We develop numerically rigorous Monte Carlo approaches for computing probabilistic reachability in hybrid systems subject to random and nondeterministic parameters. Instead of standard simulation we use δ-complete SMT procedures, which enable formal reasoning for nonlinear systems up to a user-definable numeric precision. Monte Carlo approaches for probability estimation assume that sampling is possible for the real system at hand. However, when using δ-complete simulation one instead samples from an overapproximation of the real random variable. In this paper, we introduce a Monte Carlo-SMT approach for computing probabilistic reachability confidence intervals that are both statistically and numerically rigorous. We apply our technique to hybrid systems involving nonlinear differential equations.

This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. It also introduces new benchmarks within this category, and recommends next steps for this category towards next year’s edition of the competition. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Spring/Summer 2020.

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In particular, we consider hybrid systems with nonlinear dynamics (Lipschitzcontinuous ordinary differential equations) and random parameters, and we synthesize PID controllers such that the resulting closed-loop systems satisfy safety and performance constraints given as probabilistic bounded reachability properties. Our technique leverages SMT solvers over the reals and nonlinear differential equations to provide formal guarantees that the synthesized controllers satisfy such properties. These controllers are also robust by design since they minimize the probability of reaching an unsafe state in the presence of random disturbances. We apply our approach to the problem of insulin regulation for type 1 diabetes, synthesizing controllers with robust responses to large random meal disturbances, thereby enabling them to maintain blood glucose levels within healthy, safe ranges. arXiv:1707.05229v2 [cs.SY]

Background Remission duration and treatment response following phototherapy for psoriasis are highly variable and factors influencing these are poorly understood. Objectives Our primary outcome was to investigate whether selected clinical/serum biomarkers were associated with remission duration, and secondly with psoriasis clearance at the end of phototherapy. In addition, we looked at whether early trajectory of UVB clearance was associated with final clearance outcome. MethodsWe performed a prospective cohort study of 100 psoriasis patients, routinely prescribed Narrowband UVB and measured selected clinical and biochemical biomarkers, including weekly PASI (psoriasis area and severity index) scores. Patients were followed up for 18 months. ResultsThe median time to relapse was 6 months (95% CI 5-18) if PASI90 was achieved, and 4 months (95% CI 3-9) if less than PASI90 was achieved. Achieving PASI100 did not result in prolonged remission. On UVB completion, the median final PASI (n = 96) was 1.0 (IQR 0.5, 1.6) with 78 (81%) achieving PASI75 and 39 (41%) achieving PASI90.Improved PASI90 response was significantly associated with lower BMI, higher baseline PASI, non-smoking status and lower cumulative NbUVB. Serum levels of C-reactive protein (CRP) and vitamin D were not associated with clearance or remission duration. Early treatment response from weeks 2-3 was predictive of final outcome. For example, achieving PASI30 at week 3 was significantly associated with PASI90 at the end of the course [36/77 (51%) vs. 2/24 (8%), P < 0.001].Conclusions Raised BMI and positive smoking status predicted poorer phototherapy response. For the first time, we have shown that PASI clearance trajectory over the first 2-3 weeks of UVB, can predict psoriasis clearance. This is an important new step towards developing psoriasis personalized prescribing, which can now be formally tested in clinical trials. These simple clinical measures can be used to inform patient treatment expectations; allowing treatment modifications and/or switching to alternative therapies.

Despite increased understanding about psoriasis pathophysiology, currently there is a lack of predictive computational models. We developed a personalisable ordinary differential equations model of human epidermis and psoriasis that incorporates immune cells and cytokine stimuli to regulate the transition between two stable steady states of clinically healthy (non-lesional) and disease (lesional psoriasis, plaque) skin. In line with experimental data, an immune stimulus initiated transition from healthy skin to psoriasis and apoptosis of immune and epidermal cells induced by UVB phototherapy returned the epidermis back to the healthy state. Notably, our model was able to distinguish disease flares. The flexibility of our model permitted the development of a patient-specific “UVB sensitivity” parameter that reflected subject-specific sensitivity to apoptosis and enabled simulation of individual patients’ clinical response trajectory. In a prospective clinical study of 94 patients, serial individual UVB doses and clinical response (Psoriasis Area Severity Index) values collected over the first three weeks of UVB therapy informed estimation of the “UVB sensitivity” parameter and the prediction of individual patient outcome at the end of phototherapy. An important advance of our model is its potential for direct clinical application through early assessment of response to UVB therapy, and for individualised optimisation of phototherapy regimes to improve clinical outcome. Additionally by incorporating the complex interaction of immune cells and epidermal keratinocytes, our model provides a basis to study and predict outcomes to biologic therapies in psoriasis.