Gluing techniques in triangular geometry

ISSN:0033-560

A Model for the Genesis of Arterial Pressure Mayer Waves from Heart Rate and Sympathetic Activity

Both theoretic models and cross-spectral analyses suggest that an oscillating sympathetic nervous outflow generates the low frequency arterial pressure fluctuations termed Mayer waves. Fluctuations in heart rate also have been suggested to relate closely to Mayer waves, but empiric models have not assessed the joint causative influences of hemt rate and sympathetic activity. Therefore, we constructed a model based simply upon the hemodynamic equation deriving from Ohm's Law. With this model, we determined time relations and relative contributions of heart rate and sympathetic activity to the genesis of arterial pressure Mayer waves. We assessed data from eight healthy young volunteers in the basal state and in a high sympathetic state known to produce concurrent increases in sympathetic nervous outflow and Mayer wave amplitude. We fit the Mayer waves (0.05-0.20 Hz) in mean arterial pressure by the weighted sum ofleading oscillations in heart rate and sympathetic nerve activity. This model of our data showed heart rate oscillations leading by 2-3.75 seconds were responsible for almost half of the variance in arterial pressure (basal R^2=0.435±0.140, high sympathetic R^2=0.438±0.180). Surprisingly, sympathetic activity (lead 0-5 seconds) contributed only modestly to the explained variance in Mayer waves during either sympathetic state (basal: ∆R^2=0.046±0.026; heightened: ∆R^2=0.085±0.036). Thus, it appears that heart rate oscillations contribute to Mayer waves in a simple linear fashion, whereas sympathetic fluctuations contribute little to Mayer waves in this way. Although these results do not exclude an important vascular sympathetic role, they do suggest that additional Ji1ctors, such as sympathetic transduction into vascular resistance, modulate its influence.Binda and Fred Shuman Foundation; National Institute on Aging (AG14376)

A Model for the Genesis of Arterial Pressure Mayer Waves from Heart Rate and Sympathetic Activity

Both theoretic models and cross-spectral analyses suggest that an oscillating sympathetic nervous outflow generates the low frequency arterial pressure fluctuations termed Mayer waves. Fluctuations in heart rate also have been suggested to relate closely to Mayer waves, but empiric models have not assessed the joint causative influences of hemt rate and sympathetic activity. Therefore, we constructed a model based simply upon the hemodynamic equation deriving from Ohm's Law. With this model, we determined time relations and relative contributions of heart rate and sympathetic activity to the genesis of arterial pressure Mayer waves. We assessed data from eight healthy young volunteers in the basal state and in a high sympathetic state known to produce concurrent increases in sympathetic nervous outflow and Mayer wave amplitude. We fit the Mayer waves (0.05-0.20 Hz) in mean arterial pressure by the weighted sum ofleading oscillations in heart rate and sympathetic nerve activity. This model of our data showed heart rate oscillations leading by 2-3.75 seconds were responsible for almost half of the variance in arterial pressure (basal R^2=0.435±0.140, high sympathetic R^2=0.438±0.180). Surprisingly, sympathetic activity (lead 0-5 seconds) contributed only modestly to the explained variance in Mayer waves during either sympathetic state (basal: ∆R^2=0.046±0.026; heightened: ∆R^2=0.085±0.036). Thus, it appears that heart rate oscillations contribute to Mayer waves in a simple linear fashion, whereas sympathetic fluctuations contribute little to Mayer waves in this way. Although these results do not exclude an important vascular sympathetic role, they do suggest that additional Ji1ctors, such as sympathetic transduction into vascular resistance, modulate its influence.Binda and Fred Shuman Foundation; National Institute on Aging (AG14376)

From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Type I interferon-driven susceptibility to Mycobacterium tuberculosis is mediated by IL-1Ra.

The bacterium Mycobacterium tuberculosis (Mtb) causes tuberculosis and is responsible for more human mortality than any other single pathogen1. Progression to active disease occurs in only a fraction of infected individuals and is predicted by an elevated type I interferon (IFN) response2-7. Whether or how IFNs mediate susceptibility to Mtb has been difficult to study due to a lack of suitable mouse models6-11. Here, we examined B6.Sst1S congenic mice that carry the 'susceptible' allele of the Sst1 locus that results in exacerbated Mtb disease12-14. We found that enhanced production of type I IFNs was responsible for the susceptibility of B6.Sst1S mice to Mtb. Type I IFNs affect the expression of hundreds of genes, several of which have previously been implicated in susceptibility to bacterial infections6,7,15-18. Nevertheless, we found that heterozygous deficiency in just a single IFN target gene, Il1rn, which encodes interleukin-1 receptor antagonist (IL-1Ra), is sufficient to reverse IFN-driven susceptibility to Mtb in B6.Sst1S mice. In addition, antibody-mediated neutralization of IL-1Ra provided therapeutic benefit to Mtb-infected B6.Sst1S mice. Our results illustrate the value of the B6.Sst1S mouse to model IFN-driven susceptibility to Mtb, and demonstrate that IL-1Ra is an important mediator of type I IFN-driven susceptibility to Mtb infections in vivo

Blanchfield and Seifert algebra in high-dimensional boundary link theory I: Algebraic K-theory

The classification of high-dimensional mu-component boundary links motivates decomposition theorems for the algebraic K-groups of the group ring A[F_mu] and the noncommutative Cohn localization Sigma^{-1}A[F_mu], for any mu>0 and an arbitrary ring A, with F_mu the free group on mu generators and Sigma the set of matrices over A[F_mu] which become invertible over A under the augmentation A[F_mu] to A. Blanchfield A[F_mu]-modules and Seifert A-modules are abstract algebraic analogues of the exteriors and Seifert surfaces of boundary links. Algebraic transversality for A[F_mu]-module chain complexes is used to establish a long exact sequence relating the algebraic K-groups of the Blanchfield and Seifert modules, and to obtain the decompositions of K_*(A[F_mu]) and K_*(Sigma^{-1}A[F_mu]) subject to a stable flatness condition on Sigma^{-1}A[F_mu] for the higher K-groups.Comment: This is the version published by Geometry & Topology on 2 November 200

Von Neumann rho invariants and torsion in the topological knot concordance group

We discuss an infinite class of metabelian Von Neumann rho-invariants. Each one is a homomorphism from the monoid of knots to the real line. In general they are not well defined on the concordance group. Nonetheless, we show that they pass to well defined homomorphisms from the subgroup of the concordance group generated by anisotropic knots. Thus, the computation of even one of these invariants can be used to conclude that a knot is of infinite order. We introduce a method to give a computable bound on these invariants. Finally we compute this bound to get a new and explicit infinite set of twist knots which is linearly independent in the concordance group and whose every member is of algebraic order 2 .Comment: 33 pages, 14 figures. Clarifications made to theorem statements and definitions, Lemma 5.9 strengthened as needed, A citation error is corrected. Updated to agree with version in publicatio