Proving equivalence between imperative and MapReduce implementations using program transformations

Distributed programs are often formulated in popular functional frameworks like MapReduce, Spark and Thrill, but writing efficient algorithms for such frameworks is usually a non-trivial task. As the costs of running faulty algorithms at scale can be severe, it is highly desirable to verify their correctness. We propose to employ existing imperative reference implementations as specifications for MapReduce implementations. To this end, we present a novel verification approach in which equivalence between an imperative and a MapReduce implementation is established by a series of program transformations. In this paper, we present how the equivalence framework can be used to prove equivalence between an imperative implementation of the PageRank algorithm and its MapReduce variant. The eight individual transformation steps are individually presented and explained

Early Detection of Bipolar Disorders: Current State of the Art and Research Approaches

Bipolar affective disorders (BD) are severe, recurrent and disabling disorders with devastating consequences for individuals, families and the society. Although this personal burden and costs for the health system provide a compelling rationale for development of early detection and early intervention strategies in BD, the development of at-risk criteria for BD is still in an early stage of research. In this paper we review the literature of clinical data that investigate at-risk criteria. Moreover, we will discuss methodological problems associated with the definition of being at high-risk for developing bipolar disorders and show the different research approaches that deal with the investigation of at-risk criteria and appropriate intervention for BD. If prospective studies confirm the at-risk criteria for BD, then there is potential to develop preventive measures in BD with opportunities to ameliorate the severity of or even prevent BD

Challenging control over emotions in borderline personality disorder: A tDCS study

Background: Deficient cognitive control (CC) over emotional distraction is a central characteristic of borderline personality disorder (BPD). Reduced activation of the left dorsolateral prefrontal cortex (dlPFC) has been linked to this deficit. This study investigates whether it is possible to ameliorate CC deficits via anodal tDCS over the left dlPFC in BPD. Furthermore, we investigate whether the extent of CC impairment influences how well one responds to tDCS. Methods: The effect of a single-session tDCS (1 mA for 20 min, reference electrode on the contralateral mastoid bone) to the left dlPFC (F3) on the CC of patients with BPD (N = 20) and healthy control participants (HCs, N = 20) was examined in a double-blinded, balanced randomized, sham-controlled crossover trial. A delayed response working memory task with negative, neutral and positive pictures presented during the delay period was conducted to assess CC. Stimulation was applied simultaneously with the task. Results: Negative pictures caused prolonged response times as compared to a control condition in patients with BPD and HCs. Anodal tDCS to the left dlPFC did not significantly reduce this interference effect in the overall sample. Further analyses showed, however, that participants with impaired CC profited the most from anodal tDCS. In the subgroup of participants who actually showed an interference effect we found the expected significant amelioration of CC under tDCS. Conclusions: The present study demonstrates that anodal tDCS applied to the left dlPFC improves deficient CC. Thereby, base-level performance moderates tDCS effects. Hence, tDCS might be suitable to support behavioral trainings to enhance CC specifically in people whose impairments in CC are comparably high

Challenging control over emotions in borderline personality disorder-a tDCS study

Background: Deficient cognitive control (CC) over emotional distraction is a central characteristic of borderline personality disorder (BPD). Reduced activation of the left dorsolateral prefrontal cortex (dlPFC) has been linked to this deficit. This study investigates whether it is possible to ameliorate CC deficits via anodal tDCS over the left dlPFC in BPD. Furthermore, we investigate whether the extent of CC impairment influences how well one responds to tDCS. Methods: The effect of a single-session tDCS (1 mA for 20 min, reference electrode on the contralateral mastoid bone) to the left dlPFC (F3) on the CC of patients with BPD (N = 20) and healthy control participants (HCs, N = 20) was examined in a double-blinded, balanced randomized, sham-controlled crossover trial. A delayed response working memory task with negative, neutral and positive pictures presented during the delay period was conducted to assess CC. Stimulation was applied simultaneously with the task. Results: Negative pictures caused prolonged response times as compared to a control condition in patients with BPD and HCs. Anodal tDCS to the left dlPFC did not significantly reduce this interference effect in the overall sample. Further analyses showed, however, that participants with impaired CC profited the most from anodal tDCS. In the subgroup of participants who actually showed an interference effect we found the expected significant amelioration of CC under tDCS. Conclusions: The present study demonstrates that anodal tDCS applied to the left dlPFC improves deficient CC. Thereby, base-level performance moderates tDCS effects. Hence, tDCS might be suitable to support behavioral trainings to enhance CC specifically in people whose impairments in CC are comparably high

The predictive validity of bipolar at-risk (prodromal) criteria in help-seeking adolescents and young adults: a prospective study.

There are no established tools to identify individuals at risk for developing bipolar disorder. We developed a set of ultra-high-risk criteria for bipolar disorder [bipolar at-risk (BAR)]. The primary aim of the present study was to determine the predictive validity of the BAR criteria