The Large-scale ISM of SS433/W50 Revisited

With new high-resolution CO and HI data, we revisited the large-scale interstellar medium (ISM) environment toward the SS 433/W50 system. We find that two interesting molecular cloud (MC) concentrations, G39.315-1.155 and G40.331-4.302, are well aligned along the precession cone of SS 433 within a smaller opening angle of ~7deg. The kinematic features of the two MCs at ~73--84 km/s, as well as those of the corresponding atomic-gas counterparts, are consistent with the kinematic characteristics of SS 433. That is, the receding gas from SS 433 jet is probably responsible for the redshifted feature of G39.315-1.155 near the Galactic plane and the approaching one may power the blueshifted gas of G40.331-4.302 toward the observer. Moreover, the HI emission at VLSR~70--90 km/s displays the morphological resemblance with the radio nebula W50. We suggest that the VLSR=77\pm5 km/s gas is physically associated with SS 433/W50, leading to a near kinematic distance of 4.9\pm0.4 kpc for the system. The observed gas features, which are located outside the current radio boundaries of W50, are probably the fossil record of jet-ISM interactions at ~10^5 years ago. The energetic jets of the unique microquasar have profound effects on its ISM environment, which may facilitate the formation of molecular gas on the timescale of <0.1 Myr for the ram pressure of ~2x10^6 K cm-3.Comment: 1 table, 13 figures, to appear in the ApJ. Comments welcom

Full quantum treatment of Rabi oscillation driven by a pulse train and its application in ion-trap quantum computation

Rabi oscillation of a two-level system driven by a pulse train is a basic process involved in quantum computation. We present a full quantum treatment of this process and show that the population inversion of this process collapses exponentially, has no revival phenomenon, and has a dual-pulse structure in every period. As an application, we investigate the properties of this process in ion-trap quantum computation. We find that in the Cirac--Zoller computation scheme, when the wavelength of the driving field is of the order $10^{-6}$ m, the lower bound of failure probability is of the order $10^{-2}$ after about $10^2$ controlled-NOT gates. This value is approximately equal to the generally-accepted threshold in fault-tolerant quantum computation.Comment: 22 pages, 5 figur

Universal Correlation between Critical Temperature of Superconductivity and band structure features

The critical temperature (${T}_\text{c}$) of superconductors varies a lot. The factors governing the ${T}_\text{c}$ may hold key clues to understand the nature of the superconductivity. Thereby, ${T}_\text{c}$-involved correlations, such as Matthias laws, Uemura law, and cuprates doping phase diagrams, have been of great concern. However, the electronic interaction being responsible for the carriers pairing in high-${T}_\text{c}$ superconductors is still not clear, which calls for more comprehensive analyses of the experimental data in history. In this work, we propose a novel perspective for searching material gene parameters and ${T}_\text{c}$-involved correlations. By exploring holistic band structure features of diverse superconductors, we found a universal correlation between the ${T}_\text{c}$ maxima and the electron energy levels for all kinds of superconducting materials. It suggests that the ${T}_\text{c}$ maxima are determined by the energy level of secondary-outer orbitals, rather than the band structure nearby the Fermi level. The energy level of secondary-outer orbitals is a parameter corresponding to the ratio of atomic orbital hybridization, implying that the fluctuation of the orbital hybridization is another candidate of pairing glue

Perturbed Hankel determinant, correlation functions and Painlev\'e equations

We continue with the study of the Hankel determinant, $$D_{n}(t,\alpha,\beta):=\det\left(\int_{0}^{1}x^{j+k}w(x;t,\alpha,\beta)dx\right)_{j,k=0}^{n-1},$$ generated by a Pollaczek-Jacobi type weight, $$w(x;t,\alpha,\beta):=x^{\alpha}(1-x)^{\beta}{\rm e}^{-t/x}, \quad x\in [0,1], \quad \alpha>0, \quad \beta>0, \quad t\geq 0.$$ This reduces to the "pure" Jacobi weight at $t=0.$ We may take $\alpha\in \mathbb{R}$, in the situation while $t$ is strictly greater than $0.$ It was shown in Chen and Dai (2010), that the logarithmic derivative of this Hankel determinant satisfies a Jimbo-Miwa-Okamoto $\sigma$-form of Painlev\'e \uppercase\expandafter{\romannumeral5} ({\rm P_{\uppercase\expandafter{\romannumeral5}}}). In fact the logarithmic of the Hankel determinant has an integral representation in terms of a particular {\rm P_{\uppercase\expandafter{\romannumeral5}}}. \\ In this paper, we show that, under a double scaling, where $n$ the dimension of the Hankel matrix tends to $\infty$, and $t$ tends to $0^{+},$ such that $s:=2n^2t$ is finite, the double scaled Hankel determinant (effectively an operator determinant) has an integral representation in terms of a particular {\rm P_{\uppercase\expandafter{\romannumeral3}'}}. Expansions of the scaled Hankel determinant for small and large $s$ are found. A further double scaling with $\alpha=-2n+\lambda,$ where $n\rightarrow \infty$ and $t,$ tends to $0^{+},$ such that $s:=nt$ is finite. In this situation the scaled Hankel determinant has an integral representation in terms of a particular {\rm P_{\uppercase\expandafter{\romannumeral5}}}, %which can be degenerate to a particular {\rm P_{\uppercase\expandafter{\romannumeral3}}} and its small and large $s$ asymptotic expansions are also found

Critical edge behavior in the perturbed Laguerre ensemble and the Painleve V transcendent

In this paper, we consider the perturbed Laguerre unitary ensemble described by the weight function of $$w(x,t)=(x+t)^{\lambda}x^{\alpha}e^{-x}$$ with $x\geq 0,\ t>0,\ \alpha>0,\ \alpha+\lambda+1 > 0.$ The Deift-Zhou nonlinear steepest descent approach is used to analyze the limit of the eigenvalue correlation kernel. It was found that under the double scaling $s=4nt,$ $n\to \infty,$ $t\to 0$ such that $s$ is positive and finite, at the hard edge, the limiting kernel can be described by the $\varphi$-function related to a third-order nonlinear differential equation, which is equivalent to a particular Painlev\'e V (shorted as P$_{\rm V}$) transcendent via a simple transformation. Moreover, this P$_{\rm V}$ transcendent is equivalent to a general Painlev\'e P$_{\rm III}$ transcendent. For large $s,$ the P$_{\rm V}$ kernel reduces to the Bessel kernel $\mathbf{J}_{\alpha+\lambda}.$ For small $s,$ the P$_{\rm V}$ kernel reduces to another Bessel kernel $\mathbf{J}_\alpha.$ At the soft edge, the limiting kernel is the Airy kernel as the classical Laguerre weight.Comment: 53 page

Inverse Problem of Electro-seismic Conversion

When a porous rock is saturated with an electrolyte, electrical fields are coupled with seismic waves via the electro-seismic conversion. Pride derived the governing models, in which Maxwell equations are coupled with Biot equations through the electro-kinetic mobility parameter. The inverse problem of the linearized electro-seismic conversion consists in two step, namely the inversion of Biot equations and the inversion of Maxwell equations. We analyze the reconstruction of conductivity and electro-kinetic mobility parameter in Maxwell equations with internal measurements, while the internal measurements are provided by the results of the inversion of Biot equations. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determine these two parameters. Moreover, a Lipschitz type stability is proved based on the same sets of well-chosen boundary conditions

Revisiting Street-to-Aerial View Image Geo-localization and Orientation Estimation

Street-to-aerial image geo-localization, which matches a query street-view image to the GPS-tagged aerial images in a reference set, has attracted increasing attention recently. In this paper, we revisit this problem and point out the ignored issue about image alignment information. We show that the performance of a simple Siamese network is highly dependent on the alignment setting and the comparison of previous works can be unfair if they have different assumptions. Instead of focusing on the feature extraction under the alignment assumption, we show that improvements in metric learning techniques significantly boost the performance regardless of the alignment. Without leveraging the alignment information, our pipeline outperforms previous works on both panorama and cropped datasets. Furthermore, we conduct visualization to help understand the learned model and the effect of alignment information using Grad-CAM. With our discovery on the approximate rotation-invariant activation maps, we propose a novel method to estimate the orientation/alignment between a pair of cross-view images with unknown alignment information. It achieves state-of-the-art results on the CVUSA dataset.Comment: WACV 202

Multi-modal Aggregation for Video Classification

In this paper, we present a solution to Large-Scale Video Classification Challenge (LSVC2017) [1] that ranked the 1st place. We focused on a variety of modalities that cover visual, motion and audio. Also, we visualized the aggregation process to better understand how each modality takes effect. Among the extracted modalities, we found Temporal-Spatial features calculated by 3D convolution quite promising that greatly improved the performance. We attained the official metric mAP 0.8741 on the testing set with the ensemble model

Towards Randomized Testing of qq-Monomials in Multivariate Polynomials

Given any fixed integer $q\ge 2$, a $q$-monomial is of the format $\displaystyle x^{s_1}_{i_1}x^{s_2}_{i_2}...x_{i_t}^{s_t}$ such that $1\le s_j \le q-1$, $1\le j \le t$. $q$-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and $q$-monomails for prime $q$ in multivariate polynomials relies on the property that $Z_q$ is a field when $q\ge 2$ is prime. When $q>2$ is not prime, it remains open whether the problem of testing $q$-monomials can be solved in some compatible complexity. In this paper, we present a randomized $O^*(7.15^k)$ algorithm for testing $q$-monomials of degree $k$ that are found in a multivariate polynomial that is represented by a tree-like circuit with a polynomial size, thus giving a positive, affirming answer to the above question. Our algorithm works regardless of the primality of $q$ and improves upon the time complexity of the previously known algorithm for testing $q$-monomials for prime $q>7$.Comment: 21 pages, 5 figures. arXiv admin note: text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

Single-use MIMO system, Painlev\'e transcendents and double scaling

In this paper we study a particular Painlev\'e V (denoted ${\rm P_{V}}$) that arises from Multi-Input-Multi-Output (MIMO) wireless communication systems. Such a $P_V$ appears through its intimate relation with the Hankel determinant that describes the moment generating function (MGF) of the Shannon capacity. This originates through the multiplication of the Laguerre weight or the Gamma density $x^{\alpha} {\rm e}^{-x},\;x> 0,$ for $\alpha>-1$ by $(1+x/t)^{\lambda}$ with $t>0$ a scaling parameter. Here the $\lambda$ parameter "generates" the Shannon capacity, see Yang Chen and Matthew McKay, IEEE Trans. IT, 58 (2012) 4594--4634. It was found that the MGF has an integral representation as a functional of $y(t)$ and $y'(t)$, where $y(t)$ satisfies the "classical form" of $P_V$. In this paper, we consider the situation where $n,$ the number of transmit antennas, (or the size of the random matrix), tends to infinity, and the signal-to-noise ratio (SNR) $P$ tends to infinity, such that $s={4n^{2}}/{P}$ is finite. Under such double scaling the MGF, effectively an infinite determinant, has an integral representation in terms of a "lesser" $P_{III}$. We also consider the situations where $\alpha=k+1/2,\;\;k\in \mathbb{N},$ and $\alpha\in\{0,1,2,\dots\}$ $\lambda\in\{1,2,\dots\},$ linking the relevant quantity to a solution of the two dimensional sine-Gordon equation in radial coordinates and a certain discrete Painlev\'e-II. From the large $n$ asymptotic of the orthogonal polynomials, that appears naturally, we obtain the double scaled MGF for small and large $s$, together with the constant term in the large $s$ expansion. With the aid of these, we derive a number of cumulants and find that the capacity distribution function is non-Gaussian.Comment: 30 page