Maximum Waring Ranks of Monomials and Sums of Coprime Monomials

We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank

Case Report: Cerebral Revascularization in a Child With Mucopolysaccharidosis Type I

Mucopolysaccharidosis (MPS) type I is a rare lysosomal storage disorder caused by an accumulation of glycosaminoglycans (GAGs) resulting in multisystem disease. Neurological morbidity includes hydrocephalus, spinal cord compression, and cognitive decline. While many neurological symptoms have been described, stroke is not a widely-recognized manifestation of MPS I. Accordingly, patients with MPS I are not routinely evaluated for stroke, and there are no guidelines for managing stroke in patients with this disease. We report the case of a child diagnosed with MPS I who presented with overt stroke and repeated neurological symptoms with imaging findings for severe ventriculomegaly, infarction, and bilateral terminal carotid artery stenosis. Direct intracranial pressure evaluation proved negative for hydrocephalus. The patient was subsequently treated with cerebral revascularization and at a 3-year follow-up, the patient reported no further neurological events or new ischemia on cerebral imaging. Cerebral arteriopathy in patients with MPS I may be associated with GAG accumulation within the cerebrovascular system and may predispose patients to recurrent strokes. However, further studies are required to elucidate the etiology of cerebrovascular arteriopathy in the setting of MPS I. Although the natural history of steno-occlusive arteriopathy in patients with MPS I remains unclear, our findings suggest that cerebral revascularization is a safe treatment option that may mitigate the risk of future strokes and should be strongly considered within the overall management guidelines for patients with MPS I