arXiv subjects
Publications and source records attributed to Min Li.
In this paper, we investigate the dependence on initial data of solutions to the Novikov equation. We show that the solution map is not uniformly continuous dependence on the initial data in Besov spaces $B^s_{p,r}(\R),\ s>\max\{1+\frac 1p,\frac32\}$.
With the stationary solution assumption, we establish the connection between the nonlocal nonlinear Schrödinger (NNLS) equation and an elliptic equation. Then, we obtain the general stationary solutions and discuss the relevance of their smoothness and boundedness to some integral constants. Those solutions, which cover the known results in the literature, include the unbounded Jacobi elliptic-function and hyperbolic-function solutions, the bounded sn-, cn- and dn-function solutions, as well as the hyperbolic soliton solutions. By the imaginary translation transformation of the NNLS equation, we also derive the complex-amplitude stationary solutions, in which all the bounded cases obey either the \PT- or anti-\PT-symmetric relation. In particular, the complex tanh-function solution can exhibit no spatial localization in addition to the dark and anti-dark soliton profiles, which is sharp contrast with the common dark soliton. Considering the physical relevance to \PT-symmetric system, we show that the complex-amplitude stationary solutions can yield a wide class of complex and time-independent \PT-symmetric potentials, and the symmetry breaking does not occur in the \PT-symmetric linear system with the associated potentials.
In this paper, we obtain the Nth-order rational solutions for the defocusing nonlocal nonlinear Schrodinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1<=N<=4. It turns out that the asymptotic solitons are localized in the straight or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and -t with certain parametric condition. In addition, we reveal that the soliton interactions in the rational solutions with N>=2 are stronger than those in the exponential and exponential-and-rational solutions.
We present a method to capture both 3D shape and spatially varying reflectance with a multi-view photometric stereo (MVPS) technique that works for general isotropic materials. Our algorithm is suitable for perspective cameras and nearby point light sources. Our data capture setup is simple, which consists of only a digital camera, some LED lights, and an optional automatic turntable. From a single viewpoint, we use a set of photometric stereo images to identify surface points with the same distance to the camera. We collect this information from multiple viewpoints and combine it with structure-from-motion to obtain a precise reconstruction of the complete 3D shape. The spatially varying isotropic bidirectional reflectance distribution function (BRDF) is captured by simultaneously inferring a set of basis BRDFs and their mixing weights at each surface point. In experiments, we demonstrate our algorithm with two different setups: a studio setup for highest precision and a desktop setup for best usability. According to our experiments, under the studio setting, the captured shapes are accurate to 0.5 millimeters and the captured reflectance has a relative root-mean-square error (RMSE) of 9%. We also quantitatively evaluate state-of-the-art MVPS on a newly collected benchmark dataset, which is publicly available for inspiring future research.
This work, for the first time, considers confidential data collection in the context of unmanned aerial vehicle (UAV) wireless networks, where the scheduled ground sensor node (SN) intends to transmit confidential information to the UAV without being intercepted by other unscheduled ground SNs. Specifically, a full-duplex (FD) UAV collects data from each scheduled SN on the ground and generates artificial noise (AN) to prevent the scheduled SN's confidential information from being wiretapped by other unscheduled SNs. We first derive the reliability outage probability (ROP) and secrecy outage probability (SOP) of a considered fixed-rate transmission, based on which we formulate an optimization problem that maximizes the minimum average secrecy rate (ASR) subject to some specific constraints. We then transform the formulated optimization problem into a convex problem with the aid of first-order restrictive approximation technique and penalty method. The resultant problem is a generalized nonlinear convex programming (GNCP) and solving it directly still leads to a high complexity, which motivates us to further approximate this problem as a second-order cone program (SOCP) in order to reduce the computational complexity. Finally, we develop an iteration procedure based on penalty successive convex approximation (P-SCA) algorithm to pursue the solution to the formulated optimization problem. Our examination shows that the developed joint design achieves a significant performance gain compared to a benchmark scheme.
By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger equation. We reveal that the first type of solution can display a large variety of interactions among two exponential solitons and two rational solitons, in which the standard elastic interaction properties are preserved and each soliton could be either the dark or antidark type. By developing the asymptotic analysis technique, we also find that the second type of solution can exhibit the elastic interactions among four mixed asymptotic solitons. But in sharp contrast to the common solitons, the asymptotic mixed solitons have the t-dependent velocities and their phase shifts before and after interaction also grow with |t| in the logarithmical manner. In addition, we discuss the degenerate cases for such two types of mixed soliton solutions when the four-soliton interaction reduces to a three-soliton or two-soliton interaction.
We measure the photoelectron energy spectra from strong-field ionization of Kr in a two-color laser pulse consisting of a strong 400-nm field and a weak 800-nm field. The intensities of the main above-threshold ionization (ATI) and sideband peaks in the photoelectron energy spectra oscillate roughly oppositely with respect to the relative phase between the two-color components. We study the photoelectron interferometry in strong-field ATI regime from the view of interference of different electron trajectories in order to extend RABBITT type analysis to the strong-field regime. Based on the strong-field approximation model, we obtain analytical expressions for the oscillations of both ATI and sideband peaks with the relative phase. A phase shift of π/4 with respect to the field maximum of the two-color laser pulse is revealed for the interference maximum in the main ATI peak without including the effect of the atomic potential.
T0 detector, based on Multi-gap Resistive Plate Chambers (MRPC) technology, is one of the key components in the External Target Experiment. Through precision measurements of the MRPC signals, timing of the beam impact on target can be obtained and used as the start time for other detectors. A readout electronics system was designed for the T0 detector. Based on the NINO ASIC, front-end-electronics (FEE) circuits which can achieve high precision leading-edge discrimination and Charge-to-Time Conversion (QTC) were designed for the internal and external MRPCs of the T0 detector. The output pulse of the FEE is then digitized by high precision time digitization modules with Time-to-Digital Converters (TDCs), trigger matching and other control logic integrated within Field Programmable Gate Array (FPGA) devices. To evaluate the functionality and performance, we also conducted a series of tests of the electronics. Results indicate that the system functions well and the time precision of the electronics is better than 21 ps, which satisfies the application requirement.
This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori, known as side-information, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called two-sender unicast index coding (TSUIC). The main goal is to find the shortest aggregate normalized codelength, which is expressed as the optimal broadcast rate. In this work, firstly, for a given TSUIC problem, we form three independent sub-problems each consisting of the only subset of the messages, based on whether the messages are available only in one of the senders or in both senders. Then we express the optimal broadcast rate of the TSUIC problem as a function of the optimal broadcast rates of those independent sub-problems. In this way, we discover the structural characteristics of TSUIC. For the proofs of our results, we utilize confusion graphs and coding techniques used in single-sender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graph-coloring approach that is different from the normal graph coloring, which we call two-sender graph coloring, and propose a way of grouping the vertices to analyze the number of colors used. We further determine a class of TSUIC instances where a certain type of side-information can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders.
Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable reliable outdoor millimeter-wave communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and then eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for each of the survived pairs and combines with the previous measurement to determine the best one. For OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform state-of-the-art beam alignment algorithms, and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.
We use the Richardson-Lucy deconvolution algorithm to extract one dimensional (1D) spectra from LAMOST spectrum images. Compared with other deconvolution algorithms, this algorithm is much more fast. The practice on a real LAMOST image illustrates that the 1D resulting spectrum of this method has a higher SNR and resolution than those extracted by the LAMOST pipeline. Furthermore, our algorithm can effectively depress the ringings that are often shown in the 1D resulting spectra of other deconvolution methods.
Based on the strong-field approximation, we obtain analytical expressions for the initial momentum at the tunnel exit and instantaneous ionization rate of tunneling ionization in elliptically polarized laser fields with arbitrary ellipticity. The tunneling electron reveals a nonzero offset of the initial momentum at the tunnel exit in the elliptically polarized laser field. We find that the transverse and longitudinal components of this momentum offset with respect to the instantaneous field direction are directly related to the time derivatives of the instantaneous laser electric field along the angular and radial directions, respectively. We further show that the nonzero initial momentum at the tunnel exit has a significant influence on the laser phase dependence of the instantaneous ionization rate in the nonadiabatic tunneling regime.
Laser-induced electron tunneling underlies numerous emerging spectroscopic techniques to probe attosecond electron dynamics in atoms and molecules. The improvement of those techniques requires an accurate knowledge of the exit momentum for the tunneling wave packet. Here we demonstrate a photoelectron interferometric scheme to probe the electron momentum longitudinal to the tunnel direction at the tunnel exit by measuring the photoelectron holographic pattern in an orthogonally polarized two-color laser pulse. In this scheme, we use a perturbative 400-nm laser field to modulate the photoelectron holographic fringes generated by a strong 800-nm pulse. The fringe shift offers a direct experimental access to the intermediate canonical momentum of the rescattering electron, allowing us to reconstruct the momentum offset at the tunnel exit with high accuracy. Our result unambiguously proves the existence of nonzero initial longitudinal momentum at the tunnel exit and provides fundamental insights into the non-quasi-static nature of the strong-field tunneling.
We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.
Let $G$ be a connected $m$-uniform hypergraph. In this paper we mainly consider the eigenvectors of the Laplacian or signless Laplacian tensor of $G$ associated with zero eigenvalue, called the first Laplacian or signless Laplacian eigenvectors of $G$. By means of the incidence matrix of $G$, the number of first Laplacian or signless Laplaican (H- or N-)eigenvectors can be get explicitly by solving the Smith normal form of the incidence matrix over $\mathbb{Z}_m$ or $\mathbb{Z}_2$. Consequently, we prove that the number of first Laplacian (H-)eigenvectors is equal to the number of first signless Laplacian (H-)eigenvectors when zero is an (H-)eigenvalue of the signless Laplacian tensor. We establish a connection between first Laplacian (signless Laplacian) H-eigenvectors and the even (odd) bipartitions of $G$.
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the jump-diffusion coefficient to be growth superlinearly. Moreover, the method is proved to be convergent with strongly order $\frac{1}{2}$ on the discrete time level. Finally, some numerical experiments are carried out to confirm the theoretical results.
Let $G$ be a $t$-uniform hypergraph, and let $c(G)$ denote the cyclic index of the adjacency tensor of $G$. Let $m,s,t$ be positive integers such that $t \ge 2$, $s \ge 2$ and $m=st$. The generalized power $G^{m,s}$ of $G$ is obtained from $G$ by blowing up each vertex into an $s$-set and preserving the adjacency relation. It was conjectured that $c(G^{m,s})=s \cdot c(G)$. In this paper we show that the conjecture is false by giving a counterexample, and give some sufficient conditions for the conjecture holding. Finally we give an equivalent characterization of the equality in the conjecture by using a matrix equation over $\mathbb{Z}_m$.
Machine learning systems based on deep neural networks (DNNs) have gained mainstream adoption in many applications. Recently, however, DNNs are shown to be vulnerable to adversarial example attacks with slight perturbations on the inputs. Existing defense mechanisms against such attacks try to improve the overall robustness of the system, but they do not differentiate different targeted attacks even though the corresponding impacts may vary significantly. To tackle this problem, we propose a novel configurable defense mechanism in this work, wherein we are able to flexibly tune the robustness of the system against different targeted attacks to satisfy application requirements. This is achieved by refining the DNN loss function with an attack sensitive matrix to represent the impacts of different targeted attacks. Experimental results on CIFAR-10 and GTSRB data sets demonstrate the efficacy of the proposed solution.