Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201

Matching Models Across Abstraction Levels with Gaussian Processes

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, and whether such agreement holds for different parametrisations. Here we present a generally applicable statistical machine learning methodology to automatically reconcile the predictions of different models across abstraction levels. Our approach is based on defining a correction map, a random function which modifies the output of a model in order to match the statistics of the output of a different model of the same system. We use two biological examples to give a proof-of-principle demonstration of the methodology, and discuss its advantages and potential further applications.Comment: LNCS forma

Testing in the incremental design and development of complex products

Testing is an important aspect of design and development which consumes significant time and resource in many companies. However, it has received less research attention than many other activities in product development, and especially, very few publications report empirical studies of engineering testing. Such studies are needed to establish the importance of testing and inform the development of pragmatic support methods. This paper combines insights from literature study with findings from three empirical studies of testing. The case studies concern incrementally developed complex products in the automotive domain. A description of testing practice as observed in these studies is provided, confirming that testing activities are used for multiple purposes depending on the context, and are intertwined with design from start to finish of the development process, not done after it as many models depict. Descriptive process models are developed to indicate some of the key insights, and opportunities for further research are suggested

Large Scale Structure of the Universe

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

Type Ia Supernovae as Stellar Endpoints and Cosmological Tools

Empirically, Type Ia supernovae are the most useful, precise, and mature tools for determining astronomical distances. Acting as calibrated candles they revealed the presence of dark energy and are being used to measure its properties. However, the nature of the SN Ia explosion, and the progenitors involved, have remained elusive, even after seven decades of research. But now new large surveys are bringing about a paradigm shift --- we can finally compare samples of hundreds of supernovae to isolate critical variables. As a result of this, and advances in modeling, breakthroughs in understanding all aspects of SNe Ia are finally starting to happen.Comment: Invited review for Nature Communications. Final published version. Shortened, update

"Hook"-calibration of GeneChip-microarrays: Theory and algorithm

Abstract Background: The improvement of microarray calibration methods is an essential prerequisite for quantitative expression analysis. This issue requires the formulation of an appropriate model describing the basic relationship between the probe intensity and the specific transcript concentration in a complex environment of competing interactions, the estimation of the magnitude these effects and their correction using the intensity information of a given chip and, finally the development of practicable algorithms which judge the quality of a particular hybridization and estimate the expression degree from the intensity values. Results: We present the so-called hook-calibration method which co-processes the log-difference (delta) and -sum (sigma) of the perfect match (PM) and mismatch (MM) probe-intensities. The MM probes are utilized as an internal reference which is subjected to the same hybridization law as the PM, however with modified characteristics. After sequence-specific affinity correction the method fits the Langmuir-adsorption model to the smoothed delta-versus-sigma plot. The geometrical dimensions of this so-called hook-curve characterize the particular hybridization in terms of simple geometric parameters which provide information about the mean non-specific background intensity, the saturation value, the mean PM/MM-sensitivity gain and the fraction of absent probes. This graphical summary spans a metrics system for expression estimates in natural units such as the mean binding constants and the occupancy of the probe spots. The method is single-chip based, i.e. it separately uses the intensities for each selected chip. Conclusion: The hook-method corrects the raw intensities for the non-specific background hybridization in a sequence-specific manner, for the potential saturation of the probe-spots with bound transcripts and for the sequence-specific binding of specific transcripts. The obtained chip characteristics in combination with the sensitivity corrected probe-intensity values provide expression estimates scaled in natural units which are given by the binding constants of the particular hybridization.</p

New Constraints (and Motivations) for Abelian Gauge Bosons in the MeV-TeV Mass Range

We survey the phenomenological constraints on abelian gauge bosons having masses in the MeV to multi-GeV mass range (using precision electroweak measurements, neutrino-electron and neutrino-nucleon scattering, electron and muon anomalous magnetic moments, upsilon decay, beam dump experiments, atomic parity violation, low-energy neutron scattering and primordial nucleosynthesis). We compute their implications for the three parameters that in general describe the low-energy properties of such bosons: their mass and their two possible types of dimensionless couplings (direct couplings to ordinary fermions and kinetic mixing with Standard Model hypercharge). We argue that gauge bosons with very small couplings to ordinary fermions in this mass range are natural in string compactifications and are likely to be generic in theories for which the gravity scale is systematically smaller than the Planck mass - such as in extra-dimensional models - because of the necessity to suppress proton decay. Furthermore, because its couplings are weak, in the low-energy theory relevant to experiments at and below TeV scales the charge gauged by the new boson can appear to be broken, both by classical effects and by anomalies. In particular, if the new gauge charge appears to be anomalous, anomaly cancellation does not also require the introduction of new light fermions in the low-energy theory. Furthermore, the charge can appear to be conserved in the low-energy theory, despite the corresponding gauge boson having a mass. Our results reduce to those of other authors in the special cases where there is no kinetic mixing or there is no direct coupling to ordinary fermions, such as for recently proposed dark-matter scenarios.Comment: 49 pages + appendix, 21 figures. This is the final version which appears in JHE

The Formation and Evolution of the First Massive Black Holes

The first massive astrophysical black holes likely formed at high redshifts (z>10) at the centers of low mass (~10^6 Msun) dark matter concentrations. These black holes grow by mergers and gas accretion, evolve into the population of bright quasars observed at lower redshifts, and eventually leave the supermassive black hole remnants that are ubiquitous at the centers of galaxies in the nearby universe. The astrophysical processes responsible for the formation of the earliest seed black holes are poorly understood. The purpose of this review is threefold: (1) to describe theoretical expectations for the formation and growth of the earliest black holes within the general paradigm of hierarchical cold dark matter cosmologies, (2) to summarize several relevant recent observations that have implications for the formation of the earliest black holes, and (3) to look into the future and assess the power of forthcoming observations to probe the physics of the first active galactic nuclei.Comment: 39 pages, review for "Supermassive Black Holes in the Distant Universe", Ed. A. J. Barger, Kluwer Academic Publisher

The Formation of the First Massive Black Holes

Supermassive black holes (SMBHs) are common in local galactic nuclei, and SMBHs as massive as several billion solar masses already exist at redshift z=6. These earliest SMBHs may grow by the combination of radiation-pressure-limited accretion and mergers of stellar-mass seed BHs, left behind by the first generation of metal-free stars, or may be formed by more rapid direct collapse of gas in rare special environments where dense gas can accumulate without first fragmenting into stars. This chapter offers a review of these two competing scenarios, as well as some more exotic alternative ideas. It also briefly discusses how the different models may be distinguished in the future by observations with JWST, (e)LISA and other instruments.Comment: 47 pages with 306 references; this review is a chapter in "The First Galaxies - Theoretical Predictions and Observational Clues", Springer Astrophysics and Space Science Library, Eds. T. Wiklind, V. Bromm & B. Mobasher, in pres

Radiotherapy to the prostate for men with metastatic prostate cancer in the UK and Switzerland: Long-term results from the STAMPEDE randomised controlled trial.

BACKGROUND: STAMPEDE has previously reported that radiotherapy (RT) to the prostate improved overall survival (OS) for patients with newly diagnosed prostate cancer with low metastatic burden, but not those with high-burden disease. In this final analysis, we report long-term findings on the primary outcome measure of OS and on the secondary outcome measures of symptomatic local events, RT toxicity events, and quality of life (QoL). METHODS AND FINDINGS: Patients were randomised at secondary care sites in the United Kingdom and Switzerland between January 2013 and September 2016, with 1:1 stratified allocation: 1,029 to standard of care (SOC) and 1,032 to SOC+RT. No masking of the treatment allocation was employed. A total of 1,939 had metastatic burden classifiable, with 42% low burden and 58% high burden, balanced by treatment allocation. Intention-to-treat (ITT) analyses used Cox regression and flexible parametric models (FPMs), adjusted for stratification factors age, nodal involvement, the World Health Organization (WHO) performance status, regular aspirin or nonsteroidal anti-inflammatory drug (NSAID) use, and planned docetaxel use. QoL in the first 2 years on trial was assessed using prospectively collected patient responses to QLQ-30 questionnaire. Patients were followed for a median of 61.3 months. Prostate RT improved OS in patients with low, but not high, metastatic burden (respectively: 202 deaths in SOC versus 156 in SOC+RT, hazard ratio (HR) = 0·64, 95% CI 0.52, 0.79, p < 0.001; 375 SOC versus 386 SOC+RT, HR = 1.11, 95% CI 0.96, 1.28, p = 0·164; interaction p < 0.001). No evidence of difference in time to symptomatic local events was found. There was no evidence of difference in Global QoL or QLQ-30 Summary Score. Long-term urinary toxicity of grade 3 or worse was reported for 10 SOC and 10 SOC+RT; long-term bowel toxicity of grade 3 or worse was reported for 15 and 11, respectively. CONCLUSIONS: Prostate RT improves OS, without detriment in QoL, in men with low-burden, newly diagnosed, metastatic prostate cancer, indicating that it should be recommended as a SOC. TRIAL REGISTRATION: ClinicalTrials.gov NCT00268476, ISRCTN.com ISRCTN78818544