Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Singularities of Algebraic Differential Equations

We combine algebraic and geometric approaches to general systems of algebraic ordinary or partial differential equations to provide a unified framework for the definition and detection of singularities of a given system at a fixed order. Our three main results are firstly a proof that even in the case of partial differential equations regular points are generic. Secondly, we present an algorithm for the effective detection of all singularities at a given order or, more precisely, for the determination of a regularity decomposition. Finally, we give a rigorous definition of a regular differential equation, a notion that is ubiquitous in the geometric theory of differential equations, and show that our algorithm extracts from each prime component a regular differential equation. Our main algorithmic tools are on the one hand the algebraic resp. differential Thomas decomposition and on the other hand the Vessiot theory of differential equations.Comment: 45 pages, 5 figure

Complex oscillations with multiple timescales - Application to neuronal dynamics

The results gathered in this thesis deal with multiple time scale dynamical systems near non-hyperbolic points, giving rise to canard-type solutions, in systems of dimension 2, 3 and 4. Bifurcation theory and numerical continuation methods adapted for such systems are used to analyse canard cycles as well as canard-induced complex oscillations in three-dimensional systems. Two families of such complex oscillations are considered: mixed-mode oscillations (MMOs) in systems with two slow variables, and bursting oscillations in systems with two fast variables. In the last chapter, we present recent results on systems with two slow and two fast variables, where both MMO-type dynamics and bursting-type dynamics can arise and where complex oscillations are also organised by canard solutions. The main application area that we consider here is that of neuroscience, more precisely low-dimensional point models of neurons displaying both sub-threshold and spiking behaviour. We focus on analysing how canard objects allow to control the oscillatory patterns observed in these neuron models, in particular the crossings of excitability thresholds

CTRL SHIFT

CTRL SHIFT makes a case for design under contemporary computation. The abstractions of reading, writing, metaphors, mythology, code, cryptography, interfaces, and other such symbolic languages are leveraged as tools for understanding. Alternative modes of knowledge become access points through which users can subvert the control structures of software. By challenging the singular expertise of programmers, the work presented within advocates for the examination of internalized beliefs, the redistribution of networked power, and the collective sabotage of computational authority

Visual perception an information-based approach to understanding biological and artificial vision

The central issues of this dissertation are (a) what should we be doing — what problems should we be trying to solve — in order to build computer vision systems, and (b) what relevance biological vision has to the solution of these problems. The approach taken to tackle these issues centres mostly on the clarification and use of information-based ideas, and an investigation into the nature of the processes underlying perception. The primary objective is to demonstrate that information theory and extensions of it, and measurement theory are powerful tools in helping to find solutions to these problems. The quantitative meaning of information is examined, from its origins in physical theories, through Shannon information theory, Gabor representations and codes towards semantic interpretations of the term. Also the application of information theory to the understanding of the developmental and functional properties of biological visual systems is discussed. This includes a review of the current state of knowledge of the architecture and function of the early visual pathways, particularly the retina, and a discussion of the possible coding functions of cortical neurons. The nature of perception is discussed from a number of points of view: the types and function of explanation of perceptual systems and how these relate to the operation of the system; the role of the observer in describing perceptual functions in other systems or organisms; the status and role of objectivist and representational viewpoints in understanding vision; the philosophical basis of perception; the relationship between pattern recognition and perception, and the interpretation of perception in terms of a theory of measurement These two threads of research, information theory and measurement theory are brought together in an overview and reinterpretation of the cortical role in mammalian vision. Finally the application of some of the coding and recognition concepts to industrial inspection problems are described. The nature of the coding processes used are unusual in that coded images are used as the input for a simple neural network classifier, rather than a heuristic feature set The relationship between the Karhunen-Loève transform and the singular value decomposition is clarified as background the coding technique used to code the images. This coding technique has also been used to code long sequences of moving images to investigate the possibilities of recognition of people on the basis of their gait or posture and this application is briefly described