Investigation of Quantum Chaos in the Parametric Dependent System of Interacting oscillators

Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain values of the parameters from this domain, form of the classical power spectrum is in a good agreement with the quantum band profile. Local density of states is calculated. The range in which application of perturbation theory is correct has been defined.Comment: 9 figures. to be published in Mod.Phys.Lett.

Localization in Strongly Chaotic Systems

We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let

Generation of Free Fatty Acids from Phospholipids Regulates Stratum Corneum Acidification and Integrity

There is evidence that the “acid mantle” of the stratum corneum is important for both permeability barrier formation and cutaneous antimicrobial defense. The origin of the acidic pH of the stratum corneum remains conjectural, however. Both passive (e.g., eccrine/sebaceous secretions, proteolytic) and active (e.g., proton pumps) mechanisms have been proposed. We assessed here whether the free fatty acid pool, which is derived from phospholipase-mediated hydrolysis of phospholipids during cornification, contributes to stratum corneum acidification and function. Topical applications of two chemically unrelated secretory phospholipase sPLA2 inhibitors, bromphenacylbromide and 1-hexadecyl-3-trifluoroethylglycero-sn-2-phosphomethanol, for 3 d produced an increase in the pH of murine skin surface that was paralleled not only by a permeability barrier abnormality but also altered stratum corneum integrity (number of strippings required to break the barrier) and decreased stratum corneum cohesion (protein weight removed per stripping). Not only stratum corneum pH but also all of the functional abnormalities normalized when either palmitic, stearic, or linoleic acids were coapplied with the inhibitors. Moreover, exposure of intact murine stratum corneum to a neutral pH for as little as 3 h produced comparable abnormalities in stratum corneum integrity and cohesion, and further amplified the inhibitor-induced functional alterations. Furthermore, short-term applications of an acidic pH buffer to inhibitor-treated skin also reversed the abnormalities in stratum corneum integrity and cohesion, despite the ongoing decrease in free fatty acid levels. Finally, the secretory-phospholipase-inhibitor-induced alterations in integrity/cohesion were in accordance with premature dissolution of desmosomes, demonstrated both by electron microscopy and by reduced desmoglein 1 levels in the stratum corneum (shown by immunofluorescence staining and vizualized by confocal microscopy). Together, these results demonstrate: (i) the importance of phospholipid-to-free-fatty-acid processing for normal stratum corneum acidification; and (ii) the potentially important role of this pathway not only for barrier homeostasis but also for the dual functions of stratum corneum integrity and cohesion

The Lovastatin-Treated Rodent: A New Model of Barrier Disruption and Epidermal Hyperplasia

Recent studies have linked epidermal cholesterol synthesis with maintenance of the permeability barrier. To assess directly the importance of cholesterol synthesis, we applied lovastatin, a potent inhibitor of cholesterol synthesis, to hairless mouse skin. Transepidermal water loss (TEWL) began to increase after four to six daily applications. Co-application of cholesterol blocked the expected increase in TEWL, demonstrating the importance of cholesterol for development of the lesion. The histology of lovastatin-treated skin revealed epidermal hyperplasia, accompanied by accelerated DNA synthesis. Whereas cholesterol synthesis initially was reduced in lovastatin-treated epidermis, with further treatment cholesterol synthesis normalized, while fatty acid synthesis accelerated greatly. Although the total free sterol content of lovastatin-treated epidermis remained normal, the fatty acid content increased coincident with barrier disruption. Finally, morphologic abnormalities of both lamellar body structure and their deposited, intercellular contents occurred coincident with the emerging biochemical abnormalities. Thus, the abnormal barrier function in this model can be ascribed to an initial inhibition of epidermal sterol synthesis followed by an alteration in cholesterol and fatty acid synthesis, leading to an imbalance in stratum corneum lipid composition and abnormal membrane bilayer structure

The mechanisms by which lipids coordinately regulate the formation of the protein and lipid domains of the stratum corneum: Role of fatty acids, oxysterols, cholesterol sulfate and ceramides as signaling molecules

The formation of a permeability barrier between the external environment and the host is essential for survival. To provide this barrier keratinocytes undergo a complex pathway of differentiation, which culminates in keratinocyte cornification and the formation of extracellular lipid enriched lamellar membranes in the stratum corneum. The mechanisms that coordinately regulate the parallel formation of the corneocytes and lamellar membranes are unknown. The extracellular lamellar membranes are derived from the exocytosis of lamellar bodies and to synthesize lamellar bodies the keratinocyte must have abundant quantities of cholesterol, fatty acids and ceramides. These lipids could serve as signaling molecules and thereby coordinately regulate the formation of the stratum corneum. Fatty acids activate PPARs and studies have shown that PPAR activation stimulates keratinocyte differentiation. Cholesterol is converted to oxysterols that activate LXR and studies have shown that LXR activation also stimulates keratinocyte differentation. Additionally, PPAR and LXR activation also facilitates the formation of the lipid enriched lamellar membranes. Ceramides, via a number of mechanisms also stimulate keratinocyte differentiation. Recently, studies have shown that ceramides by increasing PPAR delta also increase the expression of ABCA12, which would facilitate the formation of lamellar bodies. Finally, keratinocytes accumulate a large quantity of cholesterol sulfate, which plays a key role in regulating desquamation. Cholesterol sulfate has also been shown to stimulate keratinocyte differentiation. Thus, cholesterol, cholesterol sulfate, fatty acids and ceramides all stimulate keratinocyte differentiation and thereby could coordinately regulate the formation of the stratum corneum

Pilot GWAS of Caries in African-Americans Shows Genetic Heterogeneity

Background Dental caries is the most common chronic disease in the US and disproportionately affects racial/ethnic minorities. Caries is heritable, and though genetic heterogeneity exists between ancestries for a substantial portion of loci associated with complex disease, a genome-wide association study (GWAS) of caries specifically in African Americans has not been performed previously. Methods We performed exploratory GWAS of dental caries in 109 African American adults (age \u3e 18) and 96 children (age 3–12) from the Center for Oral Health Research in Appalachia (COHRA1 cohort). Caries phenotypes (DMFS, DMFT, dft, and dfs indices) assessed by dental exams were tested for association with 5 million genotyped or imputed single nucleotide polymorphisms (SNPs), separately in the two age groups. The GWAS was performed using linear regression with adjustment for age, sex, and two principal components of ancestry. A maximum of 1 million adaptive permutations were run to determine empirical significance. Results No loci met the threshold for genome-wide significance, though some of the strongest signals were near genes previously implicated in caries such as antimicrobial peptide DEFB1 (rs2515501; p = 4.54 × 10− 6) and TUFT1 (rs11805632; p = 5.15 × 10− 6). Effect estimates of lead SNPs at suggestive loci were compared between African Americans and Caucasians (adults N = 918; children N = 983). Significant (p \u3c 5 × 10− 8) genetic heterogeneity for caries risk was found between racial groups for 50% of the suggestive loci in children, and 12–18% of the suggestive loci in adults. Conclusions The genetic heterogeneity results suggest that there may be differences in the contributions of genetic variants to caries across racial groups, and highlight the critical need for the inclusion of minorities in subsequent and larger genetic studies of caries in order to meet the goals of precision medicine and to reduce oral health disparities

Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.Comment: 4 pages, 3 figures, Revtex fil

Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page