Numerical Convolution Research Articles

Peculiarities of Applying Partial Convolutions to the Computation of Reduced Numerical Convolutions

A method is proposed that reduces the computation of the reduced digital convolution operation to a set of independent convolutions computed in Galois fields. The reduced digital convolution is understood as a modified convolution operation whose result is a function taking discrete values in the same discrete scale as the original functions. The method is based on the use of partial convolutions, reduced to computing a modulo integer q0, which is the product of several prime numbers: q0=p1p2…pn. It is shown that it is appropriate to use the expansion of the number q0, to q=p0p1p2…pn, where p0 is an additional prime number, to compute the reduced digital convolution. This corresponds to the use of additional digits in the number system used to convert to partial convolutions. The inverse procedure, i.e., reducing the result of calculations modulo q to the result corresponding to calculations modulo q0, is provided by the formula that used only integers proved in this paper. The possibilities of practical application of the obtained results are discussed.

CasOmniMVS: Cascade Omnidirectional Depth Estimation with Dynamic Spherical Sweeping

Estimating 360∘ depth from multiple cameras has been a challenging problem. However, existing methods often adopt a fixed-step spherical sweeping approach with densely sampled spheres and use numerous 3D convolutions in networks, which limits the speed of algorithms in practice. Additionally, obtaining high-precision depth maps of real scenes poses a challenge for the existing algorithms. In this paper, we design a cascade architecture using a dynamic spherical sweeping method that progressively refines the depth estimation from coarse to fine over multiple stages. The proposed method adaptively adjusts sweeping intervals and ranges based on the predicted depth and the uncertainty from the previous stage, resulting in a more efficient cost aggregation performance. The experimental results demonstrated that our method achieved state-of-the-art accuracy with reduced GPU memory usage and time consumption compared to the other methods. Furthermore, we illustrate that our method achieved satisfactory performance on real-world data, despite being trained on synthetic data, indicating its generalization potential and practical applicability.

Prediction of In Vivo Performance of Dabigatran Capsules Marketed in Nepal from In Vitro (Dissolution) Data Using Numerical Convolution Method

Prediction of In Vivo Performance of Dabigatran Capsules Marketed in Nepal from In Vitro (Dissolution) Data Using Numerical Convolution Method

Rational Approximation of Nonlinear Systems Via NL-VF

This paper presents an alternative vector fitting (VF)-based approach to generate a rational model of nonlinear system behaviors. The proposed approach, named here as nonlinear VF (NL-VF), has its fundament in the previously proposed time-domain VF (TD-VF). TD-VF generates rational models using TD input/output responses and numerical convolution. Unlike TD-VF, NL-VF utilizes input/output vectors in the frequency domain (FD) to produce a rational approximation of the corresponding transfer function/matrix. The input/output FD vectors are obtained in this paper by a numerical Laplace transform (NLT) algorithm. Alternatively, input/output TD vectors available from any solution algorithm can be transformed to FD via NLT and used in the NL-VF approach. Computational efficiency and accuracy of the NL-VF are compared with the TD-VF technique for the single-phase case. It is demonstrated that NL-VF gives more accurate results than TD-VF, in particular when the data is calculated from a time-window, which does not capture the system slow dynamics. Also, unlike TD-VF, NL-VF can handle in a natural way FD weighting, thus exhibiting error control. The proposed approach is applied in this paper to 1) a boost converter circuit, and 2) a network involving simultaneously a three-phase grid-tied photovoltaic (PV) system and a nonlinear reactor load.

An Approach to Modeling Percussive Drilling Systems

AbstractA framework for modeling the transient response of percussive drilling systems is presented. The proposed approach is based on the distributed transfer function method (DTFM), which is a semi-analytical modeling technique. Experimental results obtained from a percussion testbed for the Regolith and ice drill for the exploration of new terrains (TRIDENT) were incorporated into this modeling technique. DTFM is shown to be a convenient, modular modeling approach, capable of handling complex boundary conditions and drill rod geometries. Moreover, this technique is computationally simple and allows for straightforward incorporation of experimentally measured boundary forcing via numerical convolution, as well as control of the frequency content in the transient response. An experimental study is used to demonstrate the ability of the proposed approach to characterize unknown boundary conditions.

A simple agent-based model to simulate 3D tumor-induced angiogenesis considering the evolution of the hypoxic conditions of the cells

In tumors, angiogenesis (conformation of a new vasculature from another primal one) is produced with the releasing of tumor angiogenic factors from hypoxic cells. These angiogenic substances are distributed around the tumor micro-environment by diffusion. When they reach the primal blood vessel bed, the sprouting and branching of a new micro-vascular network is produced. These new capillaries will supply oxygen to cells so that their hypoxic state is overcome. In this work, a new and simple 3D agent-based model to simulate tumor-induced angiogenesis is presented. In this approach, the evolution of the hypoxic conditions in cells along the related conformation of the new micro-vessels is considered. The importance that the relative position of the primal vasculature and tumor structure takes in the final distribution of the new micro-vasculature has also been addressed. The diffusion of angiogenic factors and oxygen has been modelled at the targets by numerical convolution superposition of the analytical solution from the sources. Qualitative and quantitative results show the importance of tip endothelial cells in overcoming hypoxic conditions in cells at early stages of angiogenesis. At final stages, anastomosis plays an important role in the reduction of hypoxia in cells.

Prediction of Plasma Drug Concentration Profiles and Pharmacokinetic Parameters of Nifedipine Commercial Tablets using the Convolution Method

The aim of this study was to predict the blood/plasma drug concentration profiles for five brand of nifedipine present on the Saudi Arabia market by using the numerical convolution method and to estimate the pharmacokinetic parameters (Cmax, Tmax, Ka, K and Vd) by the application of the residual method to the predicted plasma drug concentration profiles. Results showed that the higher Cmax was 118.95ng/ml for brand A2 and the lower Cmax was 72.29ng/ml for brand A3. The Tmax was ranged from 2.3 hr to 4.9 hr for brands A2 and A3 respectively. The total area under plasma drug concentration curve (AUCinf.) was in lower value equal to 585.59 ng x hr/ml for brand A2 and the higher value was for brand A5 equal to 743.52ng x hr/ml. The volume of distribution was also increased from 52.5 L for free nifidipine to 72 L for brand A1. The predicted first order elimination rate constant was decreased from 0.34 hr-1 for free nifedipine to 0.17 hr-1 for brand A3. The half-life of nifedapine was increased from 2 hours for free drug to 3.93 hours for brand A3. From this study it can be concluded that brands present in the market that shows similarity in accordance to the Dissimilarity factor f1 are not always guaranty that they will be bioequivalent in vivo and vice versa. Also, this study indicates that the method of convolution is a useful tool for prediction of bioequivalence of different brands present on the market.

An efficient time-domain method for the electromagnetic transient response of multiconductor transmission lines excited by an electromagnetic field

An efficient time-domain method based on the waveform relaxation with transverse partitioning (WR-TP) techniques and the delay extraction passive compact circuit (DEPACT) macromodel is presented for evaluating the electromagnetic (EM) transient response of multiconductor transmission lines (MTLs) excited by an external EM field. Firstly, the equivalent distributed sources due to the tangential components of the electric field are introduced into the MTLs equations. Then, the TLs are divided into a cascaded of DEPACT subnetworks, where the telegrapher’s equations of lossless TLs are decoupled by applying the WR-TP techniques. And the relaxation sources over the lossy TLs are updated by using the waveform scaling algorithm, which can completely avoid performing the numerical convolution. Finally, the equivalent circuit is established and the transient responses induced on the lines can be obtained by using the circuit simulation software PSCAD.

Hydrogel-based matrices for controlled drug delivery of etamsylate: Prediction of in-vivo plasma profiles

ObjectivesTo design oral controlled release (CR) hydrogel matrix tablets of etamsylate using various hydrophilic polymers. Additionally, to predict plasma concentration-time profiles of etamsylate released from different CR matrices. MethodsCharacterization of the in-vitro release rate was performed by various model dependent and model independent approaches. A simple numerical convolution strategy was adopted to predict the in-vivo performance of all matrices from their in-vitro percent released data. The statistical analysis was conducted utilizing a student t-test and ANOVA. ResultsThe release of etamsylate from all matrices showed a deviation from Fickian transport mechanism except; F2 followed Case II release whereas, F9 and F11 obeyed Fickian diffusion. CR hydrogel based-matrices (F4 and F11) demonstrated the maximum drug retardation and satisfied the USP release limits. Concentration–time profiles of etamsylate were predicted successfully from the in-vitro release data of all prepared matrices. Pharmacokinetic parameters of etamsylate CR hydrogel matrices were significantly changed with comparison to reference product except F1. ConclusionThe designed (F2-F11) matrices had the capability to extend the plasma level of etamsylate for an adequate time. However, F4 and F11 were considered the most ideal formulations for once daily application of etamsylate. The prediction of in-vivo pharmacokinetics of etamsylate was very useful to assess the rationality of the designed matrices for the practical application in humans.

Analytical solution of reactive hybrid cells in series (HCIS) model for pollution transport through the rivers

ABSTRACT The application of accurate transport models is critical in tracer routing through river reaches. Reactive models are widely used because of the reaction and degradation properties of some pollutants with bed and bank materials, and cell-based theoretical models are among the most popular for contaminant transport simulation. This study investigates the reactive form of cells in a series model. A new analytical equation is proposed that includes a degradation term for sudden mass release in a river reach. To consider the inaccuracy of previously proposed equations, we attempted to rearrange separate transport actions such as advection, dispersion and degradation through the cells of a length unit. The cell residence times of mixed cells were equated, and the degradation action was only forced to the second cell. The parameter number of the solution was lower than in previously proposed models. Synthetic datasets of the advection–dispersion–degradation equation were used to examine model performance. The model was found to work well in the first and later units. The numerical convolution method was used in the second to fourth units, and it also fitted synthetic data. The previously proposed equation of reactive HCISD was imprecise in the convolution method.

Lightweight image super-resolution with feature enhancement residual network

Recently, single image super-resolution (SR) methods based on deep convolutional neural network (CNN) have demonstrated remarkable progress. The essence of most CNN-based models is to learn the non-linear mapping between low-resolution patches and corresponding high-resolution ones. However, numerous convolutions are applied to implement this mapping, which directly contributes to large model sizes and huge graphics memory consumption. In this paper, we propose a lightweight feature enhancement residual network (FERN) to achieve prominent performance by incorporating lightweight non-local operations into the residual block. By taking advantage of utilizing this non-locally enhanced residual block, the proposed model can capture long-range dependencies. For further improving performance, we design the structure-aware channel attention layer that explicitly boosts feature maps with more structural and textural details. Extensive experiments suggest that the proposed approach performs favorably against the state-of-the-art SR algorithms in terms of visual quality and inference time.

Analytical and numerical methods for efficient calculation of edge diffraction by an arbitrary incident signal.

In the present study, diffraction of plane and spherically spreading signals by half-planes is considered. An existing analytical impulse response is investigated, which is exact for plane and approximate for spherical incident signals. It is shown that all its primitive functions with respect to time exist and have an explicit form involving elementary functions. The primitive functions are employed to (i) prove that the convolution of the impulse response with any bounded signal is also bounded for all times, (ii) obtain analytically the diffraction response as a combination of elementary functions for any incident signal approximated piecewise by fitting polynomials, (iii) improve the performance of the numerical convolution by orders of magnitude, and (iv) handle the convolution of very coarsely sampled incident signals. An impulse response is presented for finite-length edges, which, unlike the traditional integration formulas along the edge, is an explicit form of time. Because it is based on the impulse response for infinite edges, it inherits all aforementioned benefits associated with its primitive functions. Furthermore, it offers a substantial computational benefit compared to traditional integration formulas along the edge. Finally, the requirements for the direct application of the presented results to other impulse responses are discussed.

Fast hologram generation using intermediate angular-spectrum method for high-quality compact on-axis holographic display.

In the angular-spectrum method-based computer-generated hologram, the zero-padding method is used to convert circular convolution into linear convolution. However, it will increase the calculation time and memory usage significantly. Therefore, a fast and simple method is proposed to solve the issue of the numerical convolution in the process of hologram generation by using the intermediate angular-spectrum method in this paper. Through replacing numerical Fourier transform by optical Fourier transform in the hologram generation, the calculation speed is approximately 6 times faster than that of the zero-padding method. And due to the scaling factors introduced by the Fourier lens and without the cropping operation, the reconstruction quality of the proposed method is improved significantly compared with the zero-padding method. Moreover, the optical reconstruction system is more compact than the 4-f filter system in the on-axis holographic reconstruction. Both numerical simulations and optical experiments have validated the effectiveness of the proposed method.

Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform

In statistical theory, convolutions are often avoided in favor of asymptotic approximation or simulation. Much of this is due to the fact that convolution is a challenging problem. With abundant computational resources, numerical convolution is a more viable option than in past decades. This paper proposes mathematical error bounds for the cumulative distribution function of the convolution of a finite number of independent univariate random variables. The discrete Fourier transform and its companion, the inverse discrete Fourier transform, are used to provide fast and easily obtainable mathematical error bounds for these convolutions. Examples and applications are provided to demonstrate a few possible uses of the error bounds.

Information and analytical system for assessing the quality of planning and monitoring of the process of teaching students during the semester

Monitoring the student learning process is the basis of feedback in the management of the quality of specialist training, which determines its relevance and relevance. The aim of the work is to develop a model of continuous monitoring of the quality of student training in the semester in the context of student-teacher interaction. The monitoring is built on the basis of a special mathematical model that allows solving problems of forming the recommended student assessment and assessment of the teacher’s performance discipline implemented in the corresponding information system. Formation of the recommended assessment of a student in a discipline is carried out as an accumulation from individual stages of a discipline based on data grouping methods, work with associative data sets, data convolution, database manipulation. Statistical methods allow to monitor the performance discipline of university teachers on the basis of numerical convolutions, getting it in measurable indicators. Thus, a feedback model in the student-teacher chain was obtained, which is necessary to substantiate management decision-making in the educational process.

Analysis and test of the central-blue-spot infall hallmark

Aims. The infall of material onto a protostar, in the case of optically thick line emission, produces an asymmetry in the blue- and red-wing line emissions. For an angularly resolved emission, this translates in a blue central spot in the first-order moment (intensity weighted velocity) map. Methods. An analytical expression for the first-order moment intensity as a function of the projected distance was derived, for the cases of infinite and finite infall radius. The effect of a finite angular resolution, which requires the numerical convolution with the beam, was also studied. Results. This method was applied to existing data of several star-forming regions, namely G31.41+0.31 HMC, B335, and LDN 1287, obtaining good fits to the first-order moment intensity maps, and deriving values of the central masses onto which the infall is taking place (G31.41+0.31 HMC: 70–120 M⊙; B335: 0.1 M⊙; Guitar Core of LDN 1287: 4.8 M⊙). The central-blue-spot infall hallmark appears to be a robust and reliable indicator of infall.

Generation of material removal map for freeform surface polishing with tilted polishing disk

Polishing is one of the key processes for surface finishing. It can achieve mirror-effect on surface by removing the tool masks caused by milling. Since the process is now automated, tilted polishing disk is applied more and more widely, and the prediction of material removal map is vital for polishing trajectory planning to reduce scrap rate and shorten production cycle. This work proposed an improved material removal model of tilted elastic polishing disk by considering the geometric features of contact region, contact pressure, and velocity distribution while polishing. More specifically, based on the FEM simulation results, the contact region and the pressure distribution are discussed in three diverse types according to the geometric features of surface at contact point. The material removal map is then generated by numerical convolution of this model and trajectory planned, with which the issues of material removal, such as over-polishing, under-polishing, and waviness, can be graphically illustrated. To validate the approach, case studies on both planar and freeform surfaces are conducted. Comparative study reveals that the predicted result by the approach agrees with the actual polishing very well. Moreover, according to the generated material removal map, process optimization can be carried out to adjust process parameters, such as feedrate, interval, and step, and hence, mirror-effect surface quality can be achieved.

APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

We present an accurate and easy-to-compute approximation of the transition probabilities and the associated Arrow-Debreu (AD) prices for the inhomogeneous geometric Brownian motion (IGBM) model for interest rates, default intensities or volatilities. Through this procedure, dubbed exponent expansion, transition probabilities and AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results — for time horizons up to several years — even when truncated after the first few terms. For farther time horizons, the exponent expansion can be combined with a fast numerical convolution to obtain high-precision results.

RTD Measurement, Modeling, and Analysis of Liquid Phase of Three-Tube Industrial Pulp Digester

Abstract Residence-time distribution (RTD) experiments were performed to analyze an industrial scale three-tube series continuous pulping digester’s hydrodynamic performance. An impulse of radiotracer 82Br (γ energy source) was introduced at the inlet of the first tube. The radiotracer concentration in the liquid phase was traced at the outlet of each tube. The input behavior of the radiotracer converted to a non-ideal pulse tracer input for the second and third tubes of the digester. Numerical convolution is adopted to deal with the non-ideal pulse input of the radiotracer. A modeling procedure for determining the RTD from the outlet tracer concentration data is proposed. A plug flow component followed by axial dispersion model is considered, and is adjusted after its convolution with the inlet tracer concentration data to obtain the RTD of the individual tubes. The obtained RTD data are analyzed to explain the flow behavior, degree of dispersion, and flow abnormalities existing in the digester. The mean residence-time (MRT), and dispersion number are estimated for the model components for the three tubes. The vessel dispersion number is found to decrease from tube 1 to tube 3. Overall, the conversion of the highly dispersed flow regime into the plug-flow regime is observed in the whole digester.

Seismic fragility and risk assessment of high-speed railway continuous-girder bridge under track constraint effect

The prestressed-concrete continuous-girder bridge is one of the major high-speed railway bridges that plays an essential role in the railway. Using a typical high-speed railway continuous-girder bridge as a case study, a track-bridge longitudinal interaction model has been initially established with a comprehensive consideration of the components including rail, track slab, bed plate, rail fastener, cement asphalt mortar, sliding layer, and bridge structure. The damage states of the bridge and the seismic capacity model for key structural components of the bridge under various damages were defined. A probabilistic seismic demand model was constructed for structural components according to the incremental dynamic analysis of a suite of selected ground-motion. The fragility curves of the bridge components were derived and compared with that of the bridge model without a track system. Then, the failure probability of the bridge system was estimated using the first-order boundary method. Finally, the risk of the bridge was assessed via the numerical convolution method using both the fragility curves and seismic hazard function. The results are drawn as follows: (1) Owing to the longitudinal constraint of the track system, the dynamic characteristics of the bridge are changed; (2) A total of four damage levels occurred on the bridge pier without the track system, but only light and moderate damage levels appear due to the track constraint; (3) Under the same peak ground acceleration, the damage exceeding probability of the model without the track system is significantly greater than that with the track system; (4) Under the slight and moderate damage states, the upper and lower limits of the system fragility curves are governed by bridge pier. They are governed by the bearing with very low failure probability under the extensive and complete damage states; and (5) Within the 100-year design period, the probability that the bridge structure subject to slight and moderate damages is “occasional”, while it is “very unlikely” that the structure will suffer from the extensive and complete damages.