Deciding the positivity of a sequence defined by a linear recurrence and initial conditions is, in general, a hard problem.

We consider linear recurrences with polynomial coefficients of Poincaré type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a precisely defined genericity condition. For positive sequences, the algorithm produces a certificate of positivity that is a data-structure for a proof by induction. This induction works by showing that an explicitly computed cone is contracted by the iteration of the recurrence.

Subsurface sampling systems for future planetary robotic missions which include reliable methods of generating, acquiring, and delivering samples to a scientific instrument for analysis are of extreme importance to the success of future in situ and sample return missions. Operating at remote locations the sampler needs to deal with a variety of disparate rock sources while being essential to deliver samples in different forms and to accommodate the requirements of a wide range of scientific instruments. Existing highly efficient terrestrial drilling techniques have limited space applications due to their need for large axial forces and holding torques, high power consumption and inability to efficiently duty cycle, and the use of rigid handling platforms. This paper describes the work performed at Jet Propulsion Laboratory (JPL) and Honeybee Robotics for the development of a rotary percussive drill that uses an ultrasonic/sonic drill/corer as the hammering device integrated in a sampling system capable of automatic operation in a Mars environment.

The importance of early performance assessment grows as software systems increase in terms of size, logical distribution and interaction complexity. Lack of time on the side of software developers, as well as distance between software model notations and performance model representation do not help to build an integrated software process that takes into account, from the early phases of the lifecycle, nonfunctional requirements. We work towards filling this gap by extending the capabilities of a simulative environment developed for the UML notation. Our intent is to introduce new stereotypes representing performance related items, such as resource types and job dispatchers. They allow the software designers to homogeneously represent a software architecture integrated with a running platform as well as parameterized with the resource demand that the components require.

Verification and validation (V&V) tasks, as applied to software specifications, enable early detection of analysis and design flaws prior to implementation. Several fault injection techniques for software V&V are proposed at the code level. In this paper, we address V&V analysis methods based on fault injection at the software specification level. We present a fault model and a fault injection process for UML dynamic specifications. We use a case study based on a cardiac pacemaker for illustrating the developed approach.