Conformally invariant bending energy for hypersurfaces

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the quadratic Willmore energy for a two-dimensional surface; one is intrinsic (the Weyl invariant), the other extrinsic; the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature -- which is not itself invariant -- and a quartic in the curvature. The four-dimensional energy quadratic in extrinsic curvature plays a central role in this construction.Comment: 16 page

Next-generation sequencing reveals deep intronic cryptic ABCC8 and HADH splicing founder mutations causing hyperinsulinism by pseudoexon activation

Copyright © 2013 The American Society of Human Genetics. Published by Elsevier Inc.Next-generation sequencing (NGS) enables analysis of the human genome on a scale previously unachievable by Sanger sequencing. Exome sequencing of the coding regions and conserved splice sites has been very successful in the identification of disease-causing mutations, and targeting of these regions has extended clinical diagnostic testing from analysis of fewer than ten genes per phenotype to more than 100. Noncoding mutations have been less extensively studied despite evidence from mRNA analysis for the existence of deep intronic mutations in >20 genes. We investigated individuals with hyperinsulinaemic hypoglycaemia and biochemical or genetic evidence to suggest noncoding mutations by using NGS to analyze the entire genomic regions of ABCC8 (117 kb) and HADH (94 kb) from overlapping ~10 kb PCR amplicons. Two deep intronic mutations, c.1333-1013A>G in ABCC8 and c.636+471G>T HADH, were identified. Both are predicted to create a cryptic splice donor site and an out-of-frame pseudoexon. Sequence analysis of mRNA from affected individuals' fibroblasts or lymphoblastoid cells confirmed mutant transcripts with pseudoexon inclusion and premature termination codons. Testing of additional individuals showed that these are founder mutations in the Irish and Turkish populations, accounting for 14% of focal hyperinsulinism cases and 32% of subjects with HADH mutations in our cohort. The identification of deep intronic mutations has previously focused on the detection of aberrant mRNA transcripts in a subset of disorders for which RNA is readily obtained from the target tissue or ectopically expressed at sufficient levels. Our approach of using NGS to analyze the entire genomic DNA sequence is applicable to any disease

The Schr\"odinger Wave Functional and S-branes

In this paper we will consider the minisuperspace approach to S-branes dynamics in the Schr\"odinger picture description. Time-evolution of vacuum wave functional for quantum field theory on S-brane is studied. Open string pair production is calculated. The analysis of density matrix for mixed states is also performed.Comment: 27 page

Cylindrical equilibrium shapes of fluid membranes

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore

A Nonbehavioral Theory of Saving

We present a model where the saving rate of the household sector, especially households at the bottom of the income distribution, becomes the endogenous variable that adjusts in order for full employment to be maintained over time. An increase in income inequality and the current account deficit and a consolidation of the government budget lead to a decrease in the saving rate of the household sector. Such a process is unsustainable because it leads to an increase in the household debt-to-income ratio, and maintaining it depends on some sort of asset bubble. This framework allows us to better understand the factors that led to the Great Recession and the dilemma of a repeat of this kind of unsustainable process or secular stagnation. Sustainable growth requires a decrease in income inequality, an improvement in the external position, and a relaxation of the fiscal stance of the government

Protonation States of Remote Residues Affect Binding-Release Dynamics of the Ligand but not the Conformation of apo Ferric Binding Protein

We have studied the apo (Fe3+ free) form of periplasmic ferric binding protein (FbpA) under different conditions and we have monitored the changes in the binding and release dynamics of H2PO4- that acts as a synergistic anion in the presence of Fe3+. Our simulations predict a dissociation constant of 2.2$\pm$0.2 mM which is in remarkable agreement with the experimentally measured value of 2.3$\pm$0.3 mM under the same ionization strength and pH conditions. We apply perturbations relevant for changes in environmental conditions as (i) different values of ionic strength (IS), and (ii) protonation of a group of residues to mimic a different pH environment. Local perturbations are also studied by protonation or mutation of a site distal to the binding region that is known to mechanically manipulate the hinge-like motions of FbpA. We find that while the average conformation of the protein is intact in all simulations, the H2PO4- dynamics may be substantially altered by the changing conditions. In particular, the bound fraction which is 20$\%$ for the wild type system is increased to 50$\%$ with a D52A mutation/protonation and further to over 90$\%$ at the protonation conditions mimicking those at pH 5.5. The change in the dynamics is traced to the altered electrostatic distribution on the surface of the protein which in turn affects hydrogen bonding patterns at the active site. The observations are quantified by rigorous free energy calculations. Our results lend clues as to how the environment versus single residue perturbations may be utilized for regulation of binding modes in hFbpA systems in the absence of conformational changes.Comment: 26 pages, 4 figure

Clinical approach for the classification of congenital uterine malformations

A more objective, accurate and non-invasive estimation of uterine morphology is nowadays feasible based on the use of modern imaging techniques. The validity of the current classification systems in effective categorization of the female genital malformations has been already challenged. A new clinical approach for the classification of uterine anomalies is proposed. Deviation from normal uterine anatomy is the basic characteristic used in analogy to the American Fertility Society classification. The embryological origin of the anomalies is used as a secondary parameter. Uterine anomalies are classified into the following classes: 0, normal uterus; I, dysmorphic uterus; II, septate uterus (absorption defect); III, dysfused uterus (fusion defect); IV, unilateral formed uterus (formation defect); V, aplastic or dysplastic uterus (formation defect); VI, for still unclassified cases. A subdivision of these main classes to further anatomical varieties with clinical significance is also presented. The new proposal has been designed taking into account the experience gained from the use of the currently available classification systems and intending to be as simple as possible, clear enough and accurate as well as open for further development. This proposal could be used as a starting point for a working group of experts in the field