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Mineral Reserves under Price Uncertainty
Get PDFNational reporting organizations and regulatory bodies for the minerals and mining sector are requiring publicly reported Ore-
Reserve estimates to take account of uncertainties. Whilst methodologies that account for physical uncertainty appear relatively
well developed, methodologies which can take account of economic uncertainty appear much less so. To counter this shortfall, we
present an efficient and general methodology which can quantify the effect of price uncertainty within reserve estimates, providing
both the expected reserve size and the associated distribution (box whisker plot). This statistical information can be used by
interested parties to understand precisely where the reserve risks lie, which we highlight in a worked example
On commuting graphs for elements of order 3 in symmetric groups
Get PDFThe commuting graph , where is a group and is a subset of , is the graph with vertex set
and distinct vertices being joined by an edge whenever they commute. Here the diameter of is studied when is a symmetric group and a conjugacy class of elements of order
Finite-dimensional behaviour and observability in a randomly forced PDE
Get PDFIn earlier work [D.S. Broomhead, J.P. Huke, M.R. Muldoon, and J. Stark, Iterated function system models of digital channels, Proc. R. Soc. Lond. A 460 (2004), pp. 3123�3142], aimed at developing an approach to signal processing that
can be applied as well to nonlinear systems as linear ones, we produced mathematical models of digital communications channels that took the form of iterated function systems (IFS). For finite-dimensional systems these models have
observability properties indicating they could be used for signal processing applications. Here we see how far the same approach can be taken towards the modelling of an infinite-dimensional system. The cable equation is a well-known partial differential equation (PDE) model of an imperfectly insulated uniform conductor, coupled to its surroundings by capacitive effects. (It is also much used
as a basic model in theoretical neurobiology.) In this article we study the dynamics of this system when it is subjected to randomly selected discrete input pulses. The resulting IFS has a unique finite-dimensional attractor; we use results of Falconer and Solomyak to investigate the dimension of this attractor, relating it to the physical parameters of the system. Using work of Robinson, we show
how some of the observability properties of the IFS model are retained
Lacunarity and Period-doubling
Get PDFWe show that the deviation from power laws of the scaling of chaotic measures such as Lyapunov exponents and topological entropy is periodic in the logarithm of the distance from the accumulation of period doubling. Moreover, this periodic function is asymptotically universal for each measure (for
functions in the appropriate universality class). This is related to the concept of lacunarity known to exist for scaling functions describing the mass distribution of self-similar fractal sets
Local Fusion Graphs for Symmetric Groups
Get PDFFor a group , a set of odd positive integers and a set of involutions of we define a graph . This graph, called a -local fusion graph, has vertex set with joined by an edge provided and the order of is in . In this paper we investigate when is a finite symmetric group for various choices of and
The hyperbolic Schur decomposition (extended)
No full textWe propose a hyperbolic counterpart of the Schur decomposition, with the emphasis on the preservation of structures related to some given hyperbolic scalar product. We give results regarding the existence of such a decomposition and research the properties of its block triangular factor for various structured matrices
On the volume of tubular neighborhoods of real algebraic varieties
No full textThe problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical analysis. We present a self-contained derivation of bounds on the probability that a random point, chosen uniformly from a ball, lies within a given distance of a real algebraic variety of any codimension. The bounds are given in terms of the degrees of the defining polynomials, and contain as special case an unpublished result by Ocneanu
Triangularizing Quadratic Matrix Polynomials
Get PDFWe show that any regular quadratic matrix polynomial can be reduced to an upper
triangular quadratic matrix polynomial over the complex numbers
preserving the finite and infinite elementary divisors.
We characterize the real quadratic matrix polynomials that are
triangularizable over the real numbers and show that those that are
not triangularizable over the real numbers are quasi-triangularizable
with diagonal blocks of sizes and .
We also derive complex and real Schur-like theorems for linearizations of
quadratic matrix polynomials with nonsingular leading coefficients.
In particular, we show that for any monic linearization \l I+A of an
quadratic matrix polynomial,
there exists a nonsingular matrix defined in terms of
orthonormal vectors that transforms to a companion
linearization of a (quasi)-triangular quadratic matrix polynomial.
This provides the foundation for designing numerical algorithms for the
reduction of quadratic matrix polynomials to upper (quasi)-triangular form
Decentralized LQR Joint Servo Design for a Compliant Humanoid Robot via LMI Optimisation
No full textEnhancing bipedal walking safety, robustness and
efficiency has led to design of compliant humanoid robots.
However, the links' interactions and coupling effects are often neglected in the design of their trajectory tracking controller.
Moreover, there is not a direct decentralized approach for
designing the PD-PID gains given a multivariable model of
the compliant humanoid robot. This paper proposes an LMI
formulation for designing decentralized PID gains in discrete time. It is shown that this method can be used to design a full state feedback for trajectory tracking which includes the compliance and links' interactions in the feedback design.
Numerical simulations for a compliant compass gait and a 10
DoF humanoid models are provided to illustrate the use of this method
Stochastic Reachability Analysis of Hybrid Systems
Get PDFStochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems.
Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then treats issues representing the different faces of SRA:
· stochastic reachability based on Markov process theory;
· martingale methods;
· stochastic reachability as an optimal stopping problem; and
· dynamic programming.
The book is rounded off by an appendix providing mathematical underpinning on subjects such as ordinary differential equations, probabilistic measure theory and stochastic modeling, which will help the non-expert-mathematician to appreciate the text.
Stochastic Reachability Analysis of Hybrid Systems characterizes a highly interdisciplinary area of research and is consequently of significant interest to academic researchers and graduate students from a variety of backgrounds in control engineering, applied mathematics and computer science