arXiv subjects

Quan Zhou

Publications and source records attributed to Quan Zhou.

At least 145 records · Page 8Linked to original sources

arXiv2019

Penetrative turbulent Rayleigh-Bénard convection in two and three dimensions

Penetrative turbulent Rayleigh-Bénard convection which depends on the density maximum of water near $4^\circ\rm{C}$ is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is water near $4^\circ\rm{C}$ with Prandtl number $Pr=11.57$. The considered Rayleigh numbers $Ra$ range from $10^7$ to $10^{10}$. The density inversion parameter $θ_m$ varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thickness ($F_λ=λ_t^θ/λ_b^θ$) increases with increasing $θ_m$, and the relationship between $F_λ$ and $θ_m$ seems to be independent of $Ra$. The centre temperature $θ_c$ is enhanced compared to that of Oberbeck-Boussinesq (OB) cases, as $θ_c$ is related to $F_λ$ with $1/θ_c=1/F_λ+1$, $θ_c$ is also found to have a universal relationship with $θ_m$ which is independent of $Ra$. Both the Nusselt number $Nu$ and the Reynolds number $Re$ decrease with increasing $θ_m$, the normalized Nusselt number $Nu(θ_m)/Nu(0)$ and Reynolds number $Re(θ_m)/Re(0)$ also have universal relationships with $θ_m$ which seem to be independent of both $Ra$ and the aspect ratio $Γ$. The scaling exponents of $Nu\sim Ra^α$ and $Re\sim Ra^β$ are found to be insensitive to $θ_m$ despite of the remarkable change of the flow organizations.

physics.flu-dyn↗

arXiv2019

A lossless data hiding scheme in JPEG images with segment coding

In this paper, we propose a lossless data hiding scheme in JPEG images. After quantified DCT transform, coefficients have characteristics that distribution in high frequencies is relatively sparse and absolute values are small. To improve encoding efficiency, we put forward an encoding algorithm that searches for a high frequency as terminate point and recode the coefficients above, so spare space is reserved to embed secret data and appended data with no file expansion. Receiver can obtain terminate point through data analysis, extract additional data and recover original JPEG images lossless. Experimental results show that the proposed method has a larger capacity than state-of-the-art works.

cs.CV↗

arXiv2018

Optimal real-time detection of a drifting Brownian coordinate

Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a non-zero drift. Given that the position of the Brownian particle is being observed in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, which spatial coordinate has the non-zero drift. We solve this problem in the Bayesian formulation, under any prior probabilities of the non-zero drift being in any of the three spatial coordinates, when the passage of time is penalised linearly. Finding the exact solution to the problem in three dimensions, including a rigorous treatment of its non-monotone optimal stopping boundaries, is the main contribution of the present paper. To our knowledge this is the first time that such a problem has been solved in the literature.

math.PR↗

arXiv2018

Spatial statistics of atmospheric particulate matter in China

In this paper, the spatial dynamics of the atmospheric particulate matters (resp. PM$_{10}$ and PM$_{2.5}$) are studied using turbulence methodologies. It is found experimentally that the spatial correlation function $ρ(r)$ shows a log-law on the mesoscale range, i.e., $50\le r\le 500\,{km}$, with an experimental scaling exponent $β=0.45$. The spatial structure function shows a power-law behavior on the mesoscale range $90\le r\le 500\,{km}$. The experimental scaling exponent $ζ(q)$ is convex, showing that the intermittent correction is relevant in characterizing the spatial dynamic of particulate matter. The measured singularity spectrum $f(α)$ also shows its multifractal nature. Experimentally, the particulate matter is more intermittent than the passive scalar, which could be partially due to the \red{mesoscale movements} of the atmosphere, and also due to local sources, such as local industry activities.

physics.ao-ph↗

arXiv2018

Taylor dispersion in two-dimensional bacterial turbulence

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. Two-regime power-law behavior for short and long time evolutions were identified experimentally, which were separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be $0.94$ and $0.97$ for short and long times evolutions, respectively. For the case without the mean velocity effect, the values were $0.88$ and $0.58$. Moreover, very weak intermittency correction was detected. All measured Hurst number were above $1/2$, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food.

physics.flu-dyn↗

arXiv2018

Fast Dynamic Routing Based on Weighted Kernel Density Estimation

Capsules as well as dynamic routing between them are most recently proposed structures for deep neural networks. A capsule groups data into vectors or matrices as poses rather than conventional scalars to represent specific properties of target instance. Besides of pose, a capsule should be attached with a probability (often denoted as activation) for its presence. The dynamic routing helps capsules achieve more generalization capacity with many fewer model parameters. However, the bottleneck that prevents widespread applications of capsule is the expense of computation during routing. To address this problem, we generalize existing routing methods within the framework of weighted kernel density estimation, and propose two fast routing methods with different optimization strategies. Our methods prompt the time efficiency of routing by nearly 40\% with negligible performance degradation. By stacking a hybrid of convolutional layers and capsule layers, we construct a network architecture to handle inputs at a resolution of $64\times{64}$ pixels. The proposed models achieve a parallel performance with other leading methods in multiple benchmarks.

cs.CV↗

arXiv2018

Fast model-fitting of Bayesian variable selection regression using the iterative complex factorization algorithm

Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special class of linear systems, which can increase the speed of the BVSR model-fitting tenfold. The iterative method hinges on the complex factorization of the sum of two matrices and the solution path resides in the complex domain (instead of the real domain). Compared to the Gauss-Seidel method, the complex factorization converges almost instantaneously and its error is several magnitude smaller than that of the Gauss-Seidel method. More importantly, the error is always within the pre-specified precision while the Gauss-Seidel method is not. For large problems with thousands of covariates, the complex factorization is 10 -- 100 times faster than either the Gauss-Seidel method or the direct method via the Cholesky decomposition. In BVSR, one needs to repetitively solve large penalized regression systems whose design matrices only change slightly between adjacent MCMC steps. This slight change in design matrix enables the adaptation of the iterative complex factorization method. The computational innovation will facilitate the wide-spread use of BVSR in reanalyzing genome-wide association datasets.

stat.CO↗

arXiv2018

Atom2Vec: learning atoms for materials discovery

Exciting advances have been made in artificial intelligence (AI) during the past decades. Among them, applications of machine learning (ML) and deep learning techniques brought human-competitive performances in various tasks of fields, including image recognition, speech recognition and natural language understanding. Even in Go, the ancient game of profound complexity, the AI player already beat human world champions convincingly with and without learning from human. In this work, we show that our unsupervised machines (Atom2Vec) can learn the basic properties of atoms by themselves from the extensive database of known compounds and materials. These learned properties are represented in terms of high dimensional vectors, and clustering of atoms in vector space classifies them into meaningful groups in consistent with human knowledge. We use the atom vectors as basic input units for neural networks and other ML models designed and trained to predict materials properties, which demonstrate significant accuracy.

physics.comp-ph↗

arXiv2018

Sequential rerandomization

The seminal work of Morgan and Rubin (2012) considers rerandomization for all the units at one time. In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result, Theorem 3, that given the same number of rerandomizations (in expected value), under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.

stat.AP↗

arXiv2018

Asymptotics of multivariate contingency tables with fixed marginals

We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining whether the cell has a Poisson limit or a Gaussian limit. There are three forms of Poisson convergence. The exact form is shown to be determined by the growth rates of the two smallest marginal totals. The results are generalized to contingency tables with arbitrary sizes and are further complemented with concrete examples.

math.ST↗

arXiv2018

When is it best to follow the leader?

An object is hidden in one of $N$ boxes. Initially, the probability that it is in box $i$ is $π_i(0)$. You then search in continuous time, observing box $J_t$ at time $t$, and receiving a signal as you observe: if the box you are observing does not contain the object, your signal is a Brownian motion, but if it does contain the object your signal is a Brownian motion with positive drift $μ$. It is straightforward to derive the evolution of the posterior distribution $π(t)$ for the location of the object. If $T$ denotes the first time that one of the $π_j(t)$ reaches a desired threshold $1-\varepsilon$, then the goal is to find a search policy $(J_t)_{t \geq 0}$ which minimizes the mean of $T$. This problem was studied by Posner and Rumsey (1966) and by Zigangirov (1966), who derive an expression for the mean time of a conjectured optimal policy, which we call {\em follow the leader} (FTL); at all times, observe the box with the highest posterior probability. Posner and Rumsey assert without proof that this is optimal, and Zigangirov offers a proof that if the prior distribution is uniform then FTL is optimal. In this paper, we show that if the prior is not uniform, then FTL is {\em not} always optimal; for uniform prior, the question remains open.

math.OC↗

arXiv2018

Thick distribution tails in models of cancer secondary tumors

Recent progress in microdissection and in DNA sequencing has enabled subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led to the construction of genealogies of the primary, secondary, tertiary and so forth, foci of the tumor. These studies have led to diverse conclusions concerning the Darwinian (selective) or neutral evolution in cancer. Mathematical models of development of multifocal tumors have been developed to support these claims. We report a model of development of a multifocal tumor, which is a mathematically rigorous refinement of a model of Ling et al. (2015). Guided by numerical studies and simulations, we show that the rigorous model, in the form of an infinite-type branching process, displays distributions of tumors size which have heavy tails and moments that become infinite in finite time. To demonstrate these points, we obtain bounds on the tails of the distributions of the process and infinite-series expression for the first moments. In addition to its inherent mathematical interest, the model is corroborated by recent reports of apparent super-exponential growth in cancer metastases.

q-bio.PE↗

arXiv2017

Multiple types of topological fermions in transition metal silicides

Exotic massless fermionic excitations with non-zero Berry flux, other than Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with 3-fold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe and CoGe, when the spin-orbit coupling (SOC) is considered. Their non-trivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on side surface, which is confirmed by (010) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.

cond-mat.mtrl-sci↗

arXiv2016

Intermittency measurement in two dimensional bacterial turbulence

In this paper, an experimental velocity database of a bacterial collective motion , e.g., \textit{B. subtilis}, in turbulent phase with volume filling fraction $84\%$ provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the $β-$limitation. A dual-power-law behavior separated by the viscosity scale $\ell_ν$ was observed for the $q$th-order Hilbert moment $\mathcal{L}_q(k)$. This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale $R$, e.g., the bacterial body length. The measured scaling exponents $ζ(q)$ of both the small-scale \red{(resp. $k>k_ν$) and large-scale (resp. $k<k_ν$)} motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are $μ_S=0.26$ and $μ_L=0.17$ respectively for the small- and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum $f(α)$ vs $α$. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation.

physics.flu-dyn↗

arXiv2016

The value of foresight

Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.

math.PR↗

arXiv2016

Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure

After the recognition of the possibility to implement Majorana fermions using the building blocks of solid-state matters, the detection of this peculiar particle has been an intense focus of research. Here we experimentally demonstrate a collection of Majorana fermions living in a one-dimensional transport channel at the boundary of a superconducting quantum anomalous Hall insulator thin film. A series of topological phase changes are controlled by the reversal of the magnetization, where a half-integer quantized conductance plateau (0.5e2/h) is observed as a clear signature of the Majorana phase. This transport signature can be well repeated during many magnetic reversal sweeps, and can be tracked at different temperatures, providing a promising evidence of the chiral Majorana edge modes in the system.

cond-mat.supr-con↗

arXiv2016

Dirac Fermions in Antiferromagnetic Semimetal

The analogues of elementary particles have been extensively searched for in condensed matter systems because of both scientific interests and technological applications. Recently massless Dirac fermions were found to emerge as low energy excitations in the materials named Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry $\mathcal{T}$ and inversion symmetry $\mathcal{P}$. Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where $\mathcal{T}$ and $\mathcal{P}$ are broken but their combination $\mathcal{PT}$ is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points with symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by \emph{ab initio} calculations. Our results give a new route towards the realization of Dirac materials, and provide a possible platform to study the interplay of Dirac fermion physics and magnetism.

cond-mat.mtrl-sci↗

arXiv2015

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

We propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional $s$-wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance will be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between $e^2/2h$ and $e^2/h$ with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.

cond-mat.supr-con↗