First Colonization of a Spectral Outpost in Random Matrix Theory

We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding orthogonal polynomials. We provide an analysis with an error term of order N^(-2 h) where 1/h = 2 nu+2 is the exponent of non-regularity of the effective potential, thus improving even in the usual case the analysis of the pertinent literature. The behavior of the first finite number of zeroes (eigenvalues) appearing in the new band is analyzed and connected with the location of the zeroes of certain Freud polynomials. In general all these newborn zeroes approach the point of nonregularity at the rate N^(-h) whereas one (a stray zero) lags behind at a slower rate of approach. The kernels for the correlator functions in the scaling coordinate near the emerging band are provided together with the subleading term: in particular the transition between K and K+1 eigenvalues is analyzed in detail.Comment: 32 pages, 8 figures (typo corrected in Formula 4.13); some reference added and minor correction

Nonperturbative 2D Gravity, Punctured Spheres and Θ\Theta-Vacua in String Theories

We consider a model of 2D gravity with the coefficient of the Einstein-Hilbert action having an imaginary part $\pi/2$. This is equivalent to introduce a $\Theta$-vacuum structure in the genus expansion whose effect is to convert the expansion into a series of alternating signs, presumably Borel summable. We show that the specific heat of the model has a physical behaviour. It can be represented nonperturbatively as a series in terms of integrals over moduli spaces of punctured spheres and the sum of the series can be rewritten as a unique integral over a suitable moduli space of infinitely punctured spheres. This is an explicit realization \`a la Friedan-Shenker of 2D quantum gravity. We conjecture that the expansion in terms of punctures and the genus expansion can be derived using the Duistermaat-Heckman theorem. We briefly analyze expansions in terms of punctured spheres also for multicritical models.Comment: 12 pages + 2 figures available upon request. LaTeX Fil

Thomae type formulae for singular Z_N curves

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

The RESISTANT study (Respiratory Muscle Training in Patients with Spinal Muscular Atrophy): study protocol for a randomized controlled trial

Background: Spinal Muscular Atrophy (SMA) is characterized by progressive and predominantly proximal and axial muscle atrophy and weakness. Respiratory muscle weakness results in impaired cough with recurrent respiratory tract infections, nocturnal hypoventilation, and may ultimately lead to fatal respiratory failure in the most severely affected patients. Treatment strategies to either slow down the decline or improve respiratory muscle function are wanting. Objective: The aim of this study is to assess the feasibility and efficacy of respiratory muscle training (RMT) in patients with SMA and respiratory muscle weakness. Methods: The effect of RMT in patients with SMA, aged ≥ 8 years with respiratory muscle weakness (maximum inspiratory mouth pressure [PImax] ≤ 80 Centimeters of Water Column [cmH2O]), will be investigated with a single blinded randomized sham-controlled trial consisting of a 4-month training period followed by an 8-month open label extension phase. Intervention: The RMT program will consist of a home-based, individualized training program involving 30-breathing cycles through an inspiratory and expiratory muscle training device. Patients will be instructed to perform 10 training sessions over 5–7 days per week. In the active training group, the inspiratory and expiratory threshold will be adjusted to perceived exertion (measured on a Borg scale). The sham-control group will initially receive RMT at the same frequency but against a constant, non-therapeutic resistance. After four months the sham-control group will undergo the same intervention as the active training group (i.e., delayed intervention). Individual adherence to the RMT protocol will be reviewed every two weeks by telephone/video call with a physiotherapist. Main study parameters/endpoints: We hypothesize that the RMT program will be feasible (good adherence and good acceptability) and improve inspiratory muscle strength (primary outcome measure) and expiratory muscle strength (key secondary outcome measure) as well as lung function, patient reported breathing difficulties, respiratory infections, and health related quality of life (additional secondary outcome measures, respectively) in patients with SMA. Discussion: RMT is expected to have positive effects on respiratory muscle strength in patients with SMA. Integrating RMT with recently introduced genetic therapies for SMA may improve respiratory muscle strength in this patient population. Trial registration: Retrospectively registered at clinicaltrial.gov: NCT05632666

Fatigability in spinal muscular atrophy: Validity and reliability of endurance shuttle tests

Background: To determine construct validity and test-retest reliability of Endurance Shuttle Tests as outcome measures for fatigability of remaining motor functions in children and adults with Spinal Muscular Atrophy (SMA) across the severity spectrum. Results: We assessed the Endurance Shuttle-Nine Hole Peg Test (ESNHPT),-Box and Block Test (ESBBT) and-Walk Test (ESWT) in 61 patients with SMA types 2-4, 25 healthy controls (HC) and 15 disease controls (DC). Convergent validity, discriminative validity and test-retest reliability were investigated. Additionally, we compiled the Endurance Shuttle Combined Score (ESTCS) by selecting the most relevant endurance test of each individual. 54, 70 and 73% of patients with SMA demonstrated increased fatigability on the ESNHPT, ESBBT and the ESWT. Endurance response in SMA was characterized by a decrease in muscle strength, an increase in muscle fatigue and an increase in motor adaptions, thereby confirming convergent validity. Patients with SMA showed increased drop-out rates and a shorter endurance time compared to HC and DC demonstrating good discriminative validity. Test-retest reliability was moderate to excellent (ICC's ranging from.78 to.91) with a trend towards better performance on retest. The ESTCS increased sample size and drop-out rate up to 100 and 85%. Conclusions: Fatigability is an important additional dimension of physical impairments across the severity spectrum in children and adults with SMA. The EST's are reliable and valid to document fatigability of walking, proximal-and distal arm function in SMA and thus are promising outcome measures for use in clinical trials

Longitudinal prospective cohort study to assess peripheral motor function with extensive electrophysiological techniques in patients with Spinal Muscular Atrophy (SMA): the SMA Motor Map protocol

Background: Hereditary spinal muscular atrophy (SMA) is a motor neuron disorder with a wide range in severity in children and adults. Two therapies that alter splicing of the Survival Motor Neuron 2 (SMN2) gene, i.e. nusinersen and risdiplam, improve motor function in SMA, but treatment effects vary. Experimental studies indicate that motor unit dysfunction encompasses multiple features, including abnormal function of the motor neuron, axon, neuromuscular junction and muscle fibres. The relative contributions of dysfunction of different parts of the motor unit to the clinical phenotype are unknown. Predictive biomarkers for clinical efficacy are currently lacking. The goals of this project are to study the association of electrophysiological abnormalities of the peripheral motor system in relation to 1) SMA clinical phenotypes and 2) treatment response in patients treated with SMN2-splicing modifiers (nusinersen or risdiplam). Methods: We designed an investigator-initiated, monocentre, longitudinal cohort study using electrophysiological techniques (‘the SMA Motor Map’) in Dutch children (≥ 12 years) and adults with SMA types 1–4. The protocol includes the compound muscle action potential scan, nerve excitability testing and repetitive nerve stimulation test, executed unilaterally at the median nerve. Part one cross-sectionally assesses the association of electrophysiological abnormalities in relation to SMA clinical phenotypes in treatment-naïve patients. Part two investigates the predictive value of electrophysiological changes at two-months treatment for a positive clinical motor response after one-year treatment with SMN2-splicing modifiers. We will include 100 patients in each part of the study. Discussion: This study will provide important information on the pathophysiology of the peripheral motor system of treatment-naïve patients with SMA through electrophysiological techniques. More importantly, the longitudinal analysis in patients on SMN2-splicing modifying therapies (i.e. nusinersen and risdiplam) intents to develop non-invasive electrophysiological biomarkers for treatment response in order to improve (individualized) treatment decisions. Trial registration: NL72562.041.20 (registered at https://www.toetsingonline.nl. 26–03-2020)

Monitoring Nusinersen Treatment Effects in Children with Spinal Muscular Atrophy with Quantitative Muscle MRI

Background: Spinal muscular atrophy (SMA) is caused by deficiency of survival motor neuron (SMN) protein. Intrathecal nusinersen treatment increases SMN protein in motor neurons and has been shown to improve motor function in symptomatic children with SMA. Objective: We used quantitative MRI to gain insight in microstructure and fat content of muscle during treatment and to explore its use as biomarker for treatment effect. Methods: We used a quantitative MRI protocol before start of treatment and following the 4th and 6th injection of nusinersen in 8 children with SMA type 2 and 3 during the first year of treatment. The MR protocol allowed DIXON, T2 mapping and diffusion tensor imaging acquisitions. We also assessed muscle strength and motor function scores. Results: Fat fraction of all thigh muscles with the exception of the m. adductor longus increased in all patients during treatment (+3.2%, p = 0.02). WaterT2 showed no significant changes over time (-0.7 ms, p = 0.3). DTI parameters MD and AD demonstrate a significant decrease in the hamstrings towards values observed in healthy muscle. Conclusions: Thigh muscles of children with SMA treated with nusinersen showed ongoing fatty infiltration and possible normalization of thigh muscle microstructure during the first year of nusinersen treatment. Quantitative muscle MRI shows potential as biomarker for the effects of SMA treatment strategies

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated