The oscillatory distribution of distances in random tries

We investigate \Delta_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O(1), as n\to\infty. It is demonstrated that the centered random variable \Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution, but rather oscillates between two distributions.Comment: Published at http://dx.doi.org/10.1214/105051605000000106 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uplink capacity of a variable density cellular system with multicell processing

In this work we investigate the information theoretic capacity of the uplink of a cellular system. Assuming centralised processing for all base stations, we consider a power-law path loss model along with variable cell size (variable density of Base Stations) and we formulate an average path-loss approximation. Considering a realistic Rician flat fading environment, the analytical result for the per-cell capacity is derived for a large number of users distributed over each cell. We extend this general approach to model the uplink of sectorized cellular system. To this end, we assume that the user terminals are served by perfectly directional receiver antennas, dividing the cell coverage area into perfectly non-interfering sectors. We show how the capacity is increased (due to degrees of freedom gain) in comparison to the single receiving antenna system and we investigate the asymptotic behaviour when the number of sectors grows large. We further extend the analysis to find the capacity when the multiple antennas used for each Base Station are omnidirectional and uncorrelated (power gain on top of degrees of freedom gain). We validate the numerical solutions with Monte Carlo simulations for random fading realizations and we interpret the results for the real-world systems

Pluralism without Genic Causes?

Since the fundamental challenge that I laid at the doorstep of the pluralists was to defend, with nonderivative models, a strong notion of genic cause, it is fatal that Waters has failed to meet that challenge. Waters agrees with me that there is only a single cause operating in these models, but he argues for a notion of causal ‘parsing’ to sustain the viability of some form of pluralism. Waters and his colleagues have some very interesting and important ideas about the sciences, involving pluralism and parsing or partitioning causes, but they are ideas in search of an example. He thinks he has found an example in the case of hierarchical and genic selection. I think he has not

Pluralism without Genic Causes?

Since the fundamental challenge that I laid at the doorstep of the pluralists was to defend, with nonderivative models, a strong notion of genic cause, it is fatal that Waters has failed to meet that challenge. Waters agrees with me that there is only a single cause operating in these models, but he argues for a notion of causal ‘parsing’ to sustain the viability of some form of pluralism. Waters and his colleagues have some very interesting and important ideas about the sciences, involving pluralism and parsing or partitioning causes, but they are ideas in search of an example. He thinks he has found an example in the case of hierarchical and genic selection. I think he has not

Critical Flavor Number in the Three Dimensional Thirring Model

We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors N_f varied between 2 and 18. By identifying the lattice coupling at which the chiral condensate peaks, simulations are be performed at couplings g^2(N_f) corresponding to the strong coupling limit of the continuum theory. The chiral symmetry restoring phase transition is studied as N_f is increased, and the critical number of flavors estimated as N_{fc}=6.6(1). The critical exponents measured at the transition do not agree with self-consistent solutions of the Schwinger-Dyson equations; in particular there is no evidence for the transition being of infinite order. Implications for the critical flavor number in QED_3 are briefly discussed.Comment: 4 pages, 5 figure

Lasing in metamaterial nanostructures

A self-consistent computational scheme is presented for one dimensional (1D) and two dimensional (2D) metamaterial systems with gain incorporated into the nanostructures. The gain is described by a generic four-level system. The loss compensation and the lasing behavior of the metamaterial system with gain are studied. A critical pumping rate exists for compensating the losses of the metamaterial. There exists a wide range of input signals where the composite system behaves linearly. Nonlinearities arise for stronger signals due to gain depletion. The retrieved effective parameters are presented for one layer of gain embedded in two layers of Lorentz dielectric rods and split ring resonators with two different gain inclusions: (1) gain is embedded in the gaps only and (2) gain is surrounding the SRR. When the pumping rate increases, there is a critical pumping rate that the metamaterial system starts lasing.Comment: 18 pages, 19 figures, submitted to Journal of Optics A: Pure and Applied Optic