On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

Data compression and regression based on local principal curves.

Frequently the predictor space of a multivariate regression problem of the type y = m(x_1, …, x_p ) + ε is intrinsically one-dimensional, or at least of far lower dimension than p. Usual modeling attempts such as the additive model y = m_1(x_1) + … + m_p (x_p ) + ε, which try to reduce the complexity of the regression problem by making additional structural assumptions, are then inefficient as they ignore the inherent structure of the predictor space and involve complicated model and variable selection stages. In a fundamentally different approach, one may consider first approximating the predictor space by a (usually nonlinear) curve passing through it, and then regressing the response only against the one-dimensional projections onto this curve. This entails the reduction from a p- to a one-dimensional regression problem. As a tool for the compression of the predictor space we apply local principal curves. Taking things on from the results presented in Einbeck et al. (Classification – The Ubiquitous Challenge. Springer, Heidelberg, 2005, pp. 256–263), we show how local principal curves can be parametrized and how the projections are obtained. The regression step can then be carried out using any nonparametric smoother. We illustrate the technique using data from the physical sciences

Type Ia Supernovae and Accretion Induced Collapse

Using the population synthesis binary evolution code StarTrack, we present theoretical rates and delay times of Type Ia supernovae arising from various formation channels. These channels include binaries in which the exploding white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a white dwarf accretes from a helium-rich companion and explodes as a SN Ia before reaching the Chandrasekhar mass limit. We find that using a common envelope parameterization employing energy balance with alpha=1 and lambda=1, the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a burst of star formation at t=0. Additionally, the delay time distribution of the sub-Chandrasekhar model can be divided in to two distinct evolutionary channels: the `prompt' helium-star channel with delay times < 500 Myr, and the `delayed' double white dwarf channel with delay times > 800 Myr spanning up to a Hubble time. These findings are in agreement with recent observationally-derived delay time distributions which predict that a large number of SNe Ia have delay times < 1 Gyr, with a significant fraction having delay times < 500 Myr. We find that the DDS channel is also able to account for the observed rates of SNe Ia. However, detailed simulations of white dwarf mergers have shown that most of these mergers will not lead to SNe Ia but rather to the formation of a neutron star via accretion-induced collapse. If this is true, our standard population synthesis model predicts that the only progenitor channel which can account for the rates of SNe Ia is the sub-Chandrasekhar mass scenario, and none of the other progenitors considered can fully account for the observed rates.Comment: 6 pages, 1 figure, 1 table, to appear in proceedings for "Binary Star Evolution: Mass Loss, Accretion and Mergers

Inhibitor regulation of tissue kallikrein activity in the synovial fluid of patients with rheumatoid athritis

Tissue kallikrein (TK) and 1-antitrypsin (AT)/TK complexes can be detected in SF from patients with RA if components of the fluids which interfere with the detection of TK are removed. 2-Macroglobulin (2-M) in SF was demonstrated to contain trapped proteases which were still active in amidase assays. Removal of 2-M from RA SF reduced their amidase activity. However, at least some of the remaining activity was due to TK because it was soya bean trypsin inhibitor resistant and trasylol sensitive and was partly removed by affinity chromatography on anti-TK sepharose. Removal of RF from the fluids reduced the values obtained for TK levels by ELISA. Addition of SF to human urinary kallikrein (HUK) considerably reduced the levels of TK detected suggesting the presence of a TK ELISA inhibitor in the fluids. Removal of components of >300 kDa from SF markedly reduced the TK ELISA inhibitory activity and increased the values for both the TK and l-AT/TK levels in fluids as measured by ELISA. It is considered this novel inhibitor does not bind to the active site of TK but rather binds to the site reactive with anti-TK antibodies

Schubert polynomials as integer point transforms of generalized permutahedra

We show that the dual character of the flagged Weyl module of any diagram is a positively weighted integer point transform of a generalized permutahedron. In particular, Schubert and key polynomials are positively weighted integer point transforms of generalized permutahedra. This implies several recent conjectures of Monical, Tokcan and Yong.Comment: 8 pages. Corrected title in arXiv metadata (d'oh); no change to manuscrip

Origin of the peak-dip-hump structure in the photoemission spectra of Bi2212

The famous peak-dip-hump lineshape of the (\pi,0) photoemission spectrum of the bilayer Bi HTSC in the superconducting state is shown to be a superposition of spectral features originating from different electronic states which reside at different binding energies, but are each describable by essentially identical single-particle spectral functions. The 'superconducting' peak is due to the antibonding Cu-O-related band, while the hump is mainly formed by its bonding counterpart, with a c-axis bilayer coupling induced splitting of about 140 meV.Comment: 5 pages: text + 4 figures, revtex (Fig.2 is replaced by more suitable one

Eluate derived by extracorporal antibody-based immunoadsorption elevates the cytosolic Ca2+ concentration in podocytes via B-2 kinin receptors

Background/Aim: Patients with idiopathic focal segmental glomerulosclerosis (FSGS) often develop a recurrence of the disease after kidney transplantation. In a number of FSGS patients, plasmapheresis and immunoadsorption procedures have been shown to transiently reduce proteinuria and are thought to do this by eliminating a circulating factor. Direct cellular effects of eluates from immunoadsorption procedures on podocytes, the primary target of injury in FSGS, have not yet been reported. Methods: Eluates were derived from antibody-based immunoadsorption of a patient suffering from primary FSGS, a patient with systemic lupus erythematosus, and a healthy volunteer. The cytosolic free Ca2+ concentration ({[}Ca2+](i)) of differentiated podocytes was measured by single-cell fura-2 microfluorescence measurements. Free and total immunoreactive kinin levels were measured by radioimmunoassay. Results: FSGS eluates increased the {[}Ca2+](i) levels concentration dependently (EC50 0.14 mg/ml; n = 3-19). 1 mg/ml eluate increased the {[}Ca2+](i) values reversibly from 82 +/- 12 to 1,462 +/- 370 nmol/l, and then they returned back to 100 16 nmol/l (n = 19). The eluate-induced increase of {[}Ca2+](i) consisted of an initial Ca2+ peak followed by a Ca2+ plateau which depended on the extracellular Ca2+ concentration. The eluate-induced increase of {[}Ca2+](i) was inhibited by the specific B-2 kinin receptor antagonist Hoe 140 in a concentration-dependent manner (IC50 2.47 nmol/l). In addition, prior repetitive application of bradykinin desensitized the effect of eluate on {[}Ca2+](i). A colonic epithelial cell line not reacting to bradykinin did not respond to eluate either (n = 6). Similar to FSGS eluates, the eluate preparations of both the systemic lupus patient and the healthy volunteer led to a biphasic, concentration-dependent {[}Ca2+](i) increase in poclocytes which again was inhibited by Hoe 140. Free kinins were detected in all eluate preparations. Conclusion: The procedure of antibody-based immunoadsorption leads to kinin in the eluate which elevates the {[}Ca2+](i) level of podocytes via B-2 kinin receptors. Copyright (C) 2002 S. Karger AG, Basel

Type Ia Supernovae and Accretion Induced Collapse

Using the population synthesis binary evolution code StarTrack, we present theoretical rates and delay times of Type Ia supernovae arising from various formation channels. These channels include binaries in which the exploding white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a white dwarf accretes from a helium-rich companion and explodes as a SN Ia before reaching the Chandrasekhar mass limit. We find that using a common envelope parameterization employing energy balance with alpha=1 and lambda=1, the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a burst of star formation at t=0. Additionally, the delay time distribution of the sub-Chandrasekhar model can be divided in to two distinct evolutionary channels: the `prompt' helium-star channel with delay times < 500 Myr, and the `delayed' double white dwarf channel with delay times > 800 Myr spanning up to a Hubble time. These findings are in agreement with recent observationally-derived delay time distributions which predict that a large number of SNe Ia have delay times < 1 Gyr, with a significant fraction having delay times < 500 Myr. We find that the DDS channel is also able to account for the observed rates of SNe Ia. However, detailed simulations of white dwarf mergers have shown that most of these mergers will not lead to SNe Ia but rather to the formation of a neutron star via accretion-induced collapse. If this is true, our standard population synthesis model predicts that the only progenitor channel which can account for the rates of SNe Ia is the sub-Chandrasekhar mass scenario, and none of the other progenitors considered can fully account for the observed rates.Comment: 6 pages, 1 figure, 1 table, to appear in proceedings for "Binary Star Evolution: Mass Loss, Accretion and Mergers