Minimax Estimation of Large Precision Matrices with Bandable Cholesky Factor

Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering of the variables can be interpreted through a bandable structure on the Cholesky factor of the precision matrix. However, the minimax theory has still been largely unknown, as opposed to the well established minimax results over the corresponding bandable covariance matrices. In this paper, we focus on two commonly used types of parameter spaces, and develop the optimal rates of convergence under both the operator norm and the Frobenius norm. A striking phenomenon is found: two types of parameter spaces are fundamentally different under the operator norm but enjoy the same rate optimality under the Frobenius norm, which is in sharp contrast to the equivalence of corresponding two types of bandable covariance matrices under both norms. This fundamental difference is established by carefully constructing the corresponding minimax lower bounds. Two new estimation procedures are developed: for the operator norm, our optimal procedure is based on a novel local cropping estimator targeting on all principle submatrices of the precision matrix while for the Frobenius norm, our optimal procedure relies on a delicate regression-based thresholding rule. Lepski's method is considered to achieve optimal adaptation. We further establish rate optimality in the nonparanormal model. Numerical studies are carried out to confirm our theoretical findings

Fermions tunnelling with quantum gravity correction

Quantum gravity correction is truly important to study tunnelling process of black hole. Base on the generalized uncertainty principle, we investigate the influence of quantum gravity and the result tell us that the quantum gravity correction accelerates the evaporation of black hole. Using corrected Dirac equation in curved spacetime and Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. After solving the equation of motion of the spin 1/2 field, we obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but aslo on the mass of emitted fermions. In our calculation, the quantum gravity correction accelerates the increasing of Hawking temperature during the radiation explicitly. This correction leads to the increasing of the evaporation of black hole.Comment: 5page

No-go theorem and optimization of dynamical decoupling against noise with soft cutoff

We study the performance of dynamical decoupling in suppressing decoherence caused by soft-cutoff Gaussian noise, using short-time expansion of the noise correlations and numerical optimization. For the noise with soft cutoff at high frequencies, there exists no dynamical decoupling scheme to eliminate the decoherence to arbitrary orders of the short time, regardless of the timing or pulse shaping of the control under the population conserving condition. We formulate the equations for optimizing pulse sequences that minimizes decoherence up to the highest possible order of the short time for the noise correlations with odd power terms in the short-time expansion. In particular, we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in short-time limit for the noise correlations with a linear order term in the time expansion.Comment: 11 pages, 3 figure

Backlund transformations for Burgers Equation via localization of residual symmetries

In this paper, we obtained the non-local residual symmetry related to truncated Painlev\'e expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we got the finite transformation for the localized residual symmetry. More importantly, we also localized the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the nth Backlund transformation for Burgers equation can be expressed by determinants in a compact way

New interaction solutions of Kadomtsev-Petviashvili equation

The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction solutions for KP equation is obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves is obtained, which is hard to study by other traditional methods

New symmetry reductions related with the residual symmetry of Boussinesq equation

The Backlund transformation related symmetry is nonlocal, which is hardly to apply in constructing solutions for nonlinear equations. In this paper, we first localize nonlocal residual symmetry to Lie point symmetry by introducing multiple new variables and obtain new Baaklund transformation. Then, by solving out the general form of localized the residual symmetry, we reduce the enlarged system by classical symmetry approach and obtain the corresponding reduction solutions as well as related reduction equations. The localization procedure provides a new way to investigate interaction solutions between different waves

Residual Symmetry Reductions and Interaction Solutions of (2+1)-Dimensional Burgers Equation

The (2+1)-dimensional Burgers equation has been investigated first from prospective of symmetry by localizing the nonlocal residual symmetries and then studied by a simple generalized tanh expansion method. New symmetry reduction solutions has been obtained by using the standard Lie point symmetry group approach. A new B\"{a}klund transformation for Burgers equation has been given with the generalized tanh expansion method . From this BT, interactive solutions among different nonlinear excitations which is hard to obtain by other methods has also been obtained easily

WiFE: WiFi and Vision based Intelligent Facial-Gesture Emotion Recognition

Emotion is an essential part of Artificial Intelligence (AI) and human mental health. Current emotion recognition research mainly focuses on single modality (e.g., facial expression), while human emotion expressions are multi-modal in nature. In this paper, we propose a hybrid emotion recognition system leveraging two emotion-rich and tightly-coupled modalities, i.e., facial expression and body gesture. However, unbiased and fine-grained facial expression and gesture recognition remain a major problem. To this end, unlike our rivals relying on contact or even invasive sensors, we explore the commodity WiFi signal for device-free and contactless gesture recognition, while adopting a vision-based facial expression. However, there exist two design challenges, i.e., how to improve the sensitivity of WiFi signals and how to process the large-volume, heterogeneous, and non-synchronous data contributed by the two-modalities. For the former, we propose a signal sensitivity enhancement method based on the Rician K factor theory; for the latter, we combine CNN and RNN to mine the high-level features of bi-modal data, and perform a score-level fusion for fine-grained recognition. To evaluate the proposed method, we build a first-of-its-kind Vision-CSI Emotion Database (VCED) and conduct extensive experiments. Empirical results show the superiority of the bi-modality by achieving 83.24\% recognition accuracy for seven emotions, as compared with 66.48% and 66.67% recognition accuracy by gesture-only based solution and facial-only based solution, respectively. The VCED database download link is https://github.com/purpleleaves007/WIFE-Dataset.Comment: error in experiment result

Fixed-time consensus of multiple double-integrator systems under directed topologies: A motion-planning approach

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In the context of the fixed-time consensus, we focus on both directed fixed and switching topologies. Under the directed fixed topology, a novel class of distributed algorithms are designed, which guarantee the consensus of the multi-agent system with a fixed settling time if the topology has a directed spanning tree. Under the directed periodically switching topologies, the fixedtime consensus is solved via the proposed algorithms if the topologies jointly have a directed spanning tree. In particular, the fixed settling time can be off-line pre-assigned according to task requirements. Compared with the existing results, to our best knowledge, it is the first time to solve the fixed-time consensus problem for double-integrator systems under directed topologies. Finally, a numerical example is given to illustrate the effectiveness of the analytical results

BeSense: Leveraging WiFi Channel Data and Computational Intelligence for Behavior Analysis

The ever evolving informatics technology has gradually bounded human and computer in a compact way. Understanding user behavior becomes a key enabler in many fields such as sedentary-related healthcare, human-computer interaction (HCI) and affective computing. Traditional sensor-based and vision-based user behavior analysis approaches are obtrusive in general, hindering their usage in realworld. Therefore, in this article, we first introduce WiFi signal as a new source instead of sensor and vision for unobtrusive user behaviors analysis. Then we design BeSense, a contactless behavior analysis system leveraging signal processing and computational intelligence over WiFi channel state information (CSI). We prototype BeSense on commodity low-cost WiFi devices and evaluate its performance in realworld environments. Experimental results have verified its effectiveness in recognizing user behaviors.Comment: 11 pages accepted by IEEE Computational Intelligence Magazin