109 research outputs found
Car Centres Placement Problem
Deciding on where to locate the next retail outlet is a problem with a long and distinguished history beginning with the early work of Hotelling (1929) and extended by Huff (1964). The basic idea is to view potential customers as sources of purchasing power while a retail store possesses attractiveness thus creating an interacting particle model.
Here, we address the issue of where to locate a new car center based on a limited dataset. A method for distilling aggregate population information down to sub-regions is developed to provide estimates that feed into the optimization algorithm.
Two measures were used in the optimization: (i) total market share and (ii) total attractiveness. Total market share optimization is found to lead to placing the center close to competitors, while total attractiveness optimization is found to lead to placing the center closer to centroid of the population
Modelling Asset Prices for Algorithmic and High-Frequency Trading
Algorithmic trading (AT) and high-frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this article, we employ a hidden Markov model to examine how the intraday dynamics of the stock market have changed and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit orders to profit from the bidâask spread, and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intraday states with the shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with the shortest average durations. Moreover, in 2008, the states with the shortest durations have the smallest price impact as measured by the volatility of price innovations
Topology and Duality in Abelian Lattice Theories
We show how to obtain the dual of any lattice model with inhomogeneous local
interactions based on an arbitrary Abelian group in any dimension and on
lattices with arbitrary topology. It is shown that in general the dual theory
contains disorder loops on the generators of the cohomology group of a
particular dimension. An explicit construction for altering the statistical sum
to obtain a self-dual theory, when these obstructions exist, is also given. We
discuss some applications of these results, particularly the existence of
non-trivial self-dual 2-dimensional Z_N theories on the torus. In addition we
explicitly construct the n-point functions of plaquette variables for the U(1)
gauge theory on the 2-dimensional g-tori.Comment: 11 pages, LateX, 1 epsf figure; minor typos corrected and references
update
Loops, Surfaces and Grassmann Representation in Two- and Three-Dimensional Ising Models
Starting from the known representation of the partition function of the 2-
and 3-D Ising models as an integral over Grassmann variables, we perform a
hopping expansion of the corresponding Pfaffian. We show that this expansion is
an exact, algebraic representation of the loop- and surface expansions (with
intrinsic geometry) of the 2- and 3-D Ising models. Such an algebraic calculus
is much simpler to deal with than working with the geometrical objects. For the
2-D case we show that the algebra of hopping generators allows a simple
algebraic treatment of the geometry factors and counting problems, and as a
result we obtain the corrected loop expansion of the free energy. We compute
the radius of convergence of this expansion and show that it is determined by
the critical temperature. In 3-D the hopping expansion leads to the surface
representation of the Ising model in terms of surfaces with intrinsic geometry.
Based on a representation of the 3-D model as a product of 2-D models coupled
to an auxiliary field, we give a simple derivation of the geometry factor which
prevents overcounting of surfaces and provide a classification of possible sets
of surfaces to be summed over. For 2- and 3-D we derive a compact formula for
2n-point functions in loop (surface) representation.Comment: 31 pages, 9 figure
Persistent currents in mesoscopic rings and boundary conformal field theory
A tight-binding model of electron dynamics in mesoscopic normal rings is
studied using boundary conformal field theory. The partition function is
calculated in the low energy limit and the persistent current generated as a
function of an external magnetic flux threading the ring is found. We study the
cases where there are defects and electron-electron interactions separately.
The same temperature scaling for the persistent current is found in each case,
and the functional form can be fitted, with a high degree of accuracy, to
experimental data.Comment: 6 pages, 4 enclosed postscript figure
LĂ©vy-Ito Models in Finance
We present an overview of the broad class of financial models in which the prices of assets are L Ă©vy-Ito processes driven by an n-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an n-dimensional LĂ©vy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models
Theta Sectors and Thermodynamics of a Classical Adjoint Gas
The effect of topology on the thermodynamics of a gas of adjoint
representation charges interacting via 1+1 dimensional SU(N) gauge fields is
investigated. We demonstrate explicitly the existence of multiple vacua
parameterized by the discrete superselection variable k=1,...,N. In the low
pressure limit, the k dependence of the adjoint gas equation of state is
calculated and shown to be non-trivial. Conversely, in the limit of high system
pressure, screening by the adjoint charges results in an equation of state
independent of k. Additionally, the relation of this model to adjoint QCD at
finite temperature in two dimensions and the limit of large N are discussed.Comment: 17 pages LaTeX, 3 eps figures, uses eps
Effective String Theory and Nonlinear Lorentz Invariance
We study the low-energy effective action governing the transverse
fluctuations of a long string, such as a confining flux tube in QCD. We work in
the static gauge where this action contains only the transverse excitations of
the string. The static gauge action is strongly constrained by the requirement
that the Lorentz symmetry, that is spontaneously broken by the long string
vacuum, is nonlinearly realized on the Nambu-Goldstone bosons. One solution to
the constraints (at the classical level) is the Nambu-Goto action, and the
general solution contains higher derivative corrections to this. We show that
in 2+1 dimensions, the first allowed correction to the Nambu-Goto action is
proportional to the squared curvature of the induced metric on the worldsheet.
In higher dimensions, there is a more complicated allowed correction that
appears at lower order than the curvature squared. We argue that this leading
correction is similar to, but not identical to, the one-loop determinant
(\sqrt{-h} R \Box^{-1} R) computed by Polyakov for the bosonic fundamental
string.Comment: 15 page
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