On projections of arbitrary lattices

In this paper we prove that given any two point lattices $\Lambda_1 \subset \mathbb{R}^n$ and $\Lambda_2 \subset \nobreak \mathbb{R}^{n-k}$, there is a set of $k$ vectors $\bm{v}_i \in \Lambda_1$ such that $\Lambda_2$ is, up to similarity, arbitrarily close to the projection of $\Lambda_1$ onto the orthogonal complement of the subspace spanned by $\bm{v}_1, \ldots, \bm{v}_k$. This result extends the main theorem of \cite{Sloane2} and has applications in communication theory.Comment: 11 page

Rotated Dn-lattices

AbstractBased on algebraic number theory we construct some families of rotated Dn-lattices with full diversity which can be good for signal transmission over both Gaussian and Rayleigh fading channels. Closed-form expressions for the minimum product distance of those lattices are obtained through algebraic properties

Type 0 T-Duality and the Tachyon Coupling

We consider the T-duality relations between Type 0A and 0B theories, and show that this constraints the possible couplings of the tachyon to the RR-fields. Due to the `doubling' of the RR sector in Type 0 theories, we are able to introduce a democratic formulation for the Type 0 effective actions, in which there is no Chern-Simons term in the effective action. Finally we discuss how to embed Type II solutions into Type 0 theories.Comment: some misprints corrected and a reference adde

On Communication for Distributed Babai Point Computation

We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector X∈Rn in a given lattice. We show that the protocol is optimal in the sense that it minimizes the sum rate when the components of X are mutually independent. We then investigate the error probability, i.e. the probability that the Babai point does not coincide with the nearest lattice point, motivated by the fact that for some cases, a distributed algorithm for finding the Babai point is sufficient for finding the nearest lattice point itself. Two different probability models for X are considered—uniform and Gaussian. For the uniform model, in dimensions two and three, the error probability is seen to grow with the packing density, and we demonstrate that the densest lattice in dimension two presents the worst error probability. For higher dimensions, we develop probabilistic concentration bounds as well as bounds based on geometric arguments for the error probability. The probabilistic bounds lead to the conclusion that for lattices which generate suitably thin coverings of Rn (which includes lattices that meet Rogers’ bound on the covering radius), the error probability goes to unity as n grows. Probabilistic and geometric bounds are also used to estimate the error probability under the uniform model for various lattices including the An family and the Leech lattice, Λ24 . On the other hand, for the Gaussian model, the error probability goes to zero as the lattice dimension tends to infinity, provided the noise variance is sufficiently small

Desigualdades regionais na mortalidade por câncer de colo de útero no Brasil: tendências e projeções até o ano 2030

O objetivo deste artigo é analisar a tendência temporal da mortalidade por câncer de colo de útero no Brasil e calcular uma projeção até o ano de 2030. Foram analisados os óbitos ocorridos no Brasil de 1996 a 2010 (Sistema de Informações sobre Mortalidade). Foram realizadas análises das tendências da mortalidade por meio da regressão Joinpoint, e para o cálculo das projeções foi utilizado o Nordpred. Para o Brasil, a tendência é de redução (APC = 1, 7% IC95%-2, 2; -1, 1 p < 0, 05), sendo significativa nas regiões centro oeste (APC = -1, 3% ao ano), sudeste (APC =-3, 3%) e sul (APC = -3, 9%). As regiões norte e nordeste apresntam tendência de estabilidade. Os estados do Acre (APC = -6, 5%) e Rio Grande do Sul (APC = -4, 1%) apresentaram as maiores tendências de redução. Na análise das projeções de mortalidade, haverá uma redução das taxas no Brasil a partir do primeiro período projetado, sendo mais marcante para a região sul. As taxas de mortalidade até o ano 2030 serão explicadas, em maior medida, pela redução dos risco para a doença. A mortalidade por câncer de colo de útero apresenta tendência de redução, todavia está desigualmente distribuída no Brasil, com as regiões norte e nordeste apresentando as maiores taxas. The scope of this article is to analyze the temporal trends of cervical cancer mortality in Brazil and calculate the projection of mortality through to the year 2030. Deaths that occurred within the 1996-2010 period were analyzed (Mortality Information System). Mortality trend analysis utilized the Joinpoint regression, while Nordpred was utilized for the calculation of projections. For Brazil, decreasing trends were identified (APC = 1.7% CI95%-2.2; -1.1 p < 0.05). The Midwest region presented a significant reduction trend (APC = -1.3% per year), along with the Southeast (APC = -3.3%) and South (APC = -3.9%) regions. The North and Northeast regions presented stable trends. The states of Acre (APC = -6.5%) and Rio Grande do Sul (APC = -4.1%) presented the most pronounced reduction trends. Analysis of the mortality projections revealed a reduction in mortality rates, starting from the first projected period, with a considerable reduction for the South region. Mortality rates through to the year 2030 are explained, principally, by reductions in the riskof the disease. Cervical cancer mortality presents reducing trends, however these are unequally distributed throughout the country, where the North and Northeast regions present the highest mortality rates

Hubungan Antara Pola Tutupan Lahan Terbangun Dan Laju Infiltrasi Air Hujan

Kupang City is an area in Indonesia which has a relatively low number of rainy days. This causes the supply of clean water or drinking water in Kupang City to decrease. The high infiltration rate not only increases the amount of water stored in the soil, but also reduces flooding and erosion caused by run off. This study aims to model the relationship between infiltration and discharge capability for each type of samples land by using linear regression method. For this reason, a water absorption test was conducted on the built up area based on the infiltration rate. The results of experiments and calculations using linear regression shown that area often received heavy load such as vehichles had lower infiltration rate leading to slow inundation height decrease. While areas rarely received heavy load had higher infiltration rate. Even though the difference is only around 2-3 cm / 5 minutes, it indicates that the availability of open areas is still needed to support the implementation of the zero run-off model in urban built area

Type IIB Solutions with Interpolating Supersymmetries

We study type IIB supergravity solutions with four supersymmetries that interpolate between two types widely considered in the literature: the dual of Becker and Becker's compactifications of M-theory to 3 dimensions and the dual of Strominger's torsion compactifications of heterotic theory to 4 dimensions. We find that for all intermediate solutions the internal manifold is not Calabi-Yau, but has SU(3) holonomy in a connection with a torsion given by the 3-form flux. All 3-form and 5-form fluxes, as well as the dilaton, depend on one function appearing in the supersymmetry spinor, which satisfies a nonlinear differential equation. We check that the fields corresponding to a flat bound state of D3/D5-branes lie in our class of solutions. The relations among supergravity fields that we derive should be useful in studying new gravity duals of gauge theories, as well as possibly compactifications.Comment: 27pp, v2 REVTeX4, typographical fixes and minor clarifications, v3 added ref, modified discussion of RR axion slightl

Closed String Tachyons and Semi-Classical Instabilities

We conjecture that the end point of bulk closed string tachyon decay at any non-zero coupling, is the annihilation of space time by Witten's bubble of nothing, resulting in a topological phase of the theory. In support of this we present a variety of situations in which there is a correspondence between the existence of perturbative tachyons in one regime and the semi-classical annihilation of space-time. Our discussion will include many recently investigated scenarios in string theory including Scherk-Schwarz compactifications, Melvin magnetic backgrounds, and noncompact orbifolds. We use this conjecture to investigate a possible web of dualities relating the eleven-dimensional Fabinger-Horava background with nonsupersymmetric string theories. Along the way we point out where our conjecture resolves some of the puzzles associated with bulk closed string tachyon condensation.Comment: 31 pages, 5 figures 3 figures added, typos corrected and references added. Discussion of Type 0/Heterotic s-duality extended and some other points clarified Revision of discussion on Fabinger-Horava string descendents, section on Scherk-Schwarz compactification of Horava-Witten removed, some references adde