The balanced 2-median and 2-maxian problems on a tree

This paper deals with the facility location problems with balancing on allocation clients to servers. Two bi-objective models are considered, in which one objective is the traditional p-median or p-maxian objective and the second is to minimize the maximum demand volume allocated to any facility. An edge deletion method with time complexity O(n^2) is presented for the balanced $2$-median problem on a tree. For the balanced 2-maxian problem, it is shown the optimal solution is two end vertices of the diameter of the tree, which can be obtained in a linear time.Comment: 19 page

Helical motors and formins synergize to compact chiral filopodial bundles: A theoretical perspective

Chiral actin bundles have been shown to play an important role in cell dynamics, but our understanding of the molecular mechanisms which combine to generate chirality remains incomplete. To address this, we numerically simulate a crosslinked filopodial bundle under the actions of helical myosin motors and/or formins and examine the collective buckling and twisting of the actin bundle. We first show that a number of proposed mechanisms to buckle polymerizing actin bundles without motor activity fail under biologically-realistic parameters. We then demonstrate that a simplified model of myosin spinning action at the bundle base effectively “braids” the bundle, but cannot control compaction at the fiber tips. Finally, we show that formin-mediated polymerization and motor activity can act synergitically to compact filopodium bundles, as motor activity bends filaments into shapes that activate twist forces induced by formins. Stochastic fluctuations of actin polymerization rates and slower cross linking dynamics both increase buckling and decrease compaction. We discuss implications of our findings for mechanisms of cytoskeletal chirality

On multimodality of obnoxious faclity location models

Obnoxious single facility location models are models that have the aim to find the best location for an undesired facility. Undesired is usually expressed in relation to the so-called demand points that represent locations hindered by the facility. Because obnoxious facility location models as a rule are multimodal, the standard techniques of convex analysis used for locating desirable facilities in the plane may be trapped in local optima instead of the desired global optimum. It is assumed that having more optima coincides with being harder to solve. In this thesis the multimodality of obnoxious single facility location models is investigated in order to know which models are challenging problems in facility location problems and which are suitable for site selection. Selected for this are the obnoxious facility models that appear to be most important in literature. These are the maximin model, that maximizes the minimum distance from demand point to the obnoxious facility, the maxisum model, that maximizes the sum of distance from the demand points to the facility and the minisum model, that minimizes the sum of damage of the facility to the demand points. All models are measured with the Euclidean distances and some models also with the rectilinear distance metric. Furthermore a suitable algorithm is selected for testing multimodality. Of the tested algorithms in this thesis, Multistart is most appropriate. A small numerical experiment shows that Maximin models have on average the most optima, of which the model locating an obnoxious linesegment has the most. Maximin models have few optima and are thus not very hard to solve. From the Minisum models, the models that have the most optima are models that take wind into account. In general can be said that the generic models have less optima than the weighted versions. Models that are measured with the rectilinear norm do have more solutions than the same models measured with the Euclidean norm. This can be explained for the maximin models in the numerical example because the shape of the norm coincides with a bound of the feasible area, so not all solutions are different optima. The difference found in number of optima of the Maxisum and Minisum can not be explained by this phenomenon

A Survey on Approximation Mechanism Design without Money for Facility Games

In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games

A graphical shopping interface bases on product attributes

Most recommender systems present recommended products in lists to the user. By doing so, much information is lost about the mutual similarity between recommended products. We propose to represent the mutual similarities of the recommended products in a two dimensional space, where similar products are located close to each other and dissimilar products far apart. As a dissimilarity measure we use an adaptation of Gower's similarity coefficient based on the attributes of a product. Two recommender systems are developed that use this approach. The first, the graphical recommender system, uses a description given by the user in terms of product attributes of an ideal product. The second system, the graphical shopping interface, allows the user to navigate towards the product he wants. We show a prototype application of both systems to MP3-players

Localización simple de servicios deseados y no deseados en redes con múltiples criterios

Análisis y desarrollo de varios modelos de localización de servicios deseados y no deseados en redes con múltiples criterios. Asimismo, se han propuesto algunas mejoras en modelos de localización de servicios no deseados en redes con un solo criterio. Por consiguiente, con respecto a la localización de servicios deseados sobre redes, se propone un algoritmo polinomial para solucionar el problema del cent-dian biobjetivo. También se ha estudiado la localización de un servicio en una red con múltiples objetivos tipo mediana. Asimismo, se ha desarrollado un algoritmo polinomial para solucionar el problema cent-dian multicriterio en redes con múltiples pesos por nodo y múltiples longitudes por arista. Con respecto a los problemas de localización de servicios no deseados, primero tratamos el problema de localización del 1-centro no deseado en redes. Demostramos que las cotas superiores ya propuestas en trabajos anteriores pueden ser ajustadas. Por medio de una formulación más adecuada del problema, se ha desarrollado un nuevo algoritmo polinomial el cual es más sencillo y computacionalmente más rápido que los ya divulgados en la literatura. También se ha analizado el problema de localizar una mediana no deseada en una red, obteniendo una nueva y mejor cota superior. Se presenta un nuevo algoritmo para solucionar este problema. Por otra parte, siguiendo la resolución del problema maxian, también se ha propuesto un nuevo algoritmo para solucionar el problema del anti-cent-dian en redes. Finalmente, se han estudiado los problemas del centro no deseado y de la mediana no deseada en redes multicriterio, estableciendo nuevas propiedades y reglas para eliminar aristas ineficientes. También se presenta el modelo anti-cent-dian como combinación convexa de los dos últimos problemas. Se propone una regla eficaz para quitar aristas que contienen puntos ineficientes, así como un algoritmo polinomial. Además, este modelo se puede modificar ligeramente para generalizar otros modelos presentados en la literatura

A Lagrangian relaxation approach to the edge-weighted clique problem

The $b$-clique polytope $CP^n_b$ is the convex hull of the node and edge incidence vectors of all subcliques of size at most $b$ of a complete graph on $n$ nodes. Including the Boolean quadric polytope $QP^n$ as a special case and being closely related to the quadratic knapsack polytope, it has received considerable attention in the literature. In particular, the max-cut problem is equivalent with optimizing a linear function over $QP^n_n$. The problem of optimizing linear functions over $CP^n_b$ has so far been approached via heuristic combinatorial algorithms and cutting-plane methods. We study the structure of $CP^n_b$ in further detail and present a new computational approach to the linear optimization problem based on Lucena's suggestion of integrating cutting planes into a Lagrangian relaxation of an integer programming problem. In particular, we show that the separation problem for tree inequalities becomes polynomial in our Lagrangian framework. Finally, computational results are presented. \u

Mapping flagellated swimmers to surface-slip driven swimmers.

Flagellated microswimmers are ubiquitous in natural habitats. Understanding the hydrodynamic behavior of these cells is of paramount interest, owing to their applications in bio-medical engineering and disease spreading. Since the last two decades, computational efforts have been continuously improved to accurately capture the complex hydrodynamic behavior of these model systems. However, modeling the dynamics of such swimmers with fine details is computationally expensive due to the large number of unknowns and the small time-steps required to solve the equations. In this work we propose a method to map fully resolved flagellated microswimmers to coarse, active slip driven swimmers which can be simulated at a reduced computational cost. Using the new method, the slip driven swimmers move with the same velocity, to machine precision, as the flagellated swimmers and generate a similar flow field with a controlled accuracy. The method is validated for swimming patterns near a no-slip boundary, interactions between swimmers and scattering with large obstacles