Functionalization of Polyethyleneimine with Hollow Cyclotriveratrylene and Its Subsequent Supramolecular Interaction with Doxorubicin

In this paper, a modified Cyclotriveratrylene was synthesized and linked to a branched Polyethylenimine, and this unique polymeric material was subsequently examined as a potential supramolecular carrier for Doxorubicin. Spectroscopic analysis in different solvents had shown that Doxorubicin was coordinated within the hollow-shaped unit of the armed Cyclotriveratrylene, and the nature of the host–guest complex revealed intrinsic Van der Waals interactions and hydrogen bonding between the host and guest. The strongest interaction was detected in water because of the hydrophobic effect shared between the aromatic groups of the Doxorubicin and Cyclotriveratrylene unit. Density functional theory calculations had also confirmed that in the most stable coordination of Doxorubicin with the cross-linked polymer, the aromatic rings of the Doxorubicin were localized toward the Cyclotriveratrylene core, while its aliphatic chains aligned closer with amino groups, thus forming a compact supramolecular assembly that may confer a shielding effect on Doxorubicin. These observations had emphasized the importance of supramolecular considerations when designing a novel drug delivery platform.     

Thiazonaphthalimide derivatives: Synthesis and interaction with DNA

The synthesis of several thiazonaphthalimide derivatives is described. The exclusive formation of angular rather than linear isomers was unequivocally demonstrated by NMR and single crystal X-ray diffraction. Their photophysical properties and ability to bind calf-Thymus DNA with affinities in the range of 10⁴ makes them interesting candidates to probe DNA by fluorescence.     

On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply.     

Realization of 2-solvable nilpotent groups as groups of classes of homotopy self-equivalences

Let X be a 1-connected CW-complex of finite type and ε_?(X) be the group of homotopy classes of self-equivalences of X which induce the identity on homotopy groups. In this paper, we prove that every finitely generated 2-solvable rational nilpotent group is realizable as ε_?(X) where X is the rationalization of a 1-connected CW-complex of finite type.     

Monoid of self-equivalences and free loop spaces

Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .

     

Computing the conjugate of convex piecewise linear-quadratic bivariate functions

We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and faces. Using optimal computational geometry data structures, the algorithm has a linear time worst-case complexity. We present the algorithm, and illustrate it with numerical examples. We proceed to build a toolbox for convex bivariate PLQ functions by implementing the addition, and scalar multiplication operations. Finally, we compose these operators to compute classical convex analysis operators such as the Moreau envelope, and the proximal average.     

Optimization of Schwarz waveform relaxation over short time windows

Schwarz waveform relaxation algorithms (SWR) are naturally parallel solvers for evolution partial differential equations. They are based on a decomposition of the spatial domain into subdomains, and a partition of the time interval of interest into time windows. On each time window, an iteration, during which subproblems are solved in space-time subdomains, is then used to obtain better and better approximations of the overall solution. The information exchange between subdomains in space-time is performed through classical or optimized transmission conditions (TCs). We analyze in this paper the optimization problem when the time windows are short. We use as our model problem the optimized SWR algorithm with Robin TCs applied to the heat equation. After a general convergence analysis using energy estimates, we prove that in one spatial dimension, the optimized Robin parameter scales like the inverse of the length of the time window, which is fundamentally different from the known scaling on general bounded time windows, which is like the inverse of the square root of the time window length. We illustrate our analysis with a numerical experiment.     

Feasibility of using ultrasound contrast agents to increase the size of thermal lesions induced by non-focused transducers: in vitro demonstration in tissue mimicking phantom

Miniature flat ultrasound transducers have shown to be effective for a large variety of thermal therapies, but the associated superficial heating implicates developing original strategies in order to extend therapeutic depth. The goal of the present paper is to use ultrasound contrast agents (UCA) to increase remote attenuation and heating. Theoretical simulations demonstrated that increasing attenuation from 0.27 to 0.8 Np/cm at 10 MHz beyond a distance of 18 mm from the transducer should result in longer thermal damages due to protein coagulation in a tissue mimicking phantom. Contrast agents (BR14, Bracco, Plan-les-Ouates, Switzerland) were embedded in thermo-sensitive gel and attenuations ranging from 0.27 to 1.33 Np/cm were measured at 10 MHz for concentrations of BR14 between 0 and 4.8%. Thermal damages were then induced in several gels, which had different layering configurations. Thermal damages, 12.8 mm in length, were obtained in homogeneous gels. When mixing contrast agents at a concentration of 3.2% beyond a first 18 mm-thick layer of homogeneous gel, the thermal damages reached 21.5 mm in length. This work demonstrated that contrast agents can be used for increasing attenuation remotely and extending therapeutic depth induced by a non-focused transducer. Additional work must be done in vivo in order to verify the remote-only distribution of bubbles and associated increase in attenuation.