An application of Cox regression model to the analysis of grouped pulmonary tuberculosis survival data

The recent statistical literature attests to a considerable current interest in specialised statistical methods for the analysis of time to occurrence or failure time data in medical research. Frequently the primary objective of a failure time Study concerns with the association between certain co-variates Z = (Z1, ..., Zp) and the time T > 0 to the occurrence of a certain event. For example a clinical study may be designed to compare several treatment programmes in respect to the time T to recurrence of a disease or response to treatment of a disease. The regression vector Z would include indicator components for treatment as well as other prognostic factors

Hybridization based CEGAR for Hybrid Automata with Affine Dynamics

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Co-variate analysis of tuberculosis data using Cox's regression model

A regression model which allows for analysis of censored survival data adjusting for continuous as well as discrete covariates and varying with time has been proposed by Cox. The hazard rate could be modelled as a function of both time and covariates and the hazard rate could be represented as the product of two terms, the funs representing an unadjusted force of mortality which can be estimated non-parametrically and the second adjusting for the linear combination of a particular covariate profile. In this paper an attempt is made to demonstrate the value of this model with pulmonary tuberculosis data in quantifying the effects of disease, demographic and treatment variables

Relating Syntactic and Semantic Perturbations of Hybrid Automata

We investigate how the semantics of a hybrid automaton deviates with respect to syntactic perturbations on the hybrid automaton. We consider syntactic perturbations of a hybrid automaton, wherein the syntactic representations of its elements, namely, initial sets, invariants, guards, and flows, in some logic are perturbed. Our main result establishes a continuity like property that states that small perturbations in the syntax lead to small perturbations in the semantics. More precisely, we show that for every real number epsilon>0 and natural number k, there is a real number delta>0 such that H^delta, the delta syntactic perturbation of a hybrid automaton H, is epsilon-simulation equivalent to H up to k transition steps. As a byproduct, we obtain a proof that a bounded safety verification tool such as dReach will eventually prove the safety of a safe hybrid automaton design (when only non-strict inequalities are used in all constraints) if dReach iteratively reduces the syntactic parameter delta that is used in checking approximate satisfiability. This has an immediate application in counter-example validation in a CEGAR framework, namely, when a counter-example is spurious, then we have a complete procedure for deducing the same

Specifications for decidable hybrid games

Abstract We introduce STORMED hybrid games (SHG), a generalization of STORMED Hybrid System

STORMED hybrid systems

Abstract. We introduce STORMED hybrid systems, a decidable class which is similar to o-minimal hybrid automata in that the continuous dynamics and constraints are described in an o-minimal theory. However, unlike o-minimal hybrid automata, the variables are not initialized in a memoryless fashion at discrete steps. STORMED hybrid systems require flows which are monotonic with respect to some vector in the continuous space and can be characterised as bounded-horizon systems in terms of their discrete transitions. We demonstrate that such systems admit a finite bisimulation, which can be effectively constructed provided the o-minimal theory used to describe the system is decidable. As a consequence, many verification problems for such systems have effective decision algorithms

A Decidable Class of Planar Linear Hybrid Systems

The paper shows the decidability of the reachability problem for planar, monotonic, linear hybrid automata without resets. These automata are a special class of linear hybrid automata with only two variables, whose flows in all states is monotonic along some direction in the plane, and in which the continuous variables are not reset on a discrete transition. We also prove the undecidability for the same class of automata in 4-dimensions

Conformance Testing of Boolean Programs with Multiple Faults

International audienceConformance testing is the problem of constructing a complete test suite of inputs based on a specification S such that any implementation I (of size less than a given bound) that is not equivalent to S gives a different output on the test suite than S. Typically I and S are assumed to be some type of finite automata. In this paper we consider the problem of constructing test suites for boolean programs (or more precisely modular visibly pushdown automata) that are guaranteed to catch all erroneous implementations that have at least R faults, and pass all correct implementations; if the incorrect implementation has fewer than R faults then the test suite may or may not detect it. We present a randomized algorithm for the construction of such test suites, and prove the near optimality of our test suites by proving lower bounds on the size of test suites

Pre-orders for Reasoning about Stability

Pre-orders between processes, like simulation, have played a central role in the verification and analysis of discrete-state systems. Logical characterization of such pre-orders have allowed one to verify the correctness of a system by analyzing an abstraction of the system. In this paper, we investigate whether this approach can be feasibly applied to reason about stability properties of a system. Stability is an important property of systems that have a continuous component in their state space; it stipulates that when a system is started somewhere close to its ideal starting state, its behavior is close to its ideal, desired behavior. In [6], it was shown that stability with respect to equilibrium states is not preserved by bisimulation and hence additional continuity constraints were imposed on the bisimulation relation to ensure preservation of Lyapunov stability. We first show that stability of trajectories is not invariant even under the notion of bisimulation with continuity conditions introduced in [6]. We then present the notion of uniformly continuous simulations — namely, simulation with some additional uniform continuity conditions on the relation—that can be used to reason about stability of trajectories. Finally, we show that uniformly continuous simulations are widely prevalent, by recasting many classical results on proving stability of dynamical and hybrid systems as establishing the existence of a simple, obviously stable system that simulates the desired system through uniformly continuous simulations