Closing the Gap for Pseudo-Polynomial Strip Packing

Two-dimensional packing problems are a fundamental class of optimization problems and Strip Packing is one of the most natural and famous among them. Indeed it can be defined in just one sentence: Given a set of rectangular axis parallel items and a strip with bounded width and infinite height, the objective is to find a packing of the items into the strip minimizing the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial time algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + epsilon. In this paper, we close the gap between inapproximability result and currently known algorithms by presenting an algorithm with approximation ratio 5/4 + epsilon. The algorithm relies on a new structural result which is the main accomplishment of this paper. It states that each optimal solution can be transformed with bounded loss in the objective such that it has one of a polynomial number of different forms thus making the problem tractable by standard techniques, i.e., dynamic programming. To show the conceptual strength of the approach, we extend our result to other problems as well, e.g., Strip Packing with 90 degree rotations and Contiguous Moldable Task Scheduling, and present algorithms with approximation ratio 5/4 + epsilon for these problems as well

Phenotyping the potential antagonistic knock-out of the chromatin remodeler EZH2 and CHD7 in neural stem cells and the adult brain

CHARGE syndrome describes a combination of severe developmental defects including, among other things, a delayed or retarded mental development, sometimes combined with a variety of psychological symptoms. Especially, the molecular mechanisms behind this brain phenotype is little understood, and cannot be treated effectively up to now. This syndrome is caused by a heterozygous mutation in the Chromodomain helicase protein 7 (chd7) gene, which encodes an epigenetically active protein (CHD7) mediating nucleosome sliding, and associated with open and active chromatin (H3K27ac, Feng et al., 2017). Another epigenetically active protein fulfilling an opposite task is EZH2 (the catalytic part of the polycomb repressive complex 2 (PRC2)) which silences gene expression by methylating histon 3 lysin 27. Both EZH2 and CHD7 are expressed in overlapping brain regions, and a knock-out of the respective protein has opposing effects on neuronal branching (Feng et al., 2013 and Liu, Y.). With these hints it was hypothesized that EZH2 might counteract CHD7 deficiency and could be beneficial for the CHARGE condition. In the frame of this thesis I was able to generate and analyze a CHARGE mouse (CMVCre;CHD7+/fl) that displayed a variety of CHARGE related symptoms. Heterozygous chd7 mutant mice had a reduced body weight, were significantly more active, developed sever eye malformations with narrowed palpebral fissures, significantly smaller eye diameter, a thinner retina and inner nuclear layer, and partially completely dysfunctional eyes. Furthermore, the cerebellum of CHARGE mice showed a missing anterior lobe, and a disorganized purkinje cell layer with less primary branches. Also CHARGE mice have less neurogenesis ind the hippocampus. Following the main hypothesis a genetic rescue (CMVCre;CHD7+/fl;EZH2+/fl) could restore; body and brain size, the strong eye malformations observed under CHARGE conditions, the amount of neural stem cells in the dentate gyrus, and the cerebella purkinje cell layer. Moreover, an RNA sequencing of the cerebellum tissue revealed that the gene expression of many genes in the double knock-out was indeed rescued. Furthermore, a homozygous inducible double knock-out of chd7 and ezh2 (NesCreERT2;CHD7fl/fl;EZH2fl/fl) rescued the neural stem cell pool in comparison to a chd7 single knock-out. Finally, these findings encourage me to use a very potent EZH2 inhibitor to treat neural stem cells in vitro and in vivo, thus attempting a novel CHD7 deficient treatment

Closing the Gap for Single Resource Constraint Scheduling

In the problem called single resource constraint scheduling, we are given m identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource R. A schedule of these jobs is feasible if, at each point in the schedule, the number of machines and resources required by jobs processed at this time is not exceeded. It is NP-hard to approximate this problem with a ratio better than 3/2. On the other hand, the best algorithm so far has an absolute approximation ratio of 2+?. In this paper, we present an algorithm with absolute approximation ratio (3/2+?), which closes the gap between inapproximability and best algorithm with exception of a negligible small ?

Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a configuration describes a possible placement on one of the target locations, and the IP is used to chose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and therefore be solved efficiently. As an application, we consider scheduling problems with setup times, in which a set of jobs has to be scheduled on a set of identical machines, with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/epsilon) x poly(|I|) with a single exponential term in f for the first and a double exponential one for the second case. Previously, only constant factor approximations of 5/3 and 4/3 + epsilon respectively were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine

Scheduling with Many Shared Resources

Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be executed and hence prevents the execution of jobs that need the same resource while being processed. Previously a $(2m/(m+1))$-approximation was the best known result for this problem. Furthermore, a $6/5$-approximation for the case with only two machines was known as well as a PTAS for the case with a constant number of machines. We present a simple and fast 5/3-approximation and a much more involved but still reasonable 1.5-approximation. Furthermore, we provide a PTAS for the case with only a constant number of machines, which is arguably simpler and faster than the previously known one, as well as a PTAS with resource augmentation for the general case. The approximation schemes make use of the N-fold integer programming machinery, which has found more and more applications in the field of scheduling recently. It is plausible that the latter results can be improved and extended to more general cases. Lastly, we give a $5/4 - \varepsilon$ inapproximability result for the natural problem extension where each job may need up to a constant number (in particular $3$) of different resources

XMM-Newton and Chandra observations of three X-ray faint early-type galaxies

We present XMM-Newton observations of three X-ray under-luminous elliptical galaxies, NGC 3585, NGC 4494 and NGC 5322. All three galaxies have relatively large optical luminosities (log LB=10.35-10.67 solar) but have X-ray luminosities consistent with emission from discrete sources only. In conjunction with a Chandra observation of NGC 3585, we analyse the XMM data and show that the three galaxies are dominated by discrete source emission, but do possess some X-ray emitting gas. The gas is at relatively low temperatures, kT=0.25-0.44 keV. All three galaxies show evidence of recent dynamical disturbance and formation through mergers, including kinematically distinct cores, young stellar ages, and embedded stellar disks. This leads us to conclude that the galaxies formed relatively recently and have yet to build up large X-ray halos. They are likely to be in a developmental phase where the X-ray gas has a very low density, making it undetectable outside the galaxy core. However, if the gas is a product of stellar mass loss, as seems most probable, we would expect to observe supersolar metal abundances. While abundance is not well constrained by the data, we find best fit abundances <0.1 solar for single-temperature models, and it seems unlikely that we could underestimate the metallicity by such a large factor.Comment: Accepted for publication in MNRAS, 12 pages, 8 postscript figure

Many quality measurements, but few quality measures assessing the quality of breast cancer care in women: A systematic review

BACKGROUND: Breast cancer in women is increasingly frequent, and care is complex, onerous and expensive, all of which lend urgency to improvements in care. Quality measurement is essential to monitor effectiveness and to guide improvements in healthcare. METHODS: Ten databases, including Medline, were searched electronically to identify measures assessing the quality of breast cancer care in women (diagnosis, treatment, followup, documentation of care). Eligible studies measured adherence to standards of breast cancer care in women diagnosed with, or in treatment for, any histological type of adenocarcinoma of the breast. Reference lists of studies, review articles, web sites, and files of experts were searched manually. Evidence appraisal entailed dual independent assessments of data (e.g., indicators used in quality measurement). The extent of each quality indicator's scientific validation as a measure was assessed. The American Society of Clinical Oncology (ASCO) was asked to contribute quality measures under development. RESULTS: Sixty relevant reports identified 58 studies with 143 indicators assessing adherence to quality breast cancer care. A paucity of validated indicators (n = 12), most of which assessed quality of life, only permitted a qualitative data synthesis. Most quality indicators evaluated processes of care. CONCLUSION: While some studies revealed patterns of under-use of care, all adherence data require confirmation using validated quality measures. ASCO's current development of a set of quality measures relating to breast cancer care may hold the key to conducting definitive studies