Frontiers of finance: Evolution and efficient markets

In this review article we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical models that are captable of rationalizing the empirical facrts, others taking a completely different different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological perspective and, specifically, with an evolutionary framework in which markets, instruments, institutions, and investors interact and evolve dynamically according to the "law" of economic selection. Under this view, financial agents compete and adapt, but they do not necessarily do so in an optimal fashion. Evolutionary and ecological models of financial markets is truly a new frontier whose exploration has just begun.Comment: 2 page

A method of automatically stabilizing helicopter sling loads

The effect of geometric and aerodynamic characteristics on the stability of the lateral degrees of freedom of a typical helicopter sling load is examined. The feasibility of stabilizing the suspended load by controllable fins was also studied. Linear control theory was applied to the design of a simple control law that stabilized the load over a wide range of helicopter airspeeds

An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion

We give a conditional result on the constant in the B\'aez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that $\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta}$, for some $\delta>0$, the value of this constant coincides with the lower bound given by Burnol.Comment: 9 page

The distribution of the eigenvalues of Hecke operators

For each prime $p$, we determine the distribution of the $p^{th}$ Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As $p\to\infty$, this distribution tends to the Sato--Tate distribution

Crystallization of random trigonometric polynomials

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension. In particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not Gaussian.Comment: 10 pages, 3 figure

Particle phase function measurements by a new Fiber Array Nephelometer: FAN 1

A fiber array polar nephelometer of advanced design, the FAN I is capable of in-situ phase function measurements of scattered light from man-made or natural atmospheric particles. The scattered light is measured at 100 different angles throughout 360 degrees, thus providing a potential measurement of the asymmetry of irregularly shaped particles. Phase functions can be measured at 10 to 100 Hz rates and the range of measurable single particle sizes is from 5 micron m to as large as 8mm. For particles smaller than 5 micro m the ensemble average can be measured. The FAN I is microprocessor controlled and the data may be stored on floppy disk or printed out in tabular and/or graphical form. The optical head may be separated from the computer system for operation in field or adverse conditions. Examples of laboratory measured scattering phase functions obtained with the FAN I for spherical particles is given to illustrate its measurement capabilities