Objective: the aim of this longitudinal study was to evaluate the impact of COVID-19 epidemic on Eating Disorders (EDs) patients, considering the role of pre-existing vulnerabilities. Method: 74 patients with Anorexia Nervosa (AN) or Bulimia Nervosa (BN) and 97 healthy controls (HCs) were evaluated before lockdown (T1) and during lockdown (T2). Patients were also evaluated at the beginning of treatment (T0). Questionnaires were collected to assess psychopathology, childhood trauma, attachment style, and COVID-19-related post-traumatic symptoms. Results: A different trend between patients and HCs was observed only for pathological eating behaviors. Patients experienced increased compensatory exercise during lockdown; BN patients also exacerbated binge eating. Lockdown interfered with treatment outcomes: the descending trend of ED-specific psychopathology was interrupted during the epidemic in BN patients. Previously remitted patients showed re-exacerbation of binge eating after lockdown. Household arguments and fear for the safety of loved ones predicted increased symptoms during the lockdown. BN patients reported more severe COVID-19-related post-traumatic symptomatology than AN and HCs, and these symptoms were predicted by childhood trauma and insecure attachment. Discussion: COVID-19 epidemic significantly impacted on EDs, both in terms of post-traumatic symptomatology and interference with the recovery process. Individuals with early trauma or insecure attachment were particularly vulnerable.

Abstract.In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a conditional event E|H is looked at as a three-valued quantity with values 1, or 0, or p, where p is the probability of E|H. We introduce a notion of iterated conditional random quantity of the form (X|H)|K defined as a suitable conditional random quantity, which coincides with X|HK when H ⊆ K. Based on a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity. We examine some cases of logical dependencies, by also showing that the conjunction may be a conditional event; moreover, we introduce the negation of the conjunction and by De Morgan's Law the operation of disjunction. Finally, we give the lower and upper bounds for the conjunction and the disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold.

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a complementary dual function which we call "extropy." The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of distinct measures for any quantity that is not merely an event indicator. As with entropy, the maximum extropy distribution is also the uniform distribution, and both measures are invariant with respect to permutations of their mass functions. However, they behave quite differently in their assessments of the refinement of a distribution, the axiom which concerned Shannon and Jaynes. Their duality is specified via the relationship among the entropies and extropies of course and fine partitions. We also analyze the extropy function for densities, showing that relative extropy constitutes a dual to the Kullback-Leibler divergence, widely recognized as the continuous entropy measure. These results are unified within the general structure of Bregman divergences. In this context they identify half the $L_2$ metric as the extropic dual to the entropic directed distance. We describe a statistical application to the scoring of sequential forecast distributions which provoked the discovery.Comment: Published at http://dx.doi.org/10.1214/14-STS430 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults