13,165 research outputs found
Blending methodologies in talc operations
The problem posed by Western Mining Corporation involves finding a way of improving or optimising the utilisation of batches of lower grade talc when making up orders for products of different grades. During the MISG a number of Linear Programming models were developed. These models addressed the problems of blending batches of talc for a single order and of blending to meet a series of orders for different products over a specified planning horizon. Preliminary versions of the models were tested using data supplied by Western Mining Corporation
Evaluating a weighted graph polynomial for graphs of bounded tree-width
We show that for any there is a polynomial time algorithm to evaluate the weighted graph polynomial of any graph with tree-width at most at any point. For a graph with vertices, the algorithm requires arithmetical operations, where depends only on
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
It is known that evaluating the Tutte polynomial, , of a graph, , is P-hard at all but eight specific points and one specific curve of the -plane. In contrast we show that if is a fixed constant then for graphs of tree-width at most there is an algorithm that will evaluate the polynomial at any point using only a linear number of multiplications and additions
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Counting cocircuits and convex two-colourings is #P-complete
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of counting the number of cocircuits of a graph
is #P-complete
Social learning mechanisms compared in a simple environment
Social learning can be adaptive, but little is known about the underlying mechanisms. Many researchers have focused on imitation but this may have led to simpler mechanisms being underestimated. We demonstrate in simulation that imitative learning is not always the best strategy for a group-living animal, and that the effectiveness of any such strategy will depend on details of the environment and the animal's lifestyle. We show that observations of behavioural convergence or "traditions" might suggest effective social learning, but are meaningless considered alone
The clustering coefficient of a scale-free random graph
We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the clustering coefficient of the graph process is asymptotically proportional to (log n)/n. Bollobas and Riordan have previously shown that when the constant is zero, the same expectation is asymptotically proportional to ((log n)^2)/n
Cyclic labellings with constraints at two distances
Motivated by problems in radio channel assignment, we consider the vertex-labelling of graphs with non-negative integers. The objective is to minimise the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with associated optimal assignments, for trees and cycles
Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity
We show that care is required in formulating the nonrelativistic limit of
generalized Dirac Hamiltonians which describe particles and antiparticles
interacting with static electric and/or gravitational fields. The Dirac-Coulomb
and the Dirac-Schwarzschild Hamiltonians, and the corrections to the Dirac
equation in a non-inertial frame, according to general relativity, are used as
example cases in order to investigate the unitarity of the standard and
"chiral" approaches to the Foldy-Wouthuysen transformation, and spurious
parity-breaking terms. Indeed, we find that parity-violating terms can be
generated by unitary pseudo-scalar transformations ("chiral" Foldy-Wouthuysen
transformations). Despite their interesting algebraic properties, we find that
"chiral" Foldy-Wouthuysen transformations change fundamental symmetry
properties of the Hamiltonian and do not conserve the physical interpretation
of the operators. Supplementing the discussion, we calculate the leading terms
in the Foldy-Wouthuysen transformation of the Dirac Hamiltonian with a scalar
potential (of the (1/r)-form and of the confining radially symmetric linear
form), and obtain compact expressions for the leading higher-order corrections
to the Dirac Hamiltonian in a non-inertial rotating reference frame "Mashhoon
term").Comment: 11 pages; RevTe
The effects of periodic and continuous market environments on the performance of trading agents
Simulation experiments are conducted on simple continuous double auction (CDA) markets based on the experimental economics work of Vernon Smith. CDA models within experimental economics usually consist of a sequence of discrete trading periods or âdaysâ, with allocations of stock and currency replenished at the start of each day, a situation we call âperiodicâ replenishment. In our experiments we look at both periodic and continuous-replenishment versions of the CDA. In this we build on the work of Cliff and Preist (2001) with human subjects, but we replace human traders with Zero Intelligence Plus (ZIP) trading agents, a minimal algorithm that can produce equilibrating market behaviour in CDA models. Our results indicate that continuous-replenishment (CR) CDA markets are similar to conventional periodic CDA markets in their ability to show equilibration dynamics. Secondly we show that although both models produce the same behaviour of price formation, they are different playing fields, as periodic markets are more efficient over time than their continuous counterparts. We also find, however, that the volume of trade in periodic CDA markets is concentrated in the early period of each trading day, and the market is in this sense inefficient. We look at whether ZIP agents require different parameters for optimal behaviour in each market type, and find that this is indeed the case. Overall, our conclusions mirror earlier findings on the robustness of the CDA, but we stress that a CR-CDA marketplace equilibrates in a different way to a periodic one
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