1,345 research outputs found
Phase transitions in optimal strategies for betting
Kelly's criterion is a betting strategy that maximizes the long term growth
rate, but which is known to be risky. Here, we find optimal betting strategies
that gives the highest capital growth rate while keeping a certain low value of
risky fluctuations. We then analyze the trade-off between the average and the
fluctuations of the growth rate, in models of horse races, first for two horses
then for an arbitrary number of horses, and for uncorrelated or correlated
races. We find an analog of a phase transition with a coexistence between two
optimal strategies, where one has risk and the other one does not. The above
trade-off is also embodied in a general bound on the average growth rate,
similar to thermodynamic uncertainty relations. We also prove mathematically
the absence of other phase transitions between Kelly's point and the risk free
strategy.Comment: 23 pages, 5 figure
A Poisson-Boltzmann approach for a lipid membrane in an electric field
The behavior of a non-conductive quasi-planar lipid membrane in an
electrolyte and in a static (DC) electric field is investigated theoretically
in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to
charges in the membrane lipids and in the double layers lead to corrections to
the membrane elastic moduli which are analyzed here. We show that, especially
in the low salt limit, i) the electrostatic contribution to the membrane's
surface tension due to the Debye layers crosses over from a quadratic behavior
in the externally applied voltage to a linear voltage regime. ii) the
contribution to the membrane's bending modulus due to the Debye layers
saturates for high voltages. Nevertheless, the membrane undulation instability
due to an effectively negative surface tension as predicted by linear
Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage
regime.Comment: 15 pages, 4 figure
The measurement of surface gravity
LaCoste and Romberg G and D gravity meters are normally employed when attempting high precision measurement of gravity differences on land. The capabilities and limitations of these instruments are discussed
Spin torque driven dynamics of a coupled two layer structure: interplay between conservative and dissipative coupling
In this manuscript the general concepts of spin wave theory are adapted to
the dynamics of a self-polarized system based on two layers coupled via
interlayer exchange (conservative coupling) and mutual spin torque (dissipative
coupling). An analytical description of the non-linear dynamics is proposed and
validated through numerical simulations. In contrast to the single layer model,
the phase equation of the coupled system has a contribution coming from the
dissipative part of the LLGS equation. It is shown that this is a major
contribution to the frequency mandatory to describe well the most basic
features of the dynamics of coupled systems. Using the proposed model a
specific feature of coupled dynamics is addressed: the redshift to blueshift
transition observed in the frequency current dependence of this kind of
exchange coupled systems upon increasing the applied field. It is found that
the blueshift regime can only occur in a region of field where the two linear
eigenmodes contribute equally to the steady state mode (i.e. high mode
hybridization). Finally, a general perturbed Hamiltonian equation for the
coupled system is proposed.Comment: 16 pages, 7 figue
Coherent Backscattering of light in a magnetic field
This paper describes how coherent backscattering is altered by an external
magnetic field. In the theory presented, magneto-optical effects occur inside
Mie scatterers embedded in a non-magnetic medium. Unlike previous theories
based on point-like scatterers, the decrease of coherent backscattering is
obtained in leading order of the magnetic field using rigorous Mie theory. This
decrease is strongly enhanced in the proximity of resonances, which cause the
path length of the wave inside a scatterer to be increased. Also presented is a
novel analysis of the shape of the backscattering cone in a magnetic field.Comment: 27 pages, 5 figures, Revtex, to appear in Phys. Rev.
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
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