On the asymptotic magnitude of subsets of Euclidean space

Magnitude is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of Euclidean space with finite subsets, the magnitudes of line segments, circles and Cantor sets are defined and calculated. It is observed that asymptotically these satisfy the inclusion-exclusion principle, relating them to intrinsic volumes of polyconvex sets.Comment: 23 pages. Version 2: updated to reflect more recent work, in particular, the approximation method is now known to calculate (rather than merely define) the magnitude; also minor alterations such as references adde

Protective factors as uni- or bipolar factors and their incremental validity and accuracy in predicting general recidivism

This study examined whether protective factors are unique or the opposite of risk factors and whether they have incremental validity in the prediction of general recidivism. Using a sample of 3306 Dutch forensic outpatients, this study was the first large-sample study ever performed on this topic. Results from exploratory factor analyses demonstrated a relatively stable factor structure of 14 factors, consisting of 32 of the initially included 68 risk factors and 11 of the initially included 17 protective items. The protective factors were found to be either bipolar (i.e., mirror images of risk factors) or responsivity characteristics (i.e., motivation for treatment, cognitive disability). Incremental validity for the recidivism prediction was found in one factor with internal protective items (e.g., empathy, financial management, life goals). This factor decreased the recidivism risk by 6%. However, weak predictive accuracy was found for this factor. Implications for clinical forensic practice are discussed with special focus on the risk-need-responsivity model

Multiplayer Cost Games with Simple Nash Equilibria

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We study such games and show that a large class of these games, including games where the individual objectives are mean- or discounted-payoff, or quantitative reachability, and show that they do not only have a solution, but a simple solution. We establish the existence of Nash equilibria that are composed of k memoryless strategies for each agent in a setting with k agents, one main and k-1 minor strategies. The main strategy describes what happens when all agents comply, whereas the minor strategies ensure that all other agents immediately start to co-operate against the agent who first deviates from the plan. This simplicity is important, as rational agents are an idealisation. Realistically, agents have to decide on their moves with very limited resources, and complicated strategies that require exponential--or even non-elementary--implementations cannot realistically be implemented. The existence of simple strategies that we prove in this paper therefore holds a promise of implementability.Comment: 23 page

Driving forces for Ag-induced periodic faceting of vicinal Cu(111)

Adsorption of submonolayer amounts of Ag on vicinal Cu(111) induces periodic faceting. The equilibrium structure is characterized by Ag-covered facets that alternate with clean Cu stripes. In the atomic scale, the driving force is the matching of Ag(111)-like packed rows with Cu(111) terraces underneath. This determines the preference for the facet orientation and the evolution of different phases as a function of coverage. Both Cu and Ag stripe widths can be varied smoothly in the 3-30 nm range by tuning Ag coverage, allowing to test theoretical predictions of elastic theories.Comment: 1 text, 4 figure

Acquired Brain Injury and Interventions in the Offender Population: A Systematic Review

Background and Aims: The prevalence of acquired brain injury (ABI) in offender populations appears much higher than in the general population, being estimated at 50% compared to 12%, respectively. Taking into account ABI-related cognitive and social impairments or behavioral changes in forensic treatments might be relevant and may improve treatment outcomes. The aim of the current review is to summarize and integrate the literature on psychological interventions or treatments for consequences of ABI in the forensic setting. Reviewing this literature could provide crucial information for improving treatment options for offenders with ABI, which may contribute to reducing recidivism. Methods: The PubMed/MEDLINE, PsychInfo, CINAHL, COCHRANE, and Web of Science databases were searched for studies in adult offenders with ABI that evaluated the effect of psychological interventions with a focus on ABI-related impairments and recidivism. Results: This review identified four intervention studies that met the inclusion criteria. These included an adult population (≥18-year-old) in a forensic setting (given the focus of the current review on treatment, defined here as an environment in which offenders are treated while being incarcerated or as outpatients), non-pharmacological treatments and were published in English or Dutch between 2005 and 2020. All studies reported some positive effects of the intervention on interpersonal behavior, cognition and recidivism. The aspects of the interventions that seemed most beneficial included personalized treatment and re-entry plans, support for the individual and their environment and psychoeducation about the effects of ABI. Discussion: Although positive effects were reported in the studies reviewed, all studies had methodological limitations in terms of sample size, study design and outcome measures which affects the strength of the evidence. This limits strong conclusions and generalizability to the entire offender population. Conclusion: Despite high prevalence of ABI in offender populations, interventions in forensic settings seldom address the effect of ABI. The few studies that did take ABI into account reported positive effects, but those results should be interpreted with caution. Future studies are warranted, since this does seem an important venue to improve treatment, which could eventually contribute to reducing recidivism