Spacial Domain Research Articles

Modification in spatial, extraction from transform: Keyless side-information steganography for JPEG

The state of the art steganography approaches strictly assume that the receiver has access to a steganographic key. This limitation was mitigated for images in spacial domain, but the approach does not apply to JPEG images. In this paper, we introduce a keyless steganography scheme for JPEG images. Despite the spatial domain counterpart, our approach for the JPEG domain effectively preserves higher-order statistical models that are used in steganalysis. We show that our approach does not degrade image quality either. The proposed approach is a Side-Information (SI) steganography in the sense that its input is a never-compressed image. Another characteristic of the proposed approach is the separation of the embedding modification and data extraction domains, which can initiate further studies of similar approaches in the future.

Homogenization for Nonlocal Evolution Problems with Three Different Smooth Kernels

In this paper we consider the homogenization of the evolution problem associated with a jump process that involves three different smooth kernels that govern the jumps to/from different parts of the domain. We assume that the spacial domain is divided into a sequence of two subdomains $$A_n \cup B_n$$ and we have three different smooth kernels, one that controls the jumps from $$A_n$$ to $$A_n$$ , a second one that controls the jumps from $$B_n$$ to $$B_n$$ and the third one that governs the interactions between $$A_n$$ and $$B_n$$ . Assuming that $$\chi _{A_n} (x) \rightarrow X(x)$$ weakly in $$L^\infty $$ (and then $$\chi _{B_n} (x) \rightarrow 1-X(x)$$ weakly in $$L^\infty $$ ) as $$n \rightarrow \infty $$ and that the initial condition is given by a density $$u_0$$ in $$L^2$$ we show that there is an homogenized limit system in which the three kernels and the limit function X appear. When the initial condition is a delta at one point, $$\delta _{{\bar{x}}}$$ (this corresponds to the process that starts at $${\bar{x}}$$ ) we show that there is convergence along subsequences such that $${\bar{x}} \in A_{n_j}$$ or $${\bar{x}} \in B_{n_j}$$ for every $$n_j$$ large enough. We also provide a probabilistic interpretation of this evolution equation in terms of a stochastic process that describes the movement of a particle that jumps in $$\Omega $$ according to the three different kernels and show that the underlying process converges in distribution to a limit process associated with the limit equation. We focus our analysis in Neumann type boundary conditions and briefly describe at the end how to deal with Dirichlet boundary conditions.

Capacity of axially loaded RC columns with arbitrary cross sections to Eurocode 2

Unlike older design codes, Eurocode 2 does not provide a procedure for calculation of the capacity of axially loaded columns. For that purpose, a general algorithm is developed, using the principles of structural mechanics and mathematics: It starts with constructing the P-Δ relationship (buckling curve) for the element, accounting for initial imperfections, minimum eccentricity, material nonlinearity and second order effects. Then, the respective bending moments are determined from the displacements and the P-M relationship is obtained. Finally, the axial load capacity in planar domain is determined by intersecting the P-M diagram with the interaction curve for the RC section. In spacial domain, the P-Δ relationship is defined by the respective “buckling surface”. Its intersection with the interaction surface represents a spacial curve in the (P, Mx, My) coordinate system. The axial capacity is determined as the minimum of P values along the curve. The solution is performed by numerical methods.

Mixing Local and Nonlocal Evolution Equations

In this paper, we study the homogenization of a stochastic process and its associated evolution equations in which we mix a local part (given by a Brownian motion with a reflection on the boundary) and a nonlocal part (given by a jump process with a smooth kernel). We consider a sequence of partitions of the (fixed) spacial domain into two parts (local and nonlocal) that are mixed in such a way that they both have positive density at every point in the limit. Under adequate hypotheses on the sequence of partitions, we prove convergence of the associated densities (that are solutions to an evolution equation with coupled local and nonlocal parts in two different regions of the domain) to the unique solution to a limit evolution system in which the local part disappears and the nonlocal part survives but divided into two different components. We also obtain convergence in distributions of the processes associated with the partitions and prove that the limit process has a density pair that coincides with the limit of the densities.

An efficient one-step proximal method for EIT sparse reconstruction based on nonstationary iterated Tikhonov regularization

ABSTRACT Image reconstruction of EIT mathematically is a seriously ill-posed inverse problem, which is easily affected by measurement noise. This fact leads to a relatively low spatial resolution, particularly in the accuracy of identifying object boundaries. This paper concerns with reconstructing a finite number of simple and small inclusions equipped with the homogeneous background conductivity. The sparsity with respect to the inclusions in the spacial representation domain is apriori assumed. We try to reexamine the multi-parameter constraints on mixing between -norm and -norm for attaining the sparse reconstruction as well as simultaneously enhancing the stability. On the basis of the reference approximation reconstructed by nonstationary iterated Tikhonov regularization (NITR) method, we propose a novel one-step proximal sparsity-promoting approach by one induced proximal shrink operator, abbreviated as one-step PNITR method. The proposed one-step PNITR method consists of twofold: one first performs NITR with mth iteration to generate the reference approximation, and then performs one-step proximal shrinkage processing and one forcing constraint function on it to obtain the final sparsity-promoting reconstruction. For the latter, the former aims to not only enhance higher reliability but also guarantee the sparsity. The proposed method can benefit from the double regularization effect. It is supposed to further improve the imaging quality in terms of sharpening the edges and reducing the artefacts. To validate the advantage of the proposed method, numerical simulations with synthetic data have been carried out. Also, qualitative and quantitative comparisons are conducted. Results indicate that the proposed approach can lead to substantial improvements in EIT image resolution. The performed numerical simulations show that our method is promising.

A Temporal–Spatial network embedding model for ICT supply chain market trend forecasting

Market trend forecasting for the information and communication technology (ICT) supply chain strengthens external regulation. The existing models treat the influence weight and time granularity equally, ignoring the timeliness and accuracy of trading information, which influences the result of prediction. In addition, these methods do not consider the topological and sector hierarchical relationship of enterprises. In this work, a Temporal–Spatial hybrid market trend forecasting model (TSMTF) is proposed. First, in time domain instead of modeling time-varying transaction amount, transaction event probability prediction is modeled by Hawkes​ process. Furthermore, the attention mechanism is used to optimize the accuracy of weight allocation. Second, in spacial domain, the topological dependency relation between the different enterprises with transaction information, share information, and sector information is constructed by network embedding. The experimental results show that the model is superior to other baseline algorithms in ICT data sets. The effectiveness and applicability of this method are verified by ablation experiments and examples of products in the communication industry, and the model provides a practical tool for the external management of ICT supply chain market supervision.

A two‐step accelerated Landweber‐type iteration regularization algorithm for sparse reconstruction of electrical impedance tomography

The image reconstruction of conductivity distribution in electrical impedance tomography (EIT) is a seriously ill‐posed inverse problem, which is easily affected by measurement noise. In this paper, we present a two‐step Landweber‐type iteration method and its accelerated version for sparse reconstruction of Jacobian‐based EIT problem. We aim at reconstructing a finite number of simply and small inclusions embedded at the homogeneous background conductivity. The sparsity of the inclusions with respect to the spacial domain is a prior assumed. This method we propose here contains the two‐step line searches, corresponding to the Landweber step and the approximate Landweber step equipped with a novel step parameter, respectively. To validate the advantage of the proposed method, numerical simulations have been carried out. Also, qualitative and quantitative comparisons are conducted. The results show that the proposed method significantly reduces the number of iterations and computational time needed to match an appropriate stopping criterion, relative to the conventional (one‐step) Landweber method. The performed numerical simulations show that our method is promising.

Inverse initial boundary value problem for a non-linear hyperbolic partial differential equation

In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension n ⩾ 2. In particular we consider the so called interior determination problem. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear wave equation with a time independent potential. For any small solution u = u(t, x) of our non-linear wave equation which is the perturbation of linear wave equation with time-independent potential perturbed by a divergence with respect to (t, x) of a vector whose components are quadratics with respect to ∇ t,x u(t, x). By ignoring the terms with smallness O(|∇ t,x u(t, x)|3), we will show that we can uniquely determine the potential and the coefficients of these quadratics by many boundary measurements at the boundary of the spacial domain over finite time interval and the final overdetermination at t = T. In other words, our measurement is given by the so-called the input-output map (see ()).

Challenges and opportunities in algorithmic solutions for re-balancing in bike sharing systems

In recent years, the booming of the Bike Sharing System (BSS) has played an important role in offering a convenient means of public transport. The BSS is also viewed as a solution to the first/last mile connection issue in urban cities. The BSS can be classified into dock and dock-less. However, due to imbalance in bike usage over spatial and temporal domains, stations in the BSS may exhibit overflow (full stations) or underflow (empty stations). In this paper, we will take a holistic view of the BSS design by examining the following four components: system design, system prediction, system balancing, and trip advisor. We will focus on system balancing, addressing the issue of overflow/underflow. We will look at two main methods of bike re-balancing: with trucks and with workers. Discussion on the other three components that are related to system balancing will also be given. Specifically, we will study various algorithmic solutions with the availability of data in spacial and temporal domains. Finally, we will discuss several key challenges and opportunities of the BSS design and applications as well as the future of dock and dock-less BSS in a bigger setting of the transportation system.

Constrained regional control problem of a bilinear plate equation

ABSTRACT This paper investigates a regional optimal control problem of a plate equation described by a bilinear system evolving in a spacial domain Ω. The control is distributed, bounded and acts on the velocity term. Then, we minimise a functional cost constituted of the deviation between a desired state and the reached one only on a subregion ω of Ω and the energy term. The purpose of this study is to prove that a control solution of such problem exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.

Measurement of the optical dielectric properties of thin-film materials by ultrafast time-resolved interferometry

We report a time-resolved optic interferometry (TROI) that enables to straightway probe the optical properties of traditional and special thin-film materials by feat of a phase delayed-interference between double beams of femtosecond laser synchronously traveling through vacuum (air) and sample, respectively. As a verification of measurement accuracy created by the TROI, the group and phase velocities as well as the refractive index of noncrystal thin-film HfO2, the crystal thin-film materials YAG (isotropic cubic system), and LiNbO3 (aeolotropic rigonal system), are measured by femtosecond laser pulse with 800 nm central wavelength. The data exhibit a satisfactory consequence in which even a subtle change of measurand can be ascertained by manipulating the resolution in temporal and spacial domains via the delay-line, whether the films are isotropic or aeolotropic and any different orientations of sample. Unambiguously, the presented TROI is conspicuous to the precision measurements of environment-dependent and phase-sensitive optical parameters especially involved in specific nanoscale optical devices and structured layers or coatings.

Effects of dynamic soil permeability on the wave-induced seabed response around a buried pipeline

Soil permeability is one of key factors in the prediction of the wave-induced seabed response, which needs to be considered in the design of foundation around marine installations. Most previous studies in the field treated the soil permeability as a constant or varying in spacial domain, although it depends on numerous soil parameters. In this study, the soil permeability is considered as a function of pore-water pressures as reported in the literature. With this new feature, the governing equations will become non-linear differential equations. Numerical examples demonstrate the considerable influence of dynamic soil permeability on the wave-induced pore pressure and effective stresses. It is concluded that the conventional model with constant soil permeability under-estimates the liquefaction potential.

INVERSE PROBLEMS FOR MATHEMATICAL MODELS WITH THE POINTWISE OVERDETERMINATION

In the article we examine well-posedness questions in the Sobolev spaces of an inverse source problem in the case of a quasilinear parabolic system of the second order. These problem arise when describing heat and mass transfer, diffusion, filtration, and in many other fields. The main part of the operator is linear. The unknowns occur in the nonlinear right-hand side. In particular, this class of problems includes the coefficient inverse problems on determinations of the lower order coefficients in a parabolic equation or a system. The overdetermination conditions are the values of a solution at some collection of points lying inside the spacial domain. The Dirichlet and oblique derivative problems under consideration. The problems are studied in a bounded domain with smooth boundary. However, the results can be generalized to the case of unbounded domains as well for which the corresponding solvability theorems hold. The conditions ensuring local (in time) well-posedness of the problem in the Sobolev classes are exposed. The conditions on the data are minimal. The results are sharp. The problem is reduced to an operator equation whose solvability is proven with the use of a priori bounds and the fixed point theorem. A solution possesses all generalize derivatives occurring in the system which belong to the space with and some additional necessary smoothness in some neighborhood about the overdetermination points.

Nonparametric regression using needlet kernels for spherical data

Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the needlet kernel for nonparametric regression problems whose predictor variables are defined on a sphere. Due to the localization property in the frequency domain, we prove that the regularization parameter of the kernel ridge regression associated with the needlet kernel can decrease arbitrarily fast. A natural consequence is that the regularization term for the kernel ridge regression is not necessary in the sense of rate optimality. Based on the excellent localization property in the spacial domain further, we prove that all lq(0<q≤2) kernel regularization estimates associated with the needlet kernel, including the kernel lasso estimate and kernel bridge estimate, possess almost same generalization capability for a large range of regularization parameters in the sense of rate optimality. This finding tentatively reveals that, if the needlet kernel is utilized, then the choice of q might not have a strong impact on the generalization capability in some modeling contexts. The above two properties reveal the theoretical advantages of the needlet kernel in kernel methods for spherical nonparametric regression problems.

A class of quasi-linear Allen–Cahn type equations with dynamic boundary conditions

In this paper, we consider a class of coupled systems of PDEs, denoted by (ACE)ε for ε≥0. For each ε≥0, the system (ACE)ε consists of an Allen–Cahn type equation in a bounded spacial domain Ω, and another Allen–Cahn type equation on the smooth boundary Γ:=∂Ω, and besides, these coupled equations are transmitted via the dynamic boundary conditions. In particular, the equation in Ω is derived from the non-smooth energy proposed by Visintin in his monography “Models of phase transitions”: hence, the diffusion in Ω is provided by a quasilinear form with singularity. The objective of this paper is to build a mathematical method to obtain meaningful L2-based solutions to our systems, and to see some robustness of (ACE)ε with respect to ε≥0. On this basis, we will prove two Main Theorems 1 and 2, which will be concerned with the well-posedness of (ACE)ε for each ε≥0, and the continuous dependence of solutions to (ACE)ε for the variations of ε≥0, respectively.

Fusing highly dimensional energy and connectivity features to identify affective states from EEG signals

In this paper, a novel method for affect detection is presented. The method combines both connectivity-based and channel-based features with a selection method that considerably reduces the dimensionality of the data and allows for an efficient classification. In particular, the Relative Energy (RE) and its logarithm in the spacial domain, and the Spectral Power (SP) in the frequency domain are computed for the four typical frequency bands (α, β, γ and θ), and complemented with the Mutual Information measured over all channel pairs. The resulting features are then reduced by using a hybrid method that combines supervised and unsupervised feature selection. First, Welch’s t-test is used to select the features that best separate the classes, and discard the ones that are less useful for classification. To this end, all features where the t-test yields a p-value above a threshold are eliminated. The remaining ones are further reduced by using Principal Component Analysis. Detection results are compared to state-of-the-art methods on DEAP, a database for emotion analysis composed of labeled recordings from 32 subjects while watching 40 music videos. The effect of using different classifiers is also evaluated, and a significant improvement is observed in all cases.

Measuring muscle activities during gym exercises with textile pressure mapping sensors

We present a wearable textile sensor system for monitoring muscle activity, leveraging surface pressure changes between the skin and compression garment. Our first prototype is based on an 8×16 element fabric resistive pressure mapping matrix with 1 cm spacial resolution and 50 fps refresh rate. We evaluate the prototype by monitoring leg muscles during realistic leg workouts in a gym out of the lab. The sensor covers the lower part of quadriceps of the user. The shape and movement of the two major muscles (vastus lateralis and medialis) are visible from the data visualizing during various exercises. With features extracted from spacial and temporal domains out of the pressure force mapping information, with 4 different leg exercises plus non-workout activities (relaxing, adjusting machines and walking), we have reached 81.7% average recognition accuracy on a fine-grain sliding window basis, 93.3% on an event basis, and 85.6% spotting F1-score. We further investigate the relationships between people’s perception of the exercise quality/difficulty and the variation and consistency of the force pattern. A second prototype is also developed with tether-free to explore various placements including upper-arm, chest and lower back; a brief comparison with arm-worn EMG shows our approach is comparable on the signal quality level.

Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain

Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.

Refoundation of the Cell Method Using Augmented Dual Grids

In this paper, the cell method (CM) is reformulated using augmented dual grids. In this way, the boundary of the discretized spacial domain can be properly dealt with and energetic quantities can be introduced, overcoming the well-known drawbacks of the CM. The details are given for electromagnetic boundary value problems, whose discretization can severely suffer from such drawbacks of the CM.

Fan beam image reconstruction with generalized fourier slice theorem

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N<formula>^3</formula>), where N is the number of pixel in one dimension.