Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

A Packet/Frame sync detector based on statistical mode with application to wireless-USB

Wireless Personal Area Networks (WPANs) are offering high data rates suitable for interconnecting high bandwidth personal consumer devices (Wireless HD streaming, Wireless-USB and Bluetooth EDR). ECMA-368 is the Physical (PHY) and Media Access Control (MAC) backbone of many of these wireless devices. WPAN devices tend to operate in an ad-hoc based network and therefore it is important to successfully latch onto the network and become part of one of the available piconets. This paper presents a new algorithm for detecting the Packet/Fame Sync (PFS) signal in ECMA-368 to identify piconets and aid symbol timing. The algorithm is based on correlating the received PFS symbols with the expected locally stored symbols over the 24 or 12 PFS symbols, but selecting the likely TFC based on the highest statistical mode from the 24 or 12 best correlation results. The results are very favorable showing an improvement margin in the order of 11.5dB in reference sensitivity tests between the required performance using this algorithm and the performance of comparable systems.

Wiener-System subspace identification for mobile wireless mm-wave networks

We discuss the feasibility of wireless terahertz communications links deployed in a metropolitan area and model the large-scale fading of such channels. The model takes into account reception through direct line of sight, ground and wall reflection, as well as diffraction around a corner. The movement of the receiver is modeled by an autonomous dynamic linear system in state space, whereas the geometric relations involved in the attenuation and multipath propagation of the electric field are described by a static nonlinear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a single-output Wiener model from time-domain measurements of the field intensity when the receiver motion is simulated using a constant angular speed and an exponentially decaying radius. The identification procedure is validated by using the model to perform q-step ahead predictions. The sensitivity of the algorithm to small-scale fading, detector noise, and atmospheric changes are discussed. The performance of the algorithm is tested in the diffraction zone assuming a range of emitter frequencies (2, 38, 60, 100, 140, and 400 GHz). Extensions of the simulation results to situations where a more complicated trajectory describes the motion of the receiver are also implemented, providing information on the performance of the algorithm under a worst case scenario. Finally, a sensitivity analysis to model parameters for the identified Wiener system is proposed.

Uniformization of affine dependence programs for parallel embedded system design

This paper is concerned with the uniformization of a system of afine recurrence equations. This transformation is used in the design (or compilation) of highly parallel embedded systems (VLSI systolic arrays, signal processing filters, etc.). In this paper, we present and implement an automatic system to achieve uniformization of systems of afine recurrence equations. We unify the results from many earlier papers, develop some theoretical extensions, and then propose effective uniformization algorithms. Our results can be used in any high level synthesis tool based on polyhedral representation of nested loop computations.

Uniformization tool for systolic array designs

The paper is concerned with the uniformization of a system of affine recurrence equations. This transformation is used in the design (or compilation) of highly parallel embedded systems (VLSI systolic arrays, signal processing filters, etc.). We present and implement an automatic system to achieve uniformization of systems of affine recurrence equations. We unify the results from many earlier papers, develop some theoretical extensions, and then propose effective uniformization algorithms. Our results can be used in any high level synthesis tool based on polyhedral representation of nested loop computations.

A climate change risk analysis for world ecosystems

We quantify the risks of climate-induced changes in key ecosystem processes during the 21st century by forcing a dynamic global vegetation model with multiple scenarios from 16 climate models and mapping the proportions of model runs showing forest/nonforest shifts or exceedance of natural variability in wildfire frequency and freshwater supply. Our analysis does not assign probabilities to scenarios or weights to models. Instead, we consider distribution of outcomes within three sets of model runs grouped by the amount of global warming they simulate: <2°C (including simulations in which atmospheric composition is held constant, i.e., in which the only climate change is due to greenhouse gases already emitted), 2–3°C, and >3°C. High risk of forest loss is shown for Eurasia, eastern China, Canada, Central America, and Amazonia, with forest extensions into the Arctic and semiarid savannas; more frequent wildfire in Amazonia, the far north, and many semiarid regions; more runoff north of 50°N and in tropical Africa and northwestern South America; and less runoff in West Africa, Central America, southern Europe, and the eastern U.S. Substantially larger areas are affected for global warming >3°C than for <2°C; some features appear only at higher warming levels. A land carbon sink of ≈1 Pg of C per yr is simulated for the late 20th century, but for >3°C this sink converts to a carbon source during the 21st century (implying a positive climate feedback) in 44% of cases. The risks continue increasing over the following 200 years, even with atmospheric composition held constant.

Adaptive modelling, estimation and fusion from data: a neurofuzzy approach

In a world of almost permanent and rapidly increasing electronic data availability, techniques of filtering, compressing, and interpreting this data to transform it into valuable and easily comprehensible information is of utmost importance. One key topic in this area is the capability to deduce future system behavior from a given data input. This book brings together for the first time the complete theory of data-based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data-based modelling, new concepts including extended additive and multiplicative submodels are developed and their extensions to state estimation and data fusion are derived. All these algorithms are illustrated with benchmark and real-life examples to demonstrate their efficiency. Chris Harris and his group have carried out pioneering work which has tied together the fields of neural networks and linguistic rule-based algortihms. This book is aimed at researchers and scientists in time series modeling, empirical data modeling, knowledge discovery, data mining, and data fusion.

Resource allocation analysis of the stochastic diffusion search

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

Head-controlled assistive telerobot with extended physiological proprioception capability

People with disabilities such as quadriplegia can use mouth-sticks and head-sticks as extension devices to perform desired manipulations. These extensions provide extended proprioception which allows users to directly feel forces and other perceptual cues such as texture present at the tip of the mouth-stick. Such devices are effective for two principle reasons: because of their close contact with the user's tactile and proprioceptive sensing abilities; and because they tend to be lightweight and very stiff, and can thus convey tactile and kinesthetic information with high-bandwidth. Unfortunately, traditional mouth-sticks and head-sticks are limited in workspace and in the mechanical power that can be transferred because of user mobility and strength limitations. We describe an alternative implementation of the head-stick device using the idea of a virtual head-stick: a head-controlled bilateral force-reflecting telerobot. In this system the end-effector of the slave robot moves as if it were at the tip of an imaginary extension of the user's head. The design goal is for the system is to have the same intuitive operation and extended proprioception as a regular mouth-stick effector but with augmentation of workspace volume and mechanical power. The input is through a specially modified six DOF master robot (a PerForceTM hand-controller) whose joints can be back-driven to apply forces at the user's head. The manipulation tasks in the environment are performed by a six degree-of-freedom slave robot (the Zebra-ZEROTM) with a built-in force sensor. We describe the prototype hardware/software implementation of the system, control system design, safety/disability issues, and initial evaluation tasks.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Parallel pipelined array architectures for real-time histogram computation in consumer devices

The real-time parallel computation of histograms using an array of pipelined cells is proposed and prototyped in this paper with application to consumer imaging products. The array operates in two modes: histogram computation and histogram reading. The proposed parallel computation method does not use any memory blocks. The resulting histogram bins can be stored into an external memory block in a pipelined fashion for subsequent reading or streaming of the results. The array of cells can be tuned to accommodate the required data path width in a VLSI image processing engine as present in many imaging consumer devices. Synthesis of the architectures presented in this paper in FPGA are shown to compute the real-time histogram of images streamed at over 36 megapixels at 30 frames/s by processing in parallel 1, 2 or 4 pixels per clock cycle.

Normality mining: privacy implications of behavioral profiles drawn from GPS enabled mobile phones

There is growing interest in the ways in which the location of a person can be utilized by new applications and services. Recent advances in mobile technologies have meant that the technical capability to record and transmit location data for processing is appearing in off-the-shelf handsets. This opens possibilities to profile people based on the places they visit, people they associate with, or other aspects of their complex routines determined through persistent tracking. It is possible that services offering customized information based on the results of such behavioral profiling could become commonplace. However, it may not be immediately apparent to the user that a wealth of information about them, potentially unrelated to the service, can be revealed. Further issues occur if the user agreed, while subscribing to the service, for data to be passed to third parties where it may be used to their detriment. Here, we report in detail on a short case study tracking four people, in three European member states, persistently for six weeks using mobile handsets. The GPS locations of these people have been mined to reveal places of interest and to create simple profiles. The information drawn from the profiling activity ranges from intuitive through special cases to insightful. In this paper, these results and further extensions to the technology are considered in light of European legislation to assess the privacy implications of this emerging technology.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1168 For further resources related to this article, please visit the WIREs website.