A boronate gel-based synthetic platform for closed-loop insulin delivery systems

Diabetes is one of the most devastating global diseases with an ever-increasing number of patients. Achieving persistent glycemic control in a painless and convenient way is an unmet goal for diabetes management. Insulin therapy is commonly utilized for diabetes treatment and usually relies on patient self-injection. This not only impairs a patient’s quality of life and fails to precisely control the blood glucose level but also brings the risk of life-threatening hypoglycemia. “closed-loop” insulin delivery systems could avoid these issues by providing on-demand insulin delivery. However, safety concerns limit the application of currently developed electronics-derived or enzyme-based systems. Phenylboronic acid (PBA), with the ability to reversibly bind glucose and a chemically tailored binding specificity, has attracted substantial attention in recent years. This focus review provides an overview of PBA-based versatile insulin delivery platforms developed in our group, including new PBA derivatives, glucose-responsive gels, and gel-combined medical devices, with a unique “skin layer” controlled diffusion feature.

On Krylov’s estimates for optional semimartingales

The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.

Spin-singlet to triplet Cooper pair converter interface

Combining magnetic and superconducting functionalities enables lower energy spin transfer and magnetic switching in quantum computing and information storage, owing to the dissipationless nature of quasi-particle mediated supercurrents. Here, we put forward a system where emergent spin-ordering and diffusion of Cooper pairs are achieved at a non-intrinsically magnetic nor superconducting metallo-molecular interface. Electron transport, magnetometry and low-energy muon spin rotation are used to probe time-reversal symmetry breaking in these structures. By comparing the Meissner expulsion in a system including a Cu/C60 spin-converter interface to one without, we observe a paramagnetic contribution that can be explained due to the conversion of spin-singlet Cooper pair states into odd-frequency triplet states. These results demonstrate the potential of metallo-molecular interfaces to achieve singlet to triplet Cooper pair conversion, a capability not present in either metal or molecule separately that could be used in the generation and controlled diffusion of spin polarised dissipationless currents.

On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime

We study ergodic properties of Markovian multiclass many-server queues that are uniform over scheduling policies and the size of the system. The system is heavily loaded in the Halfin–Whitt regime, and the scheduling policies are work conserving and preemptive. We provide a unified approach via a Lyapunov function method that establishes Foster–Lyapunov equations for both the limiting diffusion and the prelimit diffusion-scaled queuing processes simultaneously. We first study the limiting controlled diffusion and show that if the spare capacity (safety staffing) parameter is positive, the diffusion is exponentially ergodic uniformly over all stationary Markov controls, and the invariant probability measures have uniform exponential tails. This result is sharp because when there is no abandonment and the spare capacity parameter is negative, the controlled diffusion is transient under any Markov control. In addition, we show that if all the abandonment rates are positive, the invariant probability measures have sub-Gaussian tails regardless whether the spare capacity parameter is positive or negative. Using these results, we proceed to establish the corresponding ergodic properties for the diffusion-scaled queuing processes. In addition to providing a simpler proof of previous results in Gamarnik and Stolyar [Gamarnik D, Stolyar AL (2012) Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime: asymptotics of the stationary distribution. Queueing Systems 71(1–2):25–51], we extend these results to multiclass models with renewal arrival processes, albeit under the assumption that the mean residual life functions are bounded. For the Markovian model with Poisson arrivals, we obtain stronger results and show that the convergence to the stationary distribution is at an exponential rate uniformly over all work-conserving stationary Markov scheduling policies.