Dynamic behaviours for semi-discrete stochastic Cohen-Grossberg neural networks with time delays
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Authors: Zhang, Tianwei; Han, Sufang; Zhou, Jianwen
Abstract
By using semi-discretization technique, a discrete analogue of stochastic Cohen-Grossberg neural networks is formulated. Firstly, the existence of pth mean almost periodic sequence solutions and pth moment global exponential stability of the above semi-discrete stochastic system are investigated with the help of Krasnoselskii's fixed point theorem and some analysis techniques in stochastic theory. Secondly, the exponential stability and stochastic stabilization for a special discrete stochastic Cohen-Grossberg neural networks are studied. These findings show that stochastic disturbances and small discrete step length have negative effects on the existence of mean almost periodic solutions and moment exponential stability. But they have positive effects on the exponential stability and exponential non-stability for some special models, respectively. Besides, this paper also finds that some unstable neural networks should become exponentially stable by stochastic disturbances. In the end, some examples and computer simulations are given to demonstrate the effectiveness of the theoretical results. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
A Novel Variant in the Calcium-Sensing Receptor Associated with Familial Hypocalciuric Hypercalcemia and Low-to-Normal PTH
CASE REPORTS IN ENDOCRINOLOGY
Authors: Majumdar, Sachin K.; Jacob, Tess; Bale, Allen; Bailey, Allison; Kwon, Jeffrey; Hughes, Terence; Barbieri, Andrea L.; Laskin, William; Cohen, Paul; Carling, Tobias John Eric
Abstract
Familial hypocalciuric hypercalcemia (FHH) is considered a relatively benign condition characterized by mild elevations in serum calcium and relatively low urinary calcium excretion. It results from an elevated set point in serum calcium arising from variants in the calcium-sensing receptor (CaSR) gene but also AP2S1 and GNA11 genes, which encode for adaptor-related protein complex 2 and G11 proteins, respectively. The manifestations of FHH can vary and sometimes overlap with primary hyperparathyroidism making the diagnosis challenging. Case Presentations. We report a mother and daughter with a novel heterozygous variant in the CaSR gene resulting in a serine to leucine substitution at position 147 (S147L) of the CaSR. Both patients had mild hypercalcemia, relatively low urinary calcium excretion, elevated calcitriol, and low-to-normal intact PTH. The proband (daughter) presented with symptoms associated with hypercalcemia and was incidentally found to have a bony lesion suspicious for osteitis fibrosa cystica, and she was also diagnosed with sarcoidosis. Subtotal parathyroidectomy revealed normal-weight parathyroid glands comprised of 50-80% parathyroid epithelial cells, which has been documented as within the spectrum of normal. Her mother had no symptoms, and no intervention was pursued. Conclusion. We report a novel variant in the CaSR associated with FHH in two patients with similar biochemical features yet differing clinical manifestations. While the relationship of the bony findings and parathyroid histology with this variant remains unclear, these cases enrich our knowledge of CaSR physiology and provide further examples of how varied the manifestations of FHH can be.