Regularization Method Research Articles

Conditional stability and regularization method for inverse source for distributed order time-fractional diffusion equation

Conditional stability and regularization method for inverse source for distributed order time-fractional diffusion equation

A quasi-reversibility method for solving nonhomogeneous sideways heat equation

Abstract We consider solving a severely ill-posed problem for determining the surface temperature and heat flux distribution of the nonhomogeneous sideways heat equation by a quasi-reversibility regularization method. An analytical solution is deduced based on the Fourier transform, and then, the logarithmic-type error estimate for the regularized solution is achieved. Finally, three numerical examples, including smooth and non-smooth functions, validate the feasibility and effectiveness of the proposed approach.

DeepASD: a deep adversarial-regularized graph learning method for ASD diagnosis with multimodal data

Autism Spectrum Disorder (ASD) is a prevalent neurological condition with multiple co-occurring comorbidities that seriously affect mental health. Precisely diagnosis of ASD is crucial to intervention and rehabilitation. A single modality may not fully reflect the complex mechanisms underlying ASD, and combining multiple modalities enables a more comprehensive understanding. Here, we propose, DeepASD, an end-to-end trainable regularized graph learning method for ASD prediction, which incorporates heterogeneous multimodal data and latent inter-patient relationships to better understand the pathogenesis of ASD. DeepASD first learns cross-modal feature representations through a multimodal adversarial-regularized encoder, and then constructs adaptive patient similarity networks by leveraging the representations of each modality. DeepASD exploits inter-patient relationships to boost the ASD diagnosis that is implemented by a classifier compositing of graph neural networks. We apply DeepASD to the benchmarking Autism Brain Imaging Data Exchange (ABIDE) data with four modalities. Experimental results show that the proposed DeepASD outperforms eight state-of-the-art baselines on the benchmarking ABIDE data, showing an improvement of 13.25% in accuracy, 7.69% in AUC-ROC, and 17.10% in specificity. DeepASD holds promise for a more comprehensive insight of the complex mechanisms of ASD, leading to improved diagnosis performance.

A hybrid, nonlinear programming approach for optimizing passive shimming in MRI.

In magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming. In this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile. This study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO-SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively. The simulation study demonstrated that the magnetic field was improved from 462 to 3.6ppm, utilizing merely 1.2kg of iron in a 40cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%. The results indicated that the proposed method is expected to be effective for passive shimming.

Generalized Nash Equilibrium Seeking for Noncooperative Game With Different Monotonicities by Adaptive Neurodynamic Algorithm.

This article proposes a novel adaptive neurodynamic algorithm (ANA) to seek generalized Nash equilibrium (GNE) of the noncooperative constrained game with different monotone conditions. In the ANA, the adaptive penalty term, which acts as trajectory-dependent penalty parameters, evolves based on the degree of constraints violation until the trajectory enters the action set of noncooperative game. It is shown that the trajectory of the ANA enters the action set in finite time benefited from the adaptive penalty term. Moreover, it is proven that the trajectory exponentially (or polynomially) converges to the unique GNE when the pseudo-gradient of cost function in noncooperative game satisfies strong (or "generalized" strong) monotonicity. To the best of our knowledge, this is the first time to study the polynomial convergence of GNE seeking algorithm. Furthermore, when the pseudo-gradient mentioned above satisfies monotonicity in general, based on Tikhonov regularization method, a new ANA for finding its ε -generalized Nash equilibrium ( ε -GNE) is proposed, and the related exponential convergence of the algorithm is established. Finally, the river basin pollution game and 5G base station location game are given as examples to showcase the algorithm's effectiveness.

Bifurcations and Homoclinic Orbits of a Model Consisting of Vegetation-Prey-Predator Populations.

This study provides a comprehensive analysis of the dynamics of a three-level vertical food chain model, specifically focusing on the interactions between vegetation, herbivores, and predators in a Snowshoe hare-Canadian lynx system. By simplifying the model through dimensional analysis, we determine conditions for equilibrium existence and identify various types of bifurcations, including Saddle-Node and Hopf bifurcations. Additionally, the study explores codimension-two bifurcations such as Bogdanov-Takens (BT) and zero-Hopf bifurcations. Coefficient formulas of normal forms are derived through the use of center manifold reduction and normal form theory. The study also presents an approximation of homoclinic orbits near a BT bifurcation of the system by computing explicit asymptotics based on regular perturbation methods. Utilizing the MATLAB package MATCONT, a family of limit cycles and their associated bifurcations are computed, including limit point cycles, period-doubling bifurcations, cusp points of cycles, fold-flip bifurcations, and various resonance bifurcations (R1, R2, R3, and R4). The biological implications of the findings are discussed in detail, highlighting how the identified bifurcations and dynamics can impact the population dynamics of vegetation, herbivores, and predators in real-world ecosystems. Numerical experiments validate the theoretical results and provide further support for the conclusions.

Boron/Fe2+/H2O2 combined with resins process cost-effectively remove Ni(II) in wastewater containing Ni-EDTA: Performance and mechanism

This study proposes a green purification strategy in which mild decomplexation of Ni-EDTA into other Ni complexes facilitates the efficient removal and recovery of nickel through resin adsorption. Decomplexation of Ni-EDTA by boron/Fe2+/H2O2 (B/Fe2+/H2O2) followed by resins adsorption was conducted for Ni(II) removal in Ni-EDTA. The Ni(II) removal efficiency could only achieve 1.3 % and 6.2 % while Ni(II) coexisted with EDTA but more than 10 times of higher when Ni(II) coexisted with EDTA-relatives via the single adsorption of commercial heavy metal-affined resins (D001 and D463), which attributed to the increased binding energies of these Ni-EDTA’s degradation products complexes than Ni-EDTA based on density functional theory (DFT) calculation. In comparing to precipitation, the resin adsorption required much less mineralization of EDTA to have a better removal efficiency of Ni(II). B improved the efficiency of Ni-EDTA decompexation by accelerating the recycle of Fe3+/Fe2+. The EDTA (and TOC) removal enhanced from 48.7 % (4.7 %) to 94.7 % (11.9 %) by B/Fe2+/H2O2 process comparing to Fe2+/H2O2 process. With the high EDTA but low TOC removal efficiency after B/Fe2+/H2O2 treatment, Ni(II) removal efficiency via resins adsorption could maximum achieve 80.5 %, 2–3 times of that via regular precipitation method. In addition, B and resins exhibited good reusability in five cycles, and B/Fe2+/H2O2-resins process had excellent adaptability to different heavy metal complexes. B/Fe2+/H2O2-D463 system not only could reduce 78.4 % reagents cost compared with that of Fe2+/H2O2-precipitation process, but also could save much cost than other processes. The results provide new insights for the cost-effective treatment of EDTA-complexed heavy metal wastewater.

Roughness measurement results evaluation of 6082 aluminium alloy specimens after fatigue bending tests

In this paper, the topography of 6082 aluminium alloy specimens after fatigue bending tests was studied with a comprehensive evaluation of measurement noise caused by vibration. Roughness results were acquired by contactless Focus Variation Microscopy (FVM). Studied data were pre-processed, removing the non-measured points and outliers with regular methods, respectively, and high-frequency noise was considered. The variations in ISO 25178 roughness parameters were studied. Based on the previous studies, it was found that surfaces after fatigue bending tests can be difficult to consider when analyzing the measurement noise in a selected bandwidth. Some advantages of profile data extraction in selected directions, like horizontal, vertical or crack, were found deficient, even in studies by various functions, like autocorrelation, power spectral density, or texture direction ratio. When noise suppression methods depend on the details studied, boundary areas were extracted to compare and highlight the presence of high-frequency data characteristics. The proposed method was validated when contrasting standardised Gaussian or median filtering techniques with the spline filtering approach. A proper filter for the reduction of vibrational noise from the results of FVM topography measurements was suggested based on the proposed procedure. Finally, it was proposed how use the new method for reducing errors caused by high-frequency measurement noise in the surface topography of specimens after fatigue bending tests.

Particle swarm optimization method for parameter selecting in Tikhonov regularization method for solving inverse problems

In this article the Tikhonov method used as a regularization technique for solving the inverse problem liner operator equation of the first kind with noisy and noise-free data. We also provide the Tikhonov method's essential analysis for tackling inverse problems. Following that, we go over how to choose the Tikhonov regularization parameter by implementing the Particle Swarm Optimization (PSO) technique. The effectiveness of combining these two approaches particle swarm optimization and Tikhonov is demonstrated to be highly practicable.

Pemberdayaan Mayarakat Melalui Kuliah Kerja Nyata (KKN) Reguler Unkriswina Sumba Dibidang UMKM, Pangan Lokal, Pertanian, dan Pendidikan di Desa Mata Lombu

Kuliah Kerja Nyata (KKN) is one of the lecture programs that must be provided and implemented by every university in order to achieve one of the goals and tri dharma, namely Pengabdian Kepada Masyarakat (PKM). Mata Lombu is one of the villages selected to carry out the KKN program, but as a village in Indonesia, it is generally not free from several problems. Based on observations and social analysis carried out, there are various problems that need to be addressed including: (1) lack of community understanding regarding local food processing, (2) lack of understanding of farmers regarding preventing pests in crops, (3) lack of literacy and numeracy among students. Elementary and junior high schools in the village, (5) limited access to clean water, and (6) limitations of MSMEs (Micro, Small and Medium Enterprises) in creating jobs. Based on a number of problems found during observations and social analysis, and the description in the background, the main objective of all these programs is to fulfill community service and empowerment in Mata Lombu Village through a project action planning framework or Project Action Plan (PAP). The series of Unkriswina Sumba Regular KKN activity methods includes the stages of program planning, implementation and evaluation. The results of this activity show that this activity can increase insight, understanding and new knowledge regarding local food, making bokashi fertilizer, making natural pesticides, and tutoring, and can increase crop yields, food security, reduce the impact of environmental pollution, and increase value. increase the economy of village communities.

Bouligand–Newton type methods for non-smooth ill-posed problems

Abstract We consider Newton-type methods for solving nonlinear ill-posed inverse problems in Hilbert spaces where the forward operators are not necessarily G\^{a}teaux differentiable. Modifications are proposed with the non-existing Fr'{e}chet derivatives replaced by a family of bounded linear operators satisfying suitable properties. These bounded linear operators can be constructed by the Bouligand subderivatives which are defined as limits of Fr'{e}chet derivatives of the forward operator in differentiable points. The Bouligand subderivative mapping in general is not continuous unless the forward operator is G\^{a}teaux differentiable which
introduces challenges for convergence analysis of the corresponding Bouligand-Newton type methods. In this paper we will show that, under the discrepancy principle, these Bouligand-Newton type methods are iterative regularization methods of optimal order. Numerical results for an inverse problem arising from a non-smooth semi-linear elliptic equation are presented to test the performance of the methods.

Regularization method for reduced biquaternion neural network

A reduced biquaternion neural network (RQNN) has achieved significant success in machine learning. However, as the reduced biquaternion algebra system contains infinite zero divisors, the RQNN can be easily trapped in a local minimum and overfitting. In this paper, we propose a new regularization scheme for the RQNN to address these issues. Firstly, we propose a new operation in the reduced biquaternion domain named the reduced biquaternion complex modulus (RQCM), which can extract the scale transformation of reduced biquaternions and decrease the unreasonable network constraints caused by constrained phases. Secondly, we mathematically analyse the properties of the reduced biquaternions and obtain the geometric meaning of the RQCM. Finally, we propose an improved weight decay method using the RQCM which can better project the reduced biquaternion in terms of the scale and phase. In addition, our proposed method can effectively solve the non-differentiability of reduced biquaternion matrix and overfitting problem in the process of network parameter updating. The experimental results demonstrate that the proposed method is effective in color image classification and denoising taskas, and outperforms the state of the arts.

CSF Susceptibility Variation in Patient With Intracranial Hemorrhage: Implications for Quantitative Susceptibility Mapping Reference Selection.

Quantitative susceptibility mapping (QSM) is an emerging MRI technique with multiple clinical applications. As tissue susceptibility cannot be directly measured using MRI, QSM imaging techniques must indirectly compute susceptibility values, requiring regularization methods. CSF is a popular choice for regularization due to its near water susceptibility in healthy controls. However, the impact of pus, elevated protein, or blood dissolved in CSF on QSM regularization is not well defined. This study aimed to investigate the effects of intracranial hemorrhage (ICH) on selecting CSF as reference for QSM imaging. A total of 87 subjects, 53 with ICH (5 intraventricular, 19 subarachnoid, 27 both, and 2 intraparenchymal only) and 37 without hemorrhage (27 with MS, 10 without MS), were included in this study. Imaging was performed using 3D multiecho gradient echo, FLAIR, and multiecho complex total field inversion (mcTFI) at 3 T. McTFI with and without CSF zero-referencing regularization was generated from the 3DMEGRE data and reviewed with FLAIR images. Regions of hemorrhagic (H+) and nonhemorrhagic (H-) CSF were manually selected in reference to head CT and FLAIR images by a PGY III diagnostic radiology resident and Certificate of Added Qualification-certified neuroradiologist with 10 years' experience. Paired Student t test and one-way ANOVA were used with post hoc multicomparisons. A P value <0.05 was considered statistically significant. Areas of H- CSF were noted to have higher regularized QSM values in subjects with ICH relative to subjects without. Unregularized H- QSM values were also noted to have a systematically higher value in ICH subjects relative to subjects without blood. Subjects with MS and without ICH did not show significant difference in H- CSF regularized or unregularized QSM values. QSM values of areas suggested to not have hemorrhage on other imaging showed significantly higher QSM values in ICH subjects relative to subjects without ICH. Additionally, areas of hemorrhage did not show significant QSM value difference between regularized and unregularized QSM images. These findings suggest that, in subjects with any area of ICH, QSM values for no-hemorrhagic areas may be significantly altered using CSF regularization relative to subjects without ICH, with implications for intra- and intersubject QSM value analysis.

An existence theorem for generalized Abelian Higgs equations and its application

In this note, we construct self-dual vortices and cosmic strings from the generalized Abelian Higgs theory in which the Higgs potential is a polynomial whose degree depends on the number m . When | m | &gt; 0 , we obtain sharp existence theorems for vortices and strings corresponding to the absence and presence of gravity, respectively, over the whole plane. In the absence of gravity, we prove the existence of vortices by using a monotone iteration method. When gravity is taken into account, a regularization method and a fixed-point theorem are used to show that multiple string solutions exist under a sufficient condition imposed only on the total number of strings. In addition, a series of properties with respect to vortices and strings have also been established.

Backpropagation-Based Learning Techniques for Deep Spiking Neural Networks: A Survey.

With the adoption of smart systems, artificial neural networks (ANNs) have become ubiquitous. Conventional ANN implementations have high energy consumption, limiting their use in embedded and mobile applications. Spiking neural networks (SNNs) mimic the dynamics of biological neural networks by distributing information over time through binary spikes. Neuromorphic hardware has emerged to leverage the characteristics of SNNs, such as asynchronous processing and high activation sparsity. Therefore, SNNs have recently gained interest in the machine learning community as a brain-inspired alternative to ANNs for low-power applications. However, the discrete representation of the information makes the training of SNNs by backpropagation-based techniques challenging. In this survey, we review training strategies for deep SNNs targeting deep learning applications such as image processing. We start with methods based on the conversion from an ANN to an SNN and compare these with backpropagation-based techniques. We propose a new taxonomy of spiking backpropagation algorithms into three categories, namely, spatial, spatiotemporal, and single-spike approaches. In addition, we analyze different strategies to improve accuracy, latency, and sparsity, such as regularization methods, training hybridization, and tuning of the parameters specific to the SNN neuron model. We highlight the impact of input encoding, network architecture, and training strategy on the accuracy-latency tradeoff. Finally, in light of the remaining challenges for accurate and efficient SNN solutions, we emphasize the importance of joint hardware-software codevelopment.

Numerical prediction of passive speed and performance for multistage pump without power drive in natural flow process

With the development of engineering applications and the increase in system complexity, some particular fields, such as liquid rocket engine turbopumps, aircraft engine fuel systems, and marine natural flow cooling systems, are increasingly focusing on the performance characteristics of pumps under natural flow conditions. The pump is in the form of resistance components under natural flow conditions without a power drive. The impeller undergoes passive rotation by the impact of inlet flow. Due to the specificity of its operating conditions and performance indicators, the pump's natural flow performance cannot be evaluated by regular methods. Therefore, this paper proposed a numerical prediction method for pump natural flow performance based on a coupled computational fluid dynamics coupled with six-degrees-of freedom model. The performance of a multistage pump with guide vanes was evaluated under different natural flow conditions, and the accuracy was verified by experimental measurements. The transient variation mode of pump performance parameters with time at the initial stage of natural flow impact was analyzed. The flow field's transient evolution characteristics and the wall shear stress variation during natural flow were investigated. It was found that the impeller's passive rotational speed increases linearly with the natural flow rate, while the hydraulic loss shows an exponentially increasing trend. Meanwhile, the natural flow loss coefficient shows an exponentially decreasing trend and gradually tends to a stable value. The high turbulent kinetic energy inside the impeller is mainly distributed in the flow separation region and large velocity gradients. The distribution of shear stresses is closely related to the flow behavior inside the pump and the geometrical features of the hydraulic components.

Solutions for a flame propagation model in porous media based on Hamiltonian and regular perturbation methods

This article extends the exploration of solutions to the issue of flame propagation driven by pressure and temperature in porous media that we introduced in earlier papers. We continue to consider a p-Laplacian type operator as a mathematical formalism to model slow and fast diffusion effects, that can be given in the non-homogeneous propagation of flames. In addition, we introduce a forced convection to model any possible induced flow in the porous media. We depart from previously known models to further substantiate our driving equations. From a mathematical standpoint, our goal is to deepen in the understanding of the general behavior of solutions via analyzing their regularity, boundedness, and uniqueness. We explore stationary solutions through a Hamiltonian approach and employ a regular perturbation method. Subsequently, nonstationary solutions are derived using a singular exponential scaling and, once more, a regular perturbation approach.

A hybrid approach for power quality event identification in power systems: Elasticnet Regression decomposition and optimized probabilistic neural networks

The transformation of traditional grid networks towards smart-grid and microgrid concepts raises many critical issues, and quality in the power supply is one of the prominent ones that needs further research. Developing and applying power quality (PQ) recognition methods with efficient and reliable analysis are essential to the fast-growing issues related to modern smart power distribution systems. In this regard, a hybrid algorithm is proposed for PQ events detection and classification using Elasticnet Regression-based Variational Mode Decomposition (ER-VMD) and Salp Swarm Algorithm optimized Probabilistic Neural Network (SSA-PNN). The Elasticnet Regression (ER) process is suggested to modify the conventional VMD approach instead of the Tikhonov Regularization (TR) method to enhance performance and obtain better band-limited intrinsic mode functions. This idea results in robust and effective reconstruction features and helps to obtain accurate classification using the classifier. In the classification stage, a Salp Swarm Algorithm (SSA) based PNN is used for the PQ event, considering the relevant features obtained from ER-VMD. The system parameters often influence PNN performance, and SSA is used to determine the ideal values to improve the PNN's capacity for more accurate classification. The numerical values of the accuracy percentage, percentage of sensitivity, and percentage of specificity in the case of real-time data are found as 98.58, 100, and 98.46, respectively. The acquired comparison findings demonstrate the effectiveness and robustness of the proposed technique in terms of rapid learning speed, smaller computational complexity, robust performance for anti-noise conditions, and accurate identification and categorization.

A Novel Truncated Norm Regularization Method for Multi-Channel Color Image Denoising

A Novel Truncated Norm Regularization Method for Multi-Channel Color Image Denoising

A fast identification method of surface heat flux based on numerical pre-calibration and regularization

Abstract Identification of surface heat flux is a technique of retrieving heat flux from the measured temperature in an object. The inverse heat conduction problem abbreviated as IHCP is ill-posed, and its highly ill-conditioned characteristics lead to unstable numerical calculation. In this paper, we build an identification equation with the theory of linear superposition. The matrix of pulse sensitivity coefficient is established by formula for one-dimensional model. And a finite element pre-calibration approach is proposed to obtain the matrix of pulse sensitivity coefficient for complex three-dimensional structures. Regularization methods including Tikhonov method and algebraic reconstruction technique are utilized to reduce the sensitivity of measurement error. Numerical simulation shows that this method is efficient and accurate.