A Note on Flips in Diagonal Rectangulations

Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns { 3{14}2, 2{41}3 }. This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms

A new meta-module for efficient reconfiguration of hinged-units modular robots

We present a robust and compact meta-module for edge-hinged modular robot units such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, as well as for central-point-hinged ones such as Molecubes and Roombots. Thanks to the rotational degrees of freedom of these units, the novel meta-module is able to expand and contract, as to double/halve its length in each dimension. Moreover, for a large class of edge-hinged robots the proposed meta-module also performs the scrunch/relax and transfer operations required by any tunneling-based reconfiguration strategy, such as those designed for Crystalline and Telecube robots. These results make it possible to apply efficient geometric reconfiguration algorithms to this type of robots. We prove the size of this new meta-module to be optimal. Its robustness and performance substantially improve over previous results.Peer ReviewedPostprint (author's final draft

Bottom-up approach to manage customers, product categories, and brands simultaneously

One of the most relevant marketing objectives is to create value for both to and from customer (Kumar & Reinartz, 2016). In order to create value for customers, marketers develop and manage product categories and brands to deliver the intended value proposition. In turn, customer-centric practices aim to extract value from customers in the form of customer lifetime value (Kumar & Reinartz, 2016). Although these levels of decision-making – customer, product category, and brand – are clearly intertwined, extant marketing research has mostly addressed them separately. In this PhD dissertation, a collection of three papers is presented with the main objective of proposing and empirically applying a framework to manage customers, product categories, and brands simultaneously. The first paper is a conceptual paper in which a customer, product category, and brand (CPB) bottom-up approach is proposed to unify the performance assessment of these three perspectives and managerial implications of applying it are provided. In the second paper, methods based on the traditional recency, frequency, and monetary value (RFM) method (Fader, Hardie, & Lee, 2005b; Fader, Hardie, & Shang, 2010) are proposed to estimate customer values per product category (RFM/P). Using these methods, the CPB bottom-up approach was partially addressed, considering only customer and product category perspectives, and empirically applied using data from a financial services company and a supermarket. One of the most relevant marketing objectives is to create value for both to and from customer (Kumar & Reinartz, 2016). In order to create value for customers, marketers develop and manage product categories and brands to deliver the intended value proposition. In turn, customer-centric practices aim to extract value from customers in the form of customer lifetime value (Kumar & Reinartz, 2016). Although these levels of decision-making – customer, product category, and brand – are clearly intertwined, extant marketing research has mostly addressed them separately. In this PhD dissertation, a collection of three papers is presented with the main objective of proposing and empirically applying a framework to manage customers, product categories, and brands simultaneously. The first paper is a conceptual paper in which a customer, product category, and brand (CPB) bottom-up approach is proposed to unify the performance assessment of these three perspectives and managerial implications of applying it are provided. In the second paper, methods based on the traditional recency, frequency, and monetary value (RFM) method (Fader, Hardie, & Lee, 2005b; Fader, Hardie, & Shang, 2010) are proposed to estimate customer values per product category (RFM/P). Using these methods, the CPB bottom-up approach was partially addressed, considering only customer and product category perspectives, and empirically applied using data from a financial services company and a supermarket. The results show a better predictive accuracy of the proposed RFM/P methods over traditional RFM ones and novel managerial analyses are provided. Finally, in the third paper, the method used in the second paper is extended to additionally incorporate bran was highlighted and, through various analyses, key managerial insights that would not be possible using extant methods are provided to drive marketing efforts and increase profitability.Um dos mais relevantes objetivos do marketing é criar valor tanto a partir do cliente quanto para o cliente (Kumar & Reinartz, 2016). Para criar valor para o cliente, profissionais de marketing desenvolvem e gerem categorias de produtos e marcas para entregar a proposição de valor pretendida. Por outro lado, práticas centradas no cliente objetivam extrair valor dos clientes sob a forma de customer lifetime value. Embora esses níveis de tomada de decisão – clientes, categorias de produtos e marcas – sejam claramente interligados, pesquisas anteriores têm, na maioria dos casos, endereçado essas perceptivas separadamente. Nesta dissertação, uma coleção de três artigos é apresentada com o objetivo principal de propor e aplicar empiricamente uma abordagem para gerir simultaneamente clientes, categorias de produtos e marcas. O primeiro artigo é um artigo teórico no qual uma abordagem de gestão de baixo para cima de clientes, categorias de produtos e marcas é proposta para unificar a mensuração de performance dessas três perspectivas e implicações gerenciais a partir da adoção dessa abordagem são providas. No segundo artigo, métodos baseados no tradicional método de recência, frequência e valor monetário (RFM) (Fader Hardie, & Lee, 2005b; Fader, Hardie, & Shang, 2010) são propostos para estimar o valor dos clientes por categoria de produto (RFM/P). Usando esses métodos, a abordagem de gestão de baixo para cima de clientes, categorias de produtos e marcas foi parcialmente endereçada, considerando apenas clientes e categorias de produtos, e aplicada empiricamente usando dados de uma empresa de serviços financeiros e de um supermercado. Os resultados evidenciam uma melhor acurácia preditiva dos métodos RFM/P propostos sobre os tradicionais métodos RFM e novas análises gerenciais são apresentadas. Finalmente, no terceiro artigo, um dos modelos usados no segundo artigo é estendido para adicionalmente incorporar a marca na abordagem de gestão de baixo para 9 cima de clientes, categorias de produtos e marcas. Esse método é aplicado usando os dados de uma empresa tradicionalmente centrada em produtos, uma grande distribuidora de bens de consumo embalados. Novamente, a performance preditiva obtida foi maior do que aquela do tradicional método RFM. Além disso, a relevância da abordagem de gestão de baixo para cima de clientes, categorias de produtos e marcas foi destacada e, por meio de diversas análises, implicações gerenciais chave que não seriam possíveis utilizando métodos tradicionais foram desenvolvidas para direcionar os esforços de marketing e aumentar a lucratividade

Production matrices for geometric graphs

We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.Postprint (updated version

Space-Time Trade-offs for Stack-Based Algorithms

In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space bottleneck is a stack into memory-constrained algorithms. Given an algorithm \alg\ that runs in O(n) time using $\Theta(n)$ variables, we can modify it so that it runs in $O(n^2/s)$ time using a workspace of O(s) variables (for any $s\in o(\log n)$) or $O(n\log n/\log p)$ time using $O(p\log n/\log p)$ variables (for any $2\leq p\leq n$). We also show how the technique can be applied to solve various geometric problems, namely computing the convex hull of a simple polygon, a triangulation of a monotone polygon, the shortest path between two points inside a monotone polygon, 1-dimensional pyramid approximation of a 1-dimensional vector, and the visibility profile of a point inside a simple polygon. Our approach exceeds or matches the best-known results for these problems in constant-workspace models (when they exist), and gives the first trade-off between the size of the workspace and running time. To the best of our knowledge, this is the first general framework for obtaining memory-constrained algorithms

How land title affects child labor ?

Secure property rights are considered a key determinant of economic development. However, evaluation of the causal effects of land titling is a difficult task. Since 2004, the Brazilian government, through a program called"Papel Passado,"has issued titles to more than 85,000 families and has the goal to reach 750,000. Another topic in public policy that is crucial for developing economies is child labor force participation. In Brazil, about 5.4 million children and teenagers between 5 and 17 years old are working full time. This paper examines the direct impact of securing a property title on child labor force participation. In order to isolate the causal role of ownership security, this study uses a comparison between two close and similar communities in the City of Osasco case (a town with 650,000 people in the São Paulo metropolitan area). The key point of this case is that some units participate in the program and others do not. One of them, Jardim Canaã, received land titles in 2007; the other, Jardim DR, given fiscal constraints, will not be part of the program until 2012, and for that reason became the control group. Estimates, generated using the difference-in-difference econometric technique suggest that titling results in a substantial decrease in child labor force participation for the families that received the title compared with the others. These findings are relevant for future policy tools for dealing with informality and how it affects economic growth.Labor Policies,Access to Finance,,Debt Markets,Gender and Law

Computing Optimal Shortcuts for Networks

We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable attention recently, mostly for discrete variants of the problem. We study a fully continuous setting, where all points on the network and the inserted segment must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model, together with several results for networks that are paths, restricted to two types of shortcuts: shortcuts with a fixed orientation and simple shortcuts