The Visvalingam algorithm: metrics, measures and heuristics

This paper provides the background necessary for a clear understanding of forthcoming papers relating to the Visvalingam algorithm for line generalisation, for example on the testing and usage of its implementations. It distinguishes the algorithm from implementation-specific issues to explain why it is possible to get inconsistent but equally valid output from different implementations. By tracing relevant developments within the now-disbanded Cartographic Information Systems Research Group (CISRG) of the University of Hull, it explains why a) a partial metric-driven implementation was, and still is, sufficient for many projects but not for others; b) why the Effective Area (EA) is a measure derived from a metric; c) why this measure (EA) may serve as a heuristic indicator for in-line feature segmentation and model-based generalisation; and, d) how metrics may be combined to change the order of point elimination. The issues discussed in this paper also apply to the use of other metrics. It is hoped that the background and guidance provided in this paper will enable others to participate in further research based on the algorithm

Constrained set-up of the tGAP structure for progressive vector data transfer

A promising approach to submit a vector map from a server to a mobile client is to send a coarse representation first, which then is incrementally refined. We consider the problem of defining a sequence of such increments for areas of different land-cover classes in a planar partition. In order to submit well-generalised datasets, we propose a method of two stages: First, we create a generalised representation from a detailed dataset, using an optimisation approach that satisfies certain cartographic constraints. Second, we define a sequence of basic merge and simplification operations that transforms the most detailed dataset gradually into the generalised dataset. The obtained sequence of gradual transformations is stored without geometrical redundancy in a structure that builds up on the previously developed tGAP (topological Generalised Area Partitioning) structure. This structure and the algorithm for intermediate levels of detail (LoD) have been implemented in an object-relational database and tested for land-cover data from the official German topographic dataset ATKIS at scale 1:50 000 to the target scale 1:250 000. Results of these tests allow us to conclude that the data at lowest LoD and at intermediate LoDs is well generalised. Applying specialised heuristics the applied optimisation method copes with large datasets; the tGAP structure allows users to efficiently query and retrieve a dataset at a specified LoD. Data are sent progressively from the server to the client: First a coarse representation is sent, which is refined until the requested LoD is reached

Postquantum Br\`{e}gman relative entropies and nonlinear resource theories

We introduce the family of postquantum Br\`{e}gman relative entropies, based on nonlinear embeddings into reflexive Banach spaces (with examples given by reflexive noncommutative Orlicz spaces over semi-finite W*-algebras, nonassociative L$_p$ spaces over semi-finite JBW-algebras, and noncommutative L$_p$ spaces over arbitrary W*-algebras). This allows us to define a class of geometric categories for nonlinear postquantum inference theory (providing an extension of Chencov's approach to foundations of statistical inference), with constrained maximisations of Br\`{e}gman relative entropies as morphisms and nonlinear images of closed convex sets as objects. Further generalisation to a framework for nonlinear convex operational theories is developed using a larger class of morphisms, determined by Br\`{e}gman nonexpansive operations (which provide a well-behaved family of Mielnik's nonlinear transmitters). As an application, we derive a range of nonlinear postquantum resource theories determined in terms of this class of operations.Comment: v2: several corrections and improvements, including an extension to the postquantum (generally) and JBW-algebraic (specifically) cases, a section on nonlinear resource theories, and more informative paper's titl

Smart Nanostructures and Synthetic Quantum Systems

So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures using topological excitations of a neural-type network that can mimic natural quantum systems. These developments are a technological application of process physics which is a semantic information theory of reality in which space and quantum phenomena are emergent.Comment: LaTex,14 pages 1 eps file. To be published in BioMEMS and Smart Nanostructures, Proceedings of SPIE Conference #4590, ed. L. B. Kis

Synthetic Quantum Systems

So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the new notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures using topological excitations of a stochastic neural-type network that can mimic natural quantum systems. These developments are a technological application of process physics which is an information theory of reality in which space and quantum phenomena are emergent, and so indicates the deep origins of quantum phenomena. Analogous complex stochastic dynamical systems have recently been proposed within neurobiology to deal with the emergent complexity of biosystems, particularly the biodynamics of higher brain function. The reasons for analogous discoveries in fundamental physics and neurobiology are discussed.Comment: 16 pages, Latex, 1 eps figure fil

Geometric Aspects of Multiagent Systems

Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, interpreted systems, and the related Kripke semantics of the logic $S5_n$ (an epistemic logic with $n$-agents), the similarities with the geometric / homotopy theoretic structure of groupoid atlases is striking. These latter objects arise in problems within algebraic K-theory, an area of algebra linked to the study of decomposition and normal form theorems in linear algebra. They have a natural well structured notion of path and constructions of path objects, etc., that yield a rich homotopy theory.Comment: 14 pages, 1 eps figure, prepared for GETCO200

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde