Multi-linear measure theory and multiple stochastic integration

Summary Stochastic integration in a Lebesgue Stieltjes sense is developed in a general context of multi-linear measure theory based on the Fundamental Grothendieck Inequality and Factorization Theorem.Research partially supported by NSF Grant DMS 8601485     

Electron capture dissociation of peptide hormone changes upon opening of the tocin ring and complexation with transition metal cations

Electron capture dissociation (ECD) is an analytical technique in mass spectrometry (MS) that allows detailed structural study of biomolecules to gain insight in their function. In this work the ECD behavior of two peptide hormones oxytocin (OT1) and vasopressin (VP1) was studied. The results of OT1 and VP1 were compared to structural analogues OT2 and VP2, which have similar amino acid sequences but lack the tocin ring. The ECD results showed that both the fragment type (c/z versus b/y) and the cleavage sites (ring versus tail) changed upon opening of the tocin ring. All four peptides were complexed with three different transition metal cations (Zn²⁺, Ni²⁺ and Cu²⁺) and the ECD results were compared to those obtained from the doubly protonated species. The use of various metal ions yielded different cleavages sites within the same peptide. This can be an effect of the metal ion itself, or a consequence of a change in conformation as was suggested earlier. In addition, the type of fragment ion varied for each metal‐complexed peptide, which is in agreement with previous observations. Copyright © 2008 John Wiley & Sons, Ltd.     

The conjugacy character ofS n tends to be regular

Consider the regular and the conjugacy characters ofS _n as vectors in Euclidean space, with the standard inner product. Asn grows, the angle between them tends to zero and the ratio of their lengths tends to one. The two characters have therefore asymptotically similar decompositions into irreducible components.     

Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

Novel deletion of the E3A ubiquitin protein ligase gene detected by multiplex ligation-dependent probe amplification in a patient with Angelman syndrome

Angelman syndrome (AS) is a severe neurobehavioural disorder caused by failure of expression of the maternal copy of the imprinted domain located on 15q11-q13. There are different mechanisms leading to AS: maternal microdeletion, uniparental disomy, defects in a putative imprinting centre, mutations of the E3 ubiquitin protein ligase (UBE3A) gene. However, some of suspected cases of AS are still scored negative to all the latter mutations. Recently, it has been shown that a proportion of negative cases bear large deletions overlapping one or more exons of the UBE3A gene. These deletions are difficult to detect by conventional gene-scanning methods due to the masking effect by the non-deleted allele. In this study, we have used for the first time multiplex ligation-dependent probe amplification (MLPA) and comparative multiplex dosage analysis (CMDA) to search for large deletions affecting the UBE3A gene. Using this approach, we identified a novel causative deletion involving exon 8 in an affected sibling. Based on our results, we propose the use of MLPA as a fast, accurate and inexpensive test to detect large deletions in the UBE3A gene in a small but significant percentage of AS patients.