Journal articles on the topic 'Circular discrete convolution'

In this paper an analysis of discrete-time convolution is performed to prove that the convolution sum is polynomial multiplication without carry, whether the sequences are finite or not, by using several examples to compare the results computed using the existing approaches to the polynomial multiplication approach presented here. In the design and analysis of signals and systems the concept of convolution is very important. While software tools are available for calculating convolution, for proper understanding it is important to learn now to calculate it by hand. To this end, several popular methods are available. The idea that the convolution sum is indeed polynomial multiplication without carry is demonstrated in this paper. The concept is further extended to deconvolution, N-point circular convolution and the Z-transform approach.

This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.

This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.

In this paper, we present two systolic array algorithms for efficient Very-Large-Scale Integration (VLSI) implementations of the 1-D Modified Discrete Sine Transform (MDST) using the systolic array architectural paradigm. The new algorithms decompose the computation of the MDST into modular and regular computational structures called pseudo-circular correlation and pseudo-cycle convolution. The two computational structures for pseudo-circular correlation and pseudo-cycle convolution both have the same form. This feature can be exploited to significantly reduce the hardware complexity since the two computational structures can be computed on the same linear systolic array. Moreover, the second algorithm can be used to further reduce the hardware complexity by replacing the general multipliers from the first one with multipliers with a constant that have a significantly reduced complexity. The resulting VLSI architectures have all the advantages of a cycle convolution and circular correlation based systolic implementations, such as high-speed using concurrency, an efficient use of the VLSI technology due to its local and regular interconnection topology, and low I/O cost. Moreover, in both architectures, a cost-effective application of an obfuscation technique can be achieved with low overheads.

Future wireless communication systems are demanding a more flexible physical layer. GFDM is a block filtered multicarrier modulation scheme proposed to add multiple degrees of freedom and to cover other waveforms in a single framework. In this paper, GFDM modulation and demodulation is presented as a frequency-domain circular convolution, allowing for a reduction of the implementation complexity when MF, ZF and MMSE filters are employed as linear demodulators. The frequency-domain circular convolution shows that the DFT used in the GFDM signal generation can be seen as a precoding operation. This new point-of-view opens the possibility to use other unitary transforms, further increasing the GFDM flexibility and covering a wider set of applications. The following three precoding transforms are considered in this paper to illustrate the benefits of precoded GFDM: (i) Walsh Hadamard Transform; (ii) CAZAC transform and; (iii) Discrete Hartley Transform. The PAPR and symbol error rate of these three unitary transform combined with GFDM are analyzed as well.

In the present study, a contact problem between a spherical indenter and a half-anisotropic elastic region with a micropattern is solved under normal and tangential forces considering friction. The surface Green's function, and the discrete convolution and fast Fourier transform (DC–FFT) method are used to calculate the displacements on a contact area, and the conjugate gradient (CG) method is used to calculate the contact pressure, the contact area, shear tractions, and the stick-slip region. The influences of the shape and density (the pattern area per unit area) of the micropattern and the material anisotropy in the substrate on the friction property of the substrate are investigated. In the present study, substrates with circular and square micropatterns are used in the analysis. The results of the analysis revealed that the shear tractions are concentrated at the edges and corners of the circular and square patterns, respectively. The apparent friction coefficient varies with the direction of the anisotropic principal axis.

To reduce the computation complexity of wavelet transform, this paper presents a novel approach to be implemented. It consists of two key techniques: (1) fast number theoretic transform(FNTT) In the FNTT, linear convolution is replaced by the circular one. It can speed up the computation of 2D discrete wavelet transform. (2) In two-dimensional overlap-save method directly calculating the FNTT to the whole input sequence may meet two difficulties; namely, a big modulo obstructs the effective implementation of the FNTT and a long input sequence slows the computation of the FNTT down. To fight with such deficiencies, a new technique which is referred to as 2D overlap-save method is developed. Experiments have been conducted. The fast number theoretic transform and 2D overlap-method have been used to implement the dyadic wavelet transform and applied to contour extraction in pattern recognition.

The flows of Magnetohydrodynamics(MHD) second grade fluid between two infinite porous coaxial circular cylinders are studied. At time t=0^+, the inner cylinder begins to rotate around its axis and to slide along the same axis due to torsional and longitudinal time dependent shear stresses and the outer cylinder is also rotate around its axis and to slide along the same axis with acceleration. The exact solutions obtained with the help of discrete Laplace and finite Hankel transform, satisfy all imposed initial and boundary conditions. The solution presented in convolution product of Laplace transform . The corresponding solutions for second grade and Newtonian fluids are also obtained as limiting cases with and without MHD effect. Finally, the influence of pertinent parameters on the velocity components and shear stresses, as well as a comparison among, second grade and Newtonian fluids with and without MHD is also analyzed by graphical illustrations.

Due to model complexity, classical contact mechanics theory assumes isothermal contact processes, involving bodies with uniform temperatures and no heat transmitted or generated through or near the contact interface. This paper addresses the problem of frictional heating in non-conforming or rough contacts by investigating the thermoelastic behaviour of asperities. The heat generated in a sliding contact by interfacial friction leads to thermoelastic distortion of the contact surface, further modifying contact parameters such as pressure, gap or temperature. The thermal expansion of the contacting bodies must therefore be accounted for when solving the contact problem. The thermoelastic displacement is computed with the aid of the half-space theory and of fundamental solutions for point sources of heat located at the free surface, derived in the literature of heat conduction in solids. The linearity of conduction equations encourages the use of superposition principle in the same way as for the elastic displacement. As the thermoelastic displacement is expressed mathematically as a convolution product, methods derived in contact mechanics for elastic displacement calculation are adapted to the heat conduction equations. The influence coefficients needed to efficiently compute the convolution products are derived, and the Discrete Convolution Fast Fourier Transform technique is applied to improve the algorithm computational efficiency. A similar method is then advanced for the temperature rise on the contact interface due to arbitrary heat input. The predictions of the newly advanced computer programs are tested against existing closed-form solutions for uniform circular or ring heat sources, and a good agreement is found.

This paper aims to present a unified overview of the main Very Large-Scale Integration (VLSI) implementation solutions of forward and inverse discrete sine transforms using systolic arrays. The main features of the most important solutions to implement the forward and inverse discrete sine transform (DST) using systolic arrays are presented. One of the central ideas presented in the paper is to emphasize the advantages of using regular and modular systolic array computational structures such as cyclic convolution, circular correlation, and pseudo-band correlation in the VLSI implementation of these transforms. The use of such computational structures leads to architectures well adapted to the features of VLSI technologies, with an efficient use of the hardware structures and a reduced I/O cost that helps avoiding the so-called I/O bottleneck. With the techniques presented in this review, we have developed a new VLSI implementation of the DST using systolic arrays that allow efficient hardware implementation with reduced complexity while maintaining high-speed performances. Using a new restructuring input sequence, we have been able to efficiently reformulate the computation of the forward DST transform into a special computational structure using eight short quasi-cycle convolutions that can be computed with low complexity and where some of the coefficients are identical. This leads to a hardware structure with high throughput. The new restructuring sequence is the use of the input samples in a natural order as opposed to previous solutions, leading to a significant reduction of the hardware complexity in the pre-processing stage due to avoiding a permutation stage to reverse the order. Moreover, the proposed VLSI architecture allows an efficient incorporation of the obfuscation technique with very low overheads.

<strong><em>Goal.</em></strong><em>&nbsp;Representation of a special mathematical software for determining the angular displacements of the rotor of the induction angle sensor &ndash; resolver (rotating transformer) for applications in which the speed of the sensor&#39;s rotor is close to zero. As well as performing its experimental verification.</em>&nbsp;<strong><em>Methodology.</em></strong><em>&nbsp;The presented method is based on the determination of the phase shift angle of the output signals of the induction sensor, which is determined by comparing the obtained arrangements of signal values with a circular discrete convolution in order to achieve the most precise approximation of the obtained signal values to cosine and sine. The conversion of orthogonal components to an angle is based on the use of a digital phase detector which is use of a software comparator and inverse trigonometric functions.</em>&nbsp;<strong><em>Results.</em></strong><em>&nbsp;Based on the obtained results of mathematical modeling and experimental research, the characteristic dependencies of the angle of rotation of the rotor of the induction sensor relative to its stator, the nature of which is linear, were obtained. In addition, the estimation of measurement errors of angular displacements is carried out that occur when defining such angles by the method offered. The obtained results of the computer simulation taking into account the high signal noise, as well as the results of experimental investigations, confirm the high precision of this method and the fact that it can be used in systems where high positioning accuracy is required and the speed of the sensor shaft is close to zero.</em>&nbsp;<strong><em>Originality</em></strong><em>. This article introduces, for the first time, special mathematical software for a new method of determining the angular displacements of the rotor of an induction sensor, which is based on the determination of the orthogonal components of the signal in combination with the use of a circular discrete convolution in the determination of the phase shift angle of the induction sensor signals.</em>&nbsp;<strong><em>Practical meaning.</em></strong><em>&nbsp;The proposed method does not require the use of demodulators, counters and quadrant tables associated with conventional methods for determining the phase shift of signals. The presented method can be used to measure the full range of 0-2p angular displacements in real time, is simple and can be easily implemented using digital electronic circuitry.</em>

The crankshaft is the core part of an automobile engine, and the accuracy requirements of various shape and position errors are very high. On the basis of a synchronous measurement system, the connecting rod journal is deeply studied, including data processing and roundness evaluation. Firstly, according to the measuring processes of connecting rod journals, the real sampling angle distribution function was established, and the corresponding Gaussian weight function of each sampling angle was calculated. The weight function and the collected data corresponding to the angle were subjected to discrete cyclic convolution operation in the spatial domain to obtain the filtered effective circular contour data. Secondly, the particle swarm optimization algorithm was improved, and its inertia weight was set to decrease nonlinearly to speed up the convergence. A calculation process suitable for the evaluation of journal errors was designed. Then, the improved particle swarm optimization algorithm was used to evaluate the roundness of the corrected rod journal contour data. At last, through multiple measurement experiments, the feasibility and effectiveness of the synchronous measurement scheme and data processing method proposed in this paper are verified.

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.

Linear, time-domain analysis is used to solve the radiation problem for the forced motion of a floating body at zero forward speed. The velocity potential due to an impulsive velocity (a step change in displacement) is obtained by the solution of a pair of integral equations. The integral equations are solved numerically for bodies of arbitrary shape using discrete segments on the body surface. One of the equations must be solved by time stepping, but the kernel matrix is identical at each step and need only be inverted once. The Fourier transform of the impulse-response function gives the more conventional added-mass and damping in the frequency domain. The results for arbitrary motions may be found as a convolution of the impulse response function and the time derivatives of the motion. Comparisons are shown between the time-domain computations and published results for a sphere in heave, a sphere in sway, and a right circular cylinder in heave. Theoretical predictions and experimental results for the heave motion of a sphere released from an initial displacement are also given. In all cases the comparisons are excellent.

Butterflies are increasingly becoming model insects where basic questions surrounding the diversity of their color patterns are being investigated. Some of these color patterns consist of simple spots and eyespots. To accelerate the pace of research surrounding these discrete and circular pattern elements we trained distinct convolutional neural networks (CNNs) for detection and measurement of butterfly spots and eyespots on digital images of butterfly wings. We compared the automatically detected and segmented spot/eyespot areas with those manually annotated. These methods were able to identify and distinguish marginal eyespots from spots, as well as distinguish these patterns from less symmetrical patches of color. In addition, the measurements of an eyespot’s central area and surrounding rings were comparable with the manual measurements. These CNNs offer improvements of eyespot/spot detection and measurements relative to previous methods because it is not necessary to mathematically define the feature of interest. All that is needed is to point out the images that have those features to train the CNN.

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time Mittag-Leffler process. The approach of constructing good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process &lsquo;space-time Mittag-Leffler process&rsquo;. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a &ldquo;well-scaled&rdquo; diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the &lsquo;state density kernel&rsquo; solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time Mittag-Leffler process. The approach of constructing good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

In the first part of this paper, we presented the theoretical basics of a new method to control the bending motion of a subdomain of a thin plate. We used continuously distributed sources of self-stress, applied within the subdomain, to exactly achieve the desired result. From a practical point of view, continuously distributed self-stresses cannot be realized. Therefore, we discuss the application of discretely placed piezoelectric actuators to approximate the continuous distribution in this part. Using piezoelectric patch actuators requires the consideration of electrostatic equations as well. However, if the patches are relatively thin, the electromechanical coupling can be incorporated by means of piezoelastic (instead of elastic) stiffness (piezoelastically stiffended elastic constants). The placement of the patches is based on the discretization of the exact continuous distribution by means of piece-wise constant functions. These are calculated from a convolution integral representing the deviation of the bending motion in the controlled case from the desired one. A proper choice of test loadings allows us to eliminate representative mechanical quantities exactly and to make the resulting bending motion to match the desired one very closely; hence, to find a suboptimal approximate solution. In Part I of this paper we presented exact solutions for the axisymmetric bending of circular plates; it is also considered in Part II. For axisymmetric bending, only the radial coordinate is discretized. Hence, ring-shaped piezoelectric patch actuators are considered in this paper.

The Talbot effect concerns the periodic self-imaging along an optical axis of a free-space optical field that is periodic in an initial transverse plane. It may be modeled by a shift-invariant linear system, fully characterized by the convolution of its impulse response. Self-imaging at integer and fractional Talbot distances of point sources on a regular grid in free space may then be represented by a transmission matrix that is circulant, symmetric, and persymmetric. The free-space Talbot effect may be mapped to the Talbot effect in a multimode waveguide by imposing the anti-symmetry of the mirror-like sidewalls created by the tight confinement of light within a high-index contrast multimode waveguide. The position of the anti-symmetry axis controls the distribution of discrete lattice points in a unit cell. For different distributions, interesting features such as conditional flexibility in the placement of access ports without altering amplitude and phase relationships, omitting ports without power penalty, closed form uneven splitting ratios, and offset access ports can be derived from the MMI coupler. As a specific example, a simple 2×2 MMI coupler is shown to provide a power-splitting ratio related to the golden ratio φ. The structure is amenable to planar photonic integration on any high-index contrast platform. The predictions of the theory are confirmed by simulation and verified by experimental measurements on a golden ratio MMI coupler fabricated using an SOI process.

This dataset includes original TIFF and PNG data from original research within the project EBEAM. Precisely, there are 15 final, complex Figures, two Schemes, seven Tables, and the final PDF version of the article below: PDF of the article final version "Boosting flexible electronics with integration of two‐dimensional materials" Figure 1. Machine learning‐assisted temperature-pressure electronic skin with decoupling capability (TPD e skin) enables object recognition. (A) Principle of using machine learning to recognize objects via e‐skin. (B) Structure of a one‐dimensional convolutional neural network for TPD object recognition. (C) Breakthrough in grasping objects made from 15 different materials by prosthetics. (D) Temperature-pressure frequency waveforms generated by prosthetic grasping of 15 different materials, realized by neuromorphic coding. (E) Visualization of 15 samples of signals of different frequencies by t‐distributed stochastic neighbor embedding (t‐SNE). (F) Confusion matrices for 15 types of object recognition. (G) Cognitive outcome waveform during expiration. (H) Identification and waveform of grasping thermoplastic bottles Figure 2. Application scenarios for piezoresistive sensors based on polyetherimide (PET)/MXene designs. (A) Wireless transmission system for MXene‐based sensor signals. A Bluetooth module is used for signal transmission in response to pressure on the sensor. (B) Use of MXene‐based sensor to detect the pressure of different chess pieces and thus locate them. (C) Pressure detection during the swing of a robotic arm. (D) Utilizing the brightness of an LED to reflect changes in pressure applied to the sensor. (E) Application of the MXene‐based sensor to the skin for Joule heating experiments. (F) Temperature distribution of MXene‐based sensors at different voltages. (G) Infrared thermal imaging of the MXene‐based sensor at increasing voltage, corresponding to the test results in (F) Figure 3. Arrayed flexible graphene thermal patches for patient skin temperature and hyperthermia monitoring. (A) Illustration of the process of detecting and sensing skin temperature using graphene patches. Human skin temperature perception and auxiliary heating are achieved by integrating array‐based sensor patches into medical patches. The measured temperature signal is then processed through a readout circuit and transmitted to the phone via Bluetooth to detect the skin temperature signal in real time. Additionally, the heating temperature of graphene patches can be controlled through mobile phones. (B) Photos of a graphene capacitive sensor arranged in an 8&thinsp;&times;&thinsp;8 array composition. (C) Interface structure of the sensor array utilizing graphene as an electrode. (D) Partial enlarged view of a graphene sensor. (E) Enlarged image of the flexible substrate functional area of the graphene patch in (B). Active areas include a readout front end, an analog‐to‐digital converter, a microcontroller, an Xtal XO, Bluetooth low energy (BLE), a DC/DC converter, and a battery. (F) Framework diagram of the wireless measurement and heating system for graphene patches. The design allows precise temperature measurement by alternating between measurement and heating states Figure 4. Electronic skin, artificial retina, and electronic nose designed with machine learning algorithms. (A) Deep learning based on PdSe2 piezoresistive sensors for pulse recognition and temperature readout. Deep learning steps for converting resistance to temperatures with the input of three distinct pulse signals. The detection of pulse temperature is achieved by employing the pressure signals of pulse beats. (B) Temperature&ndash;pulse curves representing distinct pulse shapes. (C) Stabilization of training and validation losses at low values after 500 training cycles. (D) Temperature readout through deep learning with 98% accuracy. (E) MoSSe‐based artificial retina with integrated sensing, storage, and computing functions. (F) Graphene‐based artificial nose identifying four different volatile organic molecules Figure 5. (A&ndash;C) MoS2‐based field‐effect transistor employed for information encryption. (D) Image captured by the MoS2 image sensor. (E) Transfer characteristics of the MoS2 transistor, determining binary values based on the intercept of the linear fitting. (F) Histogram of the gate‐voltage intercept, with blue denoting 0 and red denoting 1; reference gate voltage is &minus;1&thinsp;V. (G) MoS2 transistor leakage current curve in the on/off state. (H) Histogram of drain current for binary data: 0 when ID&thinsp;lower 18&thinsp;&mu;A and 1 when ID&thinsp;higher 18&thinsp;&mu;A. (I) PUF pattern. (J) Sequential steps of image encryption and decryption: the image, captured by the sensor, is encrypted with a PUF key and is subsequently decrypted with the corresponding key Figure 6. Optical non‐contact control system based on a PtTex-Si sensor array for human&ndash;machine interaction. (A) Scheme of a photomultiplier transistor. (B) Optical image of the sensor array. (C) Flowchart depicting the process of shadow encoding and recognition. Converting photocurrent into a discrete signal enables instruction retrieval. (D) Process of encoding a photocurrent signal using the gradient approach. (E) Output displaying the encoding of shadows Figure 7. NbS2-MoS2‐based neurally inspired optical sensor array for high‐precision dynamic image recognition and single‐point motion trajectory extraction. (A) Schematic diagram of the structure of the NbS2-MoS2‐based vision system, which consists of a 100‐pixel NbS2-MoS2 optical sensing array. (B) Scheme and circuit diagram of the NbS2-MoS2 optical sensing array. (C) Optical micrograph of a 100‐pixel sensor array and scheme of a NbS2-MoS2 phototransistor Figure 8. Supercapacitor woven bracelet based on the MXene coaxial structure for charging a watch. (A) CV curves of a single zinc‐ion hybrid fiber supercapacitor (FSC) and two supercapacitors connected in series and parallel, respectively. (B) Plots of capacitance and energy of the supercapacitors versus length. (C) Bracelet weaving by consuming a 1.5&thinsp;m coaxial FSC. The bracelet provides electric power for a watch and LEDs in a glove Figure 9. Three‐dimensional motion detection using an MXene‐based TENG. (A) Scheme of a 4&thinsp;x&thinsp;4 TENG sensor array. The motion trajectory of a finger positioned above can be captured using the sensor array. (B) Perception of finger linear motion above the sensor. (C) Capture of the finger motion trajectory when moving in a curved path. (D) Blind navigation by installing the sensor on a walking cane. (E) Photograph of the non‐contact sensor. (F) Voltage signal output when the finger moves above the six planes (A&ndash;F) Figure 10. Graphene human&ndash;robot interfaces empowered by machine learning based on graphene acoustic transducers. (A) Auditory and vocal capabilities of the robot system empowered by the system. After training using convolutional neural networks, it can recognize different identities and emotional characteristics, allowing intelligent communication and responses. (B) Schematic representation of the graphene-PI-graphene structure formed through laser irradiation. (C) SEM image of graphene. (D) Human&ndash;robot interfaces attached to a robot. (E and F) TENG operating in microphone mode, detecting sound vibrations through surface‐charge changes. (G) TENG in loudspeaker mode, generating acoustic waves through the thermoacoustic effect Figure 11. Spiking neural network (SNN) structure based on a hybrid 2D‐CMOS microchip. (A) SNN structure. The image from the Modified National Institute of Standards and Technology (MNIST) database is edited into a column vector with 784 input neurons. Pixel intensity is encoded by the firing pattern of the input neurons. Unsupervised training of neurons connecting the input and excitation layers results in labeled trained neurons. These, together with firing patterns, are transmitted to the decision block for feedback, allowing inference of the presented images. (B) Synaptic connection evolution training conducted on 400 excitatory and 400 inhibitory layer neurons. (C) Obfuscation matrix, which provides a visual representation of dataset accuracy. (D) 50 Monte Carlo simulations of 400 excitatory and 400 inhibitory layer neurons of SNN. After 50 iterations, the system accuracy reached 90percent. (E) Schematic diagram of the neuron&ndash;synapse&ndash;neuron module circuit design based on h‐BN. (F) SPICE‐like simulation of synaptic signals from one‐transistor‐one‐memristor cells. (G) Neuronal membrane potential simulated by SPICE simulation Figure 12. Comparison between the traditional cross‐computing structure and the cyclic logic computing scheme. (A) Cross‐operation structure. The input and output memristors are in the same row and column. (B) Circular logic computational structure. The state and inverted state of the cell computer are correlated with the resistance state of the two circuits of the memristor, and the state of its neighboring cells determines the state of each cell through a cyclic logic calculation scheme. (C) Schematic diagram of the design of the memristor array to implement the cyclic logic operation scheme. (D) Design diagram of the cyclic logic calculation scheme. The mapping scheme divides the input signal into two modes-calculation and writing. The state calculation of the cellular automaton is realized through the calculation mode, whereas the cell automaton storage mode is realized through the write mode Figure 13. In‐memory computing design for a hybrid logic circuit with a MoS2‐based transistor and memristor. (A and B) I&ndash;V curves for memristors and MoS2‐based transistors, respectively. (C and D) Simple NAND and AND logic operation verification using a memristor hybrid circuit. (E and F) Measurements of both NAND and AND logic operations. (G and H) Measurement of voltage deviation by 100 simulations using Vdd and VR Figure 14. Demonstration of circular logic solutions for 1D cellular and basic cellular automata. (A) Optical image of a 1D cell automaton. (B) Circuit diagram of a 1D cell automaton. Green dotted coil indicates a basic unit. Each basic unit consists of a memory resistor and an auxiliary memory resistor. CAx and CAx represent the resistance value and resistance inverse value of the cellular automaton respectively. (C) 110 logical operation of ECA rules that describe the corresponding operation in a circular logic operation. (D) Time series in which the 110 operation triggers the signal. (E) Evolution of memory resistor states under different conversion rules Figure 15. Schematic diagram of the structure of a memristor textile network with a Ag-MoS2-HfAlOx-CNT heterostructure. (A) E‐textile memristor network with remodeled synapses at the upper layer and neuromorphic functions at the lower layer. (B) Unit device structure of the Ag-MoS2-HfAlOx-CNT heterostructure. (C) SEM images of the Ag-MoS2-HfAlOx-CNT heterostructure. (D) Artificial synaptic function simulation using the reconfigurable memristor Scheme 1. Typical applications of 2D material‐empowered flexible and wearable electronics. (1) Flexible and wearable electronics. (A) Pulse temperature measurement. (B) Rechargeable gloves. (2) Flexible energy storage and conversion. (C) E‐fabric for charging. (D) Uses of mechanical and thermal energy to create sound Scheme 2.&nbsp; Current situation and future development trend of flexible electronics Table 1. Roles of 2D materials in flexible electronics Table 2. Two-dimensional material-based flexible sensors according to their sensing from different physical signals Table 3. Four types of 2D material-based tactile sensors Table 4. Roles of 2D materials in bioelectronic devices and their features Table 5. Two-dimensional material-based flexible solid-state supercapacitors Table 6. Flexible solid-state lithium batteries from two-dimensional materials Table 7. Comparison of the performance of TENGs before and after the incorporation of 2D materials Funding: National Key Research and Development Program (No. 2022YFE0124200), National Natural Science Foundation of China (No. U2241221); Natural Science Foundation of Shandong Province for Excellent Young Scholars (YQ2022041), and the fund (No. SKT2203) from the State Key Laboratories of Transducer Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences for support; Major Scientific and Technological Innovation Project of Shandong Province (2021CXGC010603), NSFC (No. 52022037) and Taishan Scholars Project Special Funds (TSQN201812083); Foundation (No. GZKF202107) of State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology, Shandong Academy of Sciences; NSFC (No. 52071225), the National Science Center and the Czech Republic under the European Regional Development Fund (ERDF) &ldquo;Institute of Environmental Technology&mdash;Excellent Research&rdquo; (No. CZ.02.1.01/0.0/0.0/16_019/0000853); Sino-German Center for Research Promotion (SGC) for support (No. GZ 1400), European Union&rsquo;s Horizon Europe Research and Innovation Program under grant agreement No.101087143 (Electron Beam Emergent Additive Manufacturing (EBEAM)).

Magnetic surveying encounters challenges in high-precision detection and inversion on strongly magnetized bodies. Non-uniform magnetization caused by self-demagnetization and mutual magnetization makes magnetic field calculation using analytical formulas impractical. The previous discrete numerical methods have suffered from computational inefficiency or low accuracy. To resolve this issue, we develop an algorithm to solve the magnetic field integral equation for calculating the magnetization state of high-susceptibility bodies, combining the improved spatial convolution forward approach with the adaptive relaxation iteration method. To address the excessive computational burden in the magnetization field between 3-D voxel arrays of the discrete model, we construct the circular convolution kernel matrix directly when the subsurface space is divided with an equidistant grid, significantly reducing redundant computations. Then, the fast Fourier transform is used to accelerate the forward discrete circular convolution operation. In addition, we derive an iterative computation scheme that adaptively adjusts the relaxation factor based on magnetic field changes to correct the effective magnetization for algorithm convergence. From a pragmatic perspective, equating the cuboid to equal-volume sphere subdivisions is proposed to enhance computational efficiency further by about 50 per cent despite sacrificing slight accuracy. The sphere and spherical shell models validate the algorithm accuracy, efficiency, and convergence. Furthermore, we analyze the characteristics of the mutual magnetization effect among magnetic bodies under different magnetization conditions. Finally, we demonstrate the applicability of the algorithm through a realistic example. The proposed algorithm shows promise for precisely exploring highly magnetized minerals, underground pipelines, and unexploded ordnance.

AbstractIn the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

AbstractA new VLSI algorithm and its associated systolic array architecture for a prime length type IV discrete cosine transform is presented. They represent the basis of an efficient design approach for deriving a linear systolic array architecture for type IV DCT. The proposed algorithm uses a regular computational structure called pseudoband correlation structure that is appropriate for a VLSI implementation. The proposed algorithm is then mapped onto a linear systolic array with a small number of I/O channels and low I/O bandwidth. The proposed architecture can be unified with that obtained for type IV DST due to a similar kernel. A highly efficient VLSI chip can be thus obtained with good performance in the architectural topology, computing parallelism, processing speed, hardware complexity and I/O costs similar to those obtained for circular correlation and cyclic convolution computational structures.

The security of image transmission is an important issue in digital communication. As well as it is necessary to preserve and protect important information for several applications like military, medical and other services related to high confidentiality over the Internet or other unprotected networks. In this paper a proposed encryption scheme was introduced that using Lorenz system with a circular convolution and discreet cosine transform (DCT). The diffusion process was achieved using three levels of Arnold transform permutation: - namely, block level, inside each block and pixel level. The image was divided into blocks of sizes 8x8 pixels and shuffle by applying Fisher-Yates permutation image pixels. The DCT was applied to each block and multiplied by the H kernel matrix to achieve the circular convolution. Next the logistic map is used for diffusion to get the cipher image. A new key generation method is applied in order to produce the key values for generating the chaos numbers sequence. Finally applying the discreet wavelet transform (DWT) to the image will produced four quarters (LL, LH, HL and HH). The cosine of each pixel in the LL and HH quarters were computed. The sine of each pixel in the LH and HL quarters were also computed in order to generate the keys for the chaos sequence. By using this way of keys generation in every image, the differential attack possibility will be negligible

We propose spatiotemporal deep neural networks for the time-resolved reconstruction of the velocity field around a circular cylinder (DeepTRNet) based only on two flow data types: the non-time-resolved wake velocity field and sparse time-resolved velocity measurements at specific discrete points. The DeepTRNet consists of two operations, i.e., compact spatial representations extraction and sequential learning. We use the convolutional autoencoder (CAE) in DeepTRNet to extract compact spatial representations embedded in the non-time-resolved velocity field. The nonlinear CAE modes and corresponding CAE coefficients are thus obtained. Based on the nonlinear correlation analysis of the velocity field, we use the bidirectional recurrent neural networks (RNN) with the gated recurrent unit for mapping the sparse time-resolved velocity measurements to the CAE coefficients via sequential learning. The early stopping technique is used to train the DeepTRNet to avoid overfitting. With the well-trained DeepTRNet, we can reconstruct the time-resolved velocity field around the circular cylinder. The DeepTRNet is verified on the simulated datasets at two representative Reynolds numbers, 200 and 500, and the experimental dataset at Reynolds number 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. We systematically compare the DeepTRNet method and the RNN-proper orthogonal decomposition (POD) approach. The DeepTRNet can obtain the accurate time-resolved velocity field depending on the two data types mentioned above. The DeepTRNet method outperforms the RNN-POD method in the reconstruction accuracy, especially for the reconstruction of small-scale flow structures. In addition, we get the reliable velocity field even for the high-frequency components.

AbstractArtificial intelligence (AI) algorithms, encompassing machine learning and deep learning, can assist ophthalmologists in early detection of various ocular abnormalities through the analysis of retinal optical coherence tomography (OCT) images. Despite considerable progress in these algorithms, several limitations persist in medical imaging fields, where a lack of data is a common issue. Accordingly, specific image processing techniques, such as time–frequency transforms, can be employed in conjunction with AI algorithms to enhance diagnostic accuracy. This research investigates the influence of non-data-adaptive time–frequency transforms, specifically X-lets, on the classification of OCT B-scans. For this purpose, each B-scan was transformed using every considered X-let individually, and all the sub-bands were utilized as the input for a designed 2D Convolutional Neural Network (CNN) to extract optimal features, which were subsequently fed to the classifiers. Evaluating per-class accuracy shows that the use of the 2D Discrete Wavelet Transform (2D-DWT) yields superior outcomes for normal cases, whereas the circlet transform outperforms other X-lets for abnormal cases characterized by circles in their retinal structure (due to the accumulation of fluid). As a result, we propose a novel transform named CircWave by concatenating all sub-bands from the 2D-DWT and the circlet transform. The objective is to enhance the per-class accuracy of both normal and abnormal cases simultaneously. Our findings show that classification results based on the CircWave transform outperform those derived from original images or any individual transform. Furthermore, Grad-CAM class activation visualization for B-scans reconstructed from CircWave sub-bands highlights a greater emphasis on circular formations in abnormal cases and straight lines in normal cases, in contrast to the focus on irrelevant regions in original B-scans. To assess the generalizability of our method, we applied it to another dataset obtained from a different imaging system. We achieved promising accuracies of 94.5% and 90% for the first and second datasets, respectively, which are comparable with results from previous studies. The proposed CNN based on CircWave sub-bands (i.e. CircWaveNet) not only produces superior outcomes but also offers more interpretable results with a heightened focus on features crucial for ophthalmologists.