The vector on the left represents a generic neutrino state expressed in the flavor basis, and on the right is the PMNS matrix multiplied by a vector representing the same neutrino state in the mass basis. X-linked or autosomal dominant, lethal in the male, inheritance of the Melnick-Needles osteodysplasty syndrome? An undiagnosed bone dysplasia: An infinite number of possible parameterizations exist; one other common example being the Wolfenstein parameterization. Bone disease was recognized in infancy when she began to walk.
Each flavor state can thus be written as a superposition of mass eigenstates, and vice versa. The PMNS matrix, with components U ai corresponding to the amplitude of mass eigenstate i in flavor a , parameterizes the unitary transformation between the two bases:.
The vector on the left represents a generic neutrino state expressed in the flavor basis, and on the right is the PMNS matrix multiplied by a vector representing the same neutrino state in the mass basis. Due to the difficulties of detecting neutrinos , it is much more difficult to determine the individual coefficients than in the equivalent matrix for the quarks the CKM matrix. As noted above, PMNS matrix is unitary. In the simplest case, the Standard Model posits three generations of neutrinos with Dirac mass that oscillate between three neutrino mass eigenvalues, an assumption that is made when best fit values for its parameters are calculated.
The PMNS matrix is not necessarily unitary, and additional parameters are necessary to describe all possible neutrino mixing parameters in other models of neutrino oscillation and mass generation, such as the see-saw model, and in general, in the case of neutrinos that have Majorana mass rather than Dirac mass.
There are also additional mass parameters and mixing angles in a simple extension of the PMNS matrix in which there are more than three flavors of neutrinos, regardless of the character of neutrino mass. As of July , scientists studying neutrino oscillation are actively considering fits of the experimental neutrino oscillation data to an extended PMNS matrix with a fourth, light "sterile" neutrino and four mass eigenvalues, although the current experimental data tends to disfavor that possibility.
In general, there are nine degrees of freedom in any unitary three by three matrix. However, in the case of the PMNS matrix five of those real parameters can be absorbed as phases of the lepton fields and thus the PMNS matrix can be fully described by four free parameters. An infinite number of possible parameterizations exist; one other common example being the Wolfenstein parameterization.
The mixing angles have been measured by a variety of experiments see neutrino mixing for a description. From Wikipedia, the free encyclopedia. Flavour in particle physics Flavour quantum numbers Isospin: I or I 3 Charm: Osteoarthritis of the lumbar spine and hips gave much pain. Her height was normal. Striking facies comprised frog-like eyes, high forehead, full red cheeks, and receding chin. X-rays showed curved long bones, tortuous ribboned ribs, and deformed clavicles, scapula, and pelvis.
Beighton and Hamersma speculated that frontometaphyseal dysplasia and osteodysplasty MNS may be due to the same gene.
They suggested that the gene may be X-linked and that the former condition is the usual phenotype in hemizygous males and the latter condition the usual phenotype in heterozygous females. They pointed out that the manifestations in Melnick and Needles' 2 kindreds 13 affected persons; 9 females, 4 males were highly variable. Apart from one doubtful instance, no male-to-male transmission was reported.
Features emphasized by Kozlowski on the basis of 9 cases included small, deformed chest, large anterior fontanel associated with prominent forehead, and high vertebrae. One of his patients was diagnosed at the age of 37 years. They analyzed the X-chromosome inactivation pattern in this family to determine if it was related to the variable phenotype. A very skewed inactivation pattern was observed in the blood from both the mildly affected mother and one of her daughters, whereas a highly skewed inactivation pattern in buccal smear DNA was observed in the mother only.
X inactivation, therefore, did not explain the variable phenotype in this family. Von Oeyen et al. The son had omphalocele and hypoplastic kidneys. A similar case was reported by Theander and Ekberg The condition was detected sonographically at 16 weeks' gestation. Autopsy on the electively aborted fetus showed exophthalmos, prune belly sequence with urethral atresia and megacystis, tetralogy of Fallot, atrioventricular canal defect, and complete malrotation of the gut.
One of the patients described in detail died of pneumonia at age 3 after having repeated bouts of pneumonia. Van der Lely et al. He may be the oldest surviving male with this disorder. His facial features were similar to those of his mother. He was not short, but was mentally retarded. His radiologic examination showed sclerotic skull base, ribbon-like flaring of ribs, short bowed clavicles, small pelvis with thin iliac crest, and moderate flaring of the distal part of the long bones.
In addition, he had atrial septal defect, pulmonic stenosis, intestinal malrotation, and ectopic kidney. They reviewed the features in these disorders and in OPD1 and suggested that these disorders constitute a single entity.
Melnick-Needles syndrome is an X-linked dominant disorder. Most cases described are in females. Nyhan and Sakati described a family with 4 affected females in 3 successive generations. Melnick studied 4 additional families in the United States; in two, 3 generations were affected and in the other two, 2 generations.
The Melnick-Needles syndrome had been assumed to be an autosomal dominant disorder. However, Gorlin and Knier analyzed reported families with restudy of some. Melnick had reexamined the male 'cases' in the kindred he reported in and found them in fact to be normal. In all, Gorlin and Knier found 23 patients in 15 pedigrees.
Most cases were sporadic and may represent new mutations. In only 3 pedigrees was there transmission from one generation to the next, always female to female. Ter Haar et al. This disorder was later characterized as a distinct entity and named Frank-ter Haar syndrome See also review by Wettke-Schafer and Kantner Svejcar found an increased content of collagen; the sclerosing bone process may be an expression thereof. X-linked inheritance is established by the demonstration of Robertson et al.
All had mutations in exon 22 of the gene. One mutation was found in 6 individuals, a second mutation in 5, and a third mutation in a single case. The girl had an unaffected twin sister who did not carry the mutation; the unaffected mother also did not carry the mutation. The twins were born with separate amniotic sacs within a single chorion, and zygosity analysis indicated a high probability that the girls were monozygotic twins. Osteodysplasty Melnick and Needles' syndrome: