On the Optimal Control of a Random Walk with Jumps and Barriers

The modeling and optimal control of a class of random walks (RWs) is investigated in the framework of the Chapman-Kolmogorov (CK) and Fokker-Planck (FP) equations. This class of RWs includes jumps driven by a compound Poisson process and are subject to different barriers. A control mechanism is investigated that is included in the CK stochastic transition matrix and the purpose of the control is to track a desired discrete probability density function and attain a desired terminal density configuration. Existence and characterization of optimal controls are discussed. The proposed approach allows the derivation of a new FP model that accommodates the presence of the jumps and guarantees conservation of total probability in the case of reflecting barriers, which are modelled by appropriate operators. Results of numerical experiments are presented that successfully validate the proposed control framework.     

Existence of complete vector topologies with prescribed conditions

In every infinite-dimensional vector space we build a complete, non-locally convex linear Hausdorff topology under the prescribed condition that it shall be compatible with a bounded algebraic structure for the space, that is, it admits a bounded Hamel basis whose coefficient linear functionals are continuous. As a byproduct, we obtain the existence of non-locally convex topologies having the approximate and fixed point property as prescribed conditions. The obstruction of bounded Hamel bases by complete vector topologies on linear space of countable dimension is also discussed.     

Tree Oriented Pullback

Given two epimorphisms of algebras A ? B and C ? B, we consider the pullback R. We introduce a particular class of algebras, the tree oriented pullback, where there is a close relationship between the category of indecomposable modules of these algebras. This leads us to prove that if A and C are hereditary algebras, then R is a tilted algebra.     

Switching and enhanced bistability in an asymmetric nonlinear directional coupler with a metamaterial channel

We numerically simulate the propagation and switching of ultra-short pulses in a metamaterial nonlinear directional asymmetric coupler where one of the guides is a conventional medium with a positive refraction index having a decreasing Kerr nonlinearity. The second guide is based in a metamaterial. A complete study of the nonlinear dynamics of ultra-short pulses propagation and switching in this new nonlinear directional coupler, including the transmission characteristics, bistability, critical power, compression factor and extinction coefficients are presented and compared to those of a conventional coupler. We conclude that the conventional coupler has higher transmission efficiency and extinction rate when compared with the metamaterial coupler. However the metamaterial coupler presents bistability which opens the possibility of such device to be used in a large variety of optical switching, storage and logical gates. We show that the input power range leading to bistability can be optimized by controlling the profile of the nonlinear refraction index of the conventional channel.     

Synthesis and physical properties of highly branched perfluorinated polymers from AB and AB2 monomers

Highly branched perfluorinated aromatic polyether copolymers were prepared from the polycondensation of the AB₂ monomer, 3,5‐bis[(pentafluorobenzyl)oxy]benzyl alcohol with a variety of fluoroaryl and alkyl bromide AB comonomers. The structures and comonomer distribution of the resulting polymers were characterized in detail. ¹H NMR data from kinetic trials illustrated that perfluoroaryl AB comonomer distribution correlated to AB comonomer sterics. ¹⁹F NMR data revealed that fluorinated AB monomers and 3‐bromo‐1‐propanol AB monomers were distributed within the AB₂ polymer backbone, while longer alkyl bromide AB monomers, 6‐bromo‐1‐hexanol, were mostly distributed along hyperbranched polymer chain ends. In general, as AB comonomer incorporation increased for nonsterically hindered copolymers, thermal decomposition onset increased and glass transition temperatures decreased. The combined data demonstrated the effect of comonomer distribution and sterics on physical properties of AB₂‐based polymer systems. The resulting materials were used to cast thin polymer films for measurement of contact angle, which were shown to be directly related to comonomer content. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1880–1894     

The Plasticity of the Carbohydrate Recognition Domain Dictates the Exquisite Mechanism of Binding of Human Macrophage Galactose-Type Lectin

The human macrophage galactose-type lectin (MGL), expressed on macrophages and dendritic cells (DCs), modulates distinct immune cell responses by recognizing N-acetylgalactosamine (GalNAc) containing structures present on pathogens, self-glycoproteins, and tumor cells. Herein, NMR spectroscopy and molecular dynamics (MD) simulations were used to investigate the structural preferences of MGL against different GalNAc-containing structures derived from the blood group A antigen, the Forssman antigen, and the GM2 glycolipid. NMR spectroscopic analysis of the MGL carbohydrate recognition domain (MGL-CRD, C181-H316) in the absence and presence of methyl α-GalNAc (α-MeGalNAc), a simple monosaccharide, shows that the MGL-CRD is highly dynamic and its structure is strongly altered upon ligand binding. This plasticity of the MGL-CRD structure explains the ability of MGL to accommodate different GalNAc-containing molecules. However, key differences are observed in the recognition process depending on whether the GalNAc is part of the blood group A antigen, the Forssman antigen, or GM2-derived structures. These results are in accordance with molecular dynamics simulations that suggest the existence of a distinct MGL binding mechanism depending on the context of GalNAc moiety presentation. These results afford new perspectives for the rational design of GalNAc modifications that fine tune MGL immune responses in distinct biological contexts, especially in malignancy.     

Parkia pendula Seed Lectin: Potential Use to Treat Cutaneous Wounds in Healthy and Immunocompromised Mice

Parkia pendula seed lectin was used to treat cutaneous wounds of normal and immunocompromised mice, inducing cicatrization. Methotrexate (0.8 mg/kg/week) was used as immunosuppressive drug. Wounds were produced in the dorsal region (1 cm²) of female albino Swiss mice (Mus musculus), health and immunocompromised. Wounds were daily topically treated with 100 μL of the following solutions: (1) control (NaCl 0.15 M), (2) control Im (0.15 M NaCl), (3) P. pendula seed lectin (100 μg/mL), and (4) P. pendula seed lectin Im (100 μg/mL). Clinical evaluation was performed during 12 days. Biopsies for histopathology analysis and microbiological examinations were carried out in the second, seventh, and 12th days. The presence of edema and hyperemia was observed in all groups during inflammatory period. The first crust was detected from the second day, only in the groups treated with P. pendula seed lectin. Microbiological analysis of wounds from day 0 to day 2 did not show bacterium at P. pendula seed lectin group; however, Staphylococcus sp. was detected every day in the other groups. The lectin markedly induced a total wound closing at P. pendula seed lectin and P. pendula seed lectin Im groups on 11th day of evolution. The present study suggests that P. pendula seed lectin is a biomaterial potential to show pharmacological effect in the repair process of cutaneous wounds.     

Identification of Seven-coordinate LnIII Ions in a LnIII[15-MCFeIIIN(shi)-5](OAc)2Cl Species Crystallized from Methanol and Pyridine

The title metallacrown (MC) complexes Ln^III[15-MC_Fe^III_N(shi)-5](OAc)₂Cl(C₅H₅N)₆ (Ln1), where OAc^– is acetate, shi^3? is salicylhydroximate, and Ln?=?Gd and Dy, were synthesized via a self-assembly reaction in methanol and pyridine. Single crystals were grown using slow evaporation and characterized using X-ray diffraction. Seven-coordinate capped octahedron geometries were observed for the lanthanide ion in both complexes, which is uncommon for trivalent lanthanide species. The 15-MC-5 is a ruffled metallacrown archetype similar to previously reported mixed-valent manganese metallacrowns.

Graphic Abstract

The title metallacrown (MC) complexes Ln^III[15-MC_Fe^III_N(shi)-5](OAc)₂Cl(C₅H₅N)₆ (Ln1), where OAc^– is acetate, shi^3? is salicylhydroximate, and Ln?=?Gd and Dy, contains seven-coordinate capped octahedron geometries for the lanthanide ion in both complexes, which is uncommon for trivalent lanthanide species.

     

Colour switching with photochromic vinylidene-naphthofurans

A series of novel photochromic vinylidene-naphthofurans with extended conjugation, and a free hydroxyl function, were easily prepared using the Suzuki reaction. After silanization, these dyes were embedded in ormosil matrices affording solid and transparent materials that acquire different colourations (violet, green, bluish), reversibly, when exposed to the UV (Sun) light, for 2?min, at room temperature. The presence of an extra phenyl ring in some positions affects both the λ_max of absorption of the photochromic compounds in the uncoloured closed and open coloured form. After removal of the light source the materials lose progressively their colouration returning to the initial uncoloured state in less than 15?min?at room temperature.