Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Information Infrastructure for Cooperative Research in Neuroscience

The paper describes a framework for efficient sharing of knowledge between research groups, which have been working for several years without flaws. The obstacles in cooperation are connected primarily with the lack of platforms for effective exchange of experimental data, models, and algorithms. The solution to these problems is proposed by construction of the platform (EEG.pl) with the semantic aware search scheme between portals. The above approach implanted in the international cooperative projects like NEUROMATH may bring the significant progress in designing efficient methods for neuroscience research

Therapeutic Trial of Metformin and Bortezomib in a Mouse Model of Tuberous Sclerosis Complex (TSC)

Tuberous sclerosis complex (TSC) is a human genetic disorder in which loss of either TSC1 or TSC2 leads to development of hamartoma lesions, which can progress and be life-threatening or fatal. The TSC1/TSC2 protein complex regulates the state of activation of mTORC1. Tsc2+/− mice develop renal cystadenoma lesions which grow progressively. Both bortezomib and metformin have been proposed as potential therapeutics in TSC. We examined the potential benefit of 1 month treatment with bortezomib, and 4 month treatment with metformin in Tsc2+/− mice. Results were compared to vehicle treatment and treatment with the mTORC1 inhibitor rapamycin for 1 month. We used a quantitative tumor volume measurement on stained paraffin sections to assess the effect of these drugs. The median tumor volume per kidney was decreased by 99% in mice treated with rapamycin (p = 0.0004). In contrast, the median tumor volume per kidney was not significantly reduced for either the bortezomib cohort or the metformin cohort. Biochemical studies confirmed that bortezomib and metformin had their expected pharmacodynamic effects. We conclude that neither bortezomib nor metformin has significant benefit in this native Tsc2+/− mouse model, which suggests limited benefit of these compounds in the treatment of TSC hamartomas and related lesions

Tsc1-Tp53 loss induces mesothelioma in mice, and evidence for this mechanism in human mesothelioma

Mesothelioma is diagnosed in approximately 2,500 patients in the United States every year, most often arising in the pleural space, but also occurring as primary peritoneal mesothelioma. The vast majority of patients with mesothelioma die from their disease within 3 years. We developed a new mouse model of mesothelioma by bladder or intra-peritoneal injection of adenovirus Cre into mice with conditional alleles of each of Tp53 and Tsc1. Such mice began to develop malignant ascites about 6 months after injection, which was due to peritoneal mesothelioma, based on tumor morphology and immunohistochemical staining. Mesothelioma cell lines were established which showed loss of both Tsc1 and Tp53, with mTORC1 activation. Treatment of mice with malignant ascites due to mesothelioma with rapamycin led to a marked reduction in ascites, extended survival, and a 95–99% reduction in mesothelioma tumor volume, in comparison to vehicle-treated mice. To see if TSC1/TSC2 loss was a common genetic event in human mesothelioma, we examined 9 human mesothelioma cell lines, and found that 4 of 9 showed persistent activation of mTORC1 though none had loss of TSC1 or TSC2. A tissue microarray analysis of 198 human mesothelioma specimens showed that 33% of cases had reduced TSC2 expression and 60% showed activation of mTOR, indicating that mTOR activation is common in human mesothelioma and suggesting that it is a potential therapeutic target

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Hahn's Symmetric Quantum Variational Calculus

We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-201

Titania aerogels: Preparation and photocatalytic tests

Titania aerogels are suggested as promising photocatalysts [1]. In the present study aerogels were synthesised by sol-gel method combined with supercritical drying. Tetraisopropyl orthotitanate was used as a precursor, anhydrous methanol and isopropanol as solvents. Three aerogels were prepared using different ways of synthesis. Volumes and surface areas of micro- and mesopores of each aerogel were determined. XRD and SEM analyses were carried out. For comparison analyses were also performed for TiO2 P25 Degussa. Aerogels' BET surface areas ranged from 73 to 96 m2g-1. They indicate the crystalline structure of anatase. Finally photocatalytic tests were performed using water solution of p-chlorophenol and 4-hydroxybenzoic acid. Experiments were carried out in the Solar box simulating sun irradiation and on location. Aerogel Z513 prepared using 30% of precursor (tetraisopropyl orthotitanate) in isopropanol as a solvent indicates the best photocatalytic activity towards p-chlorophenol while Z516 prepared using 60% of precursor in methanol towards 4-hydroxybenzoic acid

Long-term lipoprotein apheresis in the treatment of severe familial hypercholesterolemia refractory to high intensity statin therapy: Three year experience at a lipoprotein apheresis centre

Background: Severe familial hypercholesterolemia (FH) individuals, refractory to conventional lipidloweringmedications are at exceptionally high risk of cardiovascular events. The established therapeuticoption of last choice is lipoprotein apheresis (LA). Herein, it was sought to investigate the clinical usefulnessof LA in a highly selected group of severe heterozygous FH (HeFH), as recently described by theInternational Atherosclerosis Society (IAS), for their efficacy in lipid reduction and safety.Methods: Efficacy and safety of LA were investigated in 318 sessions of 7 severe HeFH females withcardiovascular disease, over a mean period of 26.9 ± 6.5 months. Relative reduction of low density lipoproteincholesterol (LDL-C) ≥ 60%, clinical complications and vascular access problems were evaluatedand compared between the direct adsorption of lipoproteins (DALI) and lipoprotein filtration (MembraneFiltration Optimized Novel Extracorporeal Treatment [MONET]). Additionally, lipoprotein (a)[Lp(a)], total cholesterol (TC), high density lipoprotein cholesterol (HDL-C), triglycerides (TG) andfibrinogen concentrations were investigated.Results: The relative reduction of LDL-C, TC, TG and Lp(a) were 69.4 ± 12.9%, 59.7 ± 9.1, 51.5 ±± 14.2% and 71.3 ± 14.4%, respectively. A similar efficacy was found in both systems in LDL-C removal.DALI system led to larger depletions of Lp(a) (80.0 [76–83]% vs. 73.0 [64.7–78.8]%; p < 0.001).The frequency of clinical side effects and vascular access problems were low (8.5%).Conclusions: Long-term LA in severe HeFH individuals is safe and efficiently reduces LDL-C andLp(a). Higher efficacy of the DALI system than MONET in Lp(a) removal may indicate the need for individualizedapplication of the LA system in severe HeFH individuals