This article is concerned with an indefinite weight linear eigenvalue problem which is related with population dynamics. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For an arbitrary domain, it is shown that every global minimizer must be of "bang-bang" type. When the domain is an interval, it is proved that there are exactly two global minimizers, for which the weight is positive at one end of the interval and is negative in the remainder. We also consider the case of rectangular domains both mathematically and numerically.
Recent developments on universal fluctuations of growing interfaces are overviewed. Particular focus is put on experimental results in liquid-crystal turbulence, where one can directly look at statistical laws in random matrix theory as universal features of growing interfaces. Related mathematical models and concepts are also introduced.