Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Exploring DCO+^+ as a tracer of thermal inversion in the disk around the Herbig Ae star HD163296

We aim to reproduce the DCO$^+$ emission in the disk around HD163296 using a simple 2D chemical model for the formation of DCO$^+$ through the cold deuteration channel and a parametric treatment of the warm deuteration channel. We use data from ALMA in band 6 to obtain a resolved spectral imaging data cube of the DCO$^+$ $J$=3--2 line in HD163296 with a synthesized beam of 0."53$\times$ 0."42. We adopt a physical structure of the disk from the literature that reproduces the spectral energy distribution. We then apply a simplified chemical network for the formation of DCO$^+$ that uses the physical structure of the disk as parameters along with a CO abundance profile, a constant HD abundance and a constant ionization rate. Finally, from the resulting DCO$^+$ abundances, we calculate the non-LTE emission using the 3D radiative transfer code LIME. The observed DCO$^+$ emission is reproduced by a model with cold deuteration producing abundances up to $1.6\times 10^{-11}$. Warm deuteration, at a constant abundance of $3.2\times 10^{-12}$, becomes fully effective below 32 K and tapers off at higher temperatures, reproducing the lack of DCO$^+$ inside 90 AU. Throughout the DCO$^+$ emitting zone a CO abundance of $2\times 10^{-7}$ is found, with $\sim$99\% of it frozen out below 19 K. At radii where both cold and warm deuteration are active, warm deuteration contributes up to 20\% of DCO$^+$, consistent with detailed chemical models. The decrease of DCO$^+$ at large radii is attributed to a temperature inversion at 250 AU, which raises temperatures above values where cold deuteration operates. Increased photodesorption may also limit the radial extent of DCO$^+$. The corresponding return of the DCO$^+$ layer to the midplane, together with a radially increasing ionization fraction, reproduces the local DCO$^+$ emission maximum at $\sim$260 AU.Comment: 9 pages, 5 figures, accepted 7th July 201

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

Global and quadratic convergence of Newton hard-thresholding pursuit

Algorithms based on the hard thresholding principle have been well studied with sounding theoretical guarantees in the compressed sensing and more general sparsity-constrained optimization. It is widely observed in existing empirical studies that when a restricted Newton step was used (as the debiasing step), the hard-thresholding algorithms tend to meet halting conditions in a significantly low number of iterations and are very efficient. Hence, the thus obtained Newton hard-thresholding algorithms call for stronger theoretical guarantees than for their simple hard-thresholding counterparts. This paper provides a theoretical justification for the use of the restricted Newton step. We build our theory and algorithm, Newton Hard-Thresholding Pursuit (NHTP), for the sparsity-constrained optimization. Our main result shows that NHTP is quadratically convergent under the standard assumption of restricted strong convexity and smoothness. We also establish its global convergence to a stationary point under a weaker assumption. In the special case of the compressive sensing, NHTP effectively reduces to some of the existing hard-thresholding algorithms with a Newton step. Consequently, our fast convergence result justifies why those algorithms perform better than without the Newton step. The efficiency of NHTP was demonstrated on both synthetic and real data in compressed sensing and sparse logistic regression

Monotonicity and logarithmic convexity relating to the volume of the unit ball

Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence $\frac{\Omega_{n}^{1/(n\ln n)}}{\Omega_{n+1}^{1/[(n+1)\ln(n+1)]}}$ is strictly decreasing for $n\ge2$. In addition, some monotonic and concave properties of several functions relating to $\Omega_{n}$ are extended and generalized.Comment: 12 page

Parametric Fokker-Planck equation

We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented

Efficient point-based trajectory search

LNCS v. 9239 entitled: Advances in Spatial and Temporal Databases: 14th International Symposium, SSTD 2015, Hong Kong, China, August 26-28, 2015. ProceedingsTrajectory data capture the traveling history of moving objects such as people or vehicles. With the proliferation of GPS and tracking technology, huge volumes of trajectories are rapidly generated and collected. Under this, applications such as route recommendation and traveling behavior mining call for efficient trajectory retrieval. In this paper, we first focus on distance-based trajectory search; given a collection of trajectories and a set query points, the goal is to retrieve the top-k trajectories that pass as close as possible to all query points. We advance the state-of-the-art by combining existing approaches to a hybrid method and also proposing an alternative, more efficient rangebased approach. Second, we propose and study the practical variant of bounded distance-based search, which takes into account the temporal characteristics of the searched trajectories. Through an extensive experimental analysis with real trajectory data, we show that our rangebased approach outperforms previous methods by at least one order of magnitude. © Springer International Publishing Switzerland 2015.postprin

Abrupt changes in alpha decay systematics as a manifestation of collective nuclear modes

An abrupt change in $\alpha$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $\alpha$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.Comment: 6 pages, 3 figures, submitted to Phys. Rev. C, a few new references adde