Engineering design applications of surrogate-assisted optimization techniques

The construction of models aimed at learning the behaviour of a system whose responses to inputs are expensive to measure is a branch of statistical science that has been around for a very long time. Geostatistics has pioneered a drive over the last half century towards a better understanding of the accuracy of such ‘surrogate’ models of the expensive function. Of particular interest to us here are some of the even more recent advances related to exploiting such formulations in an optimization context. While the classic goal of the modelling process has been to achieve a uniform prediction accuracy across the domain, an economical optimization process may aim to bias the distribution of the learning budget towards promising basins of attraction. This can only happen, of course, at the expense of the global exploration of the space and thus finding the best balance may be viewed as an optimization problem in itself. We examine here a selection of the state of-the-art solutions to this type of balancing exercise through the prism of several simple, illustrative problems, followed by two ‘real world’ applications: the design of a regional airliner wing and the multi-objective search for a low environmental impact hous

Precipitation regime change in Western North America: The role of Atmospheric Rivers.

Daily precipitation in California has been projected to become less frequent even as precipitation extremes intensify, leading to uncertainty in the overall response to climate warming. Precipitation extremes are historically associated with Atmospheric Rivers (ARs). Sixteen global climate models are evaluated for realism in modeled historical AR behavior and contribution of the resulting daily precipitation to annual total precipitation over Western North America. The five most realistic models display consistent changes in future AR behavior, constraining the spread of the full ensemble. They, moreover, project increasing year-to-year variability of total annual precipitation, particularly over California, where change in total annual precipitation is not projected with confidence. Focusing on three representative river basins along the West Coast, we show that, while the decrease in precipitation frequency is mostly due to non-AR events, the increase in heavy and extreme precipitation is almost entirely due to ARs. This research demonstrates that examining meteorological causes of precipitation regime change can lead to better and more nuanced understanding of climate projections. It highlights the critical role of future changes in ARs to Western water resources, especially over California

Characterization of the Santa Maria del Fiore Cupola construction tools using X-ray fluorescence

This paper presents the characterization of different tools employed in the construction of the Santa Maria del Fiore cathedral in Florence; they are part of the Opera di Santa Maria del Fiore collection and are currently exhibited in the Museo dell’Opera del Duomo. The analyzed objects are turnbuckles, pulleys, three-legged lewises, and pincers; indeed, despite their uniqueness and their importance from the historical point of view, this study is the first one that investigates their alloys composition. Actually, this information can be of great interest for curators to find the best conservation strategies and to have new insights on the production techniques typical of the Renaissance. The study was performed using X-Ray Fluorescence (XRF) in order to identify the materials constituting the objects. Then, XRF spectra were analyzed using chemometric techniques, namely Principal Components Analysis (PCA), in order to investigate possible similarities among different alloys and thus provide new indications to help collocating these tools in a specific historical period

ACCELERATION OF BUILDING DESIGN OPTIMISATION THROUGH THE USE OF KRIGING SURROGATE MODELS

ABSTRACT This paper describes an experiment to test the performance of Kriging surrogate modelling optimisation techniques on a building design problem with discrete design choices. Surrogate modelling optimisation offers advantages over traditional optimisation techniques on design problems with expensive (time consuming) performance evaluation models. The techniques are tested for both single and multi-objective optimisation problems with the objective of minimising both annual CO 2 emissions predicted by a dynamic simulation and construction cost. The estimated CO 2 emissions and costs of all possible designs were first established through comprehensive analysis using a multi-processor computer, enabling the performance of the optimisation to be assessed precisely against a known single optimum or Pareto front. The performance is compared against an evolutionary algorithm (EA) searching the dynamic simulation model on the same design problem. The results show that for this design problem, Kriging surrogate modelling optimisation is effective at finding estimates of optimum designs. In the case of the single-objective optimisation it is able to find the optimum in fewer simulation calls than the stand-alone EA. In the case of the multi-objective optimisation it is capable of finding a better Pareto front if the total number of simulations is restricted, although the time cost associated with Kriging does not always mean it is worth using

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Single-molecule transcript counting of stem-cell markers in the mouse intestine

available in PMC 2012 July 1.Determining the molecular identities of adult stem cells requires technologies for sensitive transcript detection in tissues. In mouse intestinal crypts, lineage-tracing studies indicated that different genes uniquely mark spatially distinct stem-cell populations, residing either at crypt bases or at position +4, but a detailed analysis of their spatial co-expression has not been feasible. Here we apply three-colour single-molecule fluorescent in situ hybridization to study a comprehensive panel of intestinal stem-cell markers during homeostasis, ageing and regeneration. We find that the expression of all markers overlaps at crypt-base cells. This co-expression includes Lgr5, Bmi1 and mTert, genes previously suggested to mark distinct stem cells. Strikingly, Dcamkl1 tuft cells, distributed throughout the crypt axis, co-express Lgr5 and other stem-cell markers that are otherwise confined to crypt bases. We also detect significant changes in the expression of some of the markers following irradiation, indicating their potential role in the regeneration process. Our approach can enable the sensitive detection of putative stem cells in other tissues and in tumours, guiding complementary functional studies to evaluate their stem-cell properties.National Institutes of Health (U.S.) (U54CA143874)National Cancer Institute (U.S.) (Physical Sciences Oncology Center at MIT (U54CA143874))National Institutes of Health (U.S.) (NIH Pioneer award (1DP1OD003936))National Cancer Institute (U.S.) (Cancer Center Support (core) grant P30-CA14051)European Molecular Biology Organization (postdoctoral fellowship)Human Frontier Science Program (Strasbourg, France)Machiah FoundationHoward Hughes Medical Institute (Gilliam fellowship

Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Mining Markov Network Surrogates for Value-Added Optimisation

Surrogate fitness functions are a popular technique for speeding up metaheuristics, replacing calls to a costly fitness function with calls to a cheap model. However, surrogates also represent an explicit model of the fitness function, which can be exploited beyond approximating the fitness of solutions. This paper proposes that mining surrogate fitness models can yield useful additional information on the problem to the decision maker, adding value to the optimisation process. An existing fitness model based on Markov networks is presented and applied to the optimisation of glazing on a building facade. Analysis of the model reveals how its parameters point towards the global optima of the problem after only part of the optimisation run, and reveals useful properties like the relative sensitivities of the problem variables

Skin Cancers Among Albinos at a University Teaching Hospital in Northwestern Tanzania: A Retrospective Review of 64 Cases.

Skin cancers are a major risk associated with albinism and are thought to be a major cause of death in African albinos. The challenges associated with the care of these patients are numerous and need to be addressed. The aim of this study was to outline the pattern and treatment outcome of skin cancers among albinos treated at our centre and to highlight challenges associated with the care of these patients and proffer solutions for improved outcome. This was a retrospective study of all albinos with a histopathological diagnosis of skin cancer seen at Bugando Medical Centre from March 2001 to February 2010. Data collected were analyzed using descriptive statistics. A total of 64 patients were studied. The male to female ratio was 1.5:1. The median age of patients was 30 years. The median duration of illness at presentation was 24 months. The commonest reason for late presentation was financial problem. Head and the neck was the most frequent site afflicted in 46(71.8%) patients. Squamous cell carcinoma was the most common histopathological type in 75% of cases. Surgical operation was the commonest modality of treatment in 60 (93.8%) patients. Radiotherapy was given in 24(37.5%) patients. Twenty-seven (42.2%) of the patients did not complete their treatment due to lack of funds. Local recurrence following surgical treatment was recorded in 6 (30.0%) patients. Only thirty-seven (61.7%) patients were available for follow-up at 6-12 months and the remaining patients were lost to follow-up. Skin cancers are the most common cancers among albinos in our environment. Albinism and exposure to ultraviolet light appears to be the most important risk factor in the development of these cancers. Late presentation and failure to complete treatment due to financial difficulties and lack of radiotherapy services at our centre are major challenges in the care of these patients. Early institution of preventive measures, early presentation and treatment, and follow-up should be encouraged in this population for better outcome