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

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

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.

/pdf/situations-and-attitudes-57f065zg2d.pdf

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

We show how theorem proving and methods for handling real algebraic
constraints can be combined for hybrid system verification. In particular, we highlight
the interaction of deductive and algebraic reasoning that is used for handling the joint
discrete and continuous behaviour of hybrid systems. We illustrate proof tasks that occur
when verifying scenarios with cooperative traffic agents. From the experience with
these examples, we analyse proof strategies for dealing with the practical challenges for
integrated algebraic and deductive verification of hybrid systems, and we propose an
iterative background closure strategy.

/pdf/combining-deduction-and-algebraic-constraints-for-hybrid-2hyunqsphr.pdf

Combining Deduction and Algebraic Constraints for Hybrid System Analysis

Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological mo dels is often too large for classical Model Checking techniques. For these models, a statistical appro ch t Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequent ial Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Mod el Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requ i ing fewer system simulations. Another advantage of our approach is the ability to incorporate prio r B logical knowledge about the model being verified. We demonstrate our algorithm on a variety of m dels from the Systems Biology literature and show that it enables faster verification than st te-of-the-art techniques, even when no prior knowledge is available.

/pdf/statistical-model-checking-for-complex-stochastic-models-in-2l0yrxm80v.pdf

Statistical Model Checking for Complex Stochastic Models in Systems Biology

Programmable Logic Controllers (PLCs) provide a prominent choice of implementation platform for safety-critical industrial control systems. Formal verification provides ways of establishing correctness guarantees, which can be quite important for such safety-critical applications. But since PLC code does not include an analytic model of the system plant, their verification is limited to discrete properties. In this paper, we, thus, start the other way around with hybrid programs that include continuous plant models in addition to discrete control algorithms. Correctness properties of hybrid programs can be formally verified in the theorem prover KeYmaera X that implements differential dynamic logic, dL, for hybrid programs. After verifying the hybrid program, we now present an approach for translating hybrid programs into PLC code. The new HyPLC tool implements this translation of discrete control code of verified hybrid program models to PLC controller code and, vice versa, the translation of existing PLC code into the discrete control actions for a hybrid program given an additional input of the continuous dynamics of the system to be verified. This approach allows for the generation of real controller code while preserving, by compilation, the correctness of a valid and verified hybrid program. PLCs are common cyber-physical interfaces for safety-critical industrial control applications, and HyPLC serves as a pragmatic tool for bridging formal verification of complex cyber-physical systems at the algorithmic level of hybrid programs with the execution layer of concrete PLC implementations.

https://dl.acm.org/doi/pdf/10.1145/3302509.3311036

HyPLC: hybrid programmable logic controller program translation for verification

Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loops forever, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to automation of formal proofs of safety in hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.

/pdf/pegasus-a-framework-for-sound-continuous-invariant-5as31krds4.pdf

Pegasus: a framework for sound continuous invariant generation

The safety of mobile robots in dynamic environments is predicated on making sure that they do not collide with obstacles. In support of such safety arguments, we analyze and formally verify a series of increasingly powerful safety properties of controllers for avoiding both stationary and moving obstacles: (i) static safety, which ensures that no collisions can happen with stationary obstacles, (ii) passive safety, which ensures that no collisions can happen with stationary or moving obstacles while the robot moves, (iii) the stronger passive friendly safety in which the robot further maintains sufficient maneuvering distance for obstacles to avoid collision as well, and (iv) passive orientation safety, which allows for imperfect sensor coverage of the robot, i. e., the robot is aware that not everything in its environment will be visible. We complement these provably correct safety properties with liveness properties: we prove that provably safe motion is flexible enough to let the robot still navigate waypoints and pass intersections. We use hybrid system models and theorem proving techniques that describe and formally verify the robot's discrete control decisions along with its continuous, physical motion. Moreover, we formally prove that safety can still be guaranteed despite sensor uncertainty and actuator perturbation, and when control choices for more aggressive maneuvers are introduced. Our verification results are generic in the sense that they are not limited to the particular choices of one specific control algorithm but identify conditions that make them simultaneously apply to a broad class of control algorithms.

André Platzer

Papers

Combining Deduction and Algebraic Constraints for Hybrid System Analysis

Statistical Model Checking for Complex Stochastic Models in Systems Biology

HyPLC: hybrid programmable logic controller program translation for verification

Pegasus: a framework for sound continuous invariant generation

Formal Verification of Obstacle Avoidance and Navigation of Ground Robots