New lower bounds for the second variable Zagreb index

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randi?, the second Zagreb and the modified Zagreb indices.     

New bounds for locally irregular chromatic index of bipartite and subcubic graphs

A graph is locally irregular if the neighbors of every vertex v have degrees distinct from the degree of v. A locally irregular edge-coloring of a graph G is an (improper) edge-coloring such that the graph induced on the edges of any color class is locally irregular. It is conjectured that three colors suffice for a locally irregular edge-coloring. In the paper, we develop a method using which we prove four colors are enough for a locally irregular edge-coloring of any subcubic graph admiting such a coloring. We believe that our method can be further extended to prove the tight bound of three colors for such graphs. Furthermore, using a combination of existing results, we present an improvement of the bounds for bipartite graphs and general graphs, setting the best upper bounds to 7 and 220, respectively.     

THE INFORMATION TECHNOLOGY REVOLUTION AND THE UNSECURED CREDIT MARKET

The information technology (IT) revolution coincided with the transformation of the U.S. unsecured credit market. Households' borrowing increased rapidly and there was an even faster increase in bankruptcy filings. A risk of default model with asymmetric information and costly screening is introduced to study this period. When information costs are high, the design of contracts under private information prevents some households from borrowing with a risk of default. As information costs drop, households borrow more and bankruptcy filings increase. Quantitative exercises suggest that the IT revolution may have played an important role in the transformation of the unsecured credit market. (JEL E43, E44, G33)     

Initiative in work teams: adaptation and validation of the Personal Initiative at Group Level Scale / Iniciativa en los equipos de trabajo: adaptación y validación de la Escala de Iniciativa Personal a nivel Grupal

In this study, we conceptualize personal initiative as a collective construct and adapt and validate a scale to evaluate it with a sample of 308 Spanish participants belonging to 91 work teams. Personal initiative at group level is a behavioural syndrome in which the team shows an approach to work that is self-initiated, proactive, persistent, capable of modifying the atmosphere and pro organization. As a predictive variable, we analysed the climate for initiative as well as personal initiative at group level. The resulting variables that were analysed referred to organization and team performance, with the team productivity and innovation as the criteria, analysing radical innovation. The scale has suitable psychometric properties. The results show that there is a relationship between the two predictive variables. Furthermore, personal initiative at group level is related to team productivity, while the climate for initiative is related to innovation.     

‘What Was I Thinking?!’ Rhetorical Questions as a Technique to Identify and Explore Impasses in Therapy

Rhetorical questions emerging spontaneously in consultations can be used as a tool for developing self‐reflexivity and exploring the therapeutic alliance in the process of therapy with couples and families. This paper presents a technique based on the enunciation of rhetorical questions, which can point to an impasse in the process of therapy and contain a key to its resolution. The technique focuses on the distinctive feature of rhetorical questions as convening a paradoxical injunction: a question not intended as a question, while uttered as such. The technique in four steps is illustrated by examples from therapy, supervision, consultation, and self‐supervision. Its focus is the interlink between the therapeutic relationship and the process of therapy and it is informed by a second‐order cybernetics approach, dialogical practice, and the systemic literature on emotion. The technique can help develop curiosity in working with families, lead to unforeseen developments, and touch on prejudices not made explicit in previous therapeutic encounters. Whether we are acting as supervisors, therapists, or clients, the creation of a ‘secure enough’ context for rhetorical questions becomes critical to allow freeform exploration.     

Ventriloquism,racism and the politics of decoloniality in Ecuador

ABSTRACT

This article discusses two forms of discrimination against indigenous people: ventriloquism and open racism, and argues that a transition from paternalism to open intolerance has taken place in Ecuador in the context of governmental emphasis on natural resource extraction. Ventriloquism, when non-Indians speak for indigenous people, is analysed through the Sumak Kawsay (Good Living) policies of the government of Rafael Correa (2007–2017). Public racism is examined by looking at government repression against indigenous leaders and communities and Presidential speeches. The article concludes that the state’s ventriloquist and racist discourses and practices are equally rooted in the country’s colonial past. These findings are contrasted with the writings of scholars that have called the government of Mr. Correa decolonizing. The article examines the ways in which decolonial theorists informed and promoted the policies of this regime, and argues that decolonial scholars have been insufficiently self-critical and reflective of their own complicity with the state’s repressive project vis-à-vis indigenous communities.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.