Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]

In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable in this problem, hence the task reduces to a number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear

Perturbations in electromagnetic dark energy

It has been recently proposed that the presence of a temporal electromagnetic field on cosmological scales could explain the phase of accelerated expansion that the universe is currently undergoing. The field contributes as a cosmological constant and therefore, the homogeneous cosmology produced by such a model is exactly the same as that of $\Lambda$CDM. However, unlike a cosmological constant term, electromagnetic fields can acquire perturbations which in principle could affect CMB anisotropies and structure formation. In this work, we study the evolution of inhomogeneous scalar perturbations in this model. We show that provided the initial electromagnetic fluctuations generated during inflation are small, the model is perfectly compatible with both CMB and large scale structure observations at the same level of accuracy as $\Lambda$CDM.Comment: 12 pages, 3 figures. Added new comments to match the published versio

Cosmological constraints on the generalized holographic dark energy

We use the Markov ChainMonte Carlo method to investigate global constraints on the generalized holographic (GH) dark energy with flat and non-flat universe from the current observed data: the Union2 dataset of type supernovae Ia (SNIa), high-redshift Gamma-Ray Bursts (GRBs), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. The most stringent constraints on the GH model parameter are obtained. In addition, it is found that the equation of state for this generalized holographic dark energy can cross over the phantom boundary wde =-1.Comment: 14 pages, 5 figures. arXiv admin note: significant text overlap with arXiv:1105.186

Hypertrophic cardiomyopathy in South African Blacks

Hypertrophic cardiomyopathy (HCM) has been considered rare among the Black population of southern Africa. We report 7 patients with the disease who presented during a 14-month period. Current concepts in the approach to the diagnosis and treatment of HCM are discussed. It is possible that with greater awareness of the occurrence of the condition in Blacks the diagnosis of HCM will be made in more members of this population group

Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams

We consider the problem of finding the number of matrices over a finite field with a certain rank and with support that avoids a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). For general sets of entries these numbers of matrices are not polynomials in q (Stembridge 98); however, when the set of entries is a Young diagram, the numbers, up to a power of q-1, are polynomials with nonnegative coefficients (Haglund 98). In this paper, we give a number of conditions under which these numbers are polynomials in q, or even polynomials with nonnegative integer coefficients. We extend Haglund's result to complements of skew Young diagrams, and we apply this result to the case when the set of entries is the Rothe diagram of a permutation. In particular, we give a necessary and sufficient condition on the permutation for its Rothe diagram to be the complement of a skew Young diagram up to rearrangement of rows and columns. We end by giving conjectures connecting invertible matrices whose support avoids a Rothe diagram and Poincar\'e polynomials of the strong Bruhat order.Comment: 24 pages, 9 figures, 1 tabl

Heritability of specific language impairment depends on diagnostic criteria

Heritability estimates for specific language impairment (SLI) have been inconsistent. Four twin studies reported heritability of 0.5 or more, but a recent report from the Twins Early Development Study found negligible genetic influence in 4-year-olds. We considered whether the method of ascertainment influenced results and found substantially higher heritability if SLI was defined in terms of referral to speech and language pathology services than if defined by language test scores. Further analysis showed that presence of speech difficulties played a major role in determining whether a child had contact with services. Childhood language disorders that are identified by population screening are likely to have a different phenotype and different etiology from clinically referred cases. Genetic studies are more likely to find high heritability if they focus on cases who have speech difficulties and who have been referred for intervention

Heritable risk factors associated with language impairments

There is a strong genetic contribution to children’s language and literacy impairments. The aim of this study was to determine which aspects of the phenotype are familial by comparing 34 parents of probands with language/literacy impairments and 33 parents of typically developing probands. The parents responded to questionnaires regarding previous history for language/reading impairment and participated in psychometric testing. The psychometric test battery consisted of tests assessing non-verbal IQ, short-term memory, articulation, receptive grammar, reading abilities and spelling. Self-report measures demonstrated a higher prevalence of language and literacy impairments in parents of affected probands (32%) compared with parents of unaffected probands (6%). The two groups of parents differed significantly in their performance on the non-word repetition, oromotor and digit span tasks. Non-word repetition gave the best discrimination between the parent groups even when the data from the parents who actually were impaired as ascertained by direct testing or self-report were removed from the analyses. This suggests that non-word repetition serves as a marker of a family risk for language impairment. The paper concludes with a discussion of issues associated with ascertainment of specific language impairment (SLI)