Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.     

Hurewicz sets of reals without perfect subsets

We show that even for subsets of the real line that do not contain perfect sets, the Hurewicz property does not imply the property , asserting that for each countable family of open -covers of , there is a choice function whose image is a -cover of . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for , the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskiı's property .

     

A stereospecific synthesis of chiral 1,3-disubstituted bromoallenes

Optically active 1, 3-disubstituted propargyl alcohols undergo S_Ni′ rearrangements with thionyl bromide in the presence of propylene oxide to yield bromoallenes without loss of optical purity.     

The minimal cardinality where the Reznichenko property fails

A topological spaceX has the Fréchet-Urysohn property if for each subsetA ofX and each elementx inĀ, there exists a countable sequence of elements ofA which converges tox. Reznichenko introduced a natural generalization of this property, where the converging sequence of elements is replaced by a sequence of disjoint finite sets which eventually intersect each neighborhood ofx. In [5], Kočinac and Scheepers conjecture: The minimal cardinality of a setX of real numbers such thatC _p(X) does not have the weak Fréchet-Urysohn property is equal to b. (b is the minimal cardinality of an unbounded family in the Baire space^Nℕ.) We prove the Kočinac-Scheepers conjecture by showing that ifC _p(X) has the Reznichenko property, then a continuous image ofX cannot be a subbase for a non-feeble filter on ℕ. The author is partially supported by the Golda Meir Fund and the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany).     

Strong γ-sets and other singular spaces

Whereas the Gerlits-Nagy γ property is strictly weaker than the Galvin-Miller strong γ property, the corresponding strong notions for the Menger, Hurewicz, Rothberger, Gerlits-Nagy (∗), Arkhangel'ski?ˇ and Sakai properties are equivalent to the original ones. The main result is that almost each of these properties admits the game theoretic characterization suggested by the stronger notion. We also solve a related problem of Ko?inac and Scheepers, and answer a question of Iliadis.     

Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity

When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial diffusion-limited aggregation is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D = 1.71 arises only for very small angular gaps, which occur only for clusters significantly larger than M = 10(6) particles. Intermediate size gaps exhibit an effective dimension around 1.67, even for M--> infinity. They dominate the distribution for clusters with M<10(6). The largest gap approaches a finite limit extremely slowly, with a correction of order M(-0.17).     

Imaging microscopic viscosity with confocal scanning optical tweezers

The techniques of confocal microscopy and optical tweezers have shown themselves to be powerful tools in biological and medical research. We combine these methods to develop a minimally invasive instrument that is capable of making hydrodynamic measurements more rapidly than is possible with other devices. This result leads to the possibility of making scanning images of the viscosity distribution of materials around biopolymer-producing cells. 100 x 100 images can be taken with 0.5-microm spatial resolution in 3 min. An image of the viscosity distribution around a pullulan-producing cell of Aureobasidium pullulans is shown as an example.