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

Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by ordinary differential equations (ODEs) can be formally verified in differential dynamic logic (dL). The key insight is to specify ODE stability by suitably nesting the dynamic modalities of dL with first-order logic quantifiers. Elucidating the logical structure of stability properties in this way has three key benefits: i) it provides a flexible means of formally specifying various stability properties of interest, ii) it yields rigorous proofs of those stability properties from dL's axioms with dL's ODE safety and liveness proof principles, and iii) it enables formal analysis of the relationships between various stability properties which, in turn, inform proofs of those properties. These benefits are put into practice through an implementation of stability proofs for several examples in KeYmaera X, a hybrid systems theorem prover based on dL.

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Deductive Stability Proofs for Ordinary Differential Equations

Cyber-physical systems combine cyber capabilities with physical capabilities to solve problems that neither part could solve alone. This chapter provides an informal introduction to cyber-physical systems, setting the stage for this textbook. The primary purpose is a lightweight overview of the technical and nontechnical characteristics of cyber-physical systems, an overview of some of their application domains, and a discussion of their prospects and challenges. The chapter also informally outlines and explains the approach taken in this book to address crucial safety challenges in cyber-physical systems.

Cyber-Physical Systems: Overview

: We introduce differential game logic (dGL) for specifying and verifying properties of hybrid games, i.e., determined, sequential/dynamic, non-cooperative, zero-sum games of perfect information on hybrid systems that combine discrete and continuous dynamics. Unlike hybrid systems hybrid games allow choices in the system dynamics to be resolved by different players with different objectives. The logic dGL can be used to study properties of the resulting adversarial behavior. It unifies differential dynamic logic for hybrid systems with game logic. We define a regular modal semantics for dGL, present a proof calculus for dGL, and prove soundness. We identify separating axioms, i.e., the axioms that distinguish dGL and its game aspects from logics for hybrid systems. We also define an operational game semantics, prove equivalence, and prove determinacy.

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Differential Game Logic for Hybrid Games

Designing and analyzing hybrid systems, which are models for complex physical systems, is expensive and error-prone. The dissertation presented in this article intro- duces a verification logic that is suitable for analyzing the behavior of hybrid systems. It presents a proof calculus and a new deductive verification tool for hybrid systems that has been used successfully to verify aircraft and train control.

http://link.springer.com/content/pdf/10.1007/s13218-010-0014-6.pdf

Automated Theorem Proving for Hybrid Systems

First-order programming (FOP) is a new representation language that combines the strengths of mixed-integer linear programming (MILP) and rst-order logic (FOL). In this paper we describe a novel feasibility proving system for FOP formulas that combines MILP solving with instance-based methods from theorem proving. This prover allows us to perform lifted inference by repeatedly rening a propositional MILP. We prove that this procedure is sound and refutationally complete: if a formula is infeasible our solver will demonstrate this fact in nite time. We conclude by demonstrating an implementation of our decision procedure on a simple rst-order planning problem.

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André Platzer

Papers

Deductive Stability Proofs for Ordinary Differential Equations

Cyber-Physical Systems: Overview

Differential Game Logic for Hybrid Games

Automated Theorem Proving for Hybrid Systems

An Instantiation-Based Theorem Prover for First-Order Programming