Tree-valued Fleming-Viot dynamics with mutation and selection

The Fleming-Viot measure-valued diffusion is a Markov process describing the evolution of (allelic) types under mutation, selection and random reproduction. We enrich this process by genealogical relations of individuals so that the random type distribution as well as the genealogical distances in the population evolve stochastically. The state space of this tree-valued enrichment of the Fleming-Viot dynamics with mutation and selection (TFVMS) consists of marked ultrametric measure spaces, equipped with the marked Gromov-weak topology and a suitable notion of polynomials as a separating algebra of test functions. The construction and study of the TFVMS is based on a well-posed martingale problem. For existence, we use approximating finite population models, the tree-valued Moran models, while uniqueness follows from duality to a function-valued process. Path properties of the resulting process carry over from the neutral case due to absolute continuity, given by a new Girsanov-type theorem on marked metric measure spaces. To study the long-time behavior of the process, we use a duality based on ideas from Dawson and Greven [On the effects of migration in spatial Fleming-Viot models with selection and mutation (2011c) Unpublished manuscript] and prove ergodicity of the TFVMS if the Fleming-Viot measure-valued diffusion is ergodic. As a further application, we consider the case of two allelic types and additive selection. For small selection strength, we give an expansion of the Laplace transform of genealogical distances in equilibrium, which is a first step in showing that distances are shorter in the selective case.Comment: Published in at http://dx.doi.org/10.1214/11-AAP831 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Formal mutation testing for Circus

International audienceContext: The demand from industry for more dependable and scalable test-development mechanisms has fostered the use of formal models to guide the generation of tests. Despite many advancements having been obtained with state-based models, such as Finite State Machines (FSMs) and Input/Output Transition Systems (IOTSs), more advanced formalisms are required to specify large, state-rich, concurrent systems. Circus, a state-rich process algebra combining Z, CSP and a refinement calculus, is suitable for this; however, deriving tests from such models is accordingly more challenging. Recently, a testing theory has been stated for Circus, allowing the verification of process refinement based on exhaustive test sets. Objective: We investigate fault-based testing for refinement from Circus specifications using mutation. We seek the benefits of such techniques in test-set quality assertion and fault-based test-case selection. We target results relevant not only for Circus, but to any process algebra for refinement that combines CSP with a data language. Method: We present a formal definition for fault-based test sets, extending the Circus testing theory, and an extensive study of mutation operators for Circus. Using these results, we propose an approach to generate tests to kill mutants. Finally, we explain how prototype tool support can be obtained with the implementation of a mutant generator, a translator from Circus to CSP, and a refinement checker for CSP, and with

Model-Based Test Selection for Infinite-State Reactive Systems

International audienceThis paper addresses the problem of off-line selection of test cases for testing the conformance of a black-box implementation with respect to a specification, in the context of reactive systems. Efficient solutions to this problem have been proposed in the context of finite-state models, based on the ioco conformance testing theory. An extension of these is proposed in the context of infinite-state specifications, modelled as automata extended with variables. One considers the selection of test cases according to test purposes describing abstract scenarios that one wants to test. The selection of program test cases then consists in syntactical transformations of the specification model, using approximate analyses

Symbolic Test Selection Based on Approximate Analysis

International audienceThis paper addresses the problem of generating symbolic test cases for testing the conformance of a black-box implementation with respect to a specification, in the context of reactive systems. The challenge we consider is the selection of test cases according to a test purpose, which is here a set of scenarii of interest that one wants to observe during test execution. Because of the interactions that occur between the test case and the implementation, test execution can be seen as a game involving two players, in which the test case attempts to satisfy the test purpose. Efficient solutions to this problem have been proposed in the context of finite-state models, based on the use of fixpoint computations. We extend them in the context of infinite-state symbolic models, by showing how approximate fixpoint computations can be used in a conservative way. The second contribution we provide is the formalization of a quality criterium for test cases, and a result relating the quality of a generated test case to the approximations used in the selection algorithm

Semi-parametric methods for personalized treatment selection and multi-state models.

This dissertation contains three research projects on personalized medicine and a project on multi-state modelling. The idea behind personalized medicine is selecting the best treatment that maximizes interested clinical outcomes of an individual based on his or her genetic and genomic information. We propose a method for treatment assignment based on individual covariate information for a patient. Our method covers more than two treatments and it can be applied with a broad set of models and it has very desirable large sample properties. An empirical study using simulations and a real data analysis show the applicability of the proposed procedure. We then extend this idea for treatment section for survival outcomes under right-censoring by introducing re-weighted estimation to adjust the bias caused by censoring. Series of empirical studies using simulations show the desirable performance of re-weighted estimation concept in treatment selection in finite sample cases. We provide a real data application of the proposed procedure to illustrate the applicability for right-censored data. Next we propose a novel method for individualized treatment selection when the treatment response is multivariate. The proposed method uses a rank aggregation technique to estimate an ordering of treatments based on ranked lists of treatment performance measures such as smooth conditional means and conditional probability of a response for one treatment dominating others. An empirical study demonstrates very desirable performances of the proposed method in finite sample cases. We also present a data analysis using a HIV clinical trial data to show the applicability of the proposed procedure for real data. Multi-state models are extensions of simple survival models that incorporate the progression of a subject in an interconnected system such as a disease network. An important measure arising from a mutistate model is the subjects’ state occupational probabilities given baseline covariates. In the final portion of this dissertation we introduce an inverse censoring probability re-weighted semi-parametric single index model based approach to estimate conditional state occupation probabilities of a given individual in an acyclic multistate model under right-censoring. Besides obtaining a temporal regression function, we also test the potentially time varying effect of a baseline covariate on future state occupations. We show that the proposed technique has desirable finite sample performances. Its performance is competitive when compared with two other existing approaches. We illustrate the proposed methodology using two different data sets. First we re-examine a well known data set on various event times tracking the progression of a sample of leukemia patients undergoing bone marrow transplant. Our second illustration is based on the functional status of a set of spinal cord injured patients undergoing a rehabilitation program

Complete Model-Based Testing Applied to the Railway Domain

Testing is the most important verification technique to assert the correctness of an embedded system. Model-based testing (MBT) is a popular approach that generates test cases from models automatically. For the verification of safety-critical systems, complete MBT strategies are most promising. Complete testing strategies can guarantee that all errors of a certain kind are revealed by the generated test suite, given that the system-under-test fulfils several hypotheses. This work presents a complete testing strategy which is based on equivalence class abstraction. Using this approach, reactive systems, with a potentially infinite input domain but finitely many internal states, can be abstracted to finite-state machines. This allows for the generation of finite test suites providing completeness. However, for a system-under-test, it is hard to prove the validity of the hypotheses which justify the completeness of the applied testing strategy. Therefore, we experimentally evaluate the fault-detection capabilities of our equivalence class testing strategy in this work. We use a novel mutation-analysis strategy which introduces artificial errors to a SystemC model to mimic typical HW/SW integration errors. We provide experimental results that show the adequacy of our approach considering case studies from the railway domain (i.e., a speed-monitoring function and an interlocking-system controller) and from the automotive domain (i.e., an airbag controller). Furthermore, we present extensions to the equivalence class testing strategy. We show that a combination with randomisation and boundary-value selection is able to significantly increase the probability to detect HW/SW integration errors

Functional regression models in the frame work of reproducing kernel Hilbert space

The aim of this thesis is to systematically investigate some functional regression models for accurately quantifying the effect of functional predictors. In particular, three functional models are studied: functional linear regression model, functional Cox model, and function-on-scalar model. Both theoretical properties and numerical algorithms are studied in depth. The new models find broad applications in many areas. For the functional linear regression model, the focus is on testing the nullity of the slope function, and a generalized likelihood ratio test based on easily implementable data-driven estimate is proposed. The quality of the test is measured by the minimal distance between the null and the alternative space that still allows a possible test. The lower bound of the minimax decay rate of this distance is derived, and test with a distance that decays faster than the lower bound would be impossible. It is shown that the minimax optimal rate is jointly determined by the reproducing kernel and the covariance kernel and our test attains this optimal rate. Later, the test is applied to the effect of the trajectories of oxides of nitrogen (NOx) on the level of ozone (O3). In the functional Cox model, the aim is to study the Cox model with right-censored data in the presence of both functional and scalar covariates. Asymptotic properties of the maximum partial likelihood estimator is established and it is shown that the estimator achieves the minimax optimal rate of convergence under a weighted L2-risk. Implementation of the estimation approach and the selection of the smoothing parameter are discussed in detail. The finite sample performance is illustrated by simulated examples and a real application. The function-on-scalar model concentrates on developing the simultaneous model selection and estimation technique. A novel regularization method called the Grouped Smoothly Clipped Absolute Deviation (GSCAD) is proposed. The initial problem can be transferred into a dictionary learning problem, where the GSCAD can be directly applied to simultaneously learn a sparse dictionary and select the appropriate dictionary size. Efficient algorithm is designed based on the alternative direction method of multipliers (ADMM) which decomposes the joint non-convex problem with the non-convex penalty into two convex optimization problems. Several examples are presented for image denoising and image inpainting, which are competitive with the state of the art methods

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing