24,773 research outputs found
Finding All Nash Equilibria of a Finite Game Using Polynomial Algebra
The set of Nash equilibria of a finite game is the set of nonnegative
solutions to a system of polynomial equations. In this survey article we
describe how to construct certain special games and explain how to find all the
complex roots of the corresponding polynomial systems, including all the Nash
equilibria. We then explain how to find all the complex roots of the polynomial
systems for arbitrary generic games, by polyhedral homotopy continuation
starting from the solutions to the specially constructed games. We describe the
use of Groebner bases to solve these polynomial systems and to learn geometric
information about how the solution set varies with the payoff functions.
Finally, we review the use of the Gambit software package to find all Nash
equilibria of a finite game.Comment: Invited contribution to Journal of Economic Theory; includes color
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Thermoelectric properties of Bi2Te3 atomic quintuple thin films
Motivated by recent experimental realizations of quintuple atomic layer films
of Bi2Te3,the thermoelectric figure of merit, ZT, of the quintuple layer is
calculated and found to increase by a factor of 10 (ZT = 7.2) compared to that
of the bulk at room temperature. The large enhancement in ZT results from the
change in the distribution of the valence band density of modes brought about
by the quantum confinement in the thin film. The theoretical model uses ab
initio electronic structure calculations (VASP) with full quantum-mechanical
structure relaxation combined with a Landauer formalism for the linear-response
transport coefficients.Comment: 4 figures, submitted to AP
Self-Repairing Codes for Distributed Storage - A Projective Geometric Construction
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for
distributed networked storage: they not only allow stored data to be recovered
even in the presence of node failures, they also provide a repair mechanism
where as little as two live nodes can be contacted to regenerate the data of a
failed node. In this paper, we propose a new instance of self-repairing codes,
based on constructions of spreads coming from projective geometry. We study
some of their properties to demonstrate the suitability of these codes for
distributed networked storage.Comment: 5 pages, 2 figure
From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
I review how methods from mesoscopic physics can be applied to describe the
multiple wave scattering and complex wave dynamics in non-hermitian
PT-symmetric resonators, where an absorbing region is coupled symmetrically to
an amplifying region. Scattering theory serves as a convenient tool to classify
the symmetries beyond the single-channel case and leads to effective
descriptions which can be formulated in the energy domain (via Hamiltonians)
and in the time domain (via time evolution operators). These models can then be
used to identify the mesoscopic time and energy scales which govern the
spectral transition from real to complex eigenvalues. The possible presence of
magneto-optical effects (a finite vector potential) in multichannel systems
leads to a variant (termed PTT' symmetry) which imposes the same spectral
constraints as PT symmetry. I also provide multichannel versions of generalized
flux-conservation laws.Comment: 10 pages, 5 figures, minireview for a theme issue, Philosophical
Transactions of the Royal Society
Energy transport and fluctuations in small conductors
The Landauer-B\"uttiker formalism provides a simple and insightful way for
investigating many phenomena in mesoscopic physics. By this approach we derive
general formulas for the energy properties and apply them to the basic setups.
Of particular interest are the noise properties. We show that energy current
fluctuations can be induced by zero-point fluctuations and we discuss the
implications of this result.Comment: Revised and corrected versio
Tunnel Magnetoresistance of a Single-Molecule Junction
Based on the non-equilibrium Green's function (NEGF) technique and the
Landauer-B\"{u}ttiker theory, the possibility of a molecular spin-electronic
device, which consists of a single C molecule attached to two
ferromagnetic electrodes with finite cross sections, is investigated. By
studying the coherent spin-dependent transport through the energy levels of the
molecule, it is shown that the tunnel magnetoresistance (TMR) of the molecular
junction depends on the applied voltages and the number of contact points
between the device electrodes and the molecule. The TMR values more than 60%
are obtained by adjusting the related parameters.Comment: 5 pages, 3 figure
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