Algebraically special solutions in AdS/CFT

We investigate the AdS/CFT interpretation of the class of algebraically special solutions of Einstein gravity with a negative cosmological constant. Such solutions describe a CFT living in a 2+1 dimensional time-dependent geometry that, generically, has no isometries. The algebraically special condition implies that the expectation value of the CFT energy-momentum tensor is a local function of the boundary metric. When such a spacetime is slowly varying, the fluid/gravity approximation is valid and one can read off the values of certain higher order transport coefficients. To do this, we introduce a formalism for studying conformal, relativistic fluids in 2+1 dimensions that reduces everything to the manipulation of scalar quantities.Comment: 30 pages + appendices, 2 figures; v2: typos corrected, ref. adde

Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors

We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the analytical computation of all transport coefficients that appear in Navier-Stokes (NS), Bemfica-Disconzi-Noronha-Kovtun (BDNK), and second-order transient hydrodynamic theories. We solve all these formalisms in a Bjorken flow scenario and show that NS and BDNK theories display unphysical features when gradients become sufficiently large. This implies that these hydrodynamic approaches may not be suitable to describe the early stages of heavy ion collisions.Comment: 30 pages, 8 figure

Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: causality and stability

We investigate the causality and stability of three different relativistic dissipative fluid-dynamical formulations emerging from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. For this particular interaction, all transport coefficients of Navier-Stokes, Bemfica-Disconzi-Noronha-Kovtun and second-order transient theories can be computed in analytical form. We first show that Navier-Stokes theory is acausal and unstable regardless of the matching conditions. On the other hand, BDNK theory can be linearly causal and stable for a particular set of matching choices that does not contain the so-called exotic Eckart prescription. In particular, using the Li\'enard-Chipart criterion, we obtain a set of sufficient conditions that guarantee the stability of the theory. Last, second-order transient hydrodynamic theory in Landau matching is shown to be linearly causal and stable.Comment: 21 pages, 5 figure

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one

Method of moments for a relativistic single-component gas

We derive the equations of motion for all the irreducible moments of the single-particle distribution function. We find that these moment equations of motion are highly coupled, with the dynamics of lower-rank moments always being coupled to those of a higher-rank, leading to an endless tower of equations. Considering a massless gas in Bjorken flow, we investigate how this hierarchy of differential equations can be properly truncated and solved.Comment: 21 pages, 5 figure

Co-Degeneracy and Co-Treewidth: Using the Complement to Solve Dense Instances

Clique-width and treewidth are two of the most important and useful graph parameters, and several problems can be solved efficiently when restricted to graphs of bounded clique-width or treewidth. Bounded treewidth implies bounded clique-width, but not vice versa. Problems like Longest Cycle, Longest Path, MaxCut, Edge Dominating Set, and Graph Coloring are fixed-parameter tractable when parameterized by the treewidth, but they cannot be solved in FPT time when parameterized by the clique-width unless FPT = W[1], as shown by Fomin, Golovach, Lokshtanov, and Saurabh [SIAM J. Comput. 2010, SIAM J. Comput. 2014]. For a given problem that is fixed-parameter tractable when parameterized by treewidth, but intractable when parameterized by clique-width, there may exist infinite families of instances of bounded clique-width and unbounded treewidth where the problem can be solved efficiently. In this work, we initiate a systematic study of the parameters co-treewidth (the treewidth of the complement of the input graph) and co-degeneracy (the degeneracy of the complement of the input graph). We show that Longest Cycle, Longest Path, and Edge Dominating Set are FPT when parameterized by co-degeneracy. On the other hand, Graph Coloring is para-NP-complete when parameterized by co-degeneracy but FPT when parameterized by the co-treewidth. Concerning MaxCut, we give an FPT algorithm parameterized by co-treewidth, while we leave open the complexity of the problem parameterized by co-degeneracy. Additionally, we show that Precoloring Extension is fixed-parameter tractable when parameterized by co-treewidth, while this problem is known to be W[1]-hard when parameterized by treewidth. These results give evidence that co-treewidth is a useful width parameter for handling dense instances of problems for which an FPT algorithm for clique-width is unlikely to exist. Finally, we develop an algorithmic framework for co-degeneracy based on the notion of Bondy-Chvátal closure.publishedVersio

Simultaneous Therapy with Intravitreal Dexamethasone Implant and Bevacizumab for the Treatment of Macular Edema

To investigate the safety profile and benefits of a short-term simultaneous treatment regimen combining two drugs—an intravitreal implant of dexamethasone with an intravitreal injection of bevacizumab—in patients with macular edema. This was a retrospective, non-randomized, open-label case series study.  Patients were treated between April 2014 and July 2015 and were diagnosed with recurrent macular edema secondary to diabetic retinopathy and retinal vein occlusion. They underwent simultaneous treatment with an intravitreal injection of bevacizumab (1.25 mg) and an intravitreal implant of dexamethasone (0.7 mg). Patients were evaluated at baseline and at each subsequent visit with a complete ophthalmological examination and spectral-domain optical coherence tomography (OCT) scans. They were examined 24 hours after the treatment, and then followed up after 30 days and 60 days. Twenty patients (representing 20 eyes) were included in the study. At the time of injection (i.e., baseline), the best-corrected visual acuity (BCVA) was 0.758 ± 0.42 logarithm of the minimum angle of resolution (logMAR). It improved significantly to 0.51 ± 0.33 logMAR at 1 month and to 0.5 ± 0.34 logMAR at 2 months (P ≤ 0.03). The median baseline central macular thickness (CMT) was 542 µm (interquartile range, 466 – 751 µm). The median CMT decreased significantly to 321 µm (interquartile range, 288–381 µm) at 1 month and 310 µm (interquartile range, 286 – 354 µm) at 2 months (P ≤ 0.0002). The mean intraocular pressure (IOP) increased from 14.9 ± 2.29 mmHg (at baseline) to 16.5 ± 2.99 mmHg (P = 0.04) after 2 months. Two (10%) eyes showed cataract progression. There were no other ocular or systemic complications for the duration of this study. Simultaneous therapy combining a dexamethasone implant plus bevacizumab for macular edema may be an attractive treatment regimen with an acceptable safety profile

Four problems regarding representable functors

Let $R$, $S$ be two rings, $C$ an $R$-coring and ${}_{R}^C{\mathcal M}$ the category of left $C$-comodules. The category ${\bf Rep}\, ( {}_{R}^C{\mathcal M}, {}_{S}{\mathcal M} )$ of all representable functors ${}_{R}^C{\mathcal M} \to {}_{S}{\mathcal M}$ is shown to be equivalent to the opposite of the category ${}_{R}^C{\mathcal M}_S$. For $U$ an $(S,R)$-bimodule we give necessary and sufficient conditions for the induction functor $U\otimes_R - : {}_{R}^C\mathcal{M} \to {}_{S}\mathcal{M}$ to be: a representable functor, an equivalence of categories, a separable or a Frobenius functor. The latter results generalize and unify the classical theorems of Morita for categories of modules over rings and the more recent theorems obtained by Brezinski, Caenepeel et al. for categories of comodules over corings.Comment: 16 pages, the second versio

Parallel and Distributed Data Management. Introduction

The manipulation and handling of an ever increasing volume of data by current data-intensive applications require novel techniques for e?cient data management. Despite recent advances in every aspect of data management (storage, access, querying, analysis, mining), future applications are expected to scale to even higher degrees, not only in terms of volumes of data handled but also in terms of users and resources, often making use of multiple, pre-existing autonomous, distributed or heterogeneous resources