Abstract Using the calculus of variations, we prove following structure theorem for noise-stable partitions: a partition n -dimensional Euclidean space into m disjoint sets fixed Gaussian volumes that maximise their noise stability must be $(m-1)$ -dimensional, if $m-1\leq n$ . In particular, maximum in $\mathbb {R}^{n}$ is constant all satisfying $n\geq m-1$ From this result, obtain: (i) A pro...

an investigation was carried out on a young unrelated couple, both 29 years old, with two boys and three girls, 3 months to 8 years old. one boy and the mother were healthy, the other four children and the father were affected. the family, originally from the district of nour, in northern iran, near the caspian sea, was first counseled at the genetic clinic in tehran in 1984. several trips were...

thymoma is the most common neoplasm of anterior mediastinum with incidence peaks during the fourth, fifth and sixth decades of life. two-thirds of patients are asymptomatic and identified accidentally by chest x-rays . of the total, 40-70 % of patients have one or more parathymic syndromes of which myasthenia gravis (mg) is the most common and reported in 10-50% . gullain-barre syndrome (gbs) h...

conclusions there was a significant association between pms scores and the prevalence of metabolic syndrome. further studies are needed to confirm and validate the relationships between lipid profile abnormalities and metabolic disorders with pms. objectives this study was designed to investigate the association of hormonal and metabolic factors with pms among iranian women of reproductive age....

severe overgrowth and tallness is very rare in human beings. the most common cause is gigantism due to the excessive secretion of the growth hormone, especially, before the closure of long bones’ epiphyseal growth plates. there are other rare disorders that are categorized on overgrowth syndromes. herein, we report an extremely rare, or even perhaps a unique, patient from iran. the clinical and...

“Theorem of the alternative” is the generic name of different results used as an important tool in optimization. Though the early versions have been obtained under strong conditions of convexity, for the further extensions, these conditions have been weakened using generalized convexity beyond vector space structure. This is the case of the result proved by Jeyakumar [4], who used an extension ...

In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general lowdegree functions, with no constraints on the influences. We show that any real-valued function on the slice, whose degree when written as a harmonic multi-linear polynomial is o( √ n), has approximately the same dis...

In this lecture, we present a result of Khot, Kindler, Mossel and O’Donnell [1] which states that approximating MaxCut to within a factor αGW + ε, for any ε > 0, is “hard”. Here hardness is not based under the usual P 6= NP assumption, but rather a weaker conjecture called the Unique Games Conjecture (UGC). This conjecture was introduced by Khot [2] in 2002, and states that a certain very meani...

macrophage activating syndrome (mas) is a life-threatening disease seen in autoimmune diseases including lupus erythematosus, rheumatoid arthritis, still's disease, polyarteritis nodosa. it is characterized by fever, pancytopenia, liver failure, coagulopathy, and neurologic symptoms and high serum ferritin. a 27 yr. old female patient was admitted in shahid mostafa khomeini hospital (tehra...