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

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

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

Modulating spin transfer torque switching dynamics with two orthogonal spin-polarizers by varying the cell aspect ratio

We study in-plane magnetic tunnel junctions with additional perpendicular polarizer for subnanosecond-current-induced switching memories. The spin-transfer-torque switching dynamics was studied as a function of the cell aspect ratio both experimentally and by numerical simulations using the macrospin model. We show that the anisotropy field plays a significant role in the dynamics, along with the relative amplitude of the two spin-torque contributions. This was confirmed by micromagnetic simulations. Real-time measurements of the reversal were performed with samples of low and high aspect ratio. For low aspect ratios, a precessional motion of the magnetization was observed and the effect of temperature on the precession coherence was studied. For high aspect ratios, we observed magnetization reversals in less than 1 ns for high enough current densities, the final state being controlled by the current direction in the magnetic tunnel junction cell.Comment: 6 pages, 7 figure