Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution. ©2015 The Authors. Published by Elsevier Ltd.

A preliminary version of this paper was published in the proceedings of CPSNA 2013. This work was supported by the US National Science Foundation, awards NSF-CPS-1136099/1136104, the Swedish Knowledge Foundation (KK) and the Center for Research on Embedded Systems (CERES) grant number 20100314, and EPSRC grant number EP/C01037X/1.

Abstract. Developing Cyber-Physical Systems requires methods and tools to support simulation and verification of hybrid (both continuous and discrete) models. The Acumen modeling and simulation language is an open source testbed for exploring the design space of what rigorousbut-practical next-generation tools can deliver to developers of CyberPhysical Systems. Like verification tools, a design goal for Acumen is to provide rigorous results. Like simulation tools, it aims to be intuitive, practical, and scalable. However, it is far from evident whether these two goals can be achieved simultaneously. This paper explains the primary design goals for Acumen, the core challenges that must be addressed in order to achieve these goals, the "agile research method" taken by the project, the steps taken to realize these goals, the key lessons learned, and the emerging language design.

Even simple hybrid systems like the classic bouncing ball can exhibit Zeno behaviors. The existence of this type of behavior has so far forced simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad hoc restrictions to circumvent Zeno behavior or to abandon hybrid modeling. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independently of the occurrence of a given event. Such an event can then even occur an unbounded number of times, thus making it possible to handle certain types of Zeno behavior.

Background In order to estimate the prevalence and understand the spread of SARS-CoV-2 in Sweden, the Public Health Agency of Sweden, with support from the Swedish Armed Forces, conducted a series of point prevalence surveys between March and December 2020. Methods Sampling material and instructions on how to perform self-sampling of the upper respiratory tract were delivered to the homes of the participants. Samples were analysed by real-time PCR, and the participants completed questionnaires regarding symptoms. Findings The first survey in the Stockholm region in March 2020 included 707 participants and showed a SARS-CoV-2 prevalence of 2.5%. The following five surveys, performed on a national level, with between 2461 and 2983 participants, showed SARS-CoV-2 prevalences of 0.9% (April), 0.3% (May), 0.0% (August), 0.0% (September), and 0.7% (December). All positive cases who responded to questionnaires reported experiencing symptoms that occurred from 2 weeks before the date of sampling up to and including the date of sampling. Interpretation None of the individuals shown to be PCR-positive were asymptomatic at the time of sampling or in the 14 days prior to sampling. This is in contrast to many other surveys in which a substantial proportion of positive cases have been reported to be asymptomatic. Our surveys demonstrate a decreasing ratio between notified cases and the observed prevalence throughout the year, in line with increasing testing capacity and the consecutive inclusion of all symptomatic individuals in the case definition for testing.

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools.The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier.A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs.