A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Cerebral microbleeds and cognitive decline in a hemodialysis patient: Case report and review of literature

Cerebral microbleeds (CMBs) are small hemosiderin deposits indicative of prior cerebral microscopic hemorrhage and previously thought to be clinically silent. Recent population‐based cross‐sectional studies and prospective longitudinal cohort studies have revealed association between CMB and cognitive dysfunction. In the general population, CMBs are associated with age, hypertension, and cerebral amyloid angiopathy. In the chronic kidney disease (CKD) population, diminished estimated glomerular filtration rate has been found to be an independent risk factor for CMB, raising the possibility that a uremic milieu may predispose to microbleeds. In the end‐stage renal disease (ESRD) population on hemodialysis, the incidence of microbleeds is significantly higher compared with a control group without history of CKD or stroke. We present an ESRD patient on chronic hemodialysis with a history of gradual cognitive decline and progressive CMBs. Through this case and literature review, we illustrate the need to develop detection and prediction models to treat this frequent development in ESRD patients.