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Qi Wang

Publications and source records attributed to Qi Wang.

At least 757 records · Page 42Linked to original sources
arXiv2015

Boundary spikes of a Keller-Segel chemotaxis system with saturated logarithmic sensitivity

In this paper, we study the nonconstant positive steady states of a Keller-Segel chemotaxis system over a bounded domain $Ω\subset \mathbb{R}^N$, $N\geq 1$. The sensitivity function is chosen to be $ϕ(v)=\ln (v+c)$ where $c$ is a positive constant. For the chemical diffusion rate being small, we construct positive solutions with a boundary spike supported on a platform. Moreover, this spike approaches the most curved part of the boundary of the domain as the chemical diffusion rate shrinks to zero. We also conduct extensive numerical simulations to illustrate the formation of stable boundary and interior spikes of the system. These spiky solutions can be used to model the self--organized cell aggregation phenomenon in chemotaxis.

math.AP↗
arXiv2014

Local solvability of the $k$-Hessian equations

In this work, we study the existence of local solutions in $\mathbb{R}^{n}$ to $k$-Hessian equation,for which the nonhomogeneous term $f$ is permitted to change the sign or be non negative; if $f$ is $C^\infty,$ so is the local solution. We also give a classification for the second order polynomial solutions to the $k-$Hessian equation, it is the basis to construct the local solutions and obtain the uniform ellipticity of the linearized operators at such constructed local solutions.

math.AP↗
arXiv2014

Dynamic control of spin wave spectra using spin-polarized currents

We describe a method of controlling the spin wave spectra dynamically in a uniform nanostripe waveguide through spin-polarized currents. A stable periodic magnetization structure is observed when the current flows vertically through the center of nanostripe waveguide. After being excited, the spin wave is transmitted at the sides of the waveguide. Numerical simulations of spin-wave transmission and dispersion curves reveal a single, pronounced band gap. Moreover, the periodic magnetization structure can be turned on and off by the spin-polarized current. The switching process from full rejection to full transmission takes place within less than 3ns. Thus, this type magnonic waveguide can be utilized for low-dissipation spin wave based filters.

cond-mat.mtrl-sci↗
arXiv2014

Existence and stability of nonconstant positive steady states of morphogenesis models

In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady states through local bifurcation theories. We also rigorously study the stability of the nonconstant solutions when the sensitivity function are chosen to be linear and logarithmic function respectively. Finally, we present numerical solutions to illustrate the formation of stable spatially inhomogeneous patterns. Our numerical simulations suggests that this model can develop very complicated and interesting structures even over one--dimensional finite domains.

math.AP↗
arXiv2014

$C^\infty$ local solutions of elliptical $2-$Hessian equation in $\mathbb{R}^3$

In this work, we study the existence of $C^{\infty}$ local solutions to $2$-Hessian equation in $\mathbb{R}^{3}$. We consider the case that the right hand side function $f$ possibly vanishes, changes the sign, is positively or negatively defined. We also give the convexities of solutions which are related with the annulation or the sign of right-hand side function $f$. The associated linearized operator are uniformly elliptic.

math.AP↗
arXiv2014

On a shadow system of the S-K-T competition system

We study a boundary value problem with an integral constraint that arises from the modelings of species competition proposed by Lou and Ni in \cite{LN2}. Through bifurcation theories, we obtain the existence of non-constant positive solutions over one-dimensional domain, which are small perturbations from the positive constant solution of the system. Moreover, we determine the stability of the bifurcating solutions. Finally, for the diffusion rate being sufficiently small, we construct infinitely many positive solutions with single transition layer, which is represented as an approximation of a step function that. The transition-layer solution can be used to model the phenomenon of species segregation through competitions.

math.AP↗
arXiv2014

Quantifying Human Mobility Perturbation and Resilience in Natural Disasters

Human mobility is influenced by environmental change and natural disasters. Researchers have used trip distance distribution, radius of gyration of movements, and individuals' visited locations to understand and capture human mobility patterns and trajectories. However, our knowledge of human movements during natural disasters is limited owing to both a lack of empirical data and the low precision of available data. Here, we studied human mobility using high-resolution movement data from individuals in New York City during and for several days after Hurricane Sandy in 2012. We found the human movements followed truncated power-law distributions during and after Hurricane Sandy, although the β value was noticeably larger during the first 24 hours after the storm struck. Also, we examined two parameters: the center of mass and the radius of gyration of each individual's movements. We found that their values during perturbation states and steady states are highly correlated, suggesting human mobility data obtained in steady states can possibly predict the perturbation state. Our results demonstrate that human movement trajectories experienced significant perturbations during hurricanes, but also exhibited high resilience. We expect the study will stimulate future research on the perturbation and inherent resilience of human mobility under the influence of natural disasters. For example, mobility patterns in coastal urban areas could be examined as tropical cyclones approach, gain or dissipate in strength, and as the path of the storm changes. Understanding nuances of human mobility under the influence of disasters will enable more effective evacuation, emergency response planning and development of strategies and policies to reduce fatality, injury, and economic loss.

physics.soc-ph↗
arXiv2013

Three New Families of Zero-difference Balanced Functions with Applications

Zero-difference balanced (ZDB) functions integrate a number of subjects in combinatorics and algebra, and have many applications in coding theory, cryptography and communications engineering. In this paper, three new families of ZDB functions are presented. The first construction, inspired by the recent work \cite{Cai13}, gives ZDB functions defined on the abelian groups $(\gf(q_1) \times \cdots \times \gf(q_k), +)$ with new and flexible parameters. The other two constructions are based on $2$-cyclotomic cosets and yield ZDB functions on $\Z_n$ with new parameters. The parameters of optimal constant composition codes, optimal and perfect difference systems of sets obtained from these new families of ZDB functions are also summarized.

cs.IT↗
arXiv2013

From Maxout to Channel-Out: Encoding Information on Sparse Pathways

Motivated by an important insight from neural science, we propose a new framework for understanding the success of the recently proposed "maxout" networks. The framework is based on encoding information on sparse pathways and recognizing the correct pathway at inference time. Elaborating further on this insight, we propose a novel deep network architecture, called "channel-out" network, which takes a much better advantage of sparse pathway encoding. In channel-out networks, pathways are not only formed a posteriori, but they are also actively selected according to the inference outputs from the lower layers. From a mathematical perspective, channel-out networks can represent a wider class of piece-wise continuous functions, thereby endowing the network with more expressive power than that of maxout networks. We test our channel-out networks on several well-known image classification benchmarks, setting new state-of-the-art performance on CIFAR-100 and STL-10, which represent some of the "harder" image classification benchmarks.

cs.NE↗
arXiv2013

Optimization with Discrete Simultaneous Perturbation Stochastic Approximation Using Noisy Loss Function Measurements

Discrete stochastic optimization considers the problem of minimizing (or maximizing) loss functions defined on discrete sets, where only noisy measurements of the loss functions are available. The discrete stochastic optimization problem is widely applicable in practice, and many algorithms have been considered to solve this kind of optimization problem. Motivated by the efficient algorithm of simultaneous perturbation stochastic approximation (SPSA) for continuous stochastic optimization problems, we introduce the middle point discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm for the stochastic optimization of a loss function defined on a p-dimensional grid of points in Euclidean space. We show that the sequence generated by DSPSA converges to the optimal point under some conditions. Consistent with other stochastic approximation methods, DSPSA formally accommodates noisy measurements of the loss function. We also show the rate of convergence analysis of DSPSA by solving an upper bound of the mean squared error of the generated sequence. In order to compare the performance of DSPSA with the other algorithms such as the stochastic ruler algorithm (SR) and the stochastic comparison algorithm (SC), we set up a bridge between DSPSA and the other two algorithms by comparing the probability in a big-O sense of not achieving the optimal solution. We show the theoretical and numerical comparison results of DSPSA, SR, and SC. In addition, we consider an application of DSPSA towards developing optimal public health strategies for containing the spread of influenza given limited societal resources.

math.OC↗
arXiv2013

Sets of Zero-Difference Balanced Functions and Their Applications

Zero-difference balanced (ZDB) functions can be employed in many applications, e.g., optimal constant composition codes, optimal and perfect difference systems of sets, optimal frequency hopping sequences, etc. In this paper, two results are summarized to characterize ZDB functions, among which a lower bound is used to achieve optimality in applications and determine the size of preimage sets of ZDB functions. As the main contribution, a generic construction of ZDB functions is presented, and many new classes of ZDB functions can be generated. This construction is then extended to construct a set of ZDB functions, in which any two ZDB functions are related uniformly. Furthermore, some applications of such sets of ZDB functions are also introduced.

cs.IT↗
arXiv2013

Difference Balanced Functions and Their Generalized Difference Sets

Difference balanced functions from $F_{q^n}^*$ to $F_q$ are closely related to combinatorial designs and naturally define $p$-ary sequences with the ideal two-level autocorrelation. In the literature, all existing such functions are associated with the $d$-homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be $d$-homogeneous. First we characterize difference balanced functions by generalized difference sets with respect to two exceptional subgroups. We then derive several necessary and sufficient conditions for $d$-homogeneous difference balanced functions. In particular, we reveal an unexpected equivalence between the $d$-homogeneous property and multipliers of generalized difference sets. By determining these multipliers, we prove the Gong-Song conjecture for $q$ prime. Furthermore, we show that every difference balanced function must be balanced or an affine shift of a balanced function.

math.CO↗
arXiv2013

Pushing the Limits of LTE: A Survey on Research Enhancing the Standard

Cellular networks are an essential part of todays communication infrastructure. The ever-increasing demand for higher data-rates calls for a close cooperation between researchers and industry/standardization experts which hardly exists in practice. In this article we give an overview about our efforts in trying to bridge this gap. Our research group provides a standard-compliant open-source simulation platform for 3GPP LTE that enables reproducible research in a well-defined environment. We demonstrate that much innovative research under the confined framework of a real-world standard is still possible, sometimes even encouraged. With examplary samples of our research work we investigate on the potential of several important research areas under typical practical conditions.

cs.IT↗
arXiv2013

Skew Hadamard Difference Sets from Dickson Polynomials of Order 7

Skew Hadamard difference sets are an interesting topic of study for over seventy years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in $\mathbb{F}_q$ where $q \equiv 3 \bmod{4}$) were the only example in abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of $\mathcal{D}_5(x^2,u)$ is a new skew Hadamard difference set in $(\mathbb{F}_{3^m},+)$ with $m$ odd, where $\mathcal{D}_n(x,u)$ denotes the first kind of Dickson polynomials of order $n$ and $u \in \mathbb{F}_q^*$. The key observation in the proof is that $\mathcal{D}_5(x^2,u)$ is a planar function from $\mathbb{F}_{3^m}$ to $\mathbb{F}_{3^m}$ for $m$ odd. Since then a few families of new skew Hadamard difference sets have been discovered. In this paper, we prove that for all $u \in \mathbb{F}_{3^m}^*$, the set $D_u := \{\mathcal{D}_7(x^2,u) : x \in \mathbb{F}_{3^m}^* \}$ is a skew Hadamard difference set in $(\mathbb{F}_{3^m}, +)$, where $m$ is odd and $m \not \equiv 0 \pmod{3}$. The proof is more complicated and different from that of Ding-Yuan skew Hadamard difference sets since $\mathcal{D}_7(x^2,u)$ is not planar in $\mathbb{F}_{3^m}$. Furthermore, we show that such skew Hadamard difference sets are inequivalent to all existing ones for $m = 5, 7$ by comparing the triple intersection numbers.

math.CO↗
arXiv2013

Locating Multiple Multi-scale Electromagnetic Scatterers by A Single Far-field Measurement

Two inverse scattering schemes were recently developed in \cite{LiLiuShangSun} for locating multiple electromagnetic (EM) scatterers, respectively, of small size and regular size compared to the detecting EM wavelength. Both schemes make use of a single far-field measurement. The scheme of locating regular-size scatterers requires the {\it a priori} knowledge of the possible shapes, orientations and sizes of the underlying scatterer components. In this paper, we extend that imaging scheme to a much more practical setting by relaxing the requirement on the orientations and sizes. We also develop an imaging scheme of locating multiple multi-scale EM scatterers, which may include at the same time, both components of regular size and small size. For the second scheme, a novel local re-sampling technique is developed. Furthermore, more robust and accurate reconstruction can be achieved for the second scheme if an additional far-field measurement is used. Rigorous mathematical justifications are provided and numerical results are presented to demonstrate the effectiveness and the promising features of the proposed imaging schemes.

math-ph↗