Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

In this provocative book, Barwise and Perry tackle the slippery subject of \"meaning, \" a subject that has long vexed linguists, language philosophers, and logicians.

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Situations and Attitudes.

Rapid progress in machine learning and artificial intelligence (AI) has brought increasing attention to the potential impacts of AI technologies on society. In this paper we discuss one such potential impact: the problem of accidents in machine learning systems, defined as unintended and harmful behavior that may emerge from poor design of real-world AI systems. We present a list of five practical research problems related to accident risk, categorized according to whether the problem originates from having the wrong objective function ("avoiding side effects" and "avoiding reward hacking"), an objective function that is too expensive to evaluate frequently ("scalable supervision"), or undesirable behavior during the learning process ("safe exploration" and "distributional shift"). We review previous work in these areas as well as suggesting research directions with a focus on relevance to cutting-edge AI systems. Finally, we consider the high-level question of how to think most productively about the safety of forward-looking applications of AI.

Concrete Problems in AI Safety

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. We present a novel, scalable, and efficient technique for verifying properties of deep neural networks (or providing counter-examples). The technique is based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function, which is a crucial ingredient in many modern neural networks. The verification procedure tackles neural networks as a whole, without making any simplifying assumptions. We evaluated our technique on a prototype deep neural network implementation of the next-generation airborne collision avoidance system for unmanned aircraft (ACAS Xu). Results show that our technique can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods.

Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks

Logical Analysis of Hybrid Systems

We address the problem of model checking stochastic systems, i.e.~checking whether a stochastic system satisfies a certain temporal property with a probability greater (or smaller) than a fixed threshold. In particular, we present a novel Statistical Model Checking (SMC) approach based on Bayesian statistics. We show that our approach is feasible for hybrid systems with stochastic transitions, a generalization of Simulink/Stateflow models. Standard approaches to stochastic (discrete) systems require numerical solutions for large optimization problems and quickly become infeasible with larger state spaces. Generalizations of these techniques to hybrid systems with stochastic effects are even more challenging. The SMC approach was pioneered by Younes and Simmons in the discrete and non-Bayesian case. It solves the verification problem by combining randomized sampling of system traces (which is very efficient for Simulink/Stateflow) with hypothesis testing or estimation. We believe SMC is essential for scaling up to large Stateflow/Simulink models. While the answer to the verification problem is not guaranteed to be correct, we prove that Bayesian SMC can make the probability of giving a wrong answer arbitrarily small. The advantage is that answers can usually be obtained much faster than with standard, exhaustive model checking techniques. We apply our Bayesian SMC approach to a representative example of stochastic discrete-time hybrid system models in Stateflow/Simulink: a fuel control system featuring hybrid behavior and fault tolerance. We show that our technique enables faster verification than state-of-the-art statistical techniques, while retaining the same error bounds. We emphasize that Bayesian SMC is by no means restricted to Stateflow/Simulink models: we have in fact successfully applied it to very large stochastic models from Systems Biology.

Bayesian statistical model checking with application to Simulink/Stateflow verification

ion 70 admissible see substitution, admissible advance notice 458 adversarial 8, 422 analytic cut see cut and-operator 52, 123, 443 Angel 426 antecedent 177 arity 533 assignment 76, 147 differential 307, 327 nondeterministic 390 automaton hybrid 85, 91 autonomous 38 axiom 142–162, 215–217, 301–308, 327–349, 378–380, 484–494, 527 assignment 147, 486, 536 composition 153, 490 determinacy 484 duality 157, 491 iteration 155, 216, 493 modus ponens modal 161 of choice 144 of game of choice 489 solution 149, 487 test 151, 488 vacuous 162, 231, 536 axiomatics 138 axiomatization 502, 551

Logical Foundations of Cyber-Physical Systems

We generalize dynamic logic to a logic for differential-algebraic (DA) programs, i.e. discrete programs augmented with first-order differential-algebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterize interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly. For our logic, we introduce a calculus over real arithmetic with discrete induction and a new differential induction with which DA programs can be verified by exploiting their differential constraints algebraically without having to solve them. We develop the theory of differential induction and differential refinement and analyse their deductive power. As a case study, we present parametric tangential roundabout maneuvers in air traffic control and prove collision avoidance in our calculus.

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Differential-algebraic Dynamic Logic for Differential-algebraic Programs

Formal verification provides a high degree of confidence in safe system operation, but only if reality matches the verified model. Although a good model will be accurate most of the time, even the best models are incomplete. This is especially true in Cyber-Physical Systems because high-fidelity physical models of systems are expensive to develop and often intractable to verify. Conversely, reinforcement learning-based controllers are lauded for their flexibility in unmodeled environments, but do not provide guarantees of safe operation. This paper presents an approach for provably safe learning that provides the best of both worlds: the exploration and optimization capabilities of learning along with the safety guarantees of formal verification. Our main insight is that formal verification combined with verified runtime monitoring can ensure the safety of a learning agent. Verification results are preserved whenever learning agents limit exploration within the confounds of verified control choices as long as observed reality comports with the model used for off-line verification. When a model violation is detected, the agent abandons efficiency and instead attempts to learn a control strategy that guides the agent to a modeled portion of the state space. We prove that our approach toward incorporating knowledge about safe control into learning systems preserves safety guarantees, and demonstrate that we retain the empirical performance benefits provided by reinforcement learning. We also explore various points in the design space for these justified speculative controllers in a simple model of adaptive cruise control model for autonomous cars.

André Platzer

Papers

Logical Analysis of Hybrid Systems

Bayesian statistical model checking with application to Simulink/Stateflow verification

Logical Foundations of Cyber-Physical Systems

Differential-algebraic Dynamic Logic for Differential-algebraic Programs

Safe Reinforcement Learning via Formal Methods: Toward Safe Control Through Proof and Learning