Binary recurrences for which powers of two are discriminating moduli

Given a sequence of distinct positive integers $w_0 , w_1, w_2, \ldots$ and any positive integer $n$, we define the discriminator function $\mathcal{D}_{\bf w}(n)$ to be the smallest positive integer $m$ such that $w_0,\ldots, w_{n-1}$ are pairwise incongruent modulo $m$. In this paper, we classify all binary recurrent sequences $\{w_n\}_{n\geq 0}$ consisting of different integer terms such that $\mathcal{D}_{\bf w}(2^e)=2^e$ for every $e\geq 1.$ For all of these sequences it is expected that one can actually give a fairly simple description of $\mathcal{D}_{\bf w}(n)$ for every $n\ge 1.$ For two infinite families of such sequences this has been done already in 2019 by Faye, Luca and Moree, respectively Ciolan and Moree

No supportive evidence for TIA1 gene mutations in a European cohort of ALS-FTD spectrum patients

We evaluated the genetic contribution of the T cell-erestricted intracellular antigen-1 gene (TIA1) in a European cohort of frontotemporal dementia (FTD) and amyotrophic lateral sclerosis (ALS) patients. Exonic resequencing of TIA1 in 1120 patients (693 FTD, 341 ALS, 86 FTD-ALS) and 1039 controls identified in total 5 rare heterozygous missense variants, affecting the TIA1 low-complexity domain (LCD). Only 1 missense variant, p.Met290Thr, identified in a familial FTD patient with disease onset at 64 years, was absent from controls yet received a combined annotation-dependent depletion score of 11.42. By contrast, 3 of the 4 variants also detected in unaffected controls, p.Val294Glu, p.Gln318Arg, and p.Ala381Thr, had combined annotation-dependent depletion scores greater than 20. Our findings in a large European patient-control series indicate that variants in TIA1 are not a common cause of ALS and FTD. The observation of recurring TIA1 missense variants in unaffected individuals lead us to conclude that the exact genetic contribution of TIA1 to ALS and FTD pathogenesis remains to be further elucidated

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

An Investigation of Corticospinal Tract Microstructural Integrity in ARSACS Using a Profilometry MRI Analysis: Results From the PROSPAX Study

Background: Spasticity represents a core clinical feature of Autosomal Recessive Spastic Ataxia of Charlevoix-Saguenay (ARSACS) patients. Nonetheless, its pathophysiological substrate is poorly investigated. We assessed the microstructural integrity of the corticospinal tract (CST) using diffusion MRI (dMRI) via profilometry analysis to understand its possible role in the development of spasticity in ARSACS. Materials and Methods: In this multi-center prospective study, data of 37 ARSACS (M/F = 21/16; 33.4 ± 12.4 years) and 29 controls (M/F = 13/16; 42.1 ± 17.2 years) acquired within the PROSPAX consortium were collected from January 2021 to October 2022 and analyzed. Differences in terms of global CST microstructural integrity were probed, as well as a possible spatial distribution of the damage along the tract via profilometry analysis. Possible correlations between clinical severity, including the Spastic Paraplegia Rating Scale (SPRS), were also tested. Results: A significant global involvement of the CST was found in ARSACS compared to controls (all tests with p < 0.001), with a spatially defined pattern of more pronounced microstructural integrity loss occurring right below and above the pons, a structure that was also confirmed to be thickened in these patients (p < 0.001). A bilateral negative correlation emerged between the microstructural integrity of the CST and clinical indices of spasticity expressed via SPRS (p = 0.02 for both CSTs). Conclusion: A clinically meaningful microstructural involvement of CST is present in ARSACS patients, with a spatially defined pattern of damage occurring right below and above a thickened pons. An evaluation of the microstructure of this bundle might serve as a possible biomarker in this condition

High Agreement Across Laboratories Between Different Alpha‐Synuclein Seed Amplification Protocols

Background: Seed amplification assays (SAA) detect alpha-synuclein (aSYN) pathology in patient biomatrices such as cerebrospinal fluid (CSF)—potentially even before clinical manifestations. As CSF-based SAA are approaching broader use in clinical trials and research, ensuring that different laboratories obtain the same results becomes increasingly important. Methods: In this cross-laboratory, cross-aSYN-recombinant substrate and cross-protocol round-robin test, we compared SAA results from a common set of 38 CSF samples measured independently in four research laboratories of the German Center for Neurodegenerative diseases. Three laboratories (A–C) used an assay protocol adapted from Parchi's group at ISNB (Bologna, Italy); laboratory D used an assay protocol adapted from Amprion Inc. Two different manufacturers of aSYN protein were used as substrates for the SAA reaction. Results: Qualitative results were identical in at least three of the four laboratories for 37 out of 38 samples (20 positive, 17 negative). Fleiss Kappa for all four laboratories was 0.751 (z = 12, p  92%. For the number of positive replicates, Fleiss Kappa was 0.45 for a score of zero positive replicates and 0.42 for a score of four positive replicates. Conclusions: The qualitative SAA results showed a high level of agreement across research laboratories, aSYN monomers, and assay protocols. Small differences between laboratories were systematic, consistent with the notion that SAA reports biologically relevant properties. These results also underline that round-robin tests can be helpful in assessing and ensuring SAA quality across laboratories

From roadmap to a sustainable end-to-end individualized therapy pathway

The field of individualized, or N-of-1, therapy development is growing and increasingly gaining attention as a novel option for people with serious diseases, caused by unique genetic variants for whom approved therapies are not available. The N-of-1 taskforce of the International Rare Disease Research Consortium previously outlined a roadmap of aspects involved in N-of-1 therapy development and implementation. Here, this follow-up paper looks forward and reflects on how to address existing gaps to advance the current state of individualized interventions toward an integrated and sustainable treatment development model. It discusses what needs to be established for N-of-1 therapies to be developed and utilized at a larger scale, which involves features like sustainability; safety; efficacy; regulatory aspects; dedicated registries and data sharing; tools; long-term treatment monitoring; partnering with patient advocates; and reimbursement models. It closes with recommendations to shape the future of individualized therapies, focusing on ethical implications, education, creation of tools, incentives for data sharing, and innovative payment models

Differential Temporal Dynamics of Axial and Appendicular Ataxia in SCA3

Background: Disease severity in spinocerebellar ataxia type 3 (SCA3) is commonly defined by the Scale for the Assessment and Rating of Ataxia (SARA) sum score, but little is known about the contributions and progression patterns of individual items. Objectives: To investigate the temporal dynamics of SARA item scores in SCA3 patients and evaluate if clinical and demographic factors are differentially associated with evolution of axial and appendicular ataxia. Methods: In a prospective, multinational cohort study involving 11 European and 2 US sites, SARA scores were determined longitudinally in 223 SCA3 patients with a follow-up assessment after 1 year. Results: An increase in SARA score from 10 to 20 points was mainly driven by axial and speech items, with a markedly smaller contribution of appendicular items. Finger chase and nose-finger test scores not only showed the lowest variability at baseline, but also the least deterioration at follow-up. Compared with the full set of SARA items, omission of both tests would result in lower sample size requirements for therapeutic trials. Sex was associated with change in SARA sum score and appendicular, but not axial, subscore, with a significantly faster progression in men. Despite considerable interindividual variability, the average annual progression rate of SARA score was approximately three times higher in subjects with a disease duration over 10 years than in those within 10 years from onset. Conclusion: Our findings provide evidence for a difference in temporal dynamics between axial and appendicular ataxia in SCA3 patients, which will help inform the design of clinical trials and development of new (etiology-specific) outcome measures. © 2022 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.Funding agencies: This publication is an outcome of ESMI, an EU Joint Programme — Neurodegenerative Disease Research (JPND) Project (www.jpnd.eu). The project is supported through the following funding organizations under the aegis of JPND: Germany, Federal Ministry of Education and Research (BMBF; funding codes 01ED1602A/B); Netherlands, The Netherlands Organization for Health Research and Development; Portugal, Foundation for Science and Technology and Regional Fund for Science and Technology of the Azores; United Kingdom, Medical Research Council. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 643417. At the United States sites this work was in part supported by the National Ataxia Foundation.Spinocerebellar ataxia type 3Natural historyScale for the Assessment and Rating of AtaxiaDisease progressio

Monitoring equity in the delivery of health services: a Delphi process to select healthcare equity indicators

AIMS OF THE STUDY Health equity is a key component of quality of care and an objective for a growing number of quality improvement projects for deontological, ethical, public health and economic reasons. To monitor equity in the delivery of health services in Switzerland, there is a need to implement valid, measurable and actionable equity indicators, along with vulnerability stratifiers such as migrant status, which could lead to differences in quality of care. The aim of this study was to develop a set of healthcare equity indicators and stratifiers targeting inpatient and outpatient populations and to test their feasibility. METHODS A scoping literature review and inputs from a national interprofessional expert taskforce provided a set of indicators and vulnerability stratifiers. The most valid and measurable indicators and stratifiers were retained using a Delphi process. They were then operationalised, and their implementation tested in three Swiss hospitals from the three language regions. RESULTS A taskforce of 18 experts, including a patient representative, selected 11 indicators that evaluate structures, processes and outcomes, and five vulnerability stratifiers. Although most indicators and stratifiers could be implemented in all three hospitals, data availability was limited for some variables, including patient satisfaction and access to interpreters for foreign-language patients. CONCLUSIONS The equity indicators and stratifiers identified by this two-stage process have content validity, wide patient coverage and are focused on inequities in the healthcare system that are actionable through improvement projects. Both the indicators and the project methodology could be replicated in institutions aiming for more equitable care

The genetic landscape of sporadic adult-onset degenerative ataxia: a multi-modal genetic study of 377 consecutive patients from the longitudinal multi-centre SPORTAX cohort

Background: While most sporadic adult-onset neurodegenerative diseases have only a minor monogenic component, given several recently identified late adult-onset ataxia genes, the genetic burden may be substantial in sporadic adult-onset ataxias. We report systematic mapping of the genetic landscape of sporadic adult-onset ataxia in a well-characterised, multi-centre cohort, combining several multi-modal genetic screening techniques, plus longitudinal natural history data. Methods: Systematic clinico-genetic analysis of a prospective longitudinal multi-centre cohort of 377 consecutive patients with sporadic adult-onset ataxia (SPORTAX cohort), including clinically defined sporadic adult-onset ataxia of unknown aetiology (SAOA) (n = 229) and ‘clinically probable multiple system atrophy of cerebellar type’ (MSA-Ccp) (n = 148). Combined GAA-FGF14 (SCA27B) and RFC1 repeat expansion screening with next-generation sequencing (NGS) was complemented by natural history and plasma neurofilament light chain analysis in key subgroups. Findings: 85 out of 377 (22.5%) patients with sporadic adult-onset ataxia carried a pathogenic or likely pathogenic variant, thereof 67/229 (29.3%) patients with SAOA and 18/148 (12.2%) patients meeting the MSA-Ccp criteria. This included: 45/377 (11.9%) patients with GAA-FGF14≥250 repeat expansions (nine with MSA-Ccp), 17/377 (4.5%) patients with RFC1 repeat expansions (three with MSA-Ccp), and 24/377 (6.4%) patients with single nucleotide variants (SNVs) identified by NGS (six with MSA-Ccp). Five patients (1.3%) were found to have two relevant genetic variants simultaneously (dual diagnosis). Interpretation: In this cohort of sporadic adult-onset ataxia, a cohort less likely to have a monogenic cause, a substantial burden of monogenic variants was identified, particularly GAA-FGF14 and RFC1 repeat expansions. This included a substantial share of patients meeting the MSA-Ccp criteria, suggesting a reduced specificity of this clinical diagnosis and potential co-occurrence of MSA-C plus a second, independent genetic condition. These findings have important implications for the genetic work-up and counselling of patients with sporadic ataxia, even when presenting with MSA-like features. With targeted treatments for genetic ataxias now on the horizon, these findings highlight their potential utility for these patients. Funding: This work was supported by the Clinician Scientist programme “PRECISE.net” funded by the Else Kröner-Fresenius-Stiftung (to DM, AT, CW, OR, and MS), by the Deutsche Forschungsgemeinschaft (as part of the PROSPAX project), and by the Canadian Institutes of Health Research and the Fondation Groupe Monaco. Support was also provided by Humboldt Research Fellowship for Postdocs and the Hertie-Network of Excellence in Clinical Neuroscience and a Fellowship award from the Canadian Institutes of Health Research

Characterization of Lifestyle inSpinocerebellar Ataxia Type 3 andAssociation with Disease Severity

Background: Lifestyle could influence the course of hereditary ataxias, but representative data are missing. Objective: The objective of this study was to characterize lifestyle in spinocerebellar ataxia type 3 (SCA3) and investigate possible associations with disease parameters. Methods: In a prospective cohort study, data on smoking, alcohol consumption, physical activity, physiotherapy, and body mass index (BMI) were collected from 243 patients with SCA3 and 119 controls and tested for associations with age of onset, disease severity, and progression. Results: Compared with controls, patients with SCA3 were less active and consumed less alcohol. Less physical activity and alcohol abstinence were associated with more severe disease, but not with progression rates or age of onset. Smoking, BMI, or physiotherapy did not correlate with disease parameters. Conclusion: Differences in lifestyle factors of patients with SCA3 and controls as well as associations of lifestyle factors with disease severity are likely driven by the influence of symptoms on behavior. No association between lifestyle and disease progression was detected. © 2021 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder SocietyFunding agencies: This publication is an outcome of the European Spinocerebellar ataxia type 3/Machado-Joseph disease initiative (ESMI), an EU Joint Programme–Neurodegenerative Disease Research (JPND) project (see www.jpnd.eu). The project is supported through the following funding organizations under the aegis of JPND: Germany, Federal Ministry of Education and Research (funding codes 01ED1602A/B); The Netherlands, The Netherlands Organisation for Health Research and Development; Portugal, Foundation for Science and Technology (FCT); United Kingdom, Medical Research Council. This project has received funding from the European Union’s Horizon 2020 research and innovation program under Grant 643417. At the US sites, this work was in part supported by the National Ataxia Foundation and the National Institute of Neurological Disorders and Stroke Grant R01 NS080816. P.G. is supported by the National Institute for Health Research University College London Hospitals (UCLH) Biomedical Research Centre. P.G. receives also support from the North Thames Clinical Research Network (CRN). P.G. and H.G.M. work at University College London Hospitals/University College London, which receives a proportion of funding from the Department of Health’s National Institute for Health Research Biomedical Research Centres funding scheme. P.G. received funding from CureSCA3 in support of H.G.M.’s work. This work was moreover supported, in part, by the Deutsche Forschungsgemeinschaft (German Research Foundation) No. 441409627, as part of the Progression chart of Spastic ataxias (PROSPAX) consortium under the frame of the European Joint Programme on Rare Diseases (EJP RD), under the EJP RD COFUND-EJP N 825575 (to M.S., B.v.W,) and Grant 779257 “Solve-RD” from the Horizon 2020 research and innovation program to M.S