Approximate analytical solutions of systems of PDEs by homotopy analysis method

AbstractIn this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions

Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given

Clinical impact of anti-inflammatory microglia and macrophage phenotypes at glioblastoma margins

Glioblastoma is a devastating brain cancer for which effective treatments are required. Tumour-associated microglia and macrophages promote glioblastoma growth in an immune-suppressed microenvironment. Most recurrences occur at the invasive margin of the surrounding brain, yet the relationships between microglia/macrophage phenotypes, T cells and programmed death-ligand 1 (an immune checkpoint) across human glioblastoma regions are understudied. In this study, we performed a quantitative immunohistochemical analysis of 15 markers of microglia/macrophage phenotypes (including anti-inflammatory markers triggering receptor expressed on myeloid cells 2 and CD163, and the low-affinity-activating receptor CD32a), T cells, natural killer cells and programmed death-ligand 1, in 59 human IDH1-wild-type glioblastoma multi-regional samples (n = 177; 1 sample at tumour core, 2 samples at the margins: the infiltrating zone and leading edge). Assessment was made for the prognostic value of markers; the results were validated in an independent cohort. Microglia/macrophage motility and activation (Iba1, CD68), programmed death-ligand 1 and CD4+ T cells were reduced, and homeostatic microglia (P2RY12) were increased in the invasive margins compared with the tumour core. There were significant positive correlations between microglia/macrophage markers CD68 (phagocytic)/triggering receptor expressed on myeloid cells 2 (anti-inflammatory) and CD8+ T cells in the invasive margins but not in the tumour core (P < 0.01). Programmed death-ligand 1 expression was associated with microglia/macrophage markers (including anti-inflammatory) CD68, CD163, CD32a and triggering receptor expressed on myeloid cells 2, only in the leading edge of glioblastomas (P < 0.01). Similarly, there was a positive correlation between programmed death-ligand 1 expression and CD8+ T-cell infiltration in the leading edge (P < 0.001). There was no relationship between CD64 (a receptor for autoreactive T-cell responses) and CD8+/CD4+ T cells, or between the microglia/macrophage antigen presentation marker HLA-DR and microglial motility (Iba1) in the tumour margins. Natural killer cell infiltration (CD335+) correlated with CD8+ T cells and with CD68/CD163/triggering receptor expressed on myeloid cells 2 anti-inflammatory microglia/macrophages at the leading edge. In an independent large glioblastoma cohort with transcriptomic data, positive correlations between anti-inflammatory microglia/macrophage markers (triggering receptor expressed on myeloid cells 2, CD163 and CD32a) and CD4+/CD8+/programmed death-ligand 1 RNA expression were validated (P < 0.001). Finally, multivariate analysis showed that high triggering receptor expressed on myeloid cells 2, programmed death-ligand 1 and CD32a expression at the leading edge were significantly associated with poorer overall patient survival (hazard ratio = 2.05, 3.42 and 2.11, respectively), independent of clinical variables. In conclusion, anti-inflammatory microglia/macrophages, CD8+ T cells and programmed death-ligand 1 are correlated in the invasive margins of glioblastoma, consistent with immune-suppressive interactions. High triggering receptor expressed on myeloid cells 2, programmed death-ligand 1 and CD32a expression at the human glioblastoma leading edge are predictors of poorer overall survival. Given substantial interest in targeting microglia/macrophages, together with immune checkpoint inhibitors in cancer, these data have major clinical implications

Association of vital pulp therapy outcomes with tooth type, arch location, treatment type, and number of surfaces destroyed in deciduous teeth: A retrospective study

There is a paucity of information concerning vital pulp treatment outcomes in the undergraduate teaching setting. This study aimed to determine which type of deciduous molar, arch location, type of vital pulp therapy, and the number of carious surfaces involved had a better prognosis when carried out by undergraduate dental students. The method used was the review of clinical records of 590 patients with 600 deciduous molars, that visited the outpatient undergraduate dental clinics for vital pulp therapy. Statistical analysis used to determine the associations of tooth type, arch location, treatment type, and the number of carious surfaces involved in successful outcomes was logistic regression analysis with significance set at p &lt; 0.05. According to the regression analysis model results, there was a significant association based on tooth type (p &lt; 0.05) and arch location (p = 0.003). In addition, there was a significant association based on the type of treatment performed (p = 0.036). However, there was no significant association in success rates based on the number of carious surfaces involved (p = 0.873). In conclusion, second deciduous molars and maxillary deciduous molars had a better overall prognosis, and indirect pulp therapy was revealed to be more highly associated with successful treatment outcomes in comparison to ferric sulfate pulpotomy in our setting

Paraneoplastic cerebellar degeneration as a presentation of breast cancer – a case report and review of the literature

Paraneoplastic cerebellar degeneration is part of a rare spectrum of neurological syndromes whereby gynaecological, lung or breast cancers present primarily with neurological manifestations. The presence of onconeural antibodies and PET scanning help in the challenging diagnosis of these conditions but despite the treatment of the primary cancer, the prognosis for the neurological symptoms is poor

Endodontic Microbiology: A Bibliometric Analysis of the Top 50 Classics

Background: Citation analysis has emerged to play a significant role in recognition of the most useful areas of research. Endodontic microbiology has been a topic of interest for endodontists as well as periodontists and oral surgeons. This bibliometric analysis is aimed at identifying and reporting the characteristics of the top 50 cited articles on endodontic microbiology. Methods: The articles were identified through a search on Web of Science (WoS), property of Clarivate Analytics database published on endodontic microbiology. The citation information of the selected articles was recorded. The Journal of Endodontics, International Endodontic Journal, Oral Surgery Oral Medicine Oral Pathology Oral Radiology and Endodontology, Dental Traumatology, and Australian Endodontic Journal were searched in the search title. Descriptive and bivariate analyses were performed using a statistical software package SPSS. Statistical analysis was performed using Shapiro-Wilk, Kruskal-Wallis, Post hoc, Mann-Kendall trend, and Spearman-rank tests. Results: The 50 most cited articles were published from 1965 to 2012 with citation count varying from 1065 to 103 times. The total citation counts of articles recorded were 11,525 (WoS), 12,602 (Elseviers' Scopus), and 28,871 (Google Scholar). The most prolific years in terms of publications were 2001, 2002, and 2003, with five publications each, followed by 2005 with four. The year with most citations was 1998, with 1,330 citations, followed by 1965 and 2001, with 1,065 and 1,015 citations, respectively. A total of 136 authors contributed to the top 50 most cited articles with 27 corresponding institutions from 12 different countries. The most common methodological design was in vitro study, followed by clinic-laboratory study, literature review, systematic review and meta-analysis, and animal study. Conclusions: The present study provided a detailed list of the top 50 most cited and classic articles on microbiology in endodontics. This will help researchers, students, and clinicians in the field of endodontics as an impressive source of information

Microstructural and Elemental Characterization of Root Canal Sealers Using FTIR, SEM, and EDS Analysis

Background: Root canal sealers and repair materials should have the desirable physical, chemical, and biological characteristics, and an antibacterial effect if possible. There is little information available on the biocompatibility of new sealers on the market. Fourier transform infrared spectroscopy (FTIR) can offer trustworthy data to examine chemical structures; another technique for revealing the elements in the constituents that may contribute to the cytotoxicity of these sealers is scanning electron microscopy (SEM), with the goal of elemental mapping utilizing energy-dispersive X-ray spectroscopy (EDX). Methodology: All the root canal sealers were mixed as per the manufacturers’ instructions and allowed to set in molds for 24 h. Then, the samples were placed into an incubator (Memmert GmbH + Co. KG, Schwabach, Germany for 72 h, in a moist environment to allow complete chemical setting of the sealers. The organic and inorganic components of the sample were identified using FTIR with the wavelength length in the infra-red region measuring 400–450 nm. The finely crushed samples were coated with gold metal; following that, the sealer samples were examined under a scanning electron microscope (SEM) at 5000×, 10,000×, and 20,000× magnification, followed by energy-dispersive X-ray spectroscopy. Results: The surfaces of BioRoot and DiaRoot sealers revealed a relatively uniform distribution of irregular micro-sized particles aggregated in clusters, with the particle size ranging from 1 to 65 µm and 0.4 to 55 µm, respectively. OneFill, iRoot, and CeraSeal demonstrated irregularly shaped particles with particle sizes of 0.5 to 105 µm, 0.5 to 195 µm, and 0.3 to 68 µm, respectively. The EDX microanalysis revealed that oxygen, calcium, and carbon were found in all the tested sealer materials. Silicone and zirconium were absent in DiaRoot, but DiaRoot contained fluoride and ytterbium. Moreover, aluminum was noted in DiaRoot, One Fill, and CeraSeal, and chloride was only observed in BioRoot. FTIR analysis revealed strong absorption bands at 666 cm−1 and 709 cm−1 in BioRoot. Bands at 739 cm−1, 804 cm−1, 863 cm−1, 898 cm−1, and 1455 cm−1 were observed in DiaRoot. Bands at 736 cm−1 and 873 cm−1 in OneFill suggested the presence of C-H bending. Similarly, bands were observed at 937 cm−1, 885 cm−1, 743 cm−1, and 1455 cm−1 in iRoot, representing C-H stretching. Conclusions: All root canal sealers had diverse surface morphologies that contained irregular, micro-sized particles that were uniformly distributed, and they lacked heavy metals. All the experimental sealers comprised mainly calcium, oxygen, and carbon

Quantum cat maps with spin 1/2

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices. In particular, we show that the diagonal approximation of the spectral form factor for small arguments agrees with the CSE prediction. The results are confirmed by numerical investigations.Comment: 26 pages, 3 figure

Saccadic Eye Movement Abnormalities in Children with Epilepsy

Childhood onset epilepsy is associated with disrupted developmental integration of sensorimotor and cognitive functions that contribute to persistent neurobehavioural comorbidities. The role of epilepsy and its treatment on the development of functional integration of motor and cognitive domains is unclear. Oculomotor tasks can probe neurophysiological and neurocognitive mechanisms vulnerable to developmental disruptions by epilepsy-related factors. The study involved 26 patients and 48 typically developing children aged 8–18 years old who performed a prosaccade and an antisaccade task. Analyses compared medicated chronic epilepsy patients and unmedicated controlled epilepsy patients to healthy control children on saccade latency, accuracy and dynamics, errors and correction rate, and express saccades. Patients with medicated chronic epilepsy had impaired and more variable processing speed, reduced accuracy, increased peak velocity and a greater number of inhibitory errors, younger unmedicated patients also showed deficits in error monitoring. Deficits were related to reported behavioural problems in patients. Epilepsy factors were significant predictors of oculomotor functions. An earlier age at onset predicted reduced latency of prosaccades and increased express saccades, and the typical relationship between express saccades and inhibitory errors was absent in chronic patients, indicating a persistent reduction in tonic cortical inhibition and aberrant cortical connectivity. In contrast, onset in later childhood predicted altered antisaccade dynamics indicating disrupted neurotransmission in frontoparietal and oculomotor networks with greater demand on inhibitory control. The observed saccadic abnormalities are consistent with a dysmaturation of subcortical-cortical functional connectivity and aberrant neurotransmission. Eye movements could be used to monitor the impact of epilepsy on neurocognitive development and help assess the risk for poor neurobehavioural outcomes