A new order on embedded coalitions: Properties and Applications

Given a finite set of agents, an embedded coalition consists of a coalition and a partition of the rest of agents. We study a partial order on the set of embedded coalitions of a finite set of agents. An embedded coalition precedes another one if the first coalition is contained in the second and the second partition equals the first one after removing the agents in the second coalition. This poset is not a lattice. We describe the maximal lower bounds and minimal upper bounds of a finite subset, whenever they exist. It is a graded poset and we are able to count the number of elements at a given level as well as the total number of chains. The study of this structure allows us to derive results for games with externalities. In particular, we introduce a new concept of convexity and show that it is equivalent to having non-decreasing contributions to embedded coalitions of increasing size

Marginality and convexity in partition function form games

In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convex

Complete null agent for games with externalities

Game theory provides valuable tools to examine expert multi-agent systems. In a cooperative game, collaboration among agents leads to better outcomes. The most important solution for such games is the Shapley value, that coincides with the expected marginal contribution assuming equiprobability. This assumption is not plausible when externalities are present in an expert system. Generalizing the concept of marginal contributions, we propose a new family of Shapley values for situations with externalities. The properties of the Shapley value offer a rationale for its application. This family of values is characterized by extensions of Shapley's axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externalities. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, and characterize it by two additional properties

Two families of values for global games

We propose new point valued solutions for global games. We explore the implications of weakening some of the properties used by Gilboa and Lehrer (1991) in their characterization result. Our main contributions are the axiomatic characterizations of two families of values for global games

The family of lattice structure values for games with externalities

We propose and characterize a new family of Shapley values for games with coalitional externalities. To define it we generalize the concept of marginal contribution by using a lattice structure on the set of embedded coalitions. The family of lattice structure values is characterized by extensions of Shapley's axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externalities. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, which delivers balanced payoffs and characterize it by two additional properties

On Convexity in Games with Externalities

We introduce new notions of superadditivity and convexity for games with coalitional externalities. We show parallel results to the classic ones for transferable utility games without externalities. In superadditive games the grand coalition is the most efficient organization of agents. The convexity of a game is equivalent to having non decreasing contributions to larger embedded coalitions. We also see that convex games can only have negative externalitie

Some structural properties of a lattice of embedded coalitions

In this paper we investigate some structural properties of the order on the set of embedded coalitions outlined in de Clippel and Serrano (2008). Besides, we characterize the scalars associated to the basis they proposed of the vector space of partition function form games

Prospective clinical and DaT-SPECT imaging in premotor LRRK2 G2019S-associated Parkinson disease

Objective: To assess the value of baseline clinical and imaging biomarkers in a cohort of asymptomatic LRRK2 G2019S carriers for predicting conversion to Parkinson disease (PD) at 4 years. Methods: Thirty-two asymptomatic carriers of LRRK2 G2019S mutation underwent baseline and 4-year evaluation including clinical examination (Unified Parkinson?s Disease Rating Scale, part III, olfaction University of Pennsylvania Smell Identification Test [UPSIT]) and dopamine transporter (DaT) SPECT (123I-ioflupane). Visual and semiquantitative analysis of images was performed. The specific striatal binding ratio was calculated (striatal region of interest [ROI] 2 occipital ROI/ occipital ROI). Results: Three carriers, asymptomatic at baseline, had converted to PD at 4-year evaluation. Twenty-three participants were fully evaluated. PD converters had lower striatal DaT binding at baseline than nonconverters (p 50.002). A baseline scan with a ratio of bilateral striatal uptake below 1 predicted conversion to PD within the 4-year period with high sensitivity and specificity (area under the curve 1; p 5 0.006). The slope of DaT binding decline between the 2 scans was similar in PD converters and nonconverters. Age-adjusted UPSIT score at baseline and at 4 years was similar in both groups. Conclusions: Semiquantitative DaT-SPECT could be used to predict early conversion to PD in asymptomatic carriers of the LRRK2 G2019S mutation. Rate of conversion to PD at 4 years in this cohort aged ;64 years was 12%. The slope of DaT binding decline on DaT-SPECT imaging seems to be similar across different stages of the premotor perio

18F-FDG PET/CT in the follow-up of large-vessel vasculitis: A study of 37 consecutive patients

Objective 18F-FDG PET/CT has proved to be of potential value for early diagnosis of large-vessel vasculitis (LVV), which frequently involves the aorta. However, its role in the follow-up of these patients has not been well established. Our aim was to evaluate the contribution of 18F-FDG PET/CT in this clinical situation. Methods This study included 37 consecutive patients (28 women, 66.5 ± 9.9 years) with an initial 18F-FDG PET/CT positive for LVV and a mean ± standard deviation follow-up PET/CT of 7.5 ± 2.9 months after the initial scan. A semiquantitative analysis of aortic wall uptake was performed calculating the target-to-background ratio (TBR: aortic wall uptake divided by blood pool uptake). The initial and follow-up TBR as well as the clinical and laboratory outcome were compared. Results Overall, the mean TBR decreased from 1.7 ± 0.5 at the initial scan to 1.5 ± 0.3 at the time of follow-up (p = 0.0001). In the 21 patients who experienced clinical improvement following therapy the TBR also decreased from 1.8 ± 0.6 to 1.5 ± 0.3 (p = 0.0002). However, in the other 16 patients, in whom the treating physician considered that there was no clinical improvement following therapy, no statistically significant differences in TBR were found when data from the first and the follow-up PET/CT scans were compared (1.6 ± 0.3 versus 1.5 ± 0.3, p = 0.1416). Patients who experienced clinical improvement following therapy showed a nonstatistically significant higher TBR at the time of disease diagnosis (1.8 ± 0.6 versus 1.6 ± 0.3; p = 0.12). Conclusions The results obtained in the present study highlight the impact of 18F-FDG PET/CT on the management of patients with LVV.Professor Gonzalez-Gay´s research was supported by “Fondo de Investigación Sanitaria” (grant PI12/00060 and PI15/00525) from “Instituto de Salud Carlos III” (ISCIII, Health Ministry, Spain). His work is also partially supported by RETICS Programs RD12/0009 (RIER) from ISCIII (Spain) (RD16/0012/0009)

Schoolbag weight carriage in Portuguese children and adolescents: a cross-sectional study comparing possible influencing factors

Background Schoolbags and the consequences of carrying them, particularly those associated with overload, are often studied as a health concern. Modifications in gait and posture were reported when children carried loads that corresponded to more than 10% of their body weight (BW). The aims of this study were to verify the load that is carried by Portuguese students and how it is influenced by factors such as school grade, school schedule, lunch site, physical education, sex and body mass index (BMI). Acquiring a more specific knowledge of the Portuguese context and understanding the influence of these factors may allow us to generate proposals to control them in ways that benefit students.MethodsThe load carried by students in the 5th grade (10.60.4years) and 9th grade (14.70.6years) were weighed with a luggage scale on all days of the week, resulting in 680 evaluations. Data related to the school day were also collected, such as the student's lunch site, how he or she got to school and his or her school schedule for that day. Individual height and weight were also assessed. Results The 5th grade students carried greater loads than the 9th grade students, resulting in a substantial difference relative to their BW. The school loads of the 5th grade students were mostly greater than 10% of their BWs. Girls tended to carry heavier loads than boys, and overweight students also tended to carry heavier loads. Students who could eat lunch at home carried less weight, and on physical education days, the total load carried increased, but the backpacks of the 5th grade students were lighter.Conclusions The results of the current study describe excessive schoolbag weight among Portuguese students and expound on some of the factors that influence it, which can help researchers and professionals design a solution to decrease children's schoolbag loads.Funds through FCT - Portuguese Foundation for Science and Technology (UID/DTP/04045/2019) - and the European Fund for regional development (FEDER) allocated by European Union through the COMPETE 2020 Programme (POCI-01-0145-FEDER-006969), and through the Project NanoSTIMA: Macro-to-Nano Human Sensing, Towards Integrated Multimodal Health Monitoring and Analytics (NORTE-01-0145-FEDER-000016), co-financed by Fundo Europeu de Desenvolvimento Regional (FEDER) -NORTE 2020