Optimal Filling of Shapes

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal discs. We consider the properties of ideal distributions of N discs as N approaches infinity. We note an analogy with energy landscapes.Comment: 5 page

Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account.Comment: 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section

Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.Comment: 42pages, 9figures, reference added, minor chang

The Antioxidant Potential of the Mediterranean Diet in Patients at High Cardiovascular Risk: An In-Depth Review of the PREDIMED

Cardiovascular disease (CVD) is the leading global cause of death. Diet is known to be important in the prevention of CVD. The PREDIMED trial tested a relatively low-fat diet versus a high-fat Mediterranean diet (MedDiet) for the primary prevention of CVD. The resulting reduction of the CV composite outcome resulted in a paradigm shift in CV nutrition. Though many dietary factors likely contributed to this effect, this review focuses on the influence of the MedDiet on endogenous antioxidant systems and the effect of dietary polyphenols. Subgroup analysis of the PREDIMED trial revealed increased endogenous antioxidant and decreased pro-oxidant activity in the MedDiet groups. Moreover, higher polyphenol intake was associated with lower incidence of the primary outcome, overall mortality, blood pressure, inflammatory biomarkers, onset of new-onset type 2 diabetes mellitus (T2DM), and obesity. This suggests that polyphenols likely contributed to the lower incidence of the primary event in the MedDiet groups. In this article, we summarize the potential benefits of polyphenols found in the MedDiet, specifically the PREDIMED cohort. We also discuss the need for further research to confirm and expand the findings of the PREDIMED in a non-Mediterranean population and to determine the exact mechanisms of action of polyphenols

Entanglement Entropy from a Holographic Viewpoint

The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. In this article, we would like to give a quick survey of recent progresses on the holographic entanglement entropy. We focus on its gravitational aspects, so that it is comprehensible to those who are familiar with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity, minor correction

The shape influence on the overall single scattering properties of a sample in random orientation

[EN] In order to identify the type of scattering profile that corresponds to some specific shapes, we have performed calculations of some scattering properties for those shapes with a fixed size distribution. Aggregates of different numbers of spheres have been used to fit the laboratory measurements of fly ashes. The results for other shapes, such as rectangular prisms with different axial proportions, particles made of joined cubes, and particles with different fluffiness, are also shown. From all these calculations, it is concluded that the size-averaged scattering matrix elements resembles Rayleigh features, for the size distribution stopping at 1.0¿m, when either the number of spheres or cubes of the aggregates is increased, the shape becomes flatter or the particles become fluffier. We also show the effect of the refractive index on the Qsca vs. X curve in the case of strongly absorbing particles. A tendency to reach the geometric optic regime is observed instead of the Rayleigh regime using the same size distribution. © 2011 Elsevier Ltd.We are grateful to B.T. Draine and P.J. Flatau for making their DDA code available. This work was supported by ‘‘Programa Incentivo a la Investigacion de la UPV’’Vilaplana Cerda, RI.; Luna Molina, R.; Guirado, D. (2011). The shape influence on the overall single scattering properties of a sample in random orientation. Journal of Quantitative Spectroscopy and Radiative Transfer. 112(11):1838-1847. doi:10.1016/j.jqsrt.2011.01.006S183818471121

Counteracting gradients of light and soil nutrients in the understorey of Mediterranean oak forests.

The forest canopy modifies the availability of resources (light, water, and soil nutrients) in the understorey. In this paper we analyze the relationships between woody canopy density, litter accumulation, and topsoil N and P availability in the understorey of two oak forests: one in southern Portugal and the other in southern Spain. Both forests persist on low-nutrient soils, particularly poor in P. We hypothesize that direct and indirect effects of the canopy overstorey cause opposite gradients in the availability of essential resources (light and key soil nutrients) in the understorey. In both studied forests we found significant relationships between the overall canopy density, light availability, topsoil litter accumulation, and the availability of N and P, which frequently limit plant growth. Path analysis (by Shipley’s d-sep method) showed that the available data were consistent with the proposed causal model. The average values of soil variables at the end quartiles of the light-availability gradient were compared. Results showed large differences in litter accumulation (~30×) and available-N and -P topsoil concentrations (~3×) in the Spanish forest (with the wider environmental gradient). Furthermore, P increased from the ‘very low’ range to the ‘low’ or even the ‘optimum’ range of availability (according to standard plant growth criteria), which suggests potential effects on the growth of the understorey plant species. We conclude that the counteracting gradients of the essential resources -light and nutrients- in the forest understorey resulted from direct and indirect effects of the canopy overstorey, respectively. We suggest that these counteracting effects of the woody canopy on essential resources of different nature must be considered when interpreting the patterns of understorey plant populations and communities.The spanish MEC (CGL2005-05830-C03-01-BOS, DINAMED project) and the Portuguese FCT(SFRH/BD/8322/2002 grant to SMM)supported the research.Peer reviewe

Host-Directed Therapies for tackling Multi-Drug Resistant TB – learning from the Pasteur-Bechamp debates

Tuberculosis (TB) remains a global emergency causing an estimated 1.5 million deaths annually. For several decades the major focus of TB treatment has been on antibiotic development targeting Mycobacterium tuberculosis (M.tb). The lengthy TB treatment duration and poor treatment outcomes associated with multi-drug resistant TB (MDR-TB) are of major concern. The sparse new TB drug pipeline and widespread emergence of MDR-TB signal an urgent need for more innovative interventions to improve treatment outcomes. Building on the historical Pasteur-Bechamp debates on the role of the ‘microbe’ versus the ‘host internal milieu’ in disease causation, we make the case for parallel investments into host-directed therapies (HDTs). A range of potential HDTs are now available which require evaluation in randomized controlled clinical trials as adjunct therapies for shortening the duration of TB therapy and improving treatment outcomes for drug-susceptible TB and MDR-TB. Funder initiatives that may enable further research into HDTs are described