12,018 research outputs found

    Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

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    Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the kk-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

    Conditional Sampling for Max-Stable Processes with a Mixed Moving Maxima Representation

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    This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using the Poisson point process structure of such processes. For explicit calculations we restrict ourselves to the one-dimensional case and use a finite number of shape functions satisfying some regularity conditions. For more general shape functions approximation techniques are presented. Our algorithm is applied to the Smith process and the Brown-Resnick process. Finally, we compare our computational results to other approaches. Here, the algorithm for Gaussian processes with transformed marginals turns out to be surprisingly competitive.Comment: 35 pages; version accepted for publication in Extremes. The final publication is available at http://link.springer.co

    Single-cell lineage tracing in the mammary gland reveals stochastic clonal dispersion of stem/progenitor cell progeny.

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    The mammary gland undergoes cycles of growth and regeneration throughout reproductive life, a process that requires mammary stem cells (MaSCs). Whilst recent genetic fate-mapping studies using lineage-specific promoters have provided valuable insights into the mammary epithelial hierarchy, the true differentiation potential of adult MaSCs remains unclear. To address this, herein we utilize a stochastic genetic-labelling strategy to indelibly mark a single cell and its progeny in situ, combined with tissue clearing and 3D imaging. Using this approach, clones arising from a single parent cell could be visualized in their entirety. We reveal that clonal progeny contribute exclusively to either luminal or basal lineages and are distributed sporadically to branching ducts or alveoli. Quantitative analyses suggest that pools of unipotent stem/progenitor cells contribute to adult mammary gland development. Our results highlight the utility of tracing a single cell and reveal that progeny of a single proliferative MaSC/progenitor are dispersed throughout the epithelium.This work was supported by a grant from the Medical Research Council programme grant no. MR/J001023/1 (B.L-L. and C.J.W). F.M.D. was funded by a National Health and Medical Research Council CJ Martin Biomedical Fellowship (GNT1071074). O.B.H. was funded by a Wellcome Trust PhD studentship (105377/Z/14/Z)

    Large Scale Structure of the Universe

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    Galaxies are not uniformly distributed in space. On large scales the Universe displays coherent structure, with galaxies residing in groups and clusters on scales of ~1-3 Mpc/h, which lie at the intersections of long filaments of galaxies that are >10 Mpc/h in length. Vast regions of relatively empty space, known as voids, contain very few galaxies and span the volume in between these structures. This observed large scale structure depends both on cosmological parameters and on the formation and evolution of galaxies. Using the two-point correlation function, one can trace the dependence of large scale structure on galaxy properties such as luminosity, color, stellar mass, and track its evolution with redshift. Comparison of the observed galaxy clustering signatures with dark matter simulations allows one to model and understand the clustering of galaxies and their formation and evolution within their parent dark matter halos. Clustering measurements can determine the parent dark matter halo mass of a given galaxy population, connect observed galaxy populations at different epochs, and constrain cosmological parameters and galaxy evolution models. This chapter describes the methods used to measure the two-point correlation function in both redshift and real space, presents the current results of how the clustering amplitude depends on various galaxy properties, and discusses quantitative measurements of the structures of voids and filaments. The interpretation of these results with current theoretical models is also presented.Comment: Invited contribution to be published in Vol. 8 of book "Planets, Stars, and Stellar Systems", Springer, series editor T. D. Oswalt, volume editor W. C. Keel, v2 includes additional references, updated to match published versio

    The benefits system in Wales

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    This evidence supports the call for further devolution of powers in Wales, especially those that increase the ability for Wales to tackle poverty. Doing so, our work here evidence that the 10 years of austerity following the election of the Coalition Government of 2010 opened a chasm for rising socio-inequalities for Wales. This chasm has ensured that low-income people and communities in Wales were hit hard because of Covid-19 and during lockdown.In this evidence we call for further devolution of powers that will enable the Welsh Government to provide equitable financial stability for the people of Wales. Our evidence draws on our own primary research and is supported by a wealth of secondary research from academics, activists and civil society organisations who work on the frontline in supporting those in needs across Wales. This evidence discusses the current levels of poverty inWales and highlights the rising incidence of food bank use as a key identifier. Moreover, the evidence also acknowledges the potential economic impact in Wales as the pandemic dust settles and discusses the attainment (and gaps) of Local Assistance Schemes, furlough, taxation, UC, and the recent £20 uplift. Finally, we end with a significant discussion of evidence surrounding the proposal for a trial of a Universal Basic Income in Wales and discuss the link between this and the Wellbeing of Future Generations in Wales

    Likelihood inference for exponential-trawl processes

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    Integer-valued trawl processes are a class of serially correlated, stationary and infinitely divisible processes that Ole E. Barndorff-Nielsen has been working on in recent years. In this Chapter, we provide the first analysis of likelihood inference for trawl processes by focusing on the so-called exponential-trawl process, which is also a continuous time hidden Markov process with countable state space. The core ideas include prediction decomposition, filtering and smoothing, complete-data analysis and EM algorithm. These can be easily scaled up to adapt to more general trawl processes but with increasing computation efforts.Comment: 29 pages, 6 figures, forthcoming in: "A Fascinating Journey through Probability, Statistics and Applications: In Honour of Ole E. Barndorff-Nielsen's 80th Birthday", Springer, New Yor

    Therapeutic Breast Reconstruction Using Gene Therapy–Delivered IFNγ Immunotherapy

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    After mastectomy, breast reconstruction is increasingly performed using autologous tissue with the aim of improving quality of life. During this procedure, autologous tissue is excised, relocated, and reattached using vascular anastomoses at the site of the extirpated breast. The period during which the tissue is ex vivo may allow genetic modification without any systemic exposure to the vector. Could such access be used to deliver therapeutic agents using the tissue flap as a vehicle? Such delivery may be more efficient than systemic treatment, in terms of oncological outcomes. The cytokine interferon gamma (IFNγ) has antitumor effects, but systemic toxicity that could be circumvented if its effect can be localized by delivery of the IFNγ gene via gene therapy to autologous tissue used for breast reconstruction, which then releases IFNγ and exerts anti-tumor effects. In a rat model of loco-regional recurrence (LRR) using both MADB-106-Luc and MAD-MB-231-Luc breast cancer cells, autologous tissue was transduced ex vivo with an adeno-associated viral vector (AAV) encoding IFNγ. The therapeutic reconstruction released IFNγ at the LRR site and eliminated cancer cells, significantly decreased tumor burden (P<0.05), and increased survival by 33% (P<0.05) compared to sham reconstruction. Mechanistically, localized IFNγ immunotherapy stimulated M1 macrophages to target cancer cells within the regional confines of the modified tumor environment. This concept of therapeutic breast reconstruction using ex vivo gene therapy of autologous tissue offers a new application for immunotherapy in breast cancer with a dual therapeutic effect of both reconstructing the ablative defect and delivering local adjuvant immunotherapy

    Many-particle entanglement with Bose--Einstein condensates

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    We propose a method to produce entangled states of several particles starting from a Bose-Einstein condensate. In the proposal, a single fast π/2\pi/2 pulse is applied to the atoms and due to the collisional interaction, the subsequent free time evolution creates an entangled state involving all atoms in the condensate. The created entangled state is a spin-squeezed state which could be used to improve the sensitivity of atomic clocks.Comment: 4 pages. Minor modification
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