Generalized cohesiveness

We study some generalized notions of cohesiveness which arise naturally in connection with effective versions of Ramsey's Theorem. An infinite set $A$ of natural numbers is $n$--cohesive (respectively, $n$--r--cohesive) if $A$ is almost homogeneous for every computably enumerable (respectively, computable) $2$--coloring of the $n$--element sets of natural numbers. (Thus the $1$--cohesive and $1$--r--cohesive sets coincide with the cohesive and r--cohesive sets, respectively.) We consider the degrees of unsolvability and arithmetical definability levels of $n$--cohesive and $n$--r--cohesive sets. For example, we show that for all $n \ge 2$, there exists a $\Delta^0_{n+1}$ $n$--cohesive set. We improve this result for $n = 2$ by showing that there is a $\Pi^0_2$ $2$--cohesive set. We show that the $n$--cohesive and $n$--r--cohesive degrees together form a linear, non--collapsing hierarchy of degrees for $n \geq 2$. In addition, for $n \geq 2$ we characterize the jumps of $n$--cohesive degrees as exactly the degrees {\bf \geq \jump{0}{(n+1)}} and show that each $n$--r--cohesive degree has jump {\bf > \jump{0}{(n)}}

Leveraging Group Cohesiveness to Form Workflow Teams

Past literature shows that workflows will be performed with greater efficiency and/or effectiveness if workflow teams have higher group cohesiveness. The major contribution of this work in progress is the creation and implementation of a formal generalized methodology that incorporates ideas from two diverse fields: social network theory and workflow modeling, and allows optimization of work groups along group cohesiveness. In order to implement this model we present newly created algorithms to structure and represent the problem of workflow load representation, possible team sets and social network metric optimization so that standard integer programming solvers can attempt to solve it

Preference stability along time: the time cohesiveness measure

This work introduces a non-traditional perspective about the problem of measuring the stability of agents’ preferences. Specifically, the cohesiveness of preferences at different moments of time is explored under the assumption of considering dichotomous evaluations. The general concept of time cohesiveness measure is introduced as well as a particular formulation based on the consideration of any two successive moments of time, the sequential time cohesiveness measure. Moreover, some properties of the novel measure are also provided. Finally, and in order to emphasize the adaptability of our proposal to real situations, a factual case of study about clinical decision-making is presented. Concretely, the study of preference stability for life-sustaining treatments of patients with advanced cancer at end of life is analysed. The research considers patients who express their opinions on three life-sustaining treatments at four consecutive periods of time. The novel measure provides information of patients preference stability along time and considers the possibility of cancer metastasesEste trabajo forma parte del proyecto de investigación con financiación nacional: MEC-FEDER Grant ECO2016-77900-

Unit-Level Voluntary Turnover Rates and Customer Service Quality: Implications of Group Cohesiveness, Newcomer Concentration, and Size

Despite substantial growth in the service industry and emerging work on turnover consequences, little research examines how unit-level turnover rates affect essential customer-related outcomes. The authors propose an operational disruption framework to explain why voluntary turnover impairs customers’ service quality perceptions. Based on a sample of 75 work units and data from 5,631 employee surveys, 59,602 customer surveys, and organizational records, results indicate that unit-level voluntary turnover rates are negatively related to service quality perceptions. The authors also examine potential boundary conditions related to the disruption framework. Of three moderators studied (group cohesiveness, group size, and newcomer concentration), results show that turnover’s negative effects on service quality are more pronounced in larger units and in those with a greater concentration of newcomers

The weakness of being cohesive, thin or free in reverse mathematics

Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this paper, we investigate the lack of robustness of Ramsey's theorem and its consequence under the frameworks of reverse mathematics and computable reducibility. To this end, we study the degrees of unsolvability of cohesive sets for different uniformly computable sequence of sets and identify different layers of unsolvability. This analysis enables us to answer some questions of Wang about how typical sets help computing cohesive sets. We also study the impact of the number of colors in the computable reducibility between coloring statements. In particular, we strengthen the proof by Dzhafarov that cohesiveness does not strongly reduce to stable Ramsey's theorem for pairs, revealing the combinatorial nature of this non-reducibility and prove that whenever $k$ is greater than $\ell$, stable Ramsey's theorem for $n$-tuples and $k$ colors is not computably reducible to Ramsey's theorem for $n$-tuples and $\ell$ colors. In this sense, Ramsey's theorem is not robust with respect to his number of colors over computable reducibility. Finally, we separate the thin set and free set theorem from Ramsey's theorem for pairs and identify an infinite decreasing hierarchy of thin set theorems in reverse mathematics. This shows that in reverse mathematics, the strength of Ramsey's theorem is very sensitive to the number of colors in the output set. In particular, it enables us to answer several related questions asked by Cholak, Giusto, Hirst and Jockusch.Comment: 31 page

When Do People Trust Their Social Groups?

Trust facilitates cooperation and supports positive outcomes in social groups, including member satisfaction, information sharing, and task performance. Extensive prior research has examined individuals' general propensity to trust, as well as the factors that contribute to their trust in specific groups. Here, we build on past work to present a comprehensive framework for predicting trust in groups. By surveying 6,383 Facebook Groups users about their trust attitudes and examining aggregated behavioral and demographic data for these individuals, we show that (1) an individual's propensity to trust is associated with how they trust their groups, (2) smaller, closed, older, more exclusive, or more homogeneous groups are trusted more, and (3) a group's overall friendship-network structure and an individual's position within that structure can also predict trust. Last, we demonstrate how group trust predicts outcomes at both individual and group level such as the formation of new friendship ties.Comment: CHI 201

Unsolvability Cores in Classification Problems

Classification problems have been introduced by M. Ziegler as a generalization of promise problems. In this paper we are concerned with solvability and unsolvability questions with respect to a given set or language family, especially with cores of unsolvability. We generalize the results about unsolvability cores in promise problems to classification problems. Our main results are a characterization of unsolvability cores via cohesiveness and existence theorems for such cores in unsolvable classification problems. In contrast to promise problems we have to strengthen the conditions to assert the existence of such cores. In general unsolvable classification problems with more than two components exist, which possess no cores, even if the set family under consideration satisfies the assumptions which are necessary to prove the existence of cores in unsolvable promise problems. But, if one of the components is fixed we can use the results on unsolvability cores in promise problems, to assert the existence of such cores in general. In this case we speak of conditional classification problems and conditional cores. The existence of conditional cores can be related to complexity cores. Using this connection we can prove for language families, that conditional cores with recursive components exist, provided that this family admits an uniform solution for the word problem

A new measure for community structures through indirect social connections

Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is generated from the number of existing triangles around the nodes over the number of triangles that can be hypothetically constructed. This paper provides a new definition of the clustering coefficient for weighted networks under a generalized definition of triangles. Specifically, a novel concept of triangles is introduced, based on the assumption that, should the aggregate weight of two arcs be strong enough, a link between the uncommon nodes can be induced. Beyond the intuitive meaning of such generalized triangles in the social context, we also explore the usefulness of them for gaining insights into the topological structure of the underlying network. Empirical experiments on the standard networks of 500 commercial US airports and on the nervous system of the Caenorhabditis elegans support the theoretical framework and allow a comparison between our proposal and the standard definition of clustering coefficient