On a counterexample to a conjecture by Blackadar

Blackadar conjectured that if we have a split short-exact sequence 0 -> I -> A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex numbers, then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I is split. We will show how to modify their examples to find a non-semiprojective C*-algebra B with a semiprojective ideal J such that B/J is the complex numbers and the quotient map does not split.Comment: 6 page

Evaluating the Effectiveness and Cost-Effectiveness of Seizure Dogs in Persons With Medically Refractory Epilepsy in the Netherlands

__Background:__ Epilepsy is associated with a high disease burden, impacting the lives of people with epilepsy and their caregivers and family. Persons with medically refractory epilepsy experience the greatest burden, suffering from profound physical, psychological, and social consequences. Anecdotal evidence suggests these persons may benefit from a seizure dog. As the training of a seizure dog is a substantial investment, their accessibility is limited in the absence of collective reimbursement as is seen in the Netherlands. Despite sustained interest in seizure dogs, scientific knowledge on their benefits and costs remains scarce. To substantiate reimbursement decisions stronger evidence is required. The EPISODE study aims to provide this evidence by evaluating the effectiveness and cost-effectiveness of seizure dogs in adults with medically refractory epilepsy. __Methods:__ The study is designed as a stepped wedge randomized controlled trial that compares the use of seizure dogs in addition to usual care, with usual care alone. The study includes adults with epilepsy for whom current treatment options failed to achieve seizure freedom. Seizure frequency of participants should be at least two seizures per week, and the seizures should be associated with a high risk of injury or dysfunction. During the 3 year follow-up period, participants receive a seizure dog in a randomized order. Outcome measures are taken at multiple time points both before and after receiving the seizure dog. Seizure frequency is the primary outcome of the study and will be recorded continuously using a seizure diary. Questionnaires measuring seizure severity, quality of life, well-being, resource use, productivity, social participation, and caregiver burden will be completed at baseline and every 3 months thereafter. The study is designed to include a minimum of 25 participants. __Discussion:__ This protocol describes the first randomized controlled trial on seizure dogs. The study will provide comprehensive data on the effectiveness and cost effectiveness of seizure dogs in adults with medically refractory epilepsy. Broader benefits of seizure dogs for persons with epilepsy and their caregivers are taken into account, as well as the welfare of the dogs. The findings of the study can be used to inform decision-makers on the reimbursement of seizure dogs

A Resource‐Based Perspective on Organizational Citizenship and Counterproductive Work Behavior: The Role of Vitality and Core Self‐Evaluations

Although results from cross-sectional between-person studies suggest a differentiation of employees in good and bad performers, recent studies have challenged this assumption by showing that performance is also dependent on more transient states that vary within individuals. Acknowledging that individuals do not only differ in reference to others, but also in reference to themselves, we integrated the between- and within-person approach in the examination of organizational citizenship behavior (OCB) and counterproductive work behavior (CWB). We propose a model informed by conservation of resources theory in which OCB and minor CWB are predicted by within-person variation in one's level of vitality, with these relationships being moderated by trait core self-evaluations (CSE). Moderated multilevel Poisson regression analyses revealed that vitality was positively related with OCB and negatively with minor CWB. CSE moderated the relationship between vitality and OCB so that individuals high in CSE engaged in OCB regardless of their vitality levels; however, contrary to our expectations, CSE did not moderate the relationship between vitality and minor CWB. Together, these findings indicate a complex reality underlying the mechanisms that drive the enactment of OCB and CWB