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In this paper, we propose a novel convex combination algorithm based on the distributed diffusion strategy, utilizing the least mean square (LMS) approach to enhance the performance of sensor networks. By enabling communication among nodes, the algorithm achieves decentralization and improves the robustness of the network. To address the limitations of slow convergence speed and large static error associated with fixed step size errors, we introduce a convex combination strategy that integrates two filters with variable step sizes. The LMS algorithm with the convex combination variable step size assigns a higher weight to the filter with a larger step size when the error is significant, ensuring rapid convergence. Conversely, the convex combination small step size filter is assigned a higher weight when the error is small, reducing the error in the stable state. The convergence behavior of the proposed algorithm is analyzed through theoretical analysis, and its complexity is compared with that of the distributed diffusion LMS algorithm through extensive experimental simulations. The results demonstrate that the combination of the LMS algorithm with the distributed diffusion strategy offers advantages in challenging external environments, including improved convergence speed and reduced stability error. This study makes significant contributions to the existing research field by introducing a novel convex combination algorithm that addresses the shortcomings of fixed step size errors and expands the range of available algorithms. By leveraging the distributed diffusion strategy, our approach enhances the robustness of sensor networks and achieves improved performance. The findings of this study provide valuable insights for researchers working on decentralized algorithms and highlight the potential of combining the LMS algorithm with the distributed diffusion strategy in challenging environmental conditions. [ABSTRACT FROM AUTHOR]

Proximal alternating direction method of multipliers (PADMM) is a classical primal-dual splitting method for solving separable convex optimization problems with linear equality constraints, which have numerous applications in, e.g., signal and image processing, machine learning, and statistics. In this paper, we propose a new variant of PADMM, called PADMC, whose proximal centers are constructed by convex combinations of the iterates. PADMC is able to take advantage of problem structures and preserves the desirable properties of the classical PADMM. We establish iterate convergence as well as (1 / K) ergodic and (1 / K) nonergodic sublinear convergence rate results measured by function residual and feasibility violation, where K denotes the iteration number. Moreover, we propose two fast variants of PADMC, one achieves faster (1 / K 2) ergodic convergence rate when one of the component functions is strongly convex, and the other ensures faster (1 / K) nonergodic convergence rate measured by constraint violation. Finally, preliminary numerical results on the LASSO and the elastic-net regularization problems are presented to demonstrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address these issues. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters' step sizes, we propose a novel variable mixing-norm method, BC-SNQNLM-VMN, to accelerate the convergence of our BC-SNQNLM algorithm. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state. [ABSTRACT FROM AUTHOR]

In this paper, an improved high-speed adaptive filter is proposed and implemented using a field-programmable gate array platform. Specifically, a new filter structure combining systolic and convex architectures has been analyzed and compared with conventional filter architectures. The new filter structure efficiently removes power line interference noise from electrocardiogram signals at high convergence speeds. The systolic architecture is used to improve the convergence speed of the filter, and the convex architecture is used in combination to improve the signal-to-noise ratio of the filter. One fast filter was designed using the retimed delay recursive least square algorithm (recursive least square filter design with systolic architecture), and it was combined with one slow filter designed using the least mean square algorithm based on convex combination architecture. The proposed filter architectures are assessed for electrocardiogram noise cancellation, obtained from the MIT-BIH database, and the performance is compared with various filter structures in terms of the signal-to-noise ratio, convergence speed, learning behaviors, and complexity. The results show an improvement in signal-to-noise ratio of 24.2% and an increase in convergence speed of 50% when compared with conventional filter structures. [ABSTRACT FROM AUTHOR]

In our work, we introduced a distinct subclass of univalent harmonic functions referred to as a subclass of chiral functions. These functions are defined by combining the generalized Komatu operator with the integral operator (R - K), which has positive coefficients within the unit disc A. Also, we generalize the same subclass into neutrosophic complex numbers. Throughout our investigation, we establish several properties associated with these functions, including coefficient estimates, the convex formula, the integral operator, and the Hadamard product. On the other hand, we present the Neutrosophic convex formula and the neutrosophic integral operator. [ABSTRACT FROM AUTHOR]

Underwater acoustic channels often have to face the interference of impulsive noise, which is usually modeled by α-stable distribution in simulation experiments. To solve the problem of underwater acoustic channel estimation under impulsive noise, this paper proposes a convex combination–variable-step-size least mean p-norm algorithm. The algorithm incorporates a convex combination into the variable-step-size least mean p-norm algorithm and uses the convex combination of different convergence domains provided by changing the parameters of the Gaussian function to further improve the effect after convergence. The simulation results of channel estimation show that the convex combination–variable-step-size least mean p-norm algorithm provides a more stable, robust, and universal solution than the variable-step-size least mean p-norm algorithm. [ABSTRACT FROM AUTHOR]

The normalized subband adaptive filtering algorithm provides fast convergence rate for colored input signals as compared to the normalized least mean square algorithm, but it suffers from a poor convergence issue in the α -stable noise. In light of this, the normalized subband p-norm (NSPN) algorithm, which is based on the least mean p-power error (MPE) criterion, is proposed in this study. This technique is not only robust against impulsive noise samples, but it also maintains a fast convergence rate when colored input signals are used. In addition to this, we develop both the steady-state and the transient models of the NSPN algorithm and provide some insights. Then, in order to solve the problem of making a choice regarding the order p in the NSPN algorithm, we design an autonomous system and come up with the NSPN algorithm with a variable p-norm (VP-NSPN). In addition, we offer the TFC-based VP-NSPN algorithm with a fast convergence rate and low steady-state misadjustment simultaneously by making use of the tap-weights feedback-based convex combination (TFC) scheme. In conclusion, simulation results on system identification and acoustic echo cancellation are undertaken in order to validate the superiority of the proposed algorithms and validate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

We know many conjugate gradient algorithms (CG) for solving unconstrained optimization problems. In this paper, based on the three famous Liu–Storey (LS), Fletcher–Reeves (FR) and Polak–Ribiére–Polyak (PRP) conjugate gradient methods, a new hybrid CG method is proposed. Furthermore, the search direction satisfies the sufficient descent condition independent of the line search. Likewise, we prove, under the strong Wolfe line search, the global convergence of the new method. In this respect, numerical experiments are performed and reported, which show that the proposed method is efficient and promising. In virtue of this, the application of the proposed method for solving regression models of COVID-19 is provided. [ABSTRACT FROM AUTHOR]

Conventional adaptive filters for active noise control (ANC) are troubled by the trade-off between convergence speed and steady state error, especially when nonlinearity plays an important role in system model. In this paper, a hybrid ANC algorithm called FBFLANN is constructed by the collaboration of FIR and bilinear functional link artificial neural network. The characteristics of linear and nonlinear sub-filters are analyzed and utilized to facilitate the adaptability in noise reduction. A convex factor is employed to automatically balance the contribution of two sub-filters, achieving faster convergence and higher accuracy in the presence of nonlinear distortions. The mathematical working and updating rules of the controller are derived to regulate the ANC process theoretically. The effectiveness of the proposed FBFLANN algorithm is demonstrated by numerous simulation studies considering diverse nonlinear acoustic path models as well as acoustic feedback interference. Hardware ANC platform is built up to verify the real-time noise control performance in physical noisy environments. The simulation and experiment results confirm the applicability and prospects for further development of the presented architecture in noise control scenarios. [ABSTRACT FROM AUTHOR]

The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information-that is otherwise collapsed by the aggregated ranking-into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition. [ABSTRACT FROM AUTHOR]

With the aid of 𝑞-calculus, this paper introduces a new generalized p𝑝, 𝑞q-Bernardi integral operator ℬ^𝑝 𝑛,𝑞𝑓p𝑧q. Then, we define a new subclass of harmonic p𝑝, 𝑞q-starlike functions of complex order associated with the operator ℬ^𝑝 𝑛,𝑞𝑓p𝑧q. For this new subclass, a necessary and sufficient condition, compact and convex combination theorems, a distortion theorem, and extreme points are investigated. Finally, we discuss the weight mean theorem for functions belonging to this class. This research highlights the significant connections between the results presented in this study and previous works.

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address these issues. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters’ step sizes, we propose a novel variable mixing-norm method, BC-SNQNLM-VMN, to accelerate the convergence of our BC-SNQNLM algorithm. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.

This paper proposes to use the convex combination of several kernel estimators based on the ranked set sampling (RSS) scheme for estimating the underlying distribution function to construct more efficient quantiles estimation. Several different estimators of quantile function based on the simple random sampling and ranked set sampling are provided. The variance and mean-squared error of the proposed estimators are derived as explicit forms. Theoretical derivation and an intensive simulation study are used to compare the performance of the proposed method with other methods in the literature. The effect of imperfect rankings on the performance of the proposed estimators is investigated. Real data example from the China Health and Nutrition Survey is used to illustrate our proposed approach. Some discussions using another two real data are presented. It observes that the proposed estimators have different behaviours with respect to symmetric and asymmetric distributions. [ABSTRACT FROM AUTHOR]

The question of which elements of the open unit disc occur as eigenvalues of n-by-n doubly stochastic matrices has long been open, in spite of a number of intriguing partial results. By enhancing a natural, but slightly false, conjecture, we gain some new computational insights into the problem. We also apply the classical field of values to give some partial results on both the necessity of certain component polygons of P M n for other cycle lengths and the accuracy of the Perfect-Mirsky Conjecture in the neighborhoods of corners. [ABSTRACT FROM AUTHOR]

This paper studies the challenging issue of how to guarantee dwell-times of a state-dependent hysteresis switching law for switched nonlinear systems. The classical convex combination condition is utilized to construct buffer-regions. In the buffer-regions, by virtue of Lie derivative of the induced single Lyapunov function along the active vector field, the position of state at the switching instant and the evolution of state during the active interval are captured in a uniformly quantitative form via switching characteristic indices for the first time. These uniform indices are revealed as the essential attribute by which the dwell-times of hysteresis switching are guaranteed. Meanwhile, the dwell-times are associated with subsystems and can be adjusted by an introduced parameter, which ensures the adjustable multiple dwell-times for every subsystem, rather than one dwell-time for the whole systems. Moreover, for switched linear systems, the explicit expression of multiple dwell-times is obtained by using the convex condition with respect to system matrices and independent of dwell-times. A numerical example substantiates the effectiveness. [ABSTRACT FROM AUTHOR]

Negation is absolutely essential in all conversations that allows for denial, contradiction and other countering aspects of human linguistic systems. Intuitively, the negative sentences are less informative and less specific than the affirmative ones. In other words, it has more uncertainty embedded in it. If an event is uncertain, negating it will require some sort of probabilistic formulation. Yager (IEEE Trans Fuzzy Syst 25:1899–1902, 2015) gave a probabilistic definition of negation of a probability distribution based on unbiased distribution of probabilities. In the present work, a generalization of negation based on the concept of biased distribution is proposed. Some numerical examples have been discussed for determining the validity and efficacy of the proposed generalization. Finally an application in medical diagnosis has been considered. [ABSTRACT FROM AUTHOR]

Over the last twenty years, combination of adaptive filters has emerged to provide a potential solution in the development of advanced applications, such as channel equalization, active noise control, acoustic echo cancelation, adaptive beamforming, among others. Several authors have demonstrated that the combination of two filters with complementary capabilities improves the overall filter performance in comparison when a single filter is used. Commonly, these combinations employ a fast filter and slow filter to guarantee fast convergence speed and low steady-state mean square error (MSE), respectively, at the cost of increasing their computational complexity. However, those combinations have not been well analysed and compared. Currently, this aspect is crucial since most of the current convex combination of adaptive filters could be implemented in advanced embedded digital devices to be used in real-time signal processing applications. In this work, we evaluate the convex combination of adaptive filters, mainly including those based on least mean square (LMS) algorithm, the affine projection (AP) algorithm and the recursive least mean square (RLS) algorithm. We carry out an extensive performance evaluation to demonstrate the advantages and disadvantages of each approach. Specifically, we simulate them in fixed point, which makes feasible the rapid development of advanced prototypes. This aspect could be potentially valuable to the signal processing engineering communities. [ABSTRACT FROM AUTHOR]

Deep learning has been successfully exploited to various computer vision tasks, which depend on abundant annotations. The core goal of few-shot learning, in contrast, is to learn a classifier to recognize new classes from only a few labeled examples that produce a key challenge of visual recognition. However, most of the existing methods often adopt image-level features or local monodirectional manner-based similarity measures, which suffer from the interference of non-dominant objects. To tackle this limitation, we propose a Bi-Directional Local Alignment (BDLA) approach for the few-shot visual classification problem. Specifically, building upon the episodic learning mechanism, we first adopt a shared embedding network to encode the 3D tensor features with semantic information, which can effectively describe the spatial geometric representation of the image. Afterwards, we construct a forward and a backward distance by exploring the nearest neighbor search to determine the semantic region-wise feature corresponding to each local descriptor of query sets and support sets. The bi-directional distance can encourage the alignment between similar semantic information while filtering out the interference information. Finally, we design a convex combination to merge the bi-directional distance and optimize the network in an end-to-end manner. Extensive experiments also show that our proposed approach outperforms several previous methods on four standard few-shot classification datasets. [ABSTRACT FROM AUTHOR]

Recently, a golden ratio primal-dual algorithm (GRPDA) was proposed by Chang and Yang for solving structured convex optimization problems. It is a new adaptation of the classical Arrow-Hurwicz method by using a convex combination step, instead of the widely adopted extrapolation technique. The convex combination step is determined by a parameter ψ , which, to guarantee global convergence, is restricted to (1 , (1 + 5) / 2 ] . In this paper, by carrying out a refined analysis, we expand this region to (1 , 1 + 3) . Moreover, we establish ergodic sublinear convergence rate results based on function value residual and constraint violation of an equivalently reformulated constrained optimization problem, rather than the previously adopted so-called primal-dual gap function that could vanish at nonstationary points. For linear equality constrained and regularized least-squares problems, we further show that GRPDA and Chambolle-Pock’s primal-dual algorithm are equivalent provided that some parameters are chosen properly. Finally, experimental results on the LASSO and the basis pursuit problems are presented to demonstrate the performance of GRPDA with ψ being chosen in the expanded region. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to enhancing color images by modifying an affine color assignment function. This function maps colors to pixels of the enhanced gray-scale image in a way that improves the visual quality of the image, particularly in darker regions. The main goal of our method is to finely adjust saturation, correct saturation loss in specific image regions, and preserve the original image's range and hue. Our proposed method follows a two-step process. First, it enhances the intensity image using a combination of global and local histogram equalization methods. This results in an overall improved appearance by redistributing pixel intensities and enhancing contrast. Then, modified color mapping functions are applied to assign colors to each pixel of the enhanced gray-scale image. The aim is to adjust saturation by amplifying the maximally saturated color image. Additionally, we introduce two new color-weighted maps to evaluate pixel importance from the maximally saturated image. This contributes to saturation control in the final enhanced image. Compared to alternative color mapping algorithms, our model preserves the original color of pixels in challenging areas and fine-tunes saturation based on parameter settings. • Our method uses affine mapping to modify saturation and compensate for losses. • New color mapping technique improves image quality, especially in dark regions. • Modified color assignment step allows precise saturation control and range preservation. [ABSTRACT FROM AUTHOR]

The model of stochastic volatility with contemporaneous jumps is written for pricing under a partial integro-differential equation (PIDE) having a double integral and a nonsmooth initial value. To tackle this problem, first, a new radial basis function (RBF) as a convex combination of two known RBFs is given. Second, the weighting coefficients of the RBF generated finite difference (FD) method are contributed and the associated error equations are derived. To deal with the integral part, the new idea is to apply an estimate for the unknown function for every cell and do an integration of the density function. The contributed approach is competitive and reduces both the calculational efforts and elapsed time. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods (CG) are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new conjugate gradient method for unconstrained optimization. This method is a convex combination of Fletcher and Reeves (abbreviated FR), Polak–Ribiere–Polyak (abbreviated PRP) and Dai and Yuan (abbreviated DY) methods. The new conjugate gradient methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for this method. The numerical experiments are done to test the efficiency of the proposed method, which confirms its promising potentials. [ABSTRACT FROM AUTHOR]

Global quadratic stability and L 2 performance in probability (quadratic stability and L 2 gain γ in probability: abbreviated as GQ L 2 (γ) -P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQ L 2 (γ) -P, it is shown that if there exists a convex combination of subsystems achieving GQ L 2 (γ) -P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQ L 2 (γ) -P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm. [ABSTRACT FROM AUTHOR]

• TF-FxLMS algorithm is introduced to reduce the computational complexity of the traditional convex combination algorithm. • Matrix-decomposition-based structure is introduced to further reduce the computational complexity. • Compared with the traditional algorithms, the proposed algorithm can improve the performance of noise reduction. Convex combination schemes with fast tracking ability and good steady-state restoration performance have attracted wide attention in Active Noise Control (ANC) systems. The scheme can combine the outputs of multiple filters. However, the time domain filter-X least mean square (FxLMS) algorithm used in traditional convex combination structure has the problem of high computational complexity. Compared with the conventional FxLMS algorithm, the time–frequency domain FxLMS (TF-FxLMS) algorithm can compute gradient estimates and filter reference signals in the frequency domain to reduce the computation. Since the algorithm is a block processing of the signal in the frequency domain, the presence of the fast fourier transform (FFT) introduces unwanted delays which causes the rate of convergence to slow down. FFT operations should be performed at a sampling interval, which limits the real-time implementation of the algorithm. In order to reduce the computational complexity of traditional convex combination and improve the performance of the algorithm, a convex combined structure algorithm of normalized filter-X least mean square (NFxLMS) algorithm and TF-FxLMS algorithm is proposed in this paper. In addition, in order to further reduce the amount of computation, the NFxLMS algorithm is decomposed into NFxLMS algorithm and TF-FxLMS algorithm by means of partial updating of weight matrix. In this paper, the computational complexity of the proposed algorithm is analyzed and compared with the traditional algorithm. The simulation results show that the proposed algorithm has better noise reduction effect than the traditional algorithm under the noise input conditions of various driving conditions. At the same time, it has the advantage of lower computational complexity. [ABSTRACT FROM AUTHOR]

Meta-learning methods try to enhance the generalization of the meta-learning model by various tasks. Diverse tasks can provide sufficient knowledge to assist the model in understanding and capturing different types of information. The sufficient number of meta-training tasks is a crucial factor in ensuring the generalization of meta-learning algorithms. However, obtaining a sufficient number of labeled meta-training tasks is often a challenging endeavor in real-world scenarios. Some scholars have addressed the issue of inadequate tasks only by interpolating between two tasks, but they do not take into account the problem of task diversity. To resolve this concern, we propose a Multi-task Convex Combination Interpolation (MCCI) method that simultaneously considers both task quantity and task diversity issues. First, we increase the number of tasks based on interpolation techniques, which provides the possibility to extend it from 2-task interpolation to n -task interpolation. Second, we randomly select multiple tasks and perform convex combination interpolation in the n -task space, in order to increase the task diversity. Third, we prove the positive effect of the convex combination interpolation on the generalization ability and noise resistance of meta-learning algorithms in theory. Finally, we verify the generalization ability and noise resistance of the proposed MCCI on seven datasets. The extensive experimental results show the superior performance of the proposed method compared to the state-of-art methods. • The MCCI method expands interpolation space to increase task diversity. • Theoretically prove the MCCI method enhances generalization and robustness. • Validate MCCI method effectiveness across seven datasets. [Display omitted] [ABSTRACT FROM AUTHOR]

Dempster-Shafer theory (DST) and multi-criteria decision-making are widely applied mathematical tools in decision-making, though DST has some limitations in evidence fusion rule. The issues in evidence fusion are addressed through the development of combination rules, pre-processing of evidence, and generalization of evidence into interval-valued or intuitionistic belief degree. In this paper, a more flexible belief degree called the q-rung evidence set is introduced to solve the issues of standard belief degrees. Moreover, fusion of group decision-maker's belief degrees using a single fusion rule is a possible case of conflict among them. In this regard, we have employed the convex combination of two rules with different weights to generate a consensus among the decision-makers. A new aggregation method is devised to integrate the assessment of decision-maker based on the q-rung evidence set, convex combination rule, and a new score function. We have used a hypothetical case study in multi-criteria group decision-making problem for solving the patient's treatment preference problem in medical diagnosis to validate the proposed technique. The suggested technique successfully ranks the four alternatives with the comparison to the former aggregation method. [ABSTRACT FROM AUTHOR]

The literature has demonstrated that firms in the same network exhibit significant peer effects, but barely from the perspective of multiple networks. Using a novel spatial econometric model with convex combinations of multiple weight matrices, we investigate the peer effects with multifaceted network dependence structures in Chinese listed firms' R&D investment decisions, and the underlying mechanism as well as the economic consequences. Our main conclusions include: (1) A firm's R&D investment is mostly affected by its industry peer firms, followed by those with similar technical and financial characteristics, and geographical peer firms are negligible. (2) The intensity of peer effects is significantly affected by the degree of information incompleteness and market competition. (3) A firm's R&D investment can benefit its performance in the short run, while peer firms' R&D investments would inhibit its performance after a period of time. The research can provide practical guidance for market participants and regulators. [Display omitted] • We explore the peer effects in firms' R&D investment decisions with multifaceted network dependence structures. • A firm's R&D investment is mostly affected by its industry peer firms. • The intensity of peer effects is significantly affected by the degree of information incompleteness and market competition. • A firm's R&D investment can benefit its performance in the short run. • A firm's performance would be inhibited by peer firms' R&D investments after a period of time. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) employs a large antenna array and is used as a key technology in 5G communication standards. In this work, time-division duplex (TDD) is used for uplink (UL) and downlink (DL) channels as the same bandwidth can be utilized for bidirectional data transfer. This paper proposes a computationally efficient adaptive algorithm based channel estimation model. These models are applicable to multiuser MIMO (MU-MIMO) systems, which are comprised of a large number of channel coefficients. Channel state information (CSI) is acquired from estimated channel coefficients of the UL channel, and CSI of DL is obtained through channel reciprocity. The dynamic characteristics of MIMO channels are generally sparse in nature, and the degree of sparseness varies over time. Convex combination-based modeling with the introduction of l0 norm penalty to Least mean squares (LMS) algorithm develops an efficient and stable sparse channel estimation model, which is the most significant contribution of the paper. The research work presented in the paper has simultaneously focused on channel estimation using the convex combination of momentum-fractional LMS approach and equalization for massive MIMO channels. The simulation result exhibits that the proposed method outperforms the existing conventional compressed sensing (CS) based channel estimation. The UL and DL performance of the system was investigated in terms of bit error rate (BER), mean square error (MSE), and channel capacity calculated from estimated CSI. [ABSTRACT FROM AUTHOR]

Filtered‐x least mean square (FxLMS) algorithm and its variants have been prevalently applied in the field of active noise control. However, these algorithms still suffer from relatively low convergence rates and steady‐state noise reduction. In this article, we propose a new idea to improve the performance of the conventional filtered‐x least mean square/fourth (FxLMS/F) algorithm by weighting reference signal samples, thus a weighted reference signal FxLMS/F (WRS‐FxLMS/F) algorithm is presented. Besides, to solve the contradiction between convergence speed and steady‐state noise reduction, the convex combination method is combined with the WRS‐FxLMS/F algorithm, and a convex combination WRS‐FxLMS/F (CWRS‐FxLMS/F) algorithm is developed. The computational complexity of the proposed algorithms is analyzed, and the simulation results demonstrate that the proposed algorithms have better performance both in the steady‐state noise reduction and convergence rate than the traditional FxLMS, NFxLMS, and FxLMS/F algorithm. [ABSTRACT FROM AUTHOR]

The exponential sampling synchronization of complex network systems based on T–S fuzzy model is studied in this paper. Firstly, a modified Lyapunov–Krasovskii function (LKF) is designed. The linear matrix inequalities in the synchronization criterion are obtained by combining the efficient integral inequality and the free weighting matrix while processing the LKF differential results. Secondly, on the basis of Theorem 1, the full consideration of the interference caused by the time delay phenomenon in the actual production life, theorem 2 will fully solve this problem. The time delay is added during the sampling process, and the resulting synchronization criterion makes the system have better anti-interference performance than the original system. Finally, in the simulation part, two numerical simulations are proposed to verify the correctness and practical applicability of the obtained synchronization criterion. [ABSTRACT FROM AUTHOR]

Utilization of classification latent space information for downstream reconstruction and generation is an intriguing and a relatively unexplored area. In general, discriminative representations are rich in class specific features but are too sparse for reconstruction, whereas, in autoencoders the representations are dense but has limited indistinguishable class specific features, making it less suitable for classification. In this work, we propose a discriminative modelling framework that employs manipulated supervised latent representations to reconstruct and generate new samples belonging to a given class. Unlike generative modelling approaches such as GANs and VAEs that aim to model the data manifold distribution, Representation based Generations (ReGene) directly represents the given data manifold in the classification space. Such supervised representations, under certain constraints, allow for reconstructions and controlled generations using an appropriate decoder without enforcing any prior distribution. Theoretically, given a class, we show that these representations when smartly manipulated using convex combinations retain the same class label. Furthermore, they also lead to novel generation of visually realistic images. Extensive experiments on datasets of varying resolutions demonstrate that ReGene has higher classification accuracy than existing conditional generative models while being competitive in terms of FID. [ABSTRACT FROM AUTHOR]

This paper reviews some aspects of simplicial complexes. The aspects reviewed in this paper are very key in building undoubtedly strong concept as reviewed on simplicial complexes. The aspects reviewed take into a consideration: how simplices are used to construct simplicial complexes. Key areas covered at the preliminary part of this paper are simplices, face of a simplex, more on facet of a simplex, orientation of simplices, boundary of simplices, interior of a simplex etc. Geometric objects such as points, edges, triangles and tetrahedrons were the materials used in constructing simplicial complexes. We also looked at the geometric realization theorem, skeleton of simplicial complexes, maximal elements and free face, theorems under simplicial complexes and creation of simplicial complexes. At the results and discussion part, Betti numbers and Euler characteristic of simplicial complexes were computed and chimed in with real life examples. The paper was finalized by chipping in some applications of simplicial complexes. In all, the paper has opened up more and interesting study into simplicial complexes and algebraic topology at large. [ABSTRACT FROM AUTHOR]

In this article, some Bohr-type inequalities with one parameter or involving convex combination for bounded analytic functions of Schwarz functions are established. Some previous inequalities are generalized. All the results are sharp. [ABSTRACT FROM AUTHOR]