Fractional Calculus via Functional Calculus: Theory and Applications

This paper demonstrates the power of the functional-calculus definition of linear fractional (pseudo-)differential operators via generalised Fourier transforms. Firstly, we describe in detail how to get global causal solutions of linear fractional differential equations via this calculus. The solutions are represented as convolutions of the input functions with the related impulse responses. The suggested method via residue calculus separates an impulse response automatically into an exponentially damped (possibly oscillatory) part and a ''slow' relaxation. If an impulse response is stable it becomes automatically causal, otherwise one has to add a homogeneous solution to get causality. Secondly, we present examples and, moreover, verify the approach along experiments on viscolelastic rods. The quality of the method as an effective few-parameter model is impressively demonstrated: the chosen reference example PTFE (Teflon) shows that in contrast to standard classical models our model describes the behaviour in a wide frequency range within the accuracy of the measurement. Even dispersion effects are included. Thirdly, we conclude the paper with a survey of the required theory. There the attention is directed to the extension from the L-2-approach on the space of distributions cal D-

Sox2 in the differentiation of cochlear progenitor cells

HMG domain transcription factor, Sox2, is a critical gene for the development of cochlear hair cells, the receptor cells for hearing, but this has been ascribed to expansion of the progenitors that become hair cells. Here, we show that Sox2 activated Atoh1, a transcription factor important for hair cell differentiation, through an interaction with the 3′ enhancer of Atoh1. Binding to consensus sequences in the Atoh1 enhancer was dependent on the level of Sox2, and the extent of enhancer binding correlated to the extent of activation. Atoh1 activation by Sox2 was required for embryonic hair cell development: deletion of Sox2 in an inducible mutant, even after progenitor cells were fully established, halted development of hair cells, and silencing also inhibited postnatal differentiation of hair cells induced by inhibition of γ-secretase. Sox2 is thus required in the cochlea to both expand the progenitor cells and initiate their differentiation to hair cells

Fractional Equations of Curie-von Schweidler and Gauss Laws

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.Comment: 11 pages, LaTe

Does stapedotomy improve high frequency conductive hearing?

Objectives: Stapedotomy is performed to address conductive hearing deficits. While hearing thresholds reliably improve at low frequencies (LF), conductive outcomes at high frequencies (HF) are less reliable and have not been well described. Herein, we evaluate post-operative HF air-bone gap (ABG) changes and measure HF air conduction (AC) thresholds changes as a function of frequency. Methods: Retrospective review of patients who underwent primary stapedotomy with incus wire piston prosthesis between January 2016 and May 2020. Pre- and postoperative audiograms were evaluated. LF ABG was calculated as the mean ABG of thresholds at 250, 500, and 1000 Hz. HF ABG was calculated at 4 kHz. Results: Forty-six cases met criteria. Mean age at surgery was 54.0 +/- 11.7 years. The LF mean preoperative ABG was 36.9 +/- 11.0 dB and postoperatively this significantly reduced to 9.35 +/- 6.76 dB, (P \u3c .001). The HF mean preoperative ABG was 31.1 +/- 14.4 dB and postoperatively, this also significantly reduced to 14.5 +/- 12.3 dB, (P \u3c .001). The magnitude of LF ABG closure was over 1.5 times the magnitude of HF ABG closure (P \u3c .001). The gain in AC decreased with increasing frequency (P \u3c .001). Conclusion: Hearing improvement following stapedotomy is greater at low than high frequencies. Postoperative air bone gaps persist at 4 kHz. Further biomechanical and histopathologic work is necessary to localize postoperative high frequency conductive hearing deficits and improve stapedotomy hearing outcomes. Level of Evidence: 4, retrospective study

Management von Patienten mit Tracheostoma während der COVID-19-Pandemie: Literaturüberblick und Demonstration

Hintergrund Seit dem Auftreten des neuen Coronavirus im Dezember 2019 in China haben viele Länder Schwierigkeiten, die ansteigende Zahl der Infektionen, auch innerhalb des medizinischen Personals, zu kontrollieren. Es hat sich mittlerweile deutlich gezeigt, dass das neue SARS-CoV-2-Virus insbesondere über Aerosole und Tröpfchen der oberen Atemwege übertragen wird und die Infektionsgefahr bei oberen Atemwegsprozeduren deutlich erhöht ist. Ein Anteil der schwererkrankten beatmungspflichtigen Patienten benötigt ab einem gewissen Zeitpunkt eine Tracheotomie zur langfristigen Beatmung und einfacheren Entwöhnung von der Beatmungsmaschine. Diese Patienten erfordern jedoch im Anschluss eine nicht unerhebliche Betreuung durch medizinisches Pflegepersonal, und es ist bislang unklar, inwieweit die Tracheostomapflege ein Risiko für sekundäre Infektionen darstellt. Fragestellung Evaluierung der Gefahr der Tröpfchenbildung bei Trachealkanülenwechsel, Überblick zum Kanülenwechsel bei COVID-19-Patienten. Material und Methoden Literaturrecherche, quantitative und qualitative Analyse der Tröpfchenfreisetzung bei Kanülenwechsel an n = 8 Patienten, Übersicht und Checkliste für Kanülenwechsel. Ergebnisse Diese Studie demonstriert, dass beim Kanülenwechsel, insbesondere bei Einführen der neuen Kanüle, eine nicht unbeträchtliche Menge an Tröpfchen entstehen kann. Eine Aerosolbildung von Partikeln kleiner als 5 µm wurde nicht untersucht. Schlussfolgerung Unsere Ergebnisse im Zusammenhang mit der aktuellen Literatur verdeutlichen, dass die Pflege nach Tracheotomie eine hoch risikoreiche Prozedur darstellt und nur von einer kleinen Gruppe von geschultem und gut geschütztem Personal durchgeführt werden sollte

Clinical characterization of respiratory large droplet production during common airway procedures using high-speed imaging

During the COVID-19 pandemic, a significant number of healthcare workers have been infected with SARS-CoV-2. However, there remains little knowledge regarding large droplet dissemination during airway management procedures in real life settings. 12 different airway management procedures were investigated during routine clinical care. A high-speed video camera (1000 frames/second) was for imaging. Quantitative droplet characteristics as size, distance traveled, and velocity were computed. Droplets were detected in 8/12 procedures. The droplet trajectories could be divided into two distinctive patterns (type 1/2). Type 1 represented a ballistic trajectory with higher speed large droplets whereas type 2 represented a random trajectory of slower particles that persisted longer in air. The use of tracheal cannula filters reduced the amount of droplets. Respiratory droplet patterns generated during airway management procedures follow two distinctive trajectories based on the influence of aerodynamic forces. Speaking and coughing produce more droplets than non-invasive ventilation therapy confirming these behaviors as exposure risks. Even large droplets may exhibit patterns resembling the fluid dynamics smaller airborne aerosols that follow the airflow convectively and may place the healthcare provider at risk

Optogenetic stimulation of the cochlear nucleus using channelrhodopsin-2 evokes activity in the central auditory pathways

Optogenetics has become an important research tool and is being considered as the basis for several neural prostheses. However, few studies have applied optogenetics to the auditory brainstem. This study explored whether optical activation of the cochlear nucleus (CN) elicited responses in neurons in higher centers of the auditory pathway and whether it elicited an evoked response. Viral-mediated gene transfer was used to express channelrhodopsin-2 (ChR2) in the mouse CN. Blue light was delivered via an optical fiber placed near the surface of the infected CN and recordings were made in higher-level centers. Optical stimulation evoked excitatory multiunit spiking activity throughout the tonotopic axis of the central nucleus of the inferior colliculus (IC) and the auditory cortex (Actx). The pattern and magnitude of IC activity elicited by optical stimulation was comparable to that obtained with a 50 dB SPL acoustic click. This broad pattern of activity was consistent with histological confirmation of green fluorescent protein (GFP) label of cell bodies and axons throughout the CN. Increasing pulse rates up to 320 Hz did not significantly affect threshold or bandwidth of the IC responses, but rates higher than 50 Hz resulted in desynchronized activity. Optical stimulation also evoked an auditory brainstem response, which had a simpler waveform than the response to acoustic stimulation. Control cases showed no responses to optical stimulation. These data suggest that optogenetic control of central auditory neurons is feasible, but opsins with faster channel kinetics may be necessary to convey information at rates typical of many auditory signals

Paroxysmal exercise-induced dyskinesia and epilepsy is due to mutations in SLC2A1, encoding the glucose transporter GLUT1

Paroxysmal exercise-induced dyskinesia (PED) can occur in isolation or in association with epilepsy, but the genetic causes and pathophysiological mechanisms are still poorly understood. We performed a clinical evaluation and genetic analysis in a five-generation family with co-occurrence of PED and epilepsy (n = 39), suggesting that this combination represents a clinical entity. Based on a whole genome linkage analysis we screened SLC2A1, encoding the glucose transporter of the blood-brain-barrier, GLUT1 and identified heterozygous missense and frameshift mutations segregating in this and three other nuclear families with a similar phenotype. PED was characterized by choreoathetosis, dystonia or both, affecting mainly the legs. Predominant epileptic seizure types were primary generalized. A median CSF/blood glucose ratio of 0.52 (normal >0.60) in the patients and a reduced glucose uptake by mutated transporters compared with the wild-type as determined in Xenopus oocytes confirmed a pathogenic role of these mutations. Functional imaging studies implicated alterations in glucose metabolism in the corticostriate pathways in the pathophysiology of PED and in the frontal lobe cortex in the pathophysiology of epileptic seizures. Three patients were successfully treated with a ketogenic diet. In conclusion, co-occurring PED and epilepsy can be due to autosomal dominant heterozygous SLC2A1 mutations, expanding the phenotypic spectrum associated with GLUT1 deficiency and providing a potential new treatment option for this clinical syndrome

Differential roles of epigenetic changes and Foxp3 expression in regulatory T cell-specific transcriptional regulation

Naturally occurring regulatory T (Treg) cells, which specifically express the transcription factor forkhead box P3 (Foxp3), are engaged in the maintenance of immunological self-tolerance and homeostasis. By transcriptional start site cluster analysis, we assessed here how genome-wide patterns of DNA methylation or Foxp3 binding sites were associated with Treg-specific gene expression. We found that Treg-specific DNA hypomethylated regions were closely associated with Treg up-regulated transcriptional start site clusters, whereas Foxp3 binding regions had no significant correlation with either up- or down-regulated clusters in nonactivated Treg cells. However, in activated Treg cells, Foxp3 binding regions showed a strong correlation with down-regulated clusters. In accordance with these findings, the above two features of activation-dependent gene regulation in Treg cells tend to occur at different locations in the genome. The results collectively indicate that Treg-specific DNA hypomethylation is instrumental in gene up-regulation in steady state Treg cells, whereas Foxp3 down-regulates the expression of its target genes in activated Treg cells. Thus, the two events seem to play distinct but complementary roles in Treg-specific gene expression

Discovery of widespread transcription initiation at microsatellites predictable by sequence-based deep neural network

Using the Cap Analysis of Gene Expression (CAGE) technology, the FANTOM5 consortium provided one of the most comprehensive maps of transcription start sites (TSSs) in several species. Strikingly, ~72% of them could not be assigned to a specific gene and initiate at unconventional regions, outside promoters or enhancers. Here, we probe these unassigned TSSs and show that, in all species studied, a significant fraction of CAGE peaks initiate at microsatellites, also called short tandem repeats (STRs). To confirm this transcription, we develop Cap Trap RNA-seq, a technology which combines cap trapping and long read MinION sequencing. We train sequence-based deep learning models able to predict CAGE signal at STRs with high accuracy. These models unveil the importance of STR surrounding sequences not only to distinguish STR classes, but also to predict the level of transcription initiation. Importantly, genetic variants linked to human diseases are preferentially found at STRs with high transcription initiation level, supporting the biological and clinical relevance of transcription initiation at STRs. Together, our results extend the repertoire of non-coding transcription associated with DNA tandem repeats and complexify STR polymorphism