Why frequencies are natural

Research in mathematical cognition has shown that rates, and other interpretations of x/y, are hard to learn and understand. On the other hand, there is extensive evidence that the brain is endowed with a specialized mechanism for representing and manipulating the numerosities of sets – that is, frequencies. Hence, base-rates are neglected precisely because they are rates, whereas frequencies are indeed natural

Estimating probabilities from experimental frequencies

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or frequency count 'f', of each of the possible outcomes. In this work, the probability that the true distribution be 'q', given that the frequency count 'f' was sampled, is studied. Such a probability may be written as a Gibbs distribution. A thermodynamic potential, which allows an easy evaluation of the mean Kullback-Leibler divergence between the true and measured distribution, is defined. For a large number of samples, the expectation value of any function of 'q' is expanded in powers of the inverse number of samples. As an example, the moments, the entropy and the mutual information are analyzed.Comment: 10 pages, 3 figures, to be published in Physical Review

Magnetic nanocomposites at microwave frequencies

Most conventional magnetic materials used in the electronic devices are ferrites, which are composed of micrometer-size grains. But ferrites have small saturation magnetization, therefore the performance at GHz frequencies is rather poor. That is why functionalized nanocomposites comprising magnetic nanoparticles (e.g. Fe, Co) with dimensions ranging from a few nm to 100 nm, and embedded in dielectric matrices (e.g. silicon oxide, aluminium oxide) have a significant potential for the electronics industry. When the size of the nanoparticles is smaller than the critical size for multidomain formation, these nanocomposites can be regarded as an ensemble of particles in single-domain states and the losses (due for example to eddy currents) are expected to be relatively small. Here we review the theory of magnetism in such materials, and we present a novel measurement method used for the characterization of the electromagnetic properties of composites with nanomagnetic insertions. We also present a few experimental results obtained on composites consisting of iron nanoparticles in a dielectric matrix.Comment: 20 pages, 10 figures, 5 table

Space VLBI at Low Frequencies

At sufficiently low frequencies, no ground-based radio array will be able to produce high resolution images while looking through the ionosphere. A space-based array will be needed to explore the objects and processes which dominate the sky at the lowest radio frequencies. An imaging radio interferometer based on a large number of small, inexpensive satellites would be able to track solar radio bursts associated with coronal mass ejections out to the distance of Earth, determine the frequency and duration of early epochs of nonthermal activity in galaxies, and provide unique information about the interstellar medium. This would be a "space-space" VLBI mission, as only baselines between satellites would be used. Angular resolution would be limited only by interstellar and interplanetary scattering.Comment: To appear in "Astrophysical Phenomena Revealed by Space VLBI", ed. H. Hirabayashi, P. Edwards, and D. Murphy (ISAS, Japan