John V. Tucker

Bio: John V. Tucker is an academic researcher from Swansea University. The author has contributed to research in topics: Data type & Computability. The author has an hindex of 32, co-authored 180 publications receiving 3404 citations. Previous affiliations of John V. Tucker include University of Wales & University of Bristol.

Constructive Volume Geometry

Abstract: We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar elds as fundamental building blocks, CVG provides high-level algebraic representations of objects that are dened mathematically or built upon sampled or simulated datasets. It models amorphous phenomena as well as solid objects, and describes the interior as well as the exterior of objects. We also describe a hierarchical representation scheme for CVG, and a direct rendering method with a new approach for consistent sampling. The work has demonstrated the feasibility of combining a variety of graphics data types in a coherent modelling scheme.

Program Correctness over Abstract Data Types, With Error State Semantics

Abstract: Straight-Line Programs. Preliminaries: Signatures and Structures. The Programming Language. Assertions. Correctness Formulae. A Proof System Soundness. Predicates State Transformers The Weakest Precondition and Strongest Postcondition. Completeness of the Proof System. `While' Programs. Notation for Partial Functions. The Programming Language. Assertions. Correctness Formulae. A Proof System Soundness. Partial State Transformers The Weakest Precondition and Strongest Postcondition. Completeness of the Proof System. Appendix: Total Correctness for `While' Programs. Recursive Programs. The Programming Language. Assertions. Correctness Formulae. A Proof System Soundness. A Look Ahead. Inductive Computability of the Input-Output Relation. Completeness of the Proof System. Appendix: Total Correctness for Recursive Programs. Computability in an Abstract Setting. Induction Schemes. Some Important Properties. From Induction Schemes to `While' Programs. From `While' Programs to Induction Schemes. Course-of-Values Induction. From COV Induction Schemes to `While'-Array Programs. From `While'-Array Programs to COV Induction Schemes. More on Induction. The COV Inductively Definable Functions. A Survey of Computability in an Abstract Setting. A Generalized Church-Turing Thesis. Bibliography.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Real-time computing without stable states: a new framework for neural computation based on perturbations

Abstract: A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.

Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

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