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Small scale equidistribution of Hecke eigenforms at infinity

We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. We show that at scales finer than the Planck scale they do not equidistribute while at scales more coarse than the Planck scale they equidistribute on a full density subsequence of eigenforms. On a suitable set of test functions we compute the variance showing interesting transition behavior at half the Planck scale.Comment: 30 pages. Added 4 figures. Several minor correction

Tumour burden in early stage Hodgkin's disease: the single most important prognostic factor for outcome after radiotherapy.

One hundred and forty-two patients with Hodgkin's disease PS I or II were treated with total or subtotal nodal irradiation as part of a prospective randomized trial in the Danish National Hodgkin Study during the period 1971-83. They were followed till death or--at the time of this analysis--from 15 to 146 months after initiation of therapy. The initial tumour burden of each patient was assessed, combining tumour size of each involved region and number of regions involved. Tumour burden thus assessed proved to be the single most important prognostic factor with regard to disease free survival. Other known prognostic factors such as number of involved regions, mediastinal size, pathological stage, systemic symptoms, and ESR were related to tumour burden and lost their prognostic significance in a multivariate analysis. The only other factors of independent significance were histologic subtype and, to a lesser extent, sex. Combining tumour burden and histologic subtype made it possible to single out a group of patients with a very poor disease free survival. These patients also had a poorer survival from Hodgkin's disease and thus clearly candidates for additional initial treatment

Update to the study protocol Face Your Fears:Virtual reality-based cognitive behavioral therapy (VR-CBT) versus standard CBT for paranoid ideations in patients with schizophrenia spectrum disorders: a randomized clinical trial

We unfortunately need to make an update to our published study protocol that describes a significant change in the design of the study. The Committee on Health Research Ethics of the Capital Region Denmark recently rejected the approval of changing the primary outcome in the trial, on the invariable grounds that the trial has already commenced. It is therefore necessary to retain the Green Paranoid Thought Scale (GPTS) part B, ideas of persecution, as our primary outcome, and GPTS part A, ideas of social reference, as a secondary outcome, which is described opposite in our published study protocol. The exchange of outcomes has not affected participation in our trial or the informed consent. Intervention in both groups and assessments are unchanged. The two outcomes together constitute GPTS and the unifying concept we attempt to treat, namely paranoid ideations. As this is a blinded, methodologically rigorous trial, we did not have—and still do not have—access to preliminary data, and therefore, we have no knowledge of the distribution of our two intervention groups nor the potential effect of the intervention. The power calculation remains unchanged irrespective of the selection of the primary outcome. We have been fully transparent with the changes in primary and secondary outcomes on ClinicalTrials.gov throughout the trial. Due to the considerations mentioned above, we assumed that there would not be any ethical implications of the change of primary outcome. We sincerely apologize for the irregularity caused because of this assumption. Trial registration: ClinicalTrials.gov NCT04902066. Initial release April 19th, 2021.</p

CHALLENGE and Face Your Fears: Virtual Reality Treatment for Auditory Hallucinations and Paranoid Ideations

Background: Many patients suffering from schizophrenia spectrum disorders continue having distressing auditory hallucinations and paranoid ideations despite receiving current treatment. Virtual reality assisted treatment offers the potential of advancing current psychotherapies for psychotic symptoms by creating virtual environments that can elicit responses (e.g. thoughts, feelings, behaviours) mirroring real-world settings. In two large-scale randomised clinical trials, we are investigating whether targeted virtual reality assisted psychotherapy can reduce psychotic symptoms and increase daily life functioning and quality of life. The CHALLENGE trial examines whether nine sessions of virtual reality-assisted psychotherapy is superior to nine sessions of standard treatments in reducing the severity, frequency, and distress of auditory hallucinations in patients with psychosis. In the Face your Fears trial we are investigating whether virtual reality assisted cognitive behavioral therapy (CBT) is superior to standard CBT in reducing levels of paranoid ideation in patients with psychosis spectrum disorders. Methods: The CHALLENGE and Face your Fears trials are randomised, assessor-blinded parallel-groups superiority clinical trials, allocating a total of 266 and 256 patients, respectively to either the experimental intervention or a control condition. The trials are currently enrolling patients; thus, no quantitative data is available yet. The main objective of this presentation is to give a qualitative account of this new psychotherapeutic methods as it is applied in both trials. Results: Qualitative data comprising case descriptions and video material will be presented at the conference. Discussion: The preliminary findings indicate great potential for these innovative treatments albeit important concerns regarding implementation will be raised. DISCLOSURE: No significant relationships

Face Your Fears: Virtual reality-based cognitive behavioral therapy (VR-CBT) versus standard CBT for paranoid ideations in patients with schizophrenia spectrum disorders:a randomized clinical trial

Background: Schizophrenia spectrum disorders cause suffering for patients, relatives, and the surrounding society. Paranoid ideations, encompassing ideas of social reference and manifest persecutory delusions, are among the most frequent symptoms in this population and a cause of significant distress. Recent meta-analyses of cognitive behavioral therapy (CBT) for psychosis show small to moderate effect sizes in reducing paranoid ideations. Virtual reality-based CBT (VR-CBT) could improve therapy efficacy as exposure and behavioral experiments in VR can be optimized, individualized, and carried out in a safe environment. Few VR-CBT studies exist for paranoid ideations and there is a need for large-scale, methodologically rigorous trials. Methods: This study is a randomized, assessor-blinded parallel-groups multi-center superiority clinical trial, fulfilling the CONSORT criteria for non-pharmacological treatment. A total of 256 patients diagnosed with schizophrenia spectrum disorder, including schizotypal disorder (ICD-10 F20-29), will be allocated to either 10 sessions of symptom-specific CBT-VR plus treatment as usual-versus 10 sessions of standard symptom-specific CBT for paranoid ideations (CBT) plus treatment as usual. All participants will be assessed at baseline, treatment end (3 months post baseline), and then 9 months post baseline. A stratified block-randomization with concealed randomization sequence will be conducted. Independent assessors blinded to the treatment will evaluate the outcome. Analysis of outcome will be carried out with the intention to treat principles. The primary outcome is ideas of social reference measured with Green Paranoid Thought Scale Part A (GPTS-A) at the cessation of treatment at 3 months post baseline. Secondary outcomes are ideas of persecution (GPTS-B), Social Interaction Anxiety Scale (SIAS), Personal and Social Performance scale (PSP), Safety Behavior Questionnaire (SBQ), and CANTAB Emotion Recognition Task. Discussion: The trial will elucidate whether VR-CBT can enhance therapy efficacy for paranoid ideations. Additionally, Trial findings will provide evidence on the effectiveness and cost-effectiveness of VR-CBT for paranoid ideations that can guide the possible dissemination and implementation into clinical practice