SEIR Model for Transmission of Dengue Fever

In this paper, we study a system of differential equations that models the population dynamics of SEIR vector transmission of dengue fever. The model studied mathematical analysis by reviewing the fixed points and eigen values to determine the dynamic behaviour of system. The Simulations on the model for some parameter values were performed and the breeding rates results showed a state become either endemic or non-endemic. The SEIR model can be potential for modelling using real data

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

Modified Step Variational Iteration Method for Solving Fractional Biochemical Reaction Model

A new method called the modification of step variational iteration method (MoSVIM) is introduced and used to solve the fractional biochemical reaction model. The MoSVIM uses general Lagrange multipliers for construction of the correction functional for the problems, and it runs by step approach, which is to divide the interval into subintervals with time step, and the solutions are obtained at each subinterval as well adopting a nonzero auxiliary parameter ℏ to control the convergence region of series' solutions. The MoSVIM yields an analytical solution of a rapidly convergent infinite power series with easily computable terms and produces a good approximate solution on enlarged intervals for solving the fractional biochemical reaction model. The accuracy of the results obtained is in a excellent agreement with the Adam Bashforth Moulton method (ABMM)

Learners’ frequent pattern discovering in a dynamic collaborative learning environment designed based on game theory

Background and Objectives:In any educational system, the optimal output of educational approach is of particular importance. Therefore, considering the personality characters of individuals and providing educational services in accordance with their characteristics are effective factors in learning and educational efficiency improvement. Analyzing the data related to learner’s behavior in an educational environment and implicitly discovering the learner’s personality based on their behavior is a well-noticed study in recent years. Over the last few years, using learners’ information such as number of friends, the level of activities in educational forum, writing style of learner, study duration, the difficulty of solved problem, the difficulty of presented example by learners, number of clicks, number of signs in sentences, the time spent doing homework are items that has been used to personal characteristic identification. This study is aimed at using teammates’ changing / not changing data in order to learners’ personality identification. For this purpose the teammates’ changing/ not changing data extracted from a dynamic collaborative learning environment that allows leaners to change their teammate during the different sessions of learning, are used. The design and implementation of mentioned dynamic collaborative learning environment is based on game theory. Game theory provides mathematical models of conflict and collaboration between intelligent rational decision-makers. Methods: In this paper, we collect teammates’ changing/not changing information of 119 randomly selected computer engineering students from a game theoretical dynamic collaborative learning environment. At the next step, using frequent pattern mining, as a tools of data mining, some aspects of the neo big 5 personality traits of learners are identified. In this survey, in order to evaluate the results, the extracted patterns from frequent pattern mining are compared with the neo big 5 personality questionnaire that have been filled by learners. In another part of research, using the Laplace’s rule of succession, valuable predictions were made about the probability of teammate’s changing of learners during the learning process. Findings: In this study, using frequent pattern mining in learners’ behaviour, we identified some neo big 5 personality traits such as those in the first (neuroticism), second (extraversion), and third (openness to experience) dimensions, with an acceptable support value. The results of this part of research can be used in any adaptive learning environment that adapt learning process for individual learners with different personality. At the next step of our study, we predicted the probability of the teammate changing in the sessions after. At this step, we had a prediction accuracy of up to 67.44%. Using the results of this part, teammate suggestion can be made to learner based on likelihood of their teammates’ changing. That is, higher teammate changing probability, more appropriate teammate suggestion to learner. Conclusion: The results of the present study can be used in any adaptive system that requires predicting group change behaviour or identifying personality dimensions based on behaviour.   ===================================================================================== COPYRIGHTS  ©2020 The author(s). This is an open access article distributed under the terms of the Creative Commons Attribution (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, as long as the original authors and source are cited. No permission is required from the authors or the publishers.  ====================================================================================

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

Oscillations for Neutral Functional Differential Equations

We will consider a class of neutral functional differential equations. Some infinite integral conditions for the oscillation of all solutions are derived. Our results extend and improve some of the previous results in the literature

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

Patient-Centered Outcomes of Microfragmented Adipose Tissue Treatments of Knee Osteoarthritis: An Observational, Intention-to-Treat Study at Twelve Months

© 2020 Nima Heidari et al. Introduction. Microfragmented adipose tissue (MFAT) has been shown to benefit osteoarthritic patients by reducing pain and supporting tissue regeneration through a mesenchymal stem cell (MSC)-related paracrine mechanism. This observational study of 110 knees assessed patient-centered outcomes of pain, functionality, and quality of life, analyzing their variation at twelve months following one ultrasound-guided intra-articular injection of autologous MFAT for the treatment of knee osteoarthritis (KOA). Method. Inclusion criteria were as follows: VAS >50, and the presence of KOA as diagnosed on X-ray and MRI. Exclusion criteria included the following: recent injury (<3 months) of the symptomatic knee, intra-articular steroid injections performed within the last three months, and hyaluronic acid injections prior to this treatment. Changes in VAS, OKS, and EQ-5D were scored at baseline and twelve months following a single intra-articular injection of autologous MFAT. Score variation was analyzed utilizing a nonparametric paired samples Wilcoxon test. The statistical analysis is reproducible with Open Access statistical software R (version 4.0.0 or higher). The study was carried out with full patient consent, in a private practice setting. Results. Median VAS (pain) improved from 70 (IQR 20) to 30 (IQR 58) (p<0.001); median OKS (function) improved from 25 (IQR 11) to 33.5 (IQR 16) (p<0.001); and median EQ-5D (quality of life) improved from 0.62 (IQR 0.41) to 0.69 (IQR 0.28) (p<0.001). No adverse events were reported during the intraoperative, recovery, or postoperative periods. Conclusions. For patients with all grades of knee osteoarthritis who were treated with intra-articular injections of MFAT, statistically significant improvements in pain, function, and quality of life were reported. Although further research is warranted, the results are encouraging and suggest a positive role for intra-articular injection of MFAT as a treatment for knee osteoarthritis