Analyzing imputed financial data: a new approach to cluster analysis

The authors introduce a novel statistical modeling technique to cluster analysis and apply it to financial data. Their two main goals are to handle missing data and to find homogeneous groups within the data. Their approach is flexible and handles large and complex data structures with missing observations and with quantitative and qualitative measurements. The authors achieve this result by mapping the data to a new structure that is free of distributional assumptions in choosing homogeneous groups of observations. Their new method also provides insight into the number of different categories needed for classifying the data. The authors use this approach to partition a matched sample of stocks. One group offers dividend reinvestment plans, and the other does not. Their method partitions this sample with almost 97 percent accuracy even when using only easily available financial variables. One interpretation of their result is that the misclassified companies are the best candidates either to adopt a dividend reinvestment plan (if they have none) or to abandon one (if they currently offer one). The authors offer other suggestions for applications in the field of finance.

On q-power cycles in cubic graphs

International audienceIn the context of a conjecture of Erdős and Gyárfás, we consider, for any $q ≥ 2$, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every $q ≥ 3$, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning the remaining case $q = 2$ (which corresponds to the conjecture of Erdős and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only

On the longest path in a recursively partitionable graph

A connected graph $G$ with order $n \geq 1$ is said to be recursively arbitrarily partitionable (R-AP for short) if either it is isomorphic to $K_1$, or for every sequence $(n_1, \ldots , n_p)$ of positive integers summing up to $n$ there exists a partition $(V_1, \ldots , V_p)$ of $V(G)$ such that each $V_i$ induces a connected R-AP subgraph of $G$ on $n_i$ vertices. Since previous investigations, it is believed that a R-AP graph should be 'almost traceable' somehow. We first show that the longest path of a R-AP graph on $n$ vertices is not constantly lower than $n$ for every $n$. This is done by exhibiting a graph family $\mathcal{C}$ such that, for every positive constant $c \geq 1$, there is a R-AP graph in $\mathcal{C}$ that has arbitrary order $n$ and whose longest path has order $n-c$. We then investigate the largest positive constant $c' \lt 1$ such that every R-AP graph on $n$ vertices has its longest path passing through $n \cdot c'$ vertices. In particular, we show that $c' \leq \frac{2}{3}$. This result holds for R-AP graphs with arbitrary connectivity

A glimpse into the future with orthodontics’ smart brackets

O aparelho ortodôntico fixo tipo multibandas atual não permite medir ‘in-vivo’ as forças e torques aplicados ao dente individual. Para um tratamento ideal e para reduzir os efeitos iatrogênicos, o ‘Smart Bracket’ foi desenvolvido para uma próxima geração de aparelhos ortodônticos fixos fornecendo ao ortodontista uma medida quantitativa sobre as forças e torques aplicados a cada dente ao longo da terapia. O presente trabalho pretende ser uma revisão narrativa da literatura tendo como objetivo descrever o conceito de ‘Smart Bracket’, comparando-o com os aparelhos ortodônticos fixos atuais. Além disso, procura analisar e resumir o seu desenvolvimento e a evolução dos seus vários protótipos existentes. A pesquisa foi realizada entre Fevereiro e Agosto de 2020 por meio do motor de busca B-On (entre outros), para o período temporal 2005-2020, com o objectivo de sintetizar a literatura sobre o sistema, identificar seus limites e, eventualmente, recomendar novos temas de pesquisa. Adicionalmente, artigos de revisão e livros científicos foram consultados a partir de 2000 para apresentar os atuais aparelhos multibandas e seus efeitos iatrogênicos.The current multi-bracket appliances do not allow to measure ‘in-vivo’ the forces and torques applied to the individual tooth. For an ideal treatment and to reduce iatrogenic effects, the ‘Smart Bracket’ has been developed for a next generation of fixed orthodontic appliances providing the orthodontist with quantitative measure of the forces and torques applied to each tooth throughout therapy. The present work intends to be a narrative review of the literature aiming to describe the concept of ‘Smart Bracket’, comparing it with the current fixed orthodontic appliances. In addition, it seeks to analyze and summarize its development and the evolution of its various existing prototypes. The literature research was carried out between February and August 2020 using the search engine B-On (among others), for the period 2005-2020, with the aim of synthesizing the literature on the system, identifying its limits and, eventually, recommend new research topics. In addition, review articles and scientific books were consulted from 2000 onwards to present the current multiband devices and their iatrogenic effects