Mathematical background for a method on quotient signal decomposition

The blind source separation problem is discussed in this article. Focusing on the assumption of independency of the sources in the time-frequency domain, we present a mathematical formulation for the estimation problem of the number of sources. The proposed method uses the quotient of complex valued time-frequency information of only two observed signals to detect the number of sources. No fewer number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. We propose algorithms with feedback and give numerical simulations to show the method works well even for noisy case.     

Spectral stability results for higher-order operators under perturbations of the domain

We analyze the spectral behavior of higher-order elliptic operators when the domain is perturbed. We provide general spectral stability results for Dirichlet and Neumann boundary conditions. Moreover, we study the bi-harmonic operator with the so-called intermediate boundary conditions. We give special attention to this last case and analyze its behavior when the boundary of the domain has some oscillatory behavior. We will show that there is a critical oscillatory behavior and that the limit problem depends on whether we are above, below or just sitting on this critical value.     

Chaos and reproduction in sea level

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: optimal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.     

Molecularly imprinted hydrogels for sustained release of sunitinib in breast cancer therapy

The present work reports on the synthesis of a molecularly imprinted polymer (MIP) based on methacrylic acid and ethylene glycol dimethacrylate for sunitinib delivery. Sunitinib (SUT) is a tyrosine kinase inhibitor used in many cancer diseases. Like the majority of the anticancer drugs, SUT suffers of a low bioavailability, and at the same time, it is characterized by a narrow therapeutic window. In order to reduce drug systemic toxicity, we synthesized a MIP‐based drug delivery system for SUT‐controlled release. MIP was obtained by bulk polymerization through the so‐called noncovalent approach. Rebinding experiments were performed to evaluate the success of the imprinting process and the ability of MIP to bind in a specific and selective fashion the template molecule. Resulting data showed that sunitinib rebinding percentage was 70%, while nonimprinted polymer (NIP) rebinding percentage was 46%. A not significant difference was observed between MIP and NIP in semaxanib binding experiments. Moreover, the drug release profiles were studied for both MIP and NIP. A sustained release was observed from sunitinib‐loaded MIP during 24 hours, reaching 58% after 6 hours and 76% at the end‐point. NIP, on the contrary, released almost 90% of the loaded drug within 6 hours. Furthermore, the drug carrier was tested in vitro against MCF‐7 cells, in which the cytotoxic effect of sunitinib released from MIP reached the maximum after 72 hours, while NIP completed its effect within 48 hours. These results demonstrated that molecularly imprinted polymers are suitable systems for SUT release.     

Rational Design and Development of Anisotropic and Mechanically Strong Gelatin‐Based Stress Relaxing Hydrogels for Osteogenic/Chondrogenic Differentiation

Rational design and development of tailorable simple synthesis process remains a centerpiece of investigational efforts toward engineering advanced hydrogels. In this study, a green and scalable synthesis approach is developed to formulate a set of gelatin‐based macroporous hybrid hydrogels. This approach consists of four sequential steps starting from liquid‐phase pre‐crosslinking/grafting, unidirectional freezing, freeze‐drying, and finally post‐curing process. The chemical crosslinking mainly involves between epoxy groups of functionalized polyethylene glycol and functional groups of gelatin both in liquid and solid state. Importantly, this approach allows to accommodate different polymers, chitosan or hydroxyethyl cellulose, under identical benign condition. Structural and mechanical anisotropy can be tuned by the selection of polymer constituents. Overall, all hydrogels show suitable structural stability, good swellability, high porosity and pore interconnectivity, and maintenance of mechanical integrity during 3‐week‐long hydrolytic degradation. Under compression, hydrogels exhibit robust mechanical properties with nonlinear elasticity and stress‐relaxation behavior and show no sign of mechanical failure under repeated compression at 50% deformation. Biological experiment with human bone marrow mesenchymal stromal cells (hMSCs) reveals that hydrogels are biocompatible, and their physicomechanical properties are suitable to support cells growth, and osteogenic/chondrogenic differentiation, demonstrating their potential application for bone and cartilage regenerative medicine toward clinically relevant endpoints.     

Unravelling the Phytochemical Composition and the Pharmacological Properties of an Optimized Extract from the Fruit from Prunus mahaleb L.: From Traditional Liqueur Market to the Pharmacy Shelf

Prunus mahaleb L. fruit has long been used in the production of traditional liqueurs. The fruit also displayed scavenging and reducing activity, in vitro. The present study focused on unravelling peripheral and central protective effects, antimicrobial but also anti-COVID-19 properties exerted by the water extract of P. mahaleb. Anti-inflammatory effects were studied in isolated mouse colons exposed to lipopolysaccharide. Neuroprotection, measured as a blunting effect on hydrogen-peroxide-induced dopamine turnover, was investigated in hypothalamic HypoE22 cells. Antimicrobial effects were tested against different Gram+ and Gram- bacterial strains. Whereas anti-COVID-19 activity was studied in lung adenocarcinoma H1299 cells, where the gene expression of ACE2 and TMPRSS2 was measured after extract treatment. The bacteriostatic effects induced on Gram+ and Gram- strains, together with the inhibition of COX-2, TNFα, HIF1α, and VEGFA in the colon, suggest the potential of P. mahaleb water extract in contrasting the clinical symptoms related to ulcerative colitis. The inhibition of the hydrogen peroxide-induced DOPAC/DA ratio indicates promising neuroprotective effects. Finally, the downregulation of the gene expression of ACE2 and TMPRSS2 in H1299 cells, suggests the potential to inhibit SARS-CoV-2 virus entry in the human host. Overall, the results support the valorization of the local cultivation of P. mahaleb.     

A Variational Approach to the Maximization of Preferences Without Numerical Representation

Journal of Optimization Theory and Applications - We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such...     

Antimicrobial Effect and Cytotoxic Evaluation of Mg-Doped Hydroxyapatite Functionalized with Au-Nano Rods

Hydroxyapatite (HA) is the main inorganic mineral that constitutes bone matrix and represents the most used biomaterial for bone regeneration. Over the years, it has been demonstrated that HA exhibits good biocompatibility, osteoconductivity, and osteoinductivity both in vitro and in vivo, and can be prepared by synthetic and natural sources via easy fabrication strategies. However, its low antibacterial property and its fragile nature restricts its usage for bone graft applications. In this study we functionalized a MgHA scaffold with gold nanorods (AuNRs) and evaluated its antibacterial effect against S. aureus and E. coli in both suspension and adhesion and its cytotoxicity over time (1 to 24 days). Results show that the AuNRs nano-functionalization improves the antibacterial activity with 100% bacterial reduction after 24 h. The toxicity study, however, indicates a 4.38-fold cell number decrease at 24 days. Although further optimization on nano-functionalization process are needed for cytotoxicity, these data indicated that Au-NRs nano-functionalization is a very promising method for improving the antibacterial properties of HA.