Generalized Bezoutian and matrix equations

AbstractA natural generalization of the classical Bezout matrix of two polynomials is introduced for a family of several matrix polynomials. The main aim of the paper is to show that this generalized Bezoutian serves as an adequate connecting link between the class of equations in matrix polynomials M(λ)Y(λ) + Z(λ)L(λ) = R(λ) and the class of linear matrix equations AX − XB = C. Each equation in one of these classes is coupled with a certain equation in the other class so that for each couple the generalized Bezoutian corresponding to a solution (Y(λ), Z(λ)) of the equation in matrix polynomials is a solution of the matrix equation, and conversely, any solution X of the matrix equation is a generalized Bezoutian corresponding to a certain solution of the equation in matrix polynomials. In particular, either both equations are solvable or both have no solutions. Explicit formulas connecting the solutions of the two equations are given. Also, various representation formulas for the generalized Bezoutian are derived, and its relation to the resultant matrix and the greatest common divisor of several matrix polynomials is discussed

Krein systems

In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role

Innovative Financing for Global Education

Innovative financing is a growing prospect and priority in the education sector, where over 57 million children and youth do not have access to schools, and the funding gap for achieving basic education for all is estimated at $26 billion. It has made a significant difference in meeting the UN Millennium Development Goals, especially in health, by generating more than$7 billion in additional financial resources through a range of new institutions and partnerships.This paper presents a comprehensive and practical analysis of the current state of innovative financing in global education. The report argues that education is a complex sector characterized by significant barriers to investment. But it also suggests how to break through these barriers using innovative financing such as solidarity levies and private sector investments through a global education investment bank.This research, carried out by the Innovative Finance Foundation, is part of the Open Society Education Support Program's efforts to identify innovative financing mechanisms and approaches that can increase the availability and allocation of resources for education systems

On Global Conservation Laws at Null Infinity

The ``standard'' expressions for total energy, linear momentum and also angular momentum of asymptotically flat Bondi metrics at null infinity are also obtained from differential conservation laws on asymptotically flat backgrounds, derived from a quadratic Lagrangian density by methods currently used in classical field theory. It is thus a matter of taste and commodity to use or not to use a reference spacetime in defining these globally conserved quantities. Backgrounds lead to N\oe ther conserved currents; the use of backgrounds is in line with classical views on conservation laws. Moreover, the conserved quantities are in principle explicitly related to the sources of gravity through Einstein's equations, while standard definitions are not. The relations depend, however, on a rule for mapping spacetimes on backgrounds

Covariation of depressive symptoms, parkinsonism, and post-dexamethasone plasma cortisol levels in a bipolar patient: simultaneous response to ECT and lithium carbonate

: A patient presented with concurrent mood congruent delusions, parkinsonism, and elevated post-dexamethasone plasma cortisol levels. This triad could result from simultaneous development of cholinergic-monoaminergic dysfunction within critical limbic and extrapyramidal loci. The magnitude of each abnormality decreased in concert during a course of electroconvulsive therapy (ECT). Remaining abnormalities disappeared during treatment with lithium. Actions of ECT and lithium on muscarinic systems are reviewed, and a strategy for testing the hypothesis that dysfunction of cholinergic-monoaminergic mechanisms develops in parallel in different neural networks is considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66202/1/j.1600-0447.1986.tb06229.x.pd

The Functional DRD3 Ser9Gly Polymorphism (rs6280) Is Pleiotropic, Affecting Reward as Well as Movement

Abnormalities of motivation and behavior in the context of reward are a fundamental component of addiction and mood disorders. Here we test the effect of a functional missense mutation in the dopamine 3 receptor (DRD3) gene (ser9gly, rs6280) on reward-associated dopamine (DA) release in the striatum. Twenty-six healthy controls (HCs) and 10 unmedicated subjects with major depressive disorder (MDD) completed two positron emission tomography (PET) scans with [11C]raclopride using the bolus plus constant infusion method. On one occasion subjects completed a sensorimotor task (control condition) and on another occasion subjects completed a gambling task (reward condition). A linear regression analysis controlling for age, sex, diagnosis, and self-reported anhedonia indicated that during receipt of unpredictable monetary reward the glycine allele was associated with a greater reduction in D2/3 receptor binding (i.e., increased reward-related DA release) in the middle (anterior) caudate (p<0.01) and the ventral striatum (p<0.05). The possible functional effect of the ser9gly polymorphism on DA release is consistent with previous work demonstrating that the glycine allele yields D3 autoreceptors that have a higher affinity for DA and display more robust intracellular signaling. Preclinical evidence indicates that chronic stress and aversive stimulation induce activation of the DA system, raising the possibility that the glycine allele, by virtue of its facilitatory effect on striatal DA release, increases susceptibility to hyperdopaminergic responses that have previously been associated with stress, addiction, and psychosis

High frequency of the IVS2-2A>G DNA sequence variation in SLC26A5, encoding the cochlear motor protein prestin, precludes its involvement in hereditary hearing loss

BACKGROUND: Cochlear outer hair cells change their length in response to variations in membrane potential. This capability, called electromotility, is believed to enable the sensitivity and frequency selectivity of the mammalian cochlea. Prestin is a transmembrane protein required for electromotility. Homozygous prestin knockout mice are profoundly hearing impaired. In humans, a single nucleotide change in SLC26A5, encoding prestin, has been reported in association with hearing loss. This DNA sequence variation, IVS2-2A>G, occurs in the exon 3 splice acceptor site and is expected to abolish splicing of exon 3. METHODS: To further explore the relationship between hearing loss and the IVS2-2A>G transition, and assess allele frequency, genomic DNA from hearing impaired and control subjects was analyzed by DNA sequencing. SLC26A5 genomic DNA sequences from human, chimp, rat, mouse, zebrafish and fruit fly were aligned and compared for evolutionary conservation of the exon 3 splice acceptor site. Alternative splice acceptor sites within intron 2 of human SLC26A5 were sought using a splice site prediction program from the Berkeley Drosophila Genome Project. RESULTS: The IVS2-2A>G variant was found in a heterozygous state in 4 of 74 hearing impaired subjects of Hispanic, Caucasian or uncertain ethnicity and 4 of 150 Hispanic or Caucasian controls (p = 0.45). The IVS2-2A>G variant was not found in 106 subjects of Asian or African American descent. No homozygous subjects were identified (n = 330). Sequence alignment of SLC26A5 orthologs demonstrated that the A nucleotide at position IVS2-2 is invariant among several eukaryotic species. Sequence analysis also revealed five potential alternative splice acceptor sites in intron 2 of human SLC26A5. CONCLUSION: These data suggest that the IVS2-2A>G variant may not occur more frequently in hearing impaired subjects than in controls. The identification of five potential alternative splice acceptor sites in intron 2 of human SLC26A5 suggests a potential mechanism by which expression of prestin might be maintained in cells carrying the SLC26A5 IVS2-2A>G DNA sequence variation. Additional studies are needed to evaluate the effect of the IVS2-2A>G transition on splicing of SLC26A5 transcripts and characterize the hearing status of individuals homozygous for the IVS2-2A>G variant

A novel BRCA-1 mutation in Arab kindred from east Jerusalem with breast and ovarian cancer

BACKGROUND: The incidence of breast cancer (BC) in Arab women is lower compared to the incidence in the Jewish population in Israel; still, it is the most common malignancy among Arab women. There is a steep rise in breast cancer incidence in the Arab population in Israel over the last 10 years that can be attributed to life style changes. But, the younger age of BC onset in Arab women compared with that of the Jewish population is suggestive of a genetic component in BC occurrence in that population. METHODS: We studied the family history of 31 women of Palestinian Arab (PA) origin affected with breast (n = 28), ovarian (n = 3) cancer. We used denaturing high performance liquid chromatography (DHPLC) to screen for mutations of BRCA1/2 in 4 women with a personal and family history highly suggestive of genetic predisposition. RESULTS: A novel BRCA1 mutation, E1373X in exon 12, was found in a patient affected with ovarian cancer. Four of her family members, 3 BC patients and a healthy individual were consequently also found to carry this mutation. Of the other 27 patients, which were screened for this specific mutation none was found to carry it. CONCLUSION: We found a novel BRCA1 mutation in a family of PA origin with a history highly compatible with BRCA1 phenotype. This mutation was not found in additional 30 PA women affected with BC or OC. Therefore full BRCA1/2 screening should be offered to patients with characteristic family history. The significance of the novel BRCA1 mutation we identified should be studied in larger population. However, it is likely that the E1373X mutation is not a founder frequent mutation in the PA population

Allele-Specific Impairment of GJB2 Expression by GJB6 Deletion del(GJB6-D13S1854)

Mutations in the GJB2 gene, which encodes connexin 26, are a frequent cause of congenital non-syndromic sensorineural hearing loss. Two large deletions, del(GJB6-D13S1830) and del(GJB6-D13S1854), which truncate GJB6 (connexin 30), cause hearing loss in individuals homozygous, or compound heterozygous for these deletions or one such deletion and a mutation in GJB2. Recently, we have demonstrated that the del(GJB6-D13S1830) deletion contributes to hearing loss due to an allele-specific lack of GJB2 mRNA expression and not as a result of digenic inheritance, as was postulated earlier. In the current study we investigated the smaller del(GJB6-D13S1854) deletion, which disrupts the expression of GJB2 at the transcriptional level in a manner similar to the more common del(GJB6-D13S1830) deletion. Interestingly, in the presence of this deletion, GJB2 expression remains minimally but reproducibly present. The relative allele-specific expression of GJB2 was assessed by reverse-transcriptase PCR and restriction digestions in three probands who were compound heterozygous for a GJB2 mutation and del(GJB6-D13S1854). Each individual carried a different sequence variant in GJB2. All three individuals expressed the mutated GJB2 allele in trans with del(GJB6-D13S1854), but expression of the GJB2 allele in cis with the deletion was almost absent. Our study clearly corroborates the hypothesis that the del(GJB6-D13S1854), similar to the larger and more common del(GJB6-D13S1830), removes (a) putative cis-regulatory element(s) upstream of GJB6 and narrows down the region of location

A Universal Critical Density Underlying the Physics of Electrons at the LaAlO3/SrTiO3 Interface

The two-dimensional electron system formed at the interface between the insulating oxides LaAlO3 and SrTiO3 exhibits ferromagnetism, superconductivity, and a wide range of unique magnetotransport properties. A key challenge is to find a unified microscopic mechanism that underlies these emergent phenomena. Here we show that a universal Lifshitz transition between d-orbitals lies at the core of the observed transport phenomena in this system. Our measurements find a critical electronic density at which the transport switches from single to multiple carriers. This density has a universal value, independent of the LaAlO3 thickness and electron mobility. The characteristics of the transition, its universality, and its compatibility with spectroscopic measurements establish it as a transition between d-orbitals of different symmetries. A simple band model, allowing for spin-orbit coupling at the atomic level, connects the observed universal transition to a range of reported magnetotransport properties. Interestingly, we also find that the maximum of the superconducting transition temperature occurs at the same critical transition, indicating a possible connection between the two phenomena. Our observations demonstrate that orbital degeneracies play an important role in the fascinating behavior observed so far in these oxides