[Accepted Manuscript] Detecting bias arising from delayed recording of time

Sometimes in studies of the dependence of survival time on explanatory variables the natural time origin for defining entry into study cannot be observed and a delayed time origin is used instead. For example, diagnosis of disease may in some patients be made only at death. The effect of such delays is investigated both theoretically and in the context of the England and Wales National Cancer Register

Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open string invariants in the spirit of Katz-Liu, defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of [C^3/Z_3], where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main object of our study is the richer case of [C^3/Z_4], where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected, version to appear on Selecta Mathematica; v3: last minute mistake found and fixed for the symmetric brane setup of [C^3/Z_4]; in pres

The small-scale manufacture of compound animal feed (ODNRI Bulletin No. 9)

This bulletin supersedes TDRI report G67 The small-scale manufacture of compound animal feed, which was first published in 1971. lt retains a similar format to G67, but the text has been extensively revised and expanded in the light of numerous enquiries dealt with by ODNRI on all aspects of feed production in the intervening years. lt is hoped that it will act as a technical and investment guide for those interested in initiating the production of compound animal feeds, as well as acting as a useful reference report for those already actively operating in this field. Chapter 1 describes the economic background to the industry; theoretical aspects of animal nutrition are dealt with in Chapter 2; these are related to the properties of the various raw materials used in feed production in Chapter 3. Chapter 4 describes the manufacturing process and examines the physical requirements for setting up plants at various scales of output, and Chapter 5 develops cost and return models for the plants described

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.htm

Some statistical aspects of causality

Die Verfasser stellen drei Varianten von Kausalität vor. Sie diskutieren Kausalität als stabile Beziehung, Kausalität als Effekt einer Intervention und Kausalität als Erklärung eines Prozesses. Darüberhinaus werden Probleme der Aggregation und des Auftretens unbeobachteter vermittelnder Variablen erörtert und die von Bradford Hill formulierten Bedingungen für das Vorliegen von Kausalität vorgestellt. Anhand eines Fallbeispiels aus der Soziologie (Entwicklung von Einstellungen in Bezug auf die Rolle des Staates) werden Abhängigkeitsbeziehungen von unabhängigen Variablen über vermittelnde Variablen zu abhängigen Variablen konstruiert. Abschließend wird auf wichtige Veröffentlichungen zum Thema Kausalität hingewiesen. (ICE

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

On the generation of the chordless four-cycle

In der graphentheoretischen Darstellung bedingter Unabhängiger spielt der stranglose Vierer-Zyklus eine besondere Rolle. Anhand der Theorie von Markov werden für vier Randvariable die bedingten Unabhängigen 'Angstzustand' (X), 'Zornzustand' (W), 'ängstlicher Charakter' (U) und 'zorniger Charakter' (V) dargestellt. Angesichts der Schwierigkeiten bei der Erzeugung solcher Systeme werden einige mögliche Datengewinnungsmechanismen entworfen. Ein stochastischer Prozeß wird formuliert. Im Mittelpunkt stehen Systeme, die einen stranglosen Vierer-Zyklus in einer konzentrischen Matrix erzeugen können, bei denen es also nur zwei spezielle bedingte Unabhängige gibt. Daneben werden noch zwei weitere Möglichkeiten für einen stranglosen Vierer-Zyklus angesprochen. (prf

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

A sweep algorithm for triangular matrices and its statistical applications

Ein Sweepoperator ist definiert für schrittweise sequentielle Invertierung von triangulären Matrizen und ihre Werte werden verglichen mit denen des Sweepoperators zur Invertierung symmetrischer Matrizen. Der Algorithus wird angewendet, um Folgeverteilungen zu untersuchen, die über einen azyklischen Graphen gebildet wurden. Drei Hauptanwendungen werden abgeleitet. Die erste dient der Prüfung einer einfachen Form für die Folgeverteilung, die nach Marginalisierung über und Konditionalisierung von beliebigen Variablensubsets in solch einem linearen System resultiert. Die zweite Anwendung betrifft die Ausweitung der Ergebnisse für lineare Systeme auf generelle Verteilungen durch die Interpretation von strukturellen Nullen in den Matrizen durch Ausdrücke für fehlende Ecken in assoziierten Graphen und symbolische Matrixtransformationen als Grafenmodifikation. Die dritte dient dem Nachweis der Equivalenz von mehreren Kriterien für das Herauslesen von Unabhängigkeitsfeststellungen aus gerichteten azyklischen Graphen. (OH)A sweep operator is defined for stepwise sequential inversion of triangular matrices and its properties are compared to those of the sweep operator for inverting symmetric matrices. The algorithm is used to study joint distributions generated over a directed acyclic graph. Three main applications are derived. The first is to prove a simple form for the joint distribution resulting after marginalising over and conditioning on arbitrary subsets of variables in such a linear system. The second is to extend the results for linear systems to general distributions by interpreting structural zeros in matrices in terms of missing edges in associated graphs and symbolic matrix transformations as modifications of graphs. The third is to show the equivalence of several criteria for reading off independence statements from directed acyclic graphs.' (author's abstract)

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page