We present a convenient trick for computing the sizes of clusters within a network. The rationale relies on the mathematics of the geometric series and the fundamental matrix of a Markov Chain.
A family of walks confined to the first orthant whose defining stepset has drift outside of the region can be challenging to sample uniformly at random for large lengths. We address this by generalizing the 2D walk sampler of Lumbroso et al. to handle 3D walks restricted to the first orthant. The sampler includes a visualizer and means to animate the walks.
Rafael Monge-Rojas, Luis A. Barboza, Rulamán Vargas-Quesada
Abstract Background In countries where sugar fortification with vitamin A is mandatory, strategies to reduce the prevalence of overweight/obesity in adolescents that involve lowering added sugar intake could lead to vitamin A inadequate intakes, since vitamin A-fortified sugar for home consumption contributes to a high proportion of this vitamin intake in the adolescent diet. Methods The study employed a hierarchical linear model to perform a mediation analysis on a cross-sectional sample of adolescents (13–18 years old) in the province of San José, Costa Rica. Results Lowering the total energy intake derived from added sugars to less than 10% significantly increases the prevalence of vitamin A inadequate intake in adolescents by 12.1% (from 29.6% to 41.7%). This is explained by the mediation model in which, the reduced adequacy of vitamin A intake is mediated by a reduction in total energy intake derived from added sugars fortified with vitamin A. Conclusions The vitamin A fortification of sugar for household consumption should be reassessed according to the current epidemiological profile in Costa Rica to promote strategies that reduce the prevalence of overweight/obesity in adolescents by lowering the consumption of added sugars without affecting vitamin A intake.
In this paper, we study the problem of deciding whether the total domination number of a given graph $G$ can be reduced using exactly one edge contraction (called 1-Edge Contraction($γ_t$)). We focus on several graph classes and determine the computational complexity of this problem. By putting together these results, we manage to obtain a complete dichotomy for $H$-free graphs.
El presente artículo indaga las maneras en que la comunicación transmedia aunada a la participación ciudadana se constituye en una estrategia para generar y fortalecer procesos de movilización social. Plantea un recorrido teórico y conceptual sobre el concepto de narrativas transmedia en marco de la movilización social y toma como ejemplo para el análisis, por su representatividad y reconocimiento en las dinámicas sociales y culturales, al colectivo de Hip- Hop Casa Kolacho, cuyas acciones se llevan a cabo en la Comuna 13 de Medellín, territorio referente en la producción del Hip-hop en la ciudad. Se investiga además la perspectiva de éstos jóvenes involucrados en la producción cultural y creativa, relacionada con el Hip-Hop en la ciudad de Medellín. Para lograrlo, se llevó a cabo un análisis de redes sociales en el que se presentan contenidos relacionados con las producciones asociadas al Centro Cultural Casa Kolacho, la aplicación de entrevistas y seguimiento de las actividades de algunos graffiteros y miembros del Colectivo Casa Kolacho.
We present a $\sqrt{e}/(\sqrt{e}-1)$-approximation algorithm for the nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on a single machine subject to release dates and precedence constraints. The previously best known approximation algorithm dates back to 1997; its performance guarantee can be made arbitrarily close to the Euler constant $e$.
In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having graceful/odd-graceful labellings.
We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all surfaces, orientable or non-orientable. This general construction requires new ideas and is more delicate than the special orientable case, but carries the same information. It thus gives a uniform combinatorial interpretation of the counting exponent $\frac{5(h-1)}{2}$ for both orientable and non-orientable maps of Euler characteristic $2-2h$ and of the algebraicity of their generating functions. It also shows the universality of the renormalization factor $n$<sup>¼</sup> for the metric of maps, on all surfaces: the renormalized profile and radius in a uniform random pointed bipartite quadrangulation of size $n$ on any fixed surface converge in distribution. Finally, it also opens the way to the study of Brownian surfaces for any compact 2-dimensional manifold.
In this paper we modify an algorithm for updating a maximal clique enumeration after an edge insertion to provide an algorithm that runs in linear time with respect to the number of cliques containing one of the edge's endpoints, whereas existing algorithms take quadratic time.
Sambhu Charan Barman, Sukumar Mondal, Madhumangal Pal
In a graph, a spanning tree is said to be a tree t-spanner of the graph if the distance between any two vertices in is at most times their distance in . The tree t-spanner has many applications in networks and distributed environments. In this paper, an algorithm is presented to find a tree -spanner on trapezoid graphs in time, where is the number of vertices of the graph.
The $\textit{parallel chip-firing game}$ is an automaton on graphs in which vertices "fire'' chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different areas of mathematics including self-organized criticality and the study of the sandpile group. In this work, we study $\textit{firing sequences}$, which describe each vertex's interaction with its neighbors in this game. Our main contribution is a complete characterization of the periodic firing sequences that can occur in a game, which have a surprisingly simple combinatorial description. We also obtain other results about local behavior of the game after introducing the concept of $\textit{motors}$.
The face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity.
A \emph{wheel} is a graph made of a cycle of length at least~4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph $G$ and whose question is "does $G$ contains a wheel as an induced subgraph" is NP-complete. We also settle the complexity of several similar problems.
We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set. Applications of this generic algorithm range from cost minimization to condensed matter physics. In this paper, we analyze the distribution of the bin loads produced by this algorithm, considering, for example, largest and smallest loads, loads of subsets of the bins, and the likelihood of bins having equal loads.
The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of the general linear groups. In particular, we show that the descent set is preserved by Sundaram's correspondence. This gives a direct combinatorial interpretation of the branching rules for the defining representations of the symplectic groups; equivalently, for the Frobenius character of the action of a symmetric group on an isotypic subspace in a tensor power of the defining representation of a symplectic group.
The crossing number of a graph $G$ is the minimum number of pairwise intersections of edges among all drawings of $G$. In this paper, we study the crossing number of $K_{n,n}-nK_2$, $K_n\times P_2$, $K_n\times P_3$ and $K_n\times C_4$.
This paper develops an analytic theory for the study of some Pólya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equations are developed, and when they can be solved, they lead to characterization of the exact distributions underlying the urn evolution. We give a few illustrative examples.