Acid‐Labile Thermoresponsive Copolymers That Combine Fast pH‐Triggered Hydrolysis and High Stability under Neutral Conditions

Biodegradable polymeric materials are intensively used in biomedical applications. Of particular interest for drug‐delivery applications are polymers that are stable at pH 7.4, that is, in the blood stream, but rapidly hydrolyze under acidic conditions, such as those encountered in the endo/lysosome or the tumor microenvironment. However, an increase in the acidic‐degradation rate of acid‐labile groups goes hand in hand with higher instability of the polymer at pH 7.4 or during storage, thus posing an intrinsic limitation on fast degradation under acidic conditions. Herein, we report that a combination of acid‐labile dimethyldioxolane side chains and hydroxyethyl side chains leads to acid‐degradable thermoresponsive polymers that are quickly hydrolyzed under slightly acidic conditions but stable at pH 7.4 or during storage. We ascribe these properties to high hydration of the hydroxy‐containing collapsed polymer globules in conjunction with autocatalytic acceleration of the hydrolysis reactions by the hydroxy groups.     

Space–time fractional diffusion on bounded domains

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space–time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.     

Blow-Up Results for Space-Time Fractional Stochastic Partial Differential Equations

Potential Analysis - Consider non-linear time-fractional stochastic reaction-diffusion equations of the following type, $$ \partial^{\beta}_{t}u_{t}(x)=-\nu(-{\Delta})^{\alpha/2}...     

Higher order PDE's and iterated processes

We introduce a class of stochastic processes based on symmetric -stable processes, for . These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric -stable process. We call them -time processes. They generalize Brownian time processes studied in Allouba and Zheng (2001), Allouba (2002), (2003), and they introduce new interesting examples. We establish the connection of -time processes to some higher order PDE's for rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.

     

Engineering Polymer Hydrogel Nanoparticles for Lymph Node‐Targeted Delivery

The induction of antigen‐specific adaptive immunity exclusively occurs in lymphoid organs. As a consequence, the efficacy by which vaccines reach these tissues strongly affects the efficacy of the vaccine. Here, we report the design of polymer hydrogel nanoparticles that efficiently target multiple immune cell subsets in the draining lymph nodes. Nanoparticles are fabricated by infiltrating mesoporous silica particles (ca. 200 nm) with poly(methacrylic acid) followed by disulfide‐based crosslinking and template removal. PEGylation of these nanoparticles does not affect their cellular association in vitro, but dramatically improves their lymphatic drainage in vivo. The functional relevance of these observations is further illustrated by the increased priming of antigen‐specific T cells. Our findings highlight the potential of engineered hydrogel nanoparticles for the lymphatic delivery of antigens and immune‐modulating compounds.     

Time dependent random fields on spherical non-homogeneous surfaces

We introduce a class of isotropic time dependent random fields on the non-homogeneous sphere which is represented by a time-changed spherical Brownian motion of order ν∈(0,1]$\nu \in (0,1]$. We can capture some anisotropies in Cosmology with this model. This process is a time-changed rotational diffusion (TRD) or the stochastic solution to the equation involving the spherical Laplace operator and a time-fractional derivative of order ν$\nu$. TRD is a diffusion on the non-homogeneous sphere and therefore, the spherical coordinates given by TRD represent the coordinates of a non-homogeneous sphere by means of which an isotropic random field is indexed. The time dependent random fields we present in this work are therefore realized through composition and can be viewed as isotropic random field on randomly varying sphere.     

Distributed-order fractional diffusions on bounded domains

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. This paper provides explicit strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions.