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Let f be a Drinfeld modular form of level Γ 0 () which is an eigenform for the Hecke operator T ( a prime of q [ T ]). We study the relations between the Fourier coefficients of f and the -adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of T f to provide bounds and estimates on the slopes and, in particular, to find necessary conditions for "large" slopes, whose existence is closely connected with conjectures on oldforms and newforms. [ABSTRACT FROM AUTHOR]

Egocentric video has recently emerged as a potential solution for monitoring hand function in individuals living with tetraplegia in the community, especially for its ability to detect functional use in the home environment. The aim of this study was to develop and validate a wearable vision-based system for measuring hand use in the home among individuals living with tetraplegia. Several deep learning algorithms for detecting functional hand–object interactions were developed and compared. The most accurate algorithm was used to extract measures of hand function from 65 h of unscripted video recorded at home by 20 participants with tetraplegia. These measures were: the percentage of interaction time over total recording time (Perc); the average duration of individual interactions (Dur); and the number of interactions per hour (Num). To demonstrate the clinical validity of the technology, egocentric measures were correlated with validated clinical assessments of hand function and independence (Graded Redefined Assessment of Strength, Sensibility and Prehension [GRASSP], Upper Extremity Motor Score [UEMS], and Spinal Cord Independent Measure [SCIM]). Hand–object interactions were automatically detected with a median F1-score of 0.80 (0.67–0.87). Our results demonstrated that higher UEMS and better prehension were related to greater time spent interacting, whereas higher SCIM and better hand sensation resulted in a higher number of interactions performed during the egocentric video recordings. For the first time, measures of hand function automatically estimated in an unconstrained environment in individuals with tetraplegia have been validated against internationally accepted measures of hand function. Future work will necessitate a formal evaluation of the reliability and responsiveness of the egocentric-based performance measures for hand use. [ABSTRACT FROM AUTHOR]

Purpose: Choking on food is a leading cause of accidental death in several populations, including children, people with intellectual/developmental disability, and older adults in residential care facilities. One contributor to choking risk is incomplete oral processing and failure to convert food to a cohesive, nonsticky bolus with a maximum particle size that will not block the airway. Clinical tests of mastication do not evaluate properties of chewed food boluses. We characterized expectorated boluses, after oral processing, using methods developed by the International Dysphagia Diet Standardisation Initiative (IDDSI). Method: Seventeen adults without dysphagia (seven women and 10 men), aged 23–55 years, chewed samples of a cracker, a raw baby carrot, and a circular, dome-shaped gummy candy. Chewing metrics were obtained up to the point when the person indicated that they were ready to swallow. The bolus was then either expectorated or swallowed; IDDSI tests were used to characterize the expectorated boluses. Results: Measures of chewing did not differ between spit and swallow conditions. Expectorated cracker and carrot boluses had maximum particle size consistent with IDDSI Level SB6 Soft & Bite-Sized foods or lower. The gummy candy samples remained at IDDSI Level RG7 Regular food consistency. Conclusions: This study suggests that expectorated ready-to-swallow boluses are representative of boluses that are swallowed and that oral processing in adults without dysphagia typically results in boluses at IDDSI’s Level SB6 or lower. IDDSI’s testing methods provide a practical method for evaluating oral processing by characterizing expectorated ready-to-swallow boluses and may guide food texture recommendations for persons who have increased risk of choking. [ABSTRACT FROM AUTHOR]

Let p = (P) be any prime of F q [ t ] , let m be any ideal of F q [ t ] not divisible by p and consider the space of Drinfeld cusp forms of level m p , i.e. for the modular group Γ 0 (m p). Using degeneracy maps, traces and Fricke involutions we offer definitions for p -oldforms and p -newforms which turn out to be subspaces stable with respect to the action of the Atkin operator U P. We provide eigenvalues and/or slopes for p -oldforms and p -newforms and a condition to get the whole space of cusp forms as the direct sum between them. [ABSTRACT FROM AUTHOR]

We generalize some results of Greither and Popescu to a geometric Galois cover X → Y which appears naturally for example in extensions generated by p n -torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz–Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in [1]) with Goss ζ -function. [ABSTRACT FROM AUTHOR]

We study the Atkin Ut operator for Drinfeld cusp forms. In particular, we define newforms and oldforms of level Γ0(t) and we study basic properties of their slopes. Moreover, we find an explicit formula for the matrix associated to the action of Ut on Γ1(t)-invariant cusp forms using Teitelbaum's interpretation as harmonic cocycles. [ABSTRACT FROM AUTHOR]

Let A be an abelian variety defined over a global function field F of positive characteristic p and let K / F be a p -adic Lie extension with Galois group G . We provide a formula for the (truncated) Euler characteristic χ ( G , S e l A ( K ) p ) of the p -part of the Selmer group of A over K . In the special case G ≃ Z p d and A a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of S e l A ( K ) p is related to special values of a p -adic L -function. [ABSTRACT FROM AUTHOR]

We study the action of Atkin U t -operator on Drinfeld cusp forms for Γ 1 (t) and Γ (t) using Teitelbaum's interpretation as harmonic cocycles. For small weights k ≤ 2 q , we provide eigenvalues and eigenforms and prove U t is diagonalizable in odd characteristic, pointing out that non-diagonalizability in even characteristic depends on antidiagonal blocks. [ABSTRACT FROM AUTHOR]

Purpose: The goals of this study were to (a) classify speech movements of patients with amyotrophic lateral sclerosis (ALS) in presymptomatic and symptomatic phases of bulbar function decline relying solely on kinematic features of lips and jaw and (b) identify the most important measures that detect the transition between early and late bulbar changes. Method: One hundred ninety-two recordings obtained from 64 patients with ALS were considered for the analysis. Feature selection and classification algorithms were used to analyze lip and jaw movements recorded with Optotrak Certus (Northern Digital Inc.) during a sentence task. A feature set, which included 35 measures of movement range, velocity, acceleration, jerk, and area measures of lips and jaw, was used to classify sessions according to the speaking rate into presymptomatic (> 160 words per minute) and symptomatic (< 160 words per minute) groups. Results: Presymptomatic and symptomatic phases of bulbar decline were distinguished with high accuracy (87%), relying only on lip and jaw movements. The best features that allowed detecting the differences between early and later bulbar stages included cumulative path of lower lip and jaw, peak values of velocity, acceleration, and jerk of lower lip and jaw. Conclusion: The results established a relationship between facial kinematics and bulbar function decline in ALS. Considering that facial movements can be recorded by means of novel inexpensive and easy-to-use, videobased methods, this work supports the development of an automatic system for facial movement analysis to help clinicians in tracking the disease progression in ALS. [ABSTRACT FROM AUTHOR]

Background: The automatic analysis of facial expressions is an evolving field that finds several clinical applications. One of these applications is the study of facial bradykinesia in Parkinson's disease (PD), which is a major motor sign of this neurodegenerative illness. Facial bradykinesia consists in the reduction/loss of facial movements and emotional facial expressions called hypomimia. New method: In this work we propose an automatic method for studying facial expressions in PD patients relying on video-based. Methods: 17 Parkinsonian patients and 17 healthy control subjects were asked to show basic facial expressions, upon request of the clinician and after the imitation of a visual cue on a screen. Through an existing face tracker, the Euclidean distance of the facial model from a neutral baseline was computed in order to quantify the changes in facial expressivity during the tasks. Moreover, an automatic facial expressions recognition algorithm was trained in order to study how PD expressions differed from the standard expressions. Results: Results show that control subjects reported on average higher distances than PD patients along the tasks. Comparison with existing methods: This confirms that control subjects show larger movements during both posed and imitated facial expressions. Moreover, our results demonstrate that anger and disgust are the two most impaired expressions in PD patients. Conclusions: Contactless video-based systems can be important techniques for analyzing facial expressions also in rehabilitation, in particular speech therapy, where patients could get a definite advantage from a real-time feedback about the proper facial expressions/movements to perform. [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic char ( K ) ≠ 2 , 3 and let E be an elliptic curve defined over K . Let m be a positive integer, prime with char ( K ) if char ( K ) ≠ 0 ; we denote by E [ m ] the m -torsion subgroup of E and by K m : = K ( E [ m ] ) the field obtained by adding to K the coordinates of the points of E [ m ] . Let P i : = ( x i , y i ) ( i = 1 , 2 ) be a Z -basis for E [ m ] ; then K m = K ( x 1 , y 1 , x 2 , y 2 ) . We look for small sets of generators for K m inside { x 1 , y 1 , x 2 , y 2 , ζ m } trying to emphasize the role of ζ m (a primitive m -th root of unity). In particular, we prove that K m = K ( x 1 , ζ m , y 2 ) , for any odd m ⩾ 5 . When m = p is prime and K is a number field we prove that the generating set { x 1 , ζ p , y 2 } is often minimal, while when the classical Galois representation Gal ( K p / K ) → GL 2 ( Z / p Z ) is not surjective we are sometimes able to further reduce the set of generators. We also describe explicit generators, degree and Galois groups of the extensions K m / K for m = 3 and m = 4 . [ABSTRACT FROM AUTHOR]

• Clinical rating of VFSS data is time consuming and requires specialized training. • Computer vision may help conduct automated VFSS analysis. • We detect the pharyngeal phase and localize bolus in a weakly-supervised manner. • No supervision is required in terms of bolus segmentation. • Our approach will help conduct objective clinical assessment of VFSS recordings. The videofluoroscopic swallowing study (VFSS) is a gold-standard imaging technique for assessing swallowing, but analysis and rating of VFSS recordings is time consuming and requires specialized training and expertise. Researchers have recently demonstrated that it is possible to automatically detect the pharyngeal phase of swallowing and to localize the bolus in VFSS recordings via computer vision approaches, fostering the development of novel techniques for automatic VFSS analysis. However, training of algorithms to perform these tasks requires large amounts of annotated data that are seldom available. In this paper, we demonstrate that the challenges of pharyngeal phase detection and bolus localization can be solved together using a single approach. We propose a deep-learning framework that jointly tackles pharyngeal phase detection and bolus localization in a weakly-supervised manner, requiring only the initial and final frames of the pharyngeal phase as ground truth annotations for the training. Our approach stems from the observation that bolus presence in the pharynx is the most prominent visual feature upon which to infer whether individual VFSS frames belong to the pharyngeal phase. We conducted extensive experiments with multiple convolutional neural networks (CNNs) on a dataset of 1245 bolus-level clips from 59 healthy subjects. We demonstrated that the pharyngeal phase can be detected with an F1-score higher than 0.9. Moreover, by processing the class activation maps of the CNNs, we were able to localize the bolus with promising results, obtaining correlations with ground truth trajectories higher than 0.9, without any manual annotations of bolus location used for training purposes. Once validated on a larger sample of participants with swallowing disorders, our framework will pave the way for the development of intelligent tools for VFSS analysis to support clinicians in swallowing assessment. [ABSTRACT FROM AUTHOR]

Let A be an abelian variety defined over a global field F of positive characteristic p and let F / F be a Z p N -extension, unramified outside a finite set of places of F . Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p -primary Selmer group of A . To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Z p d -extension F d / F and for any Z p d − 1 -extension contained in F d , and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z p [ [ Gal ( F / F ) ] ] in the case A is a constant abelian variety. [ABSTRACT FROM AUTHOR]

Let F be a global function field of characteristic p > 0 and A/F an abelian variety. Let K/F be an ℓ-adic Lie extension ( ℓ ≠ p) unramified outside a finite set of primes S and such that Gal( K/F) has no elements of order ℓ. We shall prove that, under certain conditions, Sel( K) has no nontrivial pseudo-null submodule. [ABSTRACT FROM AUTHOR]

Background: Left atrioventricular valve (LAVV) stenosis following an atrioventricular septal defect (AVSD) repair is a rare but potentially life-threatening complication. While echocardiographic quantification of diastolic transvalvular pressure gradients is paramount in the evaluation of a newly corrected valve function, it is hypothesized that these measured gradients are overestimated immediately following a cardiopulmonary bypass (CPB) due to the altered hemodynamics when compared to postoperative valve assessments using awake transthoracic echocardiography (TTE) upon recovery after surgery. Methods: Out of the 72 patients screened for inclusion at a tertiary center, 39 patients undergoing an AVSD repair with both intraoperative transesophageal echocardiograms (TEE, performed immediately after a CPB) and an awake TTE (performed prior to hospital discharge) were retrospectively selected. The mean (MPGs) and peak pressure gradients (PPGs) were quantified using a Doppler echocardiography and other measures of interest were recorded (e.g., a non-invasive surrogate of the cardiac output and index (CI), left ventricular ejection fraction, blood pressures and airway pressures). The variables were analyzed using the paired Student's t-tests and Spearman's correlation coefficients. Results: The MPGs were significantly higher in the intraoperative measurements when compared to the awake TTE (3.0 ± 1.2 vs. 2.3 ± 1.1 mmHg; p < 0.01); however, the PPGs did not significantly differ (6.6 ± 2.7 vs. 5.7 ± 2.8 mmHg; p = 0.06). Although the assessed intraoperative heart rates (HRs) were also higher (132 ± 17 vs. 114 ± 21 bpm; p < 0.001), there was no correlation found between the MPG and the HR, or any other parameter of interest, at either time-point. In a further analysis, a moderate to strong correlation was observed in the linear relationship between the CI and the MPG (r = 0.60; p < 0.001). During the in-hospital follow-up period, no patients died or required an intervention due to LAVV stenosis. Conclusions: The Doppler-based quantification of diastolic transvalvular LAVV mean pressure gradients using intraoperative transesophageal echocardiography seems to be prone to overestimation due to altered hemodynamics immediately after an AVSD repair. Thus, the current hemodynamic state should be taken into consideration during the intraoperative interpretation of these gradients. [ABSTRACT FROM AUTHOR]

Let Λ be a nonnoetherian Krull domain which is the inverse limit of noetherian Krull domains Λd and let M be a finitely generated Λ-module which is the inverse limit of Λd-modules Md. Under certain hypotheses on the rings Λd and on the modules Md, we define a procharacteristic ideal for M in Λ, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a nonnoetherian Iwasawa algebra Zp[[Gal(F/F)]], where F is a function field of characteristic p and Gal(F/F) ≃ Z∞p. [ABSTRACT FROM AUTHOR]

Abstract: Let p be an odd prime. Let k be an algebraic number field and let be the compositum of all the -extensions of k, so that for some finite d. We shall consider fields k with . Building on known results for quadratic fields, we shall show that the Galois group of the maximal abelian unramified pro-p-extension of is pseudo-null for several such k''s, thus confirming a conjecture of Greenberg. Moreover we shall see that pseudo-nullity can be achieved quite early, namely in a -extension, and explain the consequences of this on the capitulation of ideals in such extensions. [Copyright &y& Elsevier]

Background: Neurological disorders, such as stroke and chronic pain syndromes, profoundly impact independence and quality of life, especially when affecting upper extremity (UE) function. While conventional physical therapy has shown effectiveness in providing some neural recovery in affected individuals, there remains a need for improved interventions. Virtual reality (VR) has emerged as a promising technology-based approach for neurorehabilitation to make the patient's experience more enjoyable. Among VR-based rehabilitation paradigms, those based on fully immersive systems with headsets have gained significant attention due to their potential to enhance patient's engagement. Methods: This scoping review aims to investigate the current state of research on the use of immersive VR for UE rehabilitation in individuals with neurological diseases, highlighting benefits and limitations. We identified thirteen relevant studies through comprehensive searches in Scopus, PubMed, and IEEE Xplore databases. Eligible studies incorporated immersive VR for UE rehabilitation in patients with neurological disorders and evaluated participants' neurological and motor functions before and after the intervention using clinical assessments. Results: Most of the included studies reported improvements in the participants rehabilitation outcomes, suggesting that immersive VR represents a valuable tool for UE rehabilitation in individuals with neurological disorders. In addition, immersive VR-based interventions hold the potential for personalized and intensive training within a telerehabilitation framework. However, further studies with better design are needed for true comparison with traditional therapy. Also, the potential side effects associated with VR head-mounted displays, such as dizziness and nausea, warrant careful consideration in the development and implementation of VR-based rehabilitation programs. Conclusion: This review provides valuable insights into the application of immersive VR in UE rehabilitation, offering the foundation for future research and clinical practice. By leveraging immersive VR's potential, researchers and rehabilitation specialists can design more tailored and patient-centric rehabilitation strategies, ultimately improving the functional outcome and enhancing the quality of life of individuals with neurological diseases. [ABSTRACT FROM AUTHOR]

Speech impairment is commonly reported in Parkinson's disease and is not consistently improved by available therapies – including deep brain stimulation of the subthalamic nucleus (STN-DBS), which can worsen communication performance in some patients. Improving the outcome of STN-DBS on speech is difficult due to our incomplete understanding of the contribution of the STN to fluent speaking. To assess the relationship between subthalamic neural activity and speech production and intelligibility. We investigated bilateral STN local field potentials (LFPs) in nine parkinsonian patients chronically implanted with DBS during overt reading. LFP spectral features were correlated with clinical scores and measures of speech intelligibility. Overt reading was associated with increased beta-low ([1220) Hz) power in the left STN, whereas speech intelligibility correlated positively with beta-high ([2030) Hz) power in the right STN. We identified separate contributions from frequency and brain lateralization of the STN in the execution of an overt reading motor task and its intelligibility. This subcortical organization could be exploited for new adaptive stimulation strategies capable of identifying the occurrence of speaking behavior and facilitating its functional execution. • Speech impairment is common in Parkinson's disease (PD) • Deep brain stimulation of the subthalamic nucleus (STN) can worsen speech in PD • Left STN low-beta activity is increased during overt reading • Right STN high-beta power positively relates with speech intelligibility • Speech intelligibility can be measured with semi-automatized algorithms [ABSTRACT FROM AUTHOR]