What Is the Mechanism Driving the Reduction of Cardiovascular Events from Glucagon-like Peptide-1 Receptor Agonists?—A Mini Review

Glucagon-like peptide-1 receptor agonists (GLP-1 RAs) are considered the standard of care for type 2 diabetes in many countries worldwide. These molecules have profound anti-hyperglycaemic actions with a favourable safety profile. They are now being considered for their robust cardiovascular (CV) protective qualities in diabetic patients. Most recent CV outcome trials have reported that GLP-1 RAs reduce major adverse cardiovascular events (MACE). Furthermore, the GLP-1 RAs seem to target the atherosclerotic CV disease processes preferentially. GLP-1 RAs also improve a wide range of routinely measured surrogate markers associated with CV risk. However, mediation analysis suggests these modest improvements may contribute indirectly to the overall anti-atherogenic profile of the molecules but fall short in accounting for the significant reduction in MACE. This review explores the body of literature to understand the possible mechanisms that contribute to the CV protective profile of GLP-1 RAs.     

An algebraic structure for Faber polynomials

Let Σ be the set of functions, convergent for all |z|>1, with a Laurent series of the form f(z)=z+∑_n?0a_nz^-n. In this paper, we prove that the set of Faber polynomial sequences over Σ and the set of their normalized kth derivative sequences form groups which are isomorphic to the hitting time subgroup and the Bell^(k) subgroup of the Riordan group, respectively. Further, a relationship between such Faber polynomial sequences and Lucas and Sheffer polynomial sequences is derived.     

A new extension theorem for 3-weight modulo q linear codes over $${\mathbb{F}_ q}$$

We prove that every [n, k, d] _q code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .      

Workload and Waiting Time Analyses of MAP/G/1 Queue under D-policy

We study the workload (unfinished work) and the waiting time of the queueing system with MAP arrivals under D-policy. The D-policy stipulates that the idle server begin to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We first set up the system equations for workload and obtain the steady-state distributions of workloads at an arbitrary idle and busy points of time. We then proceed to obtain the waiting time distribution of an arbitrary customer based on the workload results. The M/G/1/D-policy queue will be investigated as a special case.