Locality-preserving allocations Problems and coloured Bin Packing

We study the following problem, introduced by Chung et al. in 2006. We are given, online or offline, a set of coloured items of different sizes, and wish to pack them into bins of equal size so that we use few bins in total (at most $\alpha$ times optimal), and that the items of each colour span few bins (at most $\beta$ times optimal). We call such allocations $(\alpha, \beta)$-approximate. As usual in bin packing problems, we allow additive constants and consider $(\alpha,\beta)$ as the asymptotic performance ratios. We prove that for \eps>0, if we desire small $\alpha$, no scheme can beat (1+\eps, \Omega(1/\eps))-approximate allocations and similarly as we desire small $\beta$, no scheme can beat (1.69103, 1+\eps)-approximate allocations. We give offline schemes that come very close to achieving these lower bounds. For the online case, we prove that no scheme can even achieve $(O(1),O(1))$-approximate allocations. However, a small restriction on item sizes permits a simple online scheme that computes (2+\eps, 1.7)-approximate allocations

Structural aspects of Hamilton-Jacobi theory

In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (`slicing vector fields') on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.Comment: 26 pages. Minor changes (some minor mistakes are corrected

The Steiner Multi Cycle Problem with Applications to a Collaborative Truckload Problem

We introduce a new problem called Steiner Multi Cycle Problem that extends the Steiner Cycle problem in the same way the Steiner Forest extends the Steiner Tree problem. In this problem we are given a complete weighted graph G=(V,E), which respects the triangle inequality, a collection of terminal sets {T_1,..., T_k}, where for each a in [k] we have a subset T_a of V and these terminal sets are pairwise disjoint. The problem is to find a set of disjoint cycles of minimum cost such that for each a in [k], all vertices of T_a belong to a same cycle. Our main interest is in a restricted case where |T_a| = 2, for each a in [k], which models a collaborative less-than-truckload problem with pickup and delivery. In this problem, we have a set of agents where each agent is associated with a set T_a containing a pair of pickup and delivery vertices. This problem arises in the scenario where a company has to periodically exchange goods between two different locations, and different companies can collaborate to create a route that visits all its pairs of locations sharing the total cost of the route. We show that even the restricted problem is NP-Hard, and present some heuristics to solve it. In particular, a constructive heuristic called Refinement Search, which uses geometric properties to determine if agents are close to each other. We performed computational experiments to compare this heuristic to a GRASP based heuristic. The Refinement Search obtained the best solutions in little computational time

Multiplicity of Nearby Free-floating Ultra-cool Dwarfs: a HST-WFPC2 search for companions

We present HST/WFPC2 observations of a sample of 134 ultra-cool objects (spectral types later than M7) coming from the DENIS, 2MASS and SDSS surveys, with distances estimated to range from 7 pc to 105 pc. Fifteen new ultra-cool binary candidates are reported here. Eleven known binaries are confirmed and orbital motion is detected in some of them. We estimate that the closest binary systems in this sample have periods between 5 and 20 years, and thus dynamical masses will be derived in the near future. For the calculation of binary frequency we restrict ourselves to systems with distances less than 20 pc. After correction of the binaries bias, we find a ratio of visual binaries (at the HST limit of detection) of around 10%, and that ~15% of the 26 objects within 20 parsecs are binary systems with separations between 1 and 8 A.U. The observed frequency of ultra-cool binaries is similar than that of binaries with G-type primaries in the separation range from 2.1 A.U. to 140 A.U. There is also a clear deficit of ultra-cool binaries with separations greater than 15 A.U., and a possible tendency for the binaries to have mass ratios near unity. Most systems have indeed visual and near-infrared brightness ratios between 1 and 0.3. We discuss our results in the framework of current scenarios for the formation and evolution of free-floating brown dwarfs.Comment: 67 pages, 14 figures, Accepted for publication in AJ, September 2003. First submission to AJ: august 2002, 5 submission

An Effective Temperature Scale for Late M and L Dwarfs, from Resonance Absorption Lines of CsI and RbI

We present Keck HIRES spectra of 6 late-M dwarfs and 11 L dwarfs. Our goal is to assign effective temperatures to the objects using detailed atmospheric models and fine analysis of the alkali resonance absorption lines of CsI and RbI. These yield mutually consistent results (+-150 K) when we use ``cleared-dust'' models, which account for the removal of refractory species from the molecular states but do not include dust opacities. We find a tendency for the RbI line to imply a slightly higher temperature, which we ascribe to an incomplete treatment of the overlying molecular opacities. The final effective temperatures we adopt are based on the CsI fits alone, though the RbI fits support the CsI temperature sequence. This work, in combination with results from the infrared, hints that dust in these atmospheres has settled out of the high atmosphere but is present in the deep photosphere. We also derive radial and rotational velocities for all the objects, finding that the previously discovered trend of rapid rotation for very low mass objects is quite pervasive. To improve on our analysis, there is a clear need for better molecular line lists and a more detailed understanding of dust formation and dynamics.Comment: 53 pages, including 20 figures and 2 Tables; accepted in Ap

Adhesion of freshwater sponge cells mediated by carbohydrate-carbohydrate interactions requires low environmental calcium

Marine ancestors of freshwater sponges had to undergo a series of physiological adaptations to colonize harsh and heterogeneous limnic environments. Besides reduced salinity, river-lake systems also have calcium concentrations far lower than seawater. Cell adhesion in sponges is mediated by calcium-dependent multivalent self-interactions of sulfated polysaccharides components of membrane-bound proteoglycans named aggregation factors. Cells of marine sponges require seawater average calcium concentration (10\xC2\xA0mM) to sustain adhesion promoted by aggregation factors. We demonstrate here that the freshwater sponge Spongilla alba can thrive in a calcium-poor aquatic environment and that their cells are able to aggregate and form primmorphs with calcium concentrations 40-fold lower than that required by marine sponges cells. We also find that their gemmules need calcium and other micronutrients to hatch and generate new sponges. The sulfated polysaccharide purified from S. alba has sulfate content and molecular size notably lower than those from marine sponges. Nuclear magnetic resonance analyses indicated that it is composed of a central backbone of non- and 2-sulfated \xCE\xB1- and \xCE\xB2-glucose units decorated with branches of \xCE\xB1-glucose. Assessments with atomic force microscopy/single-molecule force spectroscopy show that S. alba glucan requires 10-fold less calcium than sulfated polysaccharides from marine sponges to self-interact efficiently. Such an ability to retain multi-cellular morphology with low environmental calcium must have been a crucial evolutionary step for freshwater sponges to successfully colonize inland waters

Infecciones bucales producidas por virus herpes simplex: características clínicas y diagnóstico diferencial

El virus Herpes simplex (VHS) es el agente patogénico de numerosas lesiones a nivel cutáneo y mucoso, pudiendo involucrar también diversos órganos de la economía. Su alta prevalencia en la población hace que sea necesario que el odontólogo, el estomatólogo, el dermatólogo e incluso el médico generalista conozcan los diversos cuadros clínicos que puede originar dicho virus . En este artículo se revisarán las características clínicas de la infección por VHS cuando se presenta a nivel bucal y las entidades nosológicas con las que se ha de hacer un adecuado diagnóstico diferencial, con el fin de orientarse hacia una terapéutica adecuada

El cerdo como modelo experimental en Odontoestomatología. Propuesta de vía de abordaje quirúrgico

El cerdo es un animal muy utilizado en estudios experimentales, como trasplantes de corazón y cirugía abdominal, entre otros campos. En el ámbito odontológico también se emplea; en implantología y cirugía reparadora; en el campo de los biomateriales, la regeneración periodontal e incluso la odontología restauradora

A Systematic Analysis of Metal and Metalloid Concentrations in Eight Zebrafish Recirculating Water Systems

Metals and metalloids are integral to biological processes and play key roles in physiology and metabolism. Nonetheless, overexposure to some metals or lack of others can lead to serious health consequences. In this study, eight zebrafish facilities collaborated to generate a multielement analysis of their centralized recirculating water systems. We report a first set of average concentrations for 46 elements detected in zebrafish facilities. Our results help to establish an initial baseline for trouble-shooting purposes, and in general for safe ranges of metal concentrations in recirculating water systems, supporting reproducible scientific research outcomes with zebrafish