <i>egl-1</i> activity that is high enough to induce apoptosis. See text for details and molecular interpretations.</p

<i>cdc-25.2</i> expression is down-regulated by <i>ces-1</i> over-expression.

<p>Transgenic animals carrying an extra-chromosomal array of <i>ces-1</i> heat-shock plasmids and coinjection marker were used as the sample group (P_HS<i>ces-1</i>), while transgenic animals carrying an extra-chromosomal array of only coinjection marker were used as control (<i>+/+</i>). Relative expression levels of <i>cdc-25</i> genes and <i>cya-1</i> gene in control animals (<i>+/+</i>) and animals over-expressing <i>ces-1</i> (P_HS<i>ces-1</i>) were determined by real-time PCR (qPCR). Data are represented as fold change relative to control. Data shown are the means ± SEM from four independent repeats. Paired t-test was used to determine significance. The level of <i>cdc-25.2</i> in P_HS<i>ces-1</i> is significantly lower than in control. The level of <i>cdc-25.3</i> in P_HS<i>ces-1</i> is significantly higher than in control. The levels of <i>cdc-25.1</i>, <i>cdc-25.4</i>, <i>cya-1</i> are not significantly changed in response to <i>ces-1</i> over-expression. *p<0.05, **p<0.01 significantly different from the control.</p

CES-1 binds to an upstream region of the <i>cdc-25.2</i> locus.

<p>The genome-wide binding sites of the CES-1 protein were identified using ChIP-seq. Shown are the distributions of CES-1-bound regions around the genomic loci of the four <i>cdc-25</i> genes, whose transcription units are indicated by blue arrows. The black boxes correspond to the gene exons. The red arrow points to the CES-1-bound region upstream of <i>cdc-25.2</i>. Data was visualized using Integrated Genome Browser based on genome WS190 of <i>C. elegans</i> <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003884#pgen.1003884-Nicol1" target="_blank">[39]</a>.</p