Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot

In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with a fixed limiting ratio, $s$, of $M$ and $(N+1/2)$. We find out the asymptotic expansion formula (AEF) of the colored Jones polynomials of the figure eight knot with $s$ close to $1$. Nonetheless, we show that the exponential growth rate of the colored Jones polynomials of the figure eight knot with $s$ close to $1/2$ is strictly less than those with $s$ close to $1$. It is known that the Turaev Viro invariant of the figure eight knot can be expressed in terms of a sum of its colored Jones polynomials. Our results show that this sum is asymptotically equal to the sum of the terms with $s$ close to 1. As an application of the asymptotic behavior of the colored Jones polynomials, we obtain the asymptotic expansion formula for the Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible generalization of our approach so as to relate the AEF for the colored Jones polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic knots.Comment: 40 pages, 0 figure

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition component by integrating the multiresolution framework into the implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm

An Anti-C1s Monoclonal, TNT003, Inhibits Complement Activation Induced by Antibodies Against HLA.

Antibody-mediated rejection (AMR) of solid organ transplants (SOT) is characterized by damage triggered by donor-specific antibodies (DSA) binding donor Class I and II HLA (HLA-I and HLA-II) expressed on endothelial cells. While F(ab')2 portions of DSA cause cellular activation and proliferation, Fc regions activate the classical complement cascade, resulting in complement deposition and leukocyte recruitment, both hallmark features of AMR. We characterized the ability of an anti-C1s monoclonal antibody, TNT003, to inhibit HLA antibody (HLA-Ab)-induced complement activation. Complement deposition induced by HLA-Ab was evaluated using novel cell- and bead-based assays. Human aortic endothelial cells (HAEC) were cultured with HLA-Ab and human complement; production of activated complement proteins was measured by flow cytometry. Additionally, C3d deposition was measured on single antigen beads (SAB) mixed with HLA-Ab and human complement. TNT003 inhibited HLA-Ab mediated complement deposition on HAEC in a concentration-dependent manner; C3a, C4a and C5a anaphylatoxin production was also diminished by TNT003. Finally, TNT003 blocked C3d deposition induced by Class I (HLAI-Ab)- and Class II (HLAII-Ab)-specific antibodies on SAB. These data suggest TNT003 may be useful for modulating the effects of DSA, as TNT003 inhibits complement deposition and split product formation generated by HLA-I/II-Ab in vitro

Suzaku X-ray Observations of the Nearest Non-Cool Core Cluster, Antlia: Dynamically Young but with Remarkably Relaxed Outskirts

We present the results of seven Suzaku mosaic observations (>200 ks in total) of the nearest non-cool core cluster, the Antlia Cluster (or Group), beyond its degree-scale virial radius in its eastern direction. The temperature is consistent with the scaled profiles of many other clusters. Its pressure follows the universal profile. The density slope in its outskirts is significantly steeper than that of the nearest cool core cluster (Virgo) with a similar temperature as Antlia, but shallower than those of the massive clusters. The entropy increases all the way out to R_200, which is consistent in value with the baseline model predicted by a gravity heating-only mechanism in the outskirts. Antlia is quite relaxed in this direction. However, the entropy inside ~R_500 is significantly higher than the baseline model, which is similar to many other nearby low mass clusters or groups. The enclosed gas-mass fraction does not exceed the cosmic value out to 1.3R_200. Thus, there is no evidence of significant gas clumping, electron-ion non-equipartition, or departure from the hydrostatic equilibrium approximation that are suggested to explain the entropy and gas fraction anomalies found in the outskirts of some massive clusters. We also present scaling relations for the gas fraction (f_gas,200), entropy (K_200), and temperature (T_500) using 22 groups and clusters with published data in the literature. The enclosed baryon fraction at R_200 is broadly consistent with the cosmic value. The power law slope of the K_200-T_500 relation is 0.638+/-0.205. The entropy deficit at R_200 cannot be fully accounted for by the bias or deviation in the gas fraction.Comment: 24 pages, 16 figures, minor modifications to match the published version in Ap

Predictors of Cycling in College Students

Objectives: To (1) assess cycling-related questions that have been added to the electronic version of the American College Health Association National College Health Assessment II (ACHA-NCHA), (2) examine cycling prevalence, and (3) identify predictors of cycling in college students. Participants: Predominately female (69%), undergraduate (89%), and white (85%) students (N = 949) from a large, urban, northwestern, bicycle-friendly university completed the electronic version of the ACHA-NCHA II. Methods: Thirty cycling-related questions were added to the ACHA-NCHA II and a subsample of questions was analyzed. Results: Cycling questions added to the ACHA-NCHA II scale were reliable and valid, based on the psychometric data analysis. More than half (59%) of this sample cycled; of those, 58% cycled for transportation and 44% for recreation. Facilitators and barriers to cycling were different for cycling in general and cycling for transportation. Conclusions: Cycling questions added to the ACHA-NCHA II can be utilized to enhance knowledge relative to cycling on college campuses