Essential Constraints of Edge-Constrained Proximity Graphs

Given a plane forest $F = (V, E)$ of $|V| = n$ points, we find the minimum set $S \subseteq E$ of edges such that the edge-constrained minimum spanning tree over the set $V$ of vertices and the set $S$ of constraints contains $F$. We present an $O(n \log n )$-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabriel graph, $\beta$-skeleton and Delaunay triangulation. We present an algorithm that identifies the minimum set $S\subseteq E$ of edges of a given plane graph $I=(V,E)$ such that $I \subseteq CG_\beta(V, S)$ for $1 \leq \beta \leq 2$, where $CG_\beta(V, S)$ is the constraint $\beta$-skeleton over the set $V$ of vertices and the set $S$ of constraints. The running time of our algorithm is $O(n)$, provided that the constrained Delaunay triangulation of $I$ is given.Comment: 24 pages, 22 figures. A preliminary version of this paper appeared in the Proceedings of 27th International Workshop, IWOCA 2016, Helsinki, Finland. It was published by Springer in the Lecture Notes in Computer Science (LNCS) serie

A Multi-Objective Optimization for Supply Chain Network Using the Bees Algorithm

A supply chain is a complex network which involves the products, services and information flows between suppliers and customers. A typical supply chain is composed of different levels, hence, there is a need to optimize the supply chain by finding the optimum configuration of the network in order to get a good compromise between the multi-objectives such as cost minimization and lead-time minimization. There are several multi-objective optimization methods which have been applied to find the optimum solutions set based on the Pareto front line. In this study, a swarm-based optimization method, namely, the bees algorithm is proposed in dealing with the multi-objective supply chain model to find the optimum configuration of a given supply chain problem which minimizes the total cost and the total lead-time. The supply chain problem utilized in this study is taken from literature and several experiments have been conducted in order to show the performance of the proposed model; in addition, the results have been compared to those achieved by the ant colony optimization method. The results show that the proposed bees algorithm is able to achieve better Pareto solutions for the supply chain problem

The Dropping of In-Medium Hadron Mass in Holographic QCD

We study the baryon density dependence of the vector meson spectrum using the D4/D6 system together with the compact D4 baryon vertex. We find that the vector meson mass decreases almost linearly in density at low density for small quark mass, but saturates to a finite non-zero value for large density. We also compute the density dependence of the $\eta\prime$ mass and the $\eta\prime$ velocity. We find that in medium, our model is consistent with the GMOR relation up to a few times the normal nuclear density. We compare our hQCD predictions with predictions made based on hidden local gauge theory that is constructed to model QCD.Comment: 20 pages, 7 figure

Power-Law Distributions in a Two-sided Market and Net Neutrality

"Net neutrality" often refers to the policy dictating that an Internet service provider (ISP) cannot charge content providers (CPs) for delivering their content to consumers. Many past quantitative models designed to determine whether net neutrality is a good idea have been rather equivocal in their conclusions. Here we propose a very simple two-sided market model, in which the types of the consumers and the CPs are {\em power-law distributed} --- a kind of distribution known to often arise precisely in connection with Internet-related phenomena. We derive mostly analytical, closed-form results for several regimes: (a) Net neutrality, (b) social optimum, (c) maximum revenue by the ISP, or (d) maximum ISP revenue under quality differentiation. One unexpected conclusion is that (a) and (b) will differ significantly, unless average CP productivity is very high

Cooper pairing near charged black holes

We show that a quartic contact interaction between charged fermions can lead to Cooper pairing and a superconducting instability in the background of a charged asymptotically Anti-de Sitter black hole. For a massless fermion we obtain the zero mode analytically and compute the dependence of the critical temperature T_c on the charge of the fermion. The instability we find occurs at charges above a critical value, where the fermion dispersion relation near the Fermi surface is linear. The critical temperature goes to zero as the marginal Fermi liquid is approached, together with the density of states at the Fermi surface. Besides the charge, the critical temperature is controlled by a four point function of a fermionic operator in the dual strongly coupled field theory.Comment: 1+33 pages, 4 figure

Shear Modes, Criticality and Extremal Black Holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference

Holographic DC conductivities from the open string metric

We study the DC conductivities of various holographic models using the open string metric (OSM), which is an effective metric geometrizing density and electromagnetic field effect. We propose a new way to compute the nonlinear conductivity using OSM. As far as the final conductivity formula is concerned, it is equivalent to the Karch-O'Bannon's real-action method. However, it yields a geometrical insight and technical simplifications. Especially, a real-action condition is interpreted as a regular geometry condition of OSM. As applications of the OSM method, we study several holographic models on the quantum Hall effect and strange metal. By comparing a Lifshitz background and the Light-Cone AdS, we show how an extra parameter can change the temperature scaling behavior of conductivity. Finally we discuss how OSM can be used to study other transport coefficients, such as diffusion constant, and effective temperature induced by the effective world volume horizon.Comment: 33 page

Algorithms for Colourful Simplicial Depth and Medians in the Plane

The colourful simplicial depth of a point x in the plane relative to a configuration of n points in k colour classes is exactly the number of closed simplices (triangles) with vertices from 3 different colour classes that contain x in their convex hull. We consider the problems of efficiently computing the colourful simplicial depth of a point x, and of finding a point, called a median, that maximizes colourful simplicial depth. For computing the colourful simplicial depth of x, our algorithm runs in time O(n log(n) + k n) in general, and O(kn) if the points are sorted around x. For finding the colourful median, we get a time of O(n^4). For comparison, the running times of the best known algorithm for the monochrome version of these problems are O(n log(n)) in general, improving to O(n) if the points are sorted around x for monochrome depth, and O(n^4) for finding a monochrome median.Comment: 17 pages, 8 figure

Holographic zero sound at finite temperature in the Sakai-Sugimoto model

In this paper, we study the fate of the holographic zero sound mode at finite temperature and non-zero baryon density in the deconfined phase of the Sakai-Sugimoto model of holographic QCD. We establish the existence of such a mode for a wide range of temperatures and investigate the dispersion relation, quasi-normal modes, and spectral functions of the collective excitations in four different regimes, namely, the collisionless quantum, collisionless thermal, and two distinct hydrodynamic regimes. For sufficiently high temperatures, the zero sound completely disappears, and the low energy physics is dominated by an emergent diffusive mode. We compare our findings to Landau-Fermi liquid theory and to other holographic models.Comment: 1+24 pages, 19 figures, PDFTeX, v2: some comments and references added, v3: some clarifications relating to the different regimes added, matches version accepted for publication in JHEP, v4: corrected typo in eq. (3.18

Active wetting of epithelial tissues

Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between 2D epithelial monolayers and 3D spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phenomena. By combining an active polar fluid model with measurements of physical forces as a function of tissue size, contractility, cell-cell and cell-substrate adhesion, and substrate stiffness, we show that the wetting transition results from the competition between traction forces and contractile intercellular stresses. This competition defines a new intrinsic lengthscale that gives rise to a critical size for the wetting transition in tissues, a striking feature that has no counterpart in classical wetting. Finally, we show that active shape fluctuations are dynamically amplified during tissue dewetting. Overall, we conclude that tissue spreading constitutes a prominent example of active wetting --- a novel physical scenario that may explain morphological transitions during tissue morphogenesis and tumor progression