Order Kernel Research Articles

Use of multifocal electroretinograms to determine stage of glaucoma.

To determine whether multifocal electroretinograms (mfERGs) recorded with natural pupils and skin electrodes can be used to determine the stage of open angle glaucoma (OAG). Two hundred eighteen eyes of 132 OAG patients and 62 eyes of 62 normal subjects whose best-corrected visual acuity (BCVA) was 0.1 logarithm of the minimum angle of resolution (logMAR) units (20/25) or less were studied. The mean deviations (MDs) obtained by Humphrey Visual Field Analyzer (HFA), optical coherence tomographic (OCT) images, and mfERGs were analyzed. The glaucoma was classified into 4 stages: preperimetric glaucoma (PPG), early stage, moderate stage, and advanced stage glaucoma. The parameters of the mfERGs examined were the amplitudes of the two positive peaks (P1, P2) of the second order kernels in the nasal and temporal fields within the central 15° diameter. The mean age of all participants (patients and normals) was 63.8 ± 10.8 years. With the progression of glaucoma, the amplitudes of P1 in the nasal hemifield increased and the amplitudes of P2 decreased. The nasal to temporal ratio (N/T ratio) of the P1 amplitudes and the negative slope of the line between P1 and P2 (P1P2 Slope) in the nasal field were larger at each glaucoma stage except at the PPG stage. Both the N/T amplitude ratio and P1P2 Slope were weakly but significantly correlated with the MD (r = -0.3139, P<0.0001; r = 0.4501, P<0.0001, respectively), and the OCT parameters (all P<0.0001) except the outer layer thickness. Our findings indicate that the amplitudes of P1 and P2 of the second order kernel of the mfERGs in the nasal field of the center region can be good markers for the stages of glaucoma.

Kernel-based hybrid multi-objective optimization algorithm (KHMO)

A new hybrid evolutionary algorithm named Kernel-based Hybrid Multi-Objective Optimization Algorithm (KHMO) is introduced in this work. The main novelty of this algorithm is its updating rule based on the concept of a reproducing kernel in order to properly approximate the numerical gradient. In addition, a novel numerical strategy based on the computation of a normal vector to determine a searching target direction that guides the nondominanted solutions into more propitious regions is also introduced for the first time. IGD and HV metrics are used to evaluate the performance of KHMO algorithm against other competitive multi-objective methods such as MRBFO, FDEA-I, VMEF, BiasMOSaDE and GAMODE tested on ZDT and CEC 2009 problems. Moreover, the Wilcoxon test is carried out as a comparative statistical analysis in order to detect if a significant difference exists with respect to the rest of the algorithms. The corresponding numerical results showed that the introduced KHMO algorithm gains the best overall performance among all the compared algorithms in terms of diversity, coverage and convergence in most problems. Moreover, IGD and HV curves reveal a respectable convergence rate since nearly 200 iterations are enough to offer quality solutions.

Practical Usage of Radical Isogenies for CSIDH

Recently, a radical isogeny was proposed to boost commutative supersingular isogeny Diffie–Hellman (CSIDH) implementation. Radical isogenies reduce the generation of a kernel of a small prime order when implementing CSIDH. However, when the size of the base field increases, field exponentiation, a core component of computing radical isogenies, becomes more computationally intensive. As the size of the field inevitably grows to resist a quantum attack, so it is necessary to discuss the practical utilization of the radical CSIDH. This paper presents an optimized implementation of radical isogenies and analyzes its ideal use in CSIDH-based cryptography with a review of quantum analysis. We tailored the formula for transforming Montgomery curves into the Tate normal form and further optimized the radical 2-isogeny formula and projective versions of the radical 5- and 7-isogenies. Except for CSIDH-512, using only the radical 2-isogeny for all parameters improves performance by 6% to 10%.

On a new higher order kernel for density estimation

Higher order kernels have been widely implemented for nonparametric function estimation, mainly due to their faster asymptotic rates of convergence and interpretability. This article constructs a novel higher order kernel of any pre‐specified even order by using Shannon's formula. The proposed kernels have a closed form expression and are easy to implement. We compare the constructed kernel with several popular higher order kernels in the context of density estimation. Further, we observe that the mean integrated squared error (MISE) of the density estimator corresponding to the proposed kernel is comparable with that of the popular kernels. The constructed kernel performs somewhat better for the Fejér‐de la Vallée Poussin and the ‐symmetric densities. The MISE of the corresponding kernel density estimator and a few related theoretical results are also presented.

Leading order, next-to-leading order, and nonperturbative parton collision kernels: Effects in static and evolving media

Energetic partons traveling in a strongly interacting medium lose energy by emitting radiation and through collisions with medium constituents. Non-perturbative, next-to-leading order and leading order collision kernels are implemented within AMY-McGill formalism. The resulting gluon emission rates are then evaluated and compared by considering scattering occurring in a brick of quark-gluon plasma, as well as in a realistic simulation of Pb-Pb, collisions at $\sqrt{s}=2.76$ ATeV using MARTINI. We find that the variations in quenching of hard partons resulting from using different kernels can be important, depending on the overall value of the strong coupling constant $\alpha_s$.

State of Health Prediction of Lithium-Ion Battery Based on Deep Dilated Convolution.

A battery's charging data include the timing information with respect to the charge. However, the existing State of Health (SOH) prediction methods rarely consider this information. This paper proposes a dilated convolution-based SOH prediction model to verify the influence of charging timing information on SOH prediction results. The model uses holes to fill in the standard convolutional kernel in order to expand the receptive field without adding parameters, thereby obtaining a wider range of charging timing information. Experimental data from six batteries of the same battery type were used to verify the model's effectiveness under different experimental conditions. The proposed method is able to accurately predict the battery SOH value in any range of voltage input through cross-validation, and the SDE (standard deviation of the error) is at least 0.28% lower than other methods. In addition, the influence of the position and length of the range of input voltage on the model's prediction ability is studied as well. The results of our analysis show that the proposed method is robust to different sampling positions and different sampling lengths of input data, which solves the problem of the original data being difficult to obtain due to the uncertainty of charging-discharging behaviour in actual operation.

On the Effects of Kernel Configuration in Multi-Kernel Polar Codes

Polar codes are a relatively new family of linear block codes which have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provably capacity achieving capability. They have been proposed to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The basic approach introduced by Arikan can only be used to generate polar codes of length , . To overcome this limitation, polarization kernels of size larger than (like , , and so on), have already been proposed in the literature. Additionally, kernels of different sizes can also be combined together to generate multi-kernel polar codes, further improving the flexibility of codeword lengths. These techniques undoubtedly improve the usability of polar codes for various practical implementations. However, with the availability of so many design options and parameters, designing polar codes that are optimally tuned to specific underlying system requirements becomes extremely challenging, since a variation in system parameters can result in a different choice of polarization kernel. This necessitates a structured design technique for optimal polarization circuits. We developed the DTS-parameter to quantify the best rate-matched polar codes. Thereafter, we developed and formalized a recursive technique to design polarization kernels of higher order from component smaller order. A scaled version of the DTS-parameter, namely SDTS-parameter (denoted by the symbol in this article) was used for the analytical assessment of this construction technique and validated for single-kernel polar codes. In this paper, we aim to extend the analysis of the aforementioned SDTS parameter for multi-kernel polar codes and validate their applicability in this domain as well.

STUDY OF HEAT TREATMENT EFFECT ON THE BIOLOGICAL VALUE OF PINE NUTS KERNELS

The aim of the research was to determine the optimal modes of heat treatment of pine nut kernels in order to preserve their biological value to the optimal, which will allow in the future to use this type of raw material in the technology of various types of sauces with the addition of dry whey. The article analyzes the drying kinetics of Pinus pinea Linneus pine nut kernels for 120 minutes under 4 heat treatment regimes: 20, 40, 60 and 80 ˚C. The effect of heat treatment on the composition of essential amino acids, the content of vitamin C and β-carotene was studied. Thus, the temperature of 20 and 40 ˚C ensures the maximum preservation of the biological value of the raw material, but it does not allow to achieve a significant decrease in the mass fraction of moisture, which will negatively affect the microbiological indicators of the raw material. During processing at 60 ˚С, the mass fraction of moisture in the kernels of pine nuts decreases from 7 to 5.28 %, which is likely to reduce water activity and positively affect the duration of storage. An increase in temperature to 80 ˚С significantly reduces the content of essential amino acids and β-carotene, as well as makes it impossible to achieve a technological effect (a significant decrease in moisture content) with the irrational use of energy resources. It was established that the optimal mode of heat treatment of pine nut kernels is drying at a temperature of 60 ˚С, which ensures the preservation of the biological value of the raw material and meets the recommendations for achieving satisfactory microbiological indicators.

Approximate Fourier series recursion for problems involving temporal fractional calculus

Fractional calculus constitutive models are of wide applicability. They have been used, for example, for: xanthan gum, bread dough, synthetic polymers (e.g. nylon), single collagen fibrils, semi-hard zero-fat cheese, pure ice at −35∘C, asphalt sealants, epithelial cells, gels, polymers, concrete, asphalt, rock mass, waxy crude oil, breast tissue cells, lung parenchyma, and red blood cell membranes (e.g. Bonfanti et al. (2020)). In this note we are motivated by applications to dispersive media such as lossy dielectrics and viscoelastic polymers, both of which involve constitutive laws with fading memory convolution Volterra integrals, and both of which have been modelled by fractional calculus — which implies a weakly singular Volterra kernel. To step forward in time with such a model the entire hereditary Volterra integral needs to be numerically re-computed at each time step. Done naïvely with standard quadrature this involves O(N2) operations and O(N) storage to compute over N time steps, and this severely limits the usefulness of such simple methods in large scale computations. Several alternatives addressing these shortcomings of this naïve approach have been offered in the literature, all of which can provide remedies. Here we propose another method, but ours is rather different in that we use a Fourier series proxy over much of the integration range. This allows for a recursive update to the ‘history integral’, with a much smaller effort expended in standard quadrature near the singularity. The recursive update is basically the same as that used when the Volterra kernel comprises decaying exponentials, a method which is already employed in some commercial codes. Given that this partial implementation is already in use, we intend that our method therefore has a lower ‘barrier to entry’ for incorporating fractional calculus models into commercial codes: it requires only minor surgery on the weakly singular kernel in order to apply the Fourier series proxy. This study is presented in the spirit of a discussion piece — there are several directions one could take from the basic observations presented here. We have aimed for simplicity and economy of presentation, and included just enough numerical results to give evidence that the method works. In summary, our method mitigates the O(N) storage and O(N2) storage issues using an easily implemented proxy. It can also be implemented for variable time steps. The code is available from https://github.com/variationalform/fouvol and https://hub.docker.com/u/variationalform.

ON BLOW-UP FOR A TIME–SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATION WITH EXPONENTIAL KERNEL IN TEMPORAL DERIVATIVE

In this paper, we study the blow-up of the solution to a semilinear time–space fractional diffusion equation, where the time derivative is the Caputo–type derivative with the exponential kernel (“the exponential Caputo derivative” for brevity) of order \(\alpha \in (0,1)\) and the spatial derivative is the fractional Laplacian of order \(s\in (0, 1)\). We first define a mild solution of the considered equation in terms of convolution form, where the fundamental solutions are denoted by Fox H-functions. The local existence and uniqueness of a mild solution are further obtained by using a fixed point argument. Then, a weak solution is defined by the test function and it is proved to be a mild solution. Finally, the finite time blow-up is shown. Besides, the global existence of the solution is shown too where the critical index is determined.

Characterizations of Some Groups in Terms of Centralizers

A group G is said to be n-centralizer if its number of element centralizers \(\mid {{\,\mathrm{Cent}\,}}(G)\mid =n\), an F-group if every non-central element centralizer contains no other element centralizer and a CA-group if all non-central element centralizers are abelian. For any non-abelian n-centralizer group G, we prove that \(\mid \frac{G}{Z(G)}\mid \le (n-2)^2\), if \(n \le 12\) and \(\mid \frac{G}{Z(G)}\mid \le 2(n-4)^{{log}_2^{(n-4)}}\) otherwise, which improves an earlier result. We prove that if G is an arbitrary non-abelian n-centralizer F-group, then gcd\((n-2, \mid \frac{G}{Z(G)}\mid ) \ne 1\). For a finite F-group G, we show that \(\mid {{\,\mathrm{Cent}\,}}(G)\mid \ge \frac{\mid G \mid }{2}\) iff \(G \cong A_4 \), an extraspecial 2-group or a Frobenius group with abelian kernel and complement of order 2. Among other results, for a finite group G with non-trivial center, it is proved that \(\mid {{\,\mathrm{Cent}\,}}(G)\mid = \frac{\mid G \mid }{2}\) iff G is an extraspecial 2-group. We give a family of F-groups which are not CA-groups and extend an earlier result.

Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts. We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains. We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster.

Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes

Let m ∈ N $m\in \mathbb {N}$ , P ( D ) : = ∑ | α | = 2 m ( − 1 ) m a α D α $P(D):=\sum _{|\alpha |=2m}(-1)^m a_\alpha D^\alpha$ be a 2 m $2m$ -order homogeneous elliptic operator with real constant coefficients on R n $\mathbb {R}^n$ , and V $V$ a real-valued measurable function on R n $\mathbb {R}^n$ . In this article, the authors introduce a new generalized Schechter class concerning V $V$ and show that the higher order Schrödinger operator L : = P ( D ) + V $\mathcal {L}:=P(D)+V$ possesses a heat kernel that satisfies the Gaussian upper bound and the Hölder regularity when V $V$ belongs to this new class. The Davies–Gaffney estimates for the associated semigroup and their local versions are also given. These results pave the way for many further studies on the analysis of L $\mathcal {L}$ .

800-Gb/s/carrier WDM Coherent Transmission Over 2000 km Based on Truncated PS-64QAM Utilizing MIMO Volterra Equalizer

We provided a feasible solution for 800-Gb&#x002F;s per carrier long-distance wavelength division multiplexing (WDM) coherent optical fibre transmission based on offline DSP. We experimentally demonstrate 5-carrier 125-GHz-spacing WDM coherent optical fibre transmission achieving 2000-km transmission distance and 800-Gb&#x002F;s net bit rate per carrier. We utilized 100-Gbaud truncated probabilistically shaped (TPS) polarization-multiplexed 64QAM format in this work. In terms of advanced components, the high-speed digital-to-analog converter with 35-GHz 3 dB-bandwidth and Raman-amplified ultra-large-area fibre were utilized to achieve higher baud-rate and longer transmission distance. In terms of modulation format, we changed PS to TPS to obtain a more suitable shaping depth, and make the shaped signal better suited to the DSP process of coherent optical communication, including constant modulus algorithm (CMA) equalizer. Besides, our results show that the TPS-64QAM signal with 5-bit&#x002F;symbol&#x002F;polarization entropy outperforms the standard-32QAM with a same bit rate by around 1 dB sensitivity gain. Furthermore, we proposed a multiple-input multiple-output (MIMO) Volterra equalizer (VE), which consists of a 1^st-order 2&#x2009;&#x00D7;&#x2009;2 MIMO complex-valued widely linear (WL) equalizer and a 2^nd-order real-valued nonlinear equalizer. Our proposed MIMO VE can effectively resolve the impact of In-phase&#x002F;quadrature (IQ) imbalance and IQ skew, and compensate linear and nonlinear impairments at the same time. We also utilized partial kernel VE to reduce the complexity by retaining part of the 2^nd-order kernels.

Kernel-based gradient evolution optimization method

A new hybrid metaheuristic method is proposed which is inspired from the recently proposed gradient-evolution method. This study introduces for the first time the concept of reproducing kernel in order to correctly estimate the numerical gradient which is used as an updating rule. This proposed method is called Kernel-based Gradient Evolution (GE) which inherits good exploration and exploitation abilities as well as non localization through several operators taken from the original gradient-evolution algorithm. In the proposed KGE algorithm the gradient vector is computed using a kernel reproducing function. Thus the local gradient estimation is numerically computed considering a local Taylor series expansion. The IEEE CEC 2019 test suite is considered in order to evaluate the numerical performance of the proposed KGE algorithm. A numerical comparison between some competitive methods and the one proposed in this work is reported. The obtained numerical results suggested that in terms of convergence, KGE algorithm performs in most cases significantly better than the original GE algorithm and gets respectable results against other considered methods.

Solution of fractional autonomous ordinary differential equations

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

Effect of Solvent Type, Extraction Temperature, Agitation Speed and Microwave Power on Phenolic Compound Extraction and Antioxidant Activity of Apricot Kernels ((Prunus armeniaca L.)

Background: Prunus armeniaca L. is widely cultivated around the world. High consumption of its fruit produces a large quantity of the apricot kernel. The valorization of this byproduct in terms of polyphenol compounds seems to be important. Objective: The aim of the present study is to investigate the best conditions of phenolic compound extraction from apricot kernels in order to determine the effects of different parameters, namely time, stirring speed, solvent type, temperature, and microwave power, on polyphenol yield. Methods: In this study, the effect of many parameters, such as the type of solvent (ethanol, methanol, acetone and water), the acetone concentration (40-70%, v/v), the extraction time, power of the microwave (100-900 W) and stirring speed on the extraction of Total Phenolic Content (TPC) from apricot kernels was studied, using the approach of single factor experiments. Results: The importance of agitation speed was determined for polyphenol compound extraction from apricot kernels besides time, temperature and microwave power, whereas the linear agitation in the water bath had no significant effect on the extraction of phenolic compounds. The best extraction conditions were 60% acetone, 300 W of microwave power for 5 min of extraction time, which gave a high TPC of 249.44 ±15.83 mg GAE/g DW. All the extraction conditions showed a significant effect (p &lt;0.05) on the TPC. The antioxidant capacity (DPPH-RSA) of the extract was positively correlated with TPC in all tested methods. Conclusion: It can be concluded that the importance of agitation speed was determined for the extraction of phenolic compounds from apricot kernels by maceration. However, the linear agitation in the water bath had no significant effect on the extraction. Apricot kernel seems to be a good source of polyphenols compared to other sources mentioned in the previous studies present in literature.

Optimization of the 3p keys kernel parameters by minimizing the ripple of the spectral characteristic

The ideal interpolation kernel is described by the sinc function, and its spectral characteristic is the box function. Due to the infinite length of the ideal kernel, it is not achievable. Therefore, convolutional interpolation kernels of finite length, which should better approximate the ideal kernel in a specified interval, are formed. The approximation function should have a small numerical complexity, so as to reduce the interpolation execution time. In the scientific literature, great attention is paid to the polynomial kernel of the third order. However, the time and spectral characteristic of the third-order polynomial kernels differs significantly from the shape of the ideal kernel. Therefore, the accuracy of cubic interpolation is lower. By optimizing the kernel parameters, it is possible to better approximate the ideal kernel. This will increase the accuracy of the interpolation. The first part of the paper describes a three-parameter (3P) Keys interpolation kernel, r. After that, the algorithm for optimizing the parameters of the 3P Keys kernel, is shown. First, the kernel is disassembled into components, and then, over each kernel component, Fourier transform is applied. In this way the spectral characteristic of the 3P Keys kernel, H, was determined. Then the spectral characteristic was developed in the Taylor series, HT. With the condition for the elimination of the members of the Taylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (?opt, ?opt, gopt) were determined. The second part of the paper describes an experiment, in which the interpolation accuracy of the 3P Keys kernel, was tested. Parametric cubic convolution (PCC) interpolation, with the 3P kernel, was performed over the images from the Test database. The Test database is created with standard Test images, which are intensively used in Digital Image Processing. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the accuracy of the interpolation was determined. The results (?opt, ?opt, gopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation accuracy with the proposed 3P Keys interpolation kernel, compared to the interpolation accuracy with, 1P Keys and 2P Keys interpolation kernels. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

Combination of high order kernel estimators for estimation of fruit trees biomass on critical land

This study aims to estimate fruit tree biomass with a high-order Gaussian kernel estimator. The source of the data was obtained by estimating the relationship between tree diameter (x) and tree biomass (y) which was obtained through the allometric equation y = 0.11ρx2.62 for branched trees. Data samples were taken as many as 250 obtained from 5 sub-district locations in critical land on longan and mango fruit tree vegetation. The relationship between x and y is then estimated in the form of an equation yi = m (xi) + εi where, i = 1, 2, n. The results of the analysis using the kernel estimator showed that the tree biomass estimation resulted in a smooth regression curve at an optimal bandwidth (h) score of 1.3 (GCV = 122.92) longan and 2.6 (GCV = 3523.25) mango. The relationship between MSE and bandwidth shows a very strong negative correlation with a score of r = -0.959 (p.value = 0.04) in the estimated longan biomass and r = -0.964 (p.value = 0.03) in the estimated mango biomass and is significant (α = 0.05). This means that a parallel increase in the bandwidth score will decrease the MSE score when GCV is controlled.

Removing mains interference from the mfERG by applying a post-processing digital notch filter: for the good or the bad?

PurposeIdeally, the multifocal electroretinogram (mfERG) is recorded without noticeable intrusion of mains interference. However, sometimes contamination is difficult to avoid. A post-processing digital notch filter can help to recover the retinal response even in severe cases of mains interference. While a digital filter can be designed to have little to no impact on peak times, filtering out mains interference also removes the retinal signal content of the same frequency, which may result in a change of amplitude. The present study addressed this issue in the standard first order kernel mfERG.MethodsIn 24 recordings from routine exams with no perceivable mains interference, the effects of 50-Hz and 60-Hz non-causal digital notch filters on amplitude and peak time were assessed. Furthermore, the effect of filtering on contaminated traces was demonstrated and simulated mains interference was used to provide an example of nonlinear superposition of retinal signal and mains interference.ResultsmfERG amplitudes were reduced by 0%–15% (median 6%) with the 50-Hz filter and remained virtually unaffected with the 60-Hz filter. Simulations illustrate that spurious high-frequency components can occur in the filtered signal if a strongly contaminated signal is clipped due to a limited input range of the analog-to-digital converter.ConclusionThe application of a 50-Hz digital notch filter to mfERG traces causes a mild amplitude reduction which will not normally affect the clinical interpretation of the data. The situation is even more favorable with a 60-Hz digital notch filter. Caution is necessary if the assumption of linear additivity of retinal signal and mains interference is violated.