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This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series. We investigate a kernel-based method to estimate the time-varying covariance operator and the time-varying mean function of a locally stationary functional time series. In particular, we derive the convergence rate of the kernel estimator of the covariance operator and associated eigenvalue and eigenfunctions and establish a central limit theorem for the kernel-based locally weighted sample mean. As applications of our results, we discuss the prediction of locally stationary functional time series and methods for testing the equality of time-varying mean functions in two functional samples.

In this paper, we propose a semigroup method for solving high-dimensional elliptic partial differential equations (PDEs) and the associated eigenvalue problems based on neural networks. For the PDE problems, we reformulate the original equations as variational problems with the help of semigroup operators and then solve the variational problems with neural network (NN) parameterization. The main advantages are that no mixed second-order derivative computation is needed during the stochastic gradient descent training and that the boundary conditions are taken into account automatically by the semigroup operator. Unlike popular methods like PINN \cite{raissi2019physics} and Deep Ritz \cite{weinan2018deep} where the Dirichlet boundary condition is enforced solely through penalty functions and thus changes the true solution, the proposed method is able to address the boundary conditions without penalty functions and it gives the correct true solution even when penalty functions are added, thanks to the semigroup operator. For eigenvalue problems, a primal-dual method is proposed, efficiently resolving the constraint with a simple scalar dual variable and resulting in a faster algorithm compared with the BSDE solver \cite{han2020solving} in certain problems such as the eigenvalue problem associated with the linear Schr\"odinger operator. Numerical results are provided to demonstrate the performance of the proposed methods.

In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real part, whereas, the two-bit observations of the DFT correspond to the signs of both the real and imaginary parts of the DFT. We focus on images for analysis and simulations, thus using the sign of the 2D-DFT. This choice of the class of signals is inspired by previous works on this problem. For our algorithm, we show that the expected mean squared error (MSE) in signal reconstruction is asymptotically proportional to the inverse of the sampling rate. The samples are affected by additive zero-mean noise of known distribution. We solve this signal estimation problem by designing an algorithm that uses contraction mapping, based on the Banach fixed point theorem. Numerical tests with four benchmark images are provided to show the effectiveness of our algorithm. Various metrics for image reconstruction quality assessment such as PSNR, SSIM, ESSIM, and MS-SSIM are employed. On all four benchmark images, our algorithm outperforms the state-of-the-art in all of these metrics by a significant margin.

In this paper we develop a new simple and effective isogeometric analysis for modeling thermal buckling of stiffened laminated composite plates with cutouts using level sets. We employ a first order shear deformation theory to approximate the displacement field of the stiffeners and the plate. Numerical modeling with a treatment of trimmed objects, such as internal cutouts in terms of NURBS-based isogeometric analysis presents several challenges, primarily due to need for using the tensor product of the NURBS basis functions. Due to this feature, the refinement operations can only be performed globally on the domain and not locally around the cutout. The new approach can overcome the drawbacks in modeling complex geometries with multiple-patches as the level sets are used to describe the internal cutouts; while the numerical integration is used only inside the physical domain. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout and the position and profile of the curvilinear stiffeners. The numerical examples show high reliability and efficiency of the present method compared with other published solutions and ABAQUS.

Machine learning methods such as deep neural networks (DNNs), despite their success across different domains, are known to often generate incorrect predictions with high confidence on inputs outside their training distribution. The deployment of DNNs in safety-critical domains requires detection of out-of-distribution (OOD) data so that DNNs can abstain from making predictions on those. A number of methods have been recently developed for OOD detection, but there is still room for improvement. We propose the new method iDECODe, leveraging in-distribution equivariance for conformal OOD detection. It relies on a novel base non-conformity measure and a new aggregation method, used in the inductive conformal anomaly detection framework, thereby guaranteeing a bounded false detection rate. We demonstrate the efficacy of iDECODe by experiments on image and audio datasets, obtaining state-of-the-art results. We also show that iDECODe can detect adversarial examples.

In this paper, we consider downlink low Earth orbit (LEO) satellite communication systems where multiple LEO satellites are uniformly distributed over a sphere at a certain altitude according to a homogeneous binomial point process (BPP). Based on the characteristics of the BPP, we analyze the distance distributions and the distribution cases for the serving satellite. We analytically derive the exact outage probability, and the approximated expression is obtained using the Poisson limit theorem. With these derived expressions, the system throughput maximization problem is formulated under the satellite-visibility and outage constraints. To solve this problem, we reformulate it with bounded feasible sets and propose an iterative algorithm to obtain near-optimal solutions. Simulation results perfectly match the derived exact expressions for the outage probability and system throughput. The analytical results of the approximated expressions are fairly close to those of the exact ones. It is also shown that the proposed algorithm for the throughput maximization is very close to the optimal performance obtained by a two-dimensional exhaustive search.

In this paper we study the security of the Bluetooth stream cipher E0 from the viewpoint it is a difference stream cipher, that is, it is defined by a system of explicit difference equations over the finite field GF(2). This approach highlights some issues of the Bluetooth encryption as the invertibility of its state transition map, a special set of 14 bits of its 132-bit state which when guessed imply linear equations among the other bits and finally a very small number of spurious keys compatible with a keystream of about 60 bits. Exploiting such issues, we implement an algebraic attack using Grobner bases, SAT solvers and Binary Decision Diagrams. Testing activities suggest that the version based on Grobner bases is the best one and it is able to attack E0 in about 2^79 seconds on an Intel i9 CPU. To the best of our knowledge, this work improves any previous attack based on a short keystream, hence fitting with Bluetooth specifications.

Salt and pepper noise removal is a common inverse problem in image processing. Traditional denoising methods have two limitations. First, noise characteristics are often not described accurately. For example, the noise location information is often ignored and the sparsity of the salt and pepper noise is often described by L1 norm, which cannot illustrate the sparse variables clearly. Second, conventional methods separate the contaminated image into a recovered image and a noise part, thus resulting in recovering an image with unsatisfied smooth parts and detail parts. In this study, we introduce a noise detection strategy to determine the position of the noise, and a non-convex sparsity regularization depicted by Lp quasi-norm is employed to describe the sparsity of the noise, thereby addressing the first limitation. The morphological component analysis framework with stationary Framelet transform is adopted to decompose the processed image into cartoon, texture, and noise parts to resolve the second limitation. Then, the alternating direction method of multipliers (ADMM) is employed to solve the proposed model. Finally, experiments are conducted to verify the proposed method and compare it with some current state-of-the-art denoising methods. The experimental results show that the proposed method can remove salt and pepper noise while preserving the details of the processed image.

Cloud Robotics is one of the emerging area of robotics. It has created a lot of attention due to its direct practical implications on Robotics. In Cloud Robotics, the concept of cloud computing is used to offload computational extensive jobs of the robots to the cloud. Apart from this, additional functionalities can also be offered on run to the robots on demand. Simultaneous Localization and Mapping (SLAM) is one of the computational intensive algorithm in robotics used by robots for navigation and map building in an unknown environment. Several Cloud based frameworks are proposed specifically to address the problem of SLAM, DAvinCi, Rapyuta and C2TAM are some of those framework. In this paper, we presented a detailed review of all these framework implementation for SLAM problem.

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.