Darboux transformations and Recursion operators for differential--difference equations

In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensive list of integrable differential-difference equations together with their Hamiltonian structures, recursion operators, nontrivial generalised symmetries and Darboux-Lax representations. The new results include multi-Hamiltonian structures and recursion operators for integrable Volterra type equations, integrable discretisation of derivative nonlinear Schroedinger equations such as the Kaup-Newell lattice, the Chen-Lee-Liulattice and the Ablowitz-Ramani-Segur (Gerdjikov-Ivanov) lattice. We also compute the weakly nonlocal inverse recursion operators

Representations of sl(2,?) in category O and master symmetries

We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries

Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations we derive new vector Yang-Baxter map and integrable discrete vector sine-Gordon equation on a sphere

The possible role of progranulin on anti-inflammatory effects of metformin in temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is the most prevalent and drug-resistant form of parietal epilepsy. TLE is accompanied by neuroinflammation in the brain, which involves reactive glial cells. Metformin is an old antidiabetic drug with anti-inflammatory and neuroprotective effects. Considering the importance of inflammation in epilepsy, we have investigated the effect of metformin on astrogliosis markers as well as pro and anti-inflammatory cytokines and its effect on progranulin expression (an important neuroprotective protein in epilepsy) in a rat TLE model. TLE was induced by intracerebroventricular microinjection of kainic acid. Metformin was orally administered for two weeks before the induction of epilepsy. Astrogliosis markers (GFAP and S100B), as well as IL-1β and IL- 10 levels, were detected by ELISA. The progranulin level was measured by Western blotting and immunohistochemistry in the hippocampus. Our results showed basal levels of GFAP, S100B, and pro-inflammatory cytokine increased in the epileptic rats but were significantly ameliorated after pretreatment with metformin. However, anti-inflammatory cytokine and progranulin also increased in the pre-treated rats and metformin alone group. An increment in the progranulin level emphasizes the importance of this protein in epilepsy. Hence, metformin may exert at least some of its anti-inflammatory effects by increasing progranulin level. In sum, we have concluded that progranulin can be a key mediator in epilepsy, and the anti-inflammatory action of metformin in status epilepticus is through increasing the secretion of IL-10 and inhibiting IL-1 β and astrogliosis. © 202

2-Deoxyglucose protects hippocampal neurons against kainate-induced temporal lobe epilepsy by modulating monocyte-derived macrophages (mo-MΦ) and progranulin production in the hippocampus

Inflammation is an important factor in the pathology of epilepsy with the hallmarks of resident microglia activation and infiltration of circulating monocytes in the damaged area. In the case of recovery and tissue repair, some monocytes change to macrophages (mo-MΦ) to enhance tissue repair. 2-deoxyglucose (2DG) is an analog of glucose capable of protecting the brain, and progranulin is a neurotrophic factor produced mainly by microglia and has an inflammation modulator effect. This study attempted to evaluate if one of the neuroprotective mechanisms of 2-DG is comprised of increasing monocyte-derived macrophages (mo-MΦ) and progranulin production. Status epilepticus (SE) was induced by i.c.v. injection of kainic acid (KA).2DG (125/mg/kg/day) was administered intraperitoneally. Four days later, animals were sacrificed. Their brain sections were then stained with Cresyl violet and Fluoro-Jade B to count the number of necrotic and degenerating neurons in CA3 and Hilus of dentate gyrus of the hippocampus. Lastly, immunohistochemistry was used to detect CD11b + monocyte, macrophage cells, and Progranulin level was evaluated by Western blotting. The histological analysis showed that 2DG can reduce the number of necrotic and degenerating neurons in CA3 and Hilar areas. Following KA administration, a great number of cD11b+ cells with monocyte morphology were observed in the hippocampus. 2DG not only reduced cD11b+ monocyte cells but was able to convert them to cells with the morphology of macrophages (mo-MΦ). 2DG also caused a significant increase in progranulin level in the hippocampus. Because macrophages and microglia are the most important sources of progranulin, it appears that 2DG caused the derivation of monocytes to macrophages and these cells produced progranulin with a subsequent anti-inflammation effect. In summary, it was concluded that 2DG is neuroprotective and probably one of its neuroprotective mechanisms is by modulating monocyte-derived macrophages by progranulin production. © 201

Combination therapy of curcumin and alendronate modulates bone turnover markers and enhances bone mineral density in postmenopausal women with osteoporosis

OBJECTIVE: This study evaluated the effects of combination therapy of curcumin and alendronate on BMD and bone turnover markers in postmenopausal women with osteoporosis. SUBJECTS AND METHODS: In a randomized, double-blind trial study, 60 postmenopausal women were divided into three groups: control, alendronate, and alendronate + curcumin. Each group included 20 patients. Total body, total hip, lumbar spine and femoral neck BMDs were measured by dual-energy X-ray absorptiometry (DXA) at baseline and after 12 months of therapy. Bone turnover markers such as bone-specific alkaline phosphatase (BALP), osteocalcin and C-terminal cross-linking telopeptide of type I collagen (CTx) were measured at the outset and 6 months later. RESULTS: Patients in the control group suffered a significant decrease in BMD and increased bone turnover markers at the end of study. The group treated with only alendronate showed significantly decreased levels of BALP and CTx and increased levels of osteocalcin compared to the control group. The alendronate group also showed significant increases in the total body, total hip, lumbar spine and femoral neck BMDs at the end of study compared to the control group. In the curcumin + alendronate group, BALP and CTx levels decreased and osteocalcin levels increased significantly at the end of study compared to the control and alendronate groups. BMD indexes also increased in four areas significantly at the end of study compared to the control and alendronate groups. CONCLUSION: The combination of curcumin and alendronate has beneficial effects on BMD and bone turnover markers among postmenopausal women with osteoporosis. Arch Endocrinol Metab. 2018;62(4):438-45

Mitochondrial ATP-sensitive potassium channel, MitoKATP, ameliorates mitochondrial dynamic disturbance induced by temporal lobe epilepsy

Temporal lobe epilepsy leads to a disturbance in the function and dynamic of the mitochondria. The mitoKATP channel is an important factor in controlling mitochondrial function. In this study, the protective role of mitoKATP was studied in temporal lobe epilepsy through the regulation of mitochondrial dynamic proteins. After induction of epilepsy, 5-HD (the inhibitor of mitoKATP) was administered daily for either 24 or 72 h. The results revealed an imbalance in dynamic proteins after epilepsy, specifically in the first 72 h. The disturbance in the mitochondrial dynamic worsened after blocking mitoKATP. In conclusion, mitoKATP has an important role in balancing mitochondrial dynamic proteins in epilepsy. © 2020 Elsevier B.V

'Reinette Russet'(R) and 'Galarina'(R) : two new winter hardy disease resistant apple cultivars released through joint collaboration of INRA (France) and AAFC (Canada)

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'Galarina' apple

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