Capacity-achieving ensembles for the binary erasure channel with bounded complexity

We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per information bit. This is in contrast to all previous constructions of capacity-achieving sequences of ensembles whose complexity grows at least like the log of the inverse of the gap (in rate) to capacity. The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes. We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs. The bound holds for every memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information Theor

Source integrals of asymptotic multipole moments

We derive source integrals for multipole moments that describe the behaviour of static and axially symmetric spacetimes close to spatial infinity. We assume isolated non-singular sources but will not restrict the matter content otherwise. Some future applications of these source integrals of the asymptotic multipole moments are outlined as well.Comment: 9 pages, 1 figure, contribution to the proceedings of the conference "Relativity and Gravitation - 100 Years after Einstein in Prague", June 25-29, 2012, Pragu

Cophylogeny and Biogeography of the Fungal Parasite Cyttaria and Its Host Nothofagus, Southern Beech

The obligate, biotrophic association among species of the fungal genus Cyttaria and their hosts in the plant genus Nothofagus often is cited as a classic example of cophylogeny and is one of the few cases in which the biogeography of a fungus is commonly mentioned or included in biogeographic analyses. In this study molecular and morphological data are used to examine hypotheses regarding the cophylogeny and biogeography of the 12 species of Cyttaria and their hosts, the 11 species of Nothofagus subgenera Lophozonia and Nothofagus. Our results indicate highly significant overall cophylogenetic structure, despite the fact that the associations between species of Cyttaria and Nothofagus usually do not correspond in a simple one to one relationship. Two major lineages of Cyttaria are confined to a single Nothofagus subgenus, a specificity that might account for a minimum of two codivergences. We hypothesize other major codivergences. Numerous extinction also are assumed, as are an independent parasite divergence followed by host switching to account for C. berteroi. Considering the historical association of Cyttaria and Nothofagus, our hypothesis may support the vicariance hypothesis for the trans-Antarctic distribution between Australasian and South American species of Cyttaria species hosted by subgenus Lophozonia. It also supports the hypothesis of transoceanic long distance dispersal to account for the relatively recent relationship between Australian and New Zealand Cyttaria species, which we estimate to have occurred 44.6–28.5 mya. Thus the history of these organisms is not only a reflection of the breakup of Gondwana but also of other events that have contributed to the distributions of many other southern hemisphere plants and fungi.Organismic and Evolutionary BiologyOther Research Uni

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Centrifugal Force and Ellipticity behaviour of a slowly rotating ultra compact object

Using the optical reference geometry approach, we have derived in the following, a general expression for the ellipticity of a slowly rotating fluid configuration using Newtonian force balance equation in the conformally projected absolute 3-space, in the realm of general relativity. Further with the help of Hartle-Thorne (H-T) metric for a slowly rotating compact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrifugal reversal occurs at around $R/R_s \approx 1.45$, and the ellipticity maximum at around $R/R_s \approx 2.75$. The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism

Centrifugal force induced by relativistically rotating spheroids and cylinders

Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect to axes that do not rotate as seen from infinity experiences a centrifugal force. Although the spacetime there is Minkowskian out to the inner cylinder nevertheless that space has been induced to rotate, so relative to the local inertial frame the particle is traversing a circular orbit.Comment: 12 pages, 2 figure

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio