Zeros, chaotic ratios and the computational complexity of approximating the independence polynomial

The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the polynomial is related to phase transitions, and plays an important role in the design of efficient algorithms to approximately compute evaluations of the polynomial.In this paper we directly relate the location of the complex zeros of the independence polynomial to computational hardness of approximating evaluations of the independence polynomial. We do this by moreover relating the location of zeros to chaotic behaviour of a naturally associated family of rational functions; the occupation ratios

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Lee-Yang Zeros of the antiferromagnetic Ising Model

We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising Model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees

Sphingolipid serum profiling in vitamin D deficient and dyslipidemic obese dimorphic adults

Recent studies on Saudi Arabians indicate a prevalence of dyslipidemia and vitamin D deficiency (25(OH)D) in both normal weight and obese subjects. In the present study the sphingolipid pattern was investigated in 23 normolipidemic normal weight (NW), 46 vitamin D deficient dyslipidemic normal weight (-vitDNW) and 60 vitamin D deficient dyslipidemic obese (-vitDO) men and women by HPTLC-primuline profiling and LC-MS analyses. Results indicate higher levels of total ceramide (Cer) and dihydroceramide (dhCers C18\u201322) and lower levels of total sphingomyelins (SMs) and dihydrosphingomyelin (dhSM) not only in -vitDO subjects compared to NW, but also in \u2013vitDNW individuals. A dependency on body mass index (BMI) was observed analyzing specific Cer acyl chains levels. Lower levels of C20 and 24 were observed in men and C24.2 in women, respectively. Furthermore, LC-MS analyses display dimorphic changes in NW, -vitDNW and \u2013vitDO subjects. In conclusion, LC-MS data identify the independency of the axis high Cers, dhCers and SMs from obesity per se. Furthermore, it indicates that long chains Cers levels are specific target of weight gain and that circulating Cer and SM levels are linked to sexual dimorphism status and can contribute to predict obese related co-morbidities in men and women

A theory of Plasma Membrane Calcium Pump stimulation and activity

The ATP-driven Plasma Membrane Calcium pump or Ca(2+)-ATPase (PMCA) is characterized by a high affinity to calcium and a low transport rate compared to other transmembrane calcium transport proteins. It plays a crucial role for calcium extrusion from cells. Calmodulin is an intracellular calcium buffering protein which is capable in its Ca(2+) liganded form of stimulating the PMCA by increasing both the affinity to calcium and the maximum calcium transport rate. We introduce a new model of this stimulation process and derive analytical expressions for experimental observables in order to determine the model parameters on the basis of specific experiments. We furthermore develop a model for the pumping activity. The pumping description resolves the seeming contradiction of the Ca(2+):ATP stoichiometry of 1:1 during a translocation step and the observation that the pump binds two calcium ions at the intracellular site. The combination of the calcium pumping and the stimulation model correctly describes PMCA function. We find that the processes of calmodulin-calcium complex attachment to the pump and of stimulation have to be separated. Other PMCA properties are discussed in the framework of the model. The presented model can serve as a tool for calcium dynamics simulations and provides the possibility to characterize different pump isoforms by different type-specific parameter sets.Comment: 24 pages, 6 figure

The Novel Mouse Mutation Oblivion Inactivates the PMCA2 Pump and Causes Progressive Hearing Loss

Progressive hearing loss is common in the human population, but we have few clues to the molecular basis. Mouse mutants with progressive hearing loss offer valuable insights, and ENU (N-ethyl-N-nitrosourea) mutagenesis is a useful way of generating models. We have characterised a new ENU-induced mouse mutant, Oblivion (allele symbol Obl), showing semi-dominant inheritance of hearing impairment. Obl/+ mutants showed increasing hearing impairment from post-natal day (P)20 to P90, and loss of auditory function was followed by a corresponding base to apex progression of hair cell degeneration. Obl/Obl mutants were small, showed severe vestibular dysfunction by 2 weeks of age, and were completely deaf from birth; sensory hair cells were completely degenerate in the basal turn of the cochlea, although hair cells appeared normal in the apex. We mapped the mutation to Chromosome 6. Mutation analysis of Atp2b2 showed a missense mutation (2630C→T) in exon 15, causing a serine to phenylalanine substitution (S877F) in transmembrane domain 6 of the PMCA2 pump, the resident Ca2+ pump of hair cell stereocilia. Transmembrane domain mutations in these pumps generally are believed to be incompatible with normal targeting of the protein to the plasma membrane. However, analyses of hair cells in cultured utricular maculae of Obl/Obl mice and of the mutant Obl pump in model cells showed that the protein was correctly targeted to the plasma membrane. Biochemical and biophysical characterisation showed that the pump had lost a significant portion of its non-stimulated Ca2+ exporting ability. These findings can explain the progressive loss of auditory function, and indicate the limits in our ability to predict mechanism from sequence alone

Genetic risk and a primary role for cell-mediated immune mechanisms in multiple sclerosis.

Multiple sclerosis is a common disease of the central nervous system in which the interplay between inflammatory and neurodegenerative processes typically results in intermittent neurological disturbance followed by progressive accumulation of disability. Epidemiological studies have shown that genetic factors are primarily responsible for the substantially increased frequency of the disease seen in the relatives of affected individuals, and systematic attempts to identify linkage in multiplex families have confirmed that variation within the major histocompatibility complex (MHC) exerts the greatest individual effect on risk. Modestly powered genome-wide association studies (GWAS) have enabled more than 20 additional risk loci to be identified and have shown that multiple variants exerting modest individual effects have a key role in disease susceptibility. Most of the genetic architecture underlying susceptibility to the disease remains to be defined and is anticipated to require the analysis of sample sizes that are beyond the numbers currently available to individual research groups. In a collaborative GWAS involving 9,772 cases of European descent collected by 23 research groups working in 15 different countries, we have replicated almost all of the previously suggested associations and identified at least a further 29 novel susceptibility loci. Within the MHC we have refined the identity of the HLA-DRB1 risk alleles and confirmed that variation in the HLA-A gene underlies the independent protective effect attributable to the class I region. Immunologically relevant genes are significantly overrepresented among those mapping close to the identified loci and particularly implicate T-helper-cell differentiation in the pathogenesis of multiple sclerosis

Expression of a Constitutively Active Calcineurin Encoded by an Intron-Retaining mRNA in Follicular Keratinocytes

Hair growth is a highly regulated cyclical process. Immunosuppressive immunophilin ligands such as cyclosporin A (CsA) and FK506 are known as potent hair growth modulatory agents in rodents and humans that induce active hair growth and inhibit hair follicle regression. The immunosuppressive effectiveness of these drugs has been generally attributed to inhibition of T cell activation through well-characterized pathways. Specifically, CsA and FK506 bind to intracellular proteins, principally cyclophilin A and FKBP12, respectively, and thereby inhibit the phosphatase calcineurin (Cn). The calcineurin (Cn)/NFAT pathway has an important, but poorly understood, role in the regulation of hair follicle development. Here we show that a novel-splicing variant of calcineurin Aß CnAß-FK, which is encoded by an intron-retaining mRNA and is deficient in the autoinhibitory domain, is predominantly expressed in mature follicular keratinocytes but not in the proliferating keratinocytes of rodents. CnAß-FK was weakly sensitive to Ca2+ and dephosphorylated NFATc2 under low Ca2+ levels in keratinocytes. Inhibition of Cn/NFAT induced hair growth in nude mice. Cyclin G2 was identified as a novel target of the Cn/NFATc2 pathway and its expression in follicular keratinocytes was reduced by inhibition of Cn/NFAT. Overexpression of cyclin G2 arrested the cell cycle in follicular keratinocytes in vitro and the Cn inhibitor, cyclosporin A, inhibited nuclear localization of NFATc2, resulting in decreased cyclin G2 expression in follicular keratinocytes of rats in vivo. We therefore suggest that the calcineurin/NFAT pathway has a unique regulatory role in hair follicle development