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

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

The Constrained Maximal Expression Level Owing to Haploidy Shapes Gene Content on the Mammalian X Chromosome.

X chromosomes are unusual in many regards, not least of which is their nonrandom gene content. The causes of this bias are commonly discussed in the context of sexual antagonism and the avoidance of activity in the male germline. Here, we examine the notion that, at least in some taxa, functionally biased gene content may more profoundly be shaped by limits imposed on gene expression owing to haploid expression of the X chromosome. Notably, if the X, as in primates, is transcribed at rates comparable to the ancestral rate (per promoter) prior to the X chromosome formation, then the X is not a tolerable environment for genes with very high maximal net levels of expression, owing to transcriptional traffic jams. We test this hypothesis using The Encyclopedia of DNA Elements (ENCODE) and data from the Functional Annotation of the Mammalian Genome (FANTOM5) project. As predicted, the maximal expression of human X-linked genes is much lower than that of genes on autosomes: on average, maximal expression is three times lower on the X chromosome than on autosomes. Similarly, autosome-to-X retroposition events are associated with lower maximal expression of retrogenes on the X than seen for X-to-autosome retrogenes on autosomes. Also as expected, X-linked genes have a lesser degree of increase in gene expression than autosomal ones (compared to the human/Chimpanzee common ancestor) if highly expressed, but not if lowly expressed. The traffic jam model also explains the known lower breadth of expression for genes on the X (and the Z of birds), as genes with broad expression are, on average, those with high maximal expression. As then further predicted, highly expressed tissue-specific genes are also rare on the X and broadly expressed genes on the X tend to be lowly expressed, both indicating that the trend is shaped by the maximal expression level not the breadth of expression per se. Importantly, a limit to the maximal expression level explains biased tissue of expression profiles of X-linked genes. Tissues whose tissue-specific genes are very highly expressed (e.g., secretory tissues, tissues abundant in structural proteins) are also tissues in which gene expression is relatively rare on the X chromosome. These trends cannot be fully accounted for in terms of alternative models of biased expression. In conclusion, the notion that it is hard for genes on the Therian X to be highly expressed, owing to transcriptional traffic jams, provides a simple yet robustly supported rationale of many peculiar features of X's gene content, gene expression, and evolution

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

Background!#!Since emergence of the new coronavirus in China in December 2019, many countries have been struggling to control skyrocketing numbers of infections, including among healthcare personnel. It has now been clearly demonstrated that SARS-CoV‑2 resides in the upper airways and transmits easily via aerosols and droplets, which significantly increases the risk of infection when performing upper airway procedures. Ventilated COVID-19 patients in a critical condition in the intensive care unit may require tracheotomy for long-term ventilation and to improve weaning. However, the risk of secondary infection of medical personnel performing subsequent tracheostomy care remains unclear.!##!Objective!#!This study aimed to evaluate the risk of droplet dispersion during tracheostomy tube change and overview tracheostomy tube change in COVID-19 patients.!##!Materials and methods!#!The current literature was reviewed, quantitative and qualitative analyses of droplet formation during tracheostomy tube change in n = 8 patients were performed, and an overview of and checklist for tracheostomy tube change were compiled.!##!Results!#!This study demonstrates that tracheostomy tube change, in particular insertion of the new tube, may cause significant droplet formation. The aerosolization of particles smaller than 5 µm was not analyzed.!##!Conclusion!#!Our data, together with the current literature, clearly emphasize that tracheostomy care is associated with a high infection risk and should only be performed by a small group of well-trained, maximally protected healthcare personnel

Idiopathic intracranial hypertension: A Retrospective Evaluation of the Management and Outcomes at One Large Tertiary Care Center (.pdf)

Idiopathic intracranial hypertension (IIH) is a common and potentially blinding disorder that affects most frequently young overweight women. The NORDIC IIH treatment trial defined the value of acetazolamide and weight loss in the management of IIH. The goal of this study was to reflect upon our outcomes based upon our traditional strategy for managing patients and also to explore outcomes across a greater range of visual disability than was studied in the IIH treatment trial study