Sampling and interpolation in Hilbert spaces of entire functions

Sampling theory is the study of spaces of functions which are reconstructible from their values at certain sets of points, which gives rise to a sampling formula for the underlying space. For this, it is necessary to consider spaces of functions whose values at a set of points are well-defined. In this work we consider the sampling and interpolation problems in reproducing kernel Hilbert space of entire functions, called de Branges space. Functions in such space are square integrable on the real line with respect to some weight function, and satisfying some growth conditions. Some sampling and interpolation results in the Paley-Wiener spaces, which are a primary example of de Branges spaces, are reviewed. We develop necessary conditions for sampling and interpolating sequences which generalize some well-known sampling and interpolation results in the Paley-Wiener space. The proofs of the necessary conditions rely very much on the Homogeneous Approximation Property and the Comparison Theorem that we prove in de Branges space. We also give necessary and sufficient conditions for Plancherel-Polya sequences, and sufficient conditions for interpolation in some de Branges spaces of exponential type

The effectiveness of neuromuscular warm-up strategies, that require no additional equipment, for preventing lower limb injuries during sports participation: a systematic review

PMCID: PMC3408383The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1741-7015/10/75. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

A putative relay circuit providing low-threshold mechanoreceptive input to lamina I projection neurons via vertical cells in lamina II of the rat dorsal horn

Background: Lamina I projection neurons respond to painful stimuli, and some are also activated by touch or hair movement. Neuropathic pain resulting from peripheral nerve damage is often associated with tactile allodynia (touch-evoked pain), and this may result from increased responsiveness of lamina I projection neurons to non-noxious mechanical stimuli. It is thought that polysynaptic pathways involving excitatory interneurons can transmit tactile inputs to lamina I projection neurons, but that these are normally suppressed by inhibitory interneurons. Vertical cells in lamina II provide a potential route through which tactile stimuli can activate lamina I projection neurons, since their dendrites extend into the region where tactile afferents terminate, while their axons can innervate the projection cells. The aim of this study was to determine whether vertical cell dendrites were contacted by the central terminals of low-threshold mechanoreceptive primary afferents. Results: We initially demonstrated contacts between dendritic spines of vertical cells that had been recorded in spinal cord slices and axonal boutons containing the vesicular glutamate transporter 1 (VGLUT1), which is expressed by myelinated low-threshold mechanoreceptive afferents. To confirm that the VGLUT1 boutons included primary afferents, we then examined vertical cells recorded in rats that had received injections of cholera toxin B subunit (CTb) into the sciatic nerve. We found that over half of the VGLUT1 boutons contacting the vertical cells were CTb-immunoreactive, indicating that they were of primary afferent origin. Conclusions: These results show that vertical cell dendritic spines are frequently contacted by the central terminals of myelinated low-threshold mechanoreceptive afferents. Since dendritic spines are associated with excitatory synapses, it is likely that most of these contacts were synaptic. Vertical cells in lamina II are therefore a potential route through which tactile afferents can activate lamina I projection neurons, and this pathway could play a role in tactile allodynia

Neuronal circuitry for pain processing in the dorsal horn

Neurons in the spinal dorsal horn process sensory information, which is then transmitted to several brain regions, including those responsible for pain perception. The dorsal horn provides numerous potential targets for the development of novel analgesics and is thought to undergo changes that contribute to the exaggerated pain felt after nerve injury and inflammation. Despite its obvious importance, we still know little about the neuronal circuits that process sensory information, mainly because of the heterogeneity of the various neuronal components that make up these circuits. Recent studies have begun to shed light on the neuronal organization and circuitry of this complex region

Protoplasmic Astrocytes Enhance the Ability of Neural Stem Cells to Differentiate into Neurons In Vitro

Protoplasmic astrocytes have been reported to exhibit neuroprotective effects on neurons, but there has been no direct evidence for a functional relationship between protoplasmic astrocytes and neural stem cells (NSCs). In this study, we examined neuronal differentiation of NSCs induced by protoplasmic astrocytes in a co-culture model. Protoplasmic astrocytes were isolated from new-born and NSCs from the E13-15 cortex of rats respectively. The differentiated cells labeled with neuron-specific marker β-tubulin III, were dramatically increased at 7 days in the co-culture condition. Blocking the effects of brain-derived neurotrophic factor (BDNF) with an anti-BDNF antibody reduced the number of neurons differentiated from NSCs when co-cultured with protoplasmic astrocytes. In fact, the content of BDNF in the supernatant obtained from protoplasmic astrocytes and NSCs co-culture media was significantly greater than that from control media conditions. These results indicate that protoplasmic astrocytes promote neuronal differentiation of NSCs, which is driven, at least in part, by BDNF

Non prescribed sale of antibiotics in Riyadh, Saudi Arabia: A Cross Sectional Study

Background Antibiotics sales without medical prescriptions are increasingly recognized as sources of antimicrobial misuse that can exacerbate the global burden of antibiotic resistance. We aimed to determine the percentage of pharmacies who sell antibiotics without medical prescriptions, examining the potential associated risks of such practice in Riyadh, Saudi Arabia, by simulation of different clinical scenarios. Methods A cross sectional study of a quasi-random sample of pharmacies stratified by the five regions of Riyadh. Each pharmacy was visited once by two investigators who simulated having a relative with a specific clinical illness (sore throat, acute bronchitis, otitis media, acute sinusitis, diarrhea, and urinary tract infection (UTI) in childbearing aged women). Results A total of 327 pharmacies were visited. Antibiotics were dispensed without a medical prescription in 244 (77.6%) of 327, of which 231 (95%) were dispensed without a patient request. Simulated cases of sore throat and diarrhea resulted in an antibiotic being dispensed in (90%) of encounters, followed by UTI (75%), acute bronchitis (73%), otitis media (51%) and acute sinusitis (40%). Metronidazole (89%) and ciprofloxacin (86%) were commonly given for diarrhea and UTI, respectively, whereas amoxicillin/clavulanate was dispensed (51%) for the other simulated cases. None of the pharmacists asked about antibiotic allergy history or provided information about drug interactions. Only 23% asked about pregnancy status when dispensing antibiotics for UTI-simulated cases. Conclusions We observed that an antibiotic could be obtained in Riyadh without a medical prescription or an evidence-based indication with associated potential clinical risks. Strict enforcement and adherence to existing regulations are warranted

Effects of peripheral nerve injury on parvalbumin expression in adult rat dorsal root ganglion neurons

Background: Parvalbumin (PV) is a calcium binding protein that identifies a subpopulation of proprioceptive dorsal root ganglion (DRG) neurons. Calcitonin gene-related peptide (CGRP) is also expressed in a high proportion of muscle afferents but its relationship to PV is unclear. Little is known of the phenotypic responses of muscle afferents to nerve injury. Sciatic nerve axotomy or L5 spinal nerve ligation and section (SNL) lesions were used to explore these issues in adult rats using immunocytochemistry. Results: In naive animals, the mean PV expression was 25 % of L4 or L5 dorsal root ganglion (DRG) neurons, and this was unchanged 2 weeks after sciatic nerve axotomy. Colocalization studies with the injury marker activating transcription factor 3 (ATF3) showed that approximately 24 % of PV neurons expressed ATF3 after sciatic nerve axotomy suggesting that PV may show a phenotypic switch from injured to uninjured neurons. This possibility was further assessed using the spinal nerve ligation (SNL) injury model where injured and uninjured neurons are located in different DRGs. Two weeks after L5 SNL there was no change in total PV staining and essentially all L5 PV neurons expressed ATF3. Additionally, there was no increase in PV-ir in the adjacent uninjured L4 DRG cells. Co-labelling of DRG neurons revealed that less than 2 % of PV neurons normally expressed CGRP and no colocalization was seen after injury. Conclusion: These experiments clearly show that axotomy does not produce down regulation of PV protein in the DRG. Moreover, this lack of change is not due to a phenotypic switch in PV immunoreactive (ir) neurons, or de novo expression of PV-ir in uninjured neurons after nerve injury. These results further illustrate differences that occur when muscle afferents are injured as compared to cutaneous afferents

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS