Network slices (NSs) are managed through a hierarchical architecture in recent 5G standards. Each NS is formed by connecting autonomously managed network slice subnets (NSSs) across the 5G network domains. To provision a new NS, users specify NS requirements as a network slice request (NSR). The NSR is decomposed into requirements for each NSS, and resources in each domain are allocated. This NSR decomposition is crucial as the selected decomposition affects resource usage and, ultimately, the total number of successfully provisioned NSs. Although several methods address NSR decomposition, most rely either on (i) detailed knowledge of domain-specific resource allocation mechanisms or (ii) extensive historical NS operational data. In practice, however, each domain’s internal processes act as "black boxes" in the hierarchical NS management architecture, making it infeasible to acquire detailed resource allocation algorithms. Additionally, historical data may be insufficient because network slicing remains an emerging technology. These limitations hinder the direct application of existing methods to real operational 5G networks. In this paper, we propose a multi-armed bandits (MABs)-based optimization method that formulates the NSR decomposition as a linear contextual bandits with knapsacks (linCBwK) problem and sequentially acquires the optimal decomposition policy. A MABs-based optimization approach enables us to avoid the need for domain-internal knowledge or extensive pre-collected training data. Simulations demonstrate that our method increases the total number of successfully provisioned NSs by 16.0% compared to the baseline method.

A complex-valued Hopfield neural network (CHNN) has weak noise tolerance due to rotational invariance. Some alternatives of CHNN, such as a rotor Hopfield neural network (RHNN) and a matrix-valued Hopfield neural network (MHNN), resolve rotational invariance and improve the noise tolerance. However, the RHNN and MHNN with projection rules have a different problem of self-feedbacks. If the self-feedbacks are reduced, the noise tolerance is expected to be improved further. For reduction in the self-feedbacks, the noise-robust projection rules are introduced. The stability conditions are extended, and the self-feedbacks are reduced based on the extended stability conditions. Computer simulations support that the noise tolerance is improved. In particular, the noise tolerance is more robust against an increase in the number of training patterns.

The coronavirus disease 2019 (COVID-19) pandemic has spread across the globe from the beginning of 2020 and people worldwide have been receiving news about the same from government offices, press conferences and various other media outlets. The COVID-19 Information Watcher Project started in 2020 to collect and organize reliable information sources worldwide. However, it is difficult to automatically identify reliable information sources in foreign countries for several reasons. First, what kind of information sources are reliable heavily depend on each county situation. In some countries people trust their government’s official information but in other countries they do not. Secondly, such reliable information sources often provide information in their local languages. Reliable information sources are not necessarily top-ranked by search engines. Crowdsourcing is a promising way to deal with such a case. However, crowd-sourcing platforms do not cover crowds in all countries. In this study, we report some results of our attempt to collect local information regarding COVID-19 from several countries through multi-hop crowdsourcing, in which we allow crowd workers on a crowdsourcing platform to use other platforms in other countries. We show two case studies, Russia and Afghanistan. Our results show that the multi-hop crowdsourcing is a promising way to collect COVID-19 information from different countries.

This paper addresses the problem of dynamically assigning tasks to a crowd consisting of AI and human workers. Currently, crowdsourcing the creation of AI programs is a common practice. To apply such kinds of AI programs to the set of tasks, we often take the ``all-or-nothing'' approach that waits for the AI to be good enough. However, this approach may prevent us from exploiting the answers provided by the AI until the process is completed, and also prevents the exploration of different AI candidates. Therefore, integrating the created AI, both with other AIs and human computation, to obtain a more efficient human-AI team is not trivial. In this paper, we propose a method that addresses these issues by adopting a ``divide-and-conquer'' strategy for AI worker evaluation. Here, the assignment is optimal when the number of task assignments to humans is minimal, as long as the final results satisfy a given quality requirement. This paper presents some theoretical analyses of the proposed method and an extensive set of experiments conducted with open benchmarks and real-world datasets. The results show that the algorithm can assign many more tasks than the baselines to AI when it is difficult for AIs to satisfy the quality requirement for the whole set of tasks. They also show that it can flexibly change the number of tasks assigned to multiple AI workers in accordance with the performance of the available AI workers.

Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a multistate neural associative memory. However, the stability conditions have been insufficient for the projection rule. In this work, the stability conditions are extended and applied to improvement of the projection rule. The computer simulations suggest improved noise tolerance.

Multistate Hopfield models, such as complex-valued Hopfield neural networks (CHNNs), have been used as multistate neural associative memories. Quaternion-valued Hopfield neural networks (QHNNs) reduce the number of weight parameters of CHNNs. The CHNNs and QHNNs have weak noise tolerance by the inherent property of rotational invariance. Klein Hopfield neural networks (KHNNs) improve the noise tolerance by resolving rotational invariance. However, the KHNNs have another disadvantage of self-feedback, a major factor of deterioration in noise tolerance. In this work, the stability conditions of KHNNs are extended. Moreover, the projection rule for KHNNs is modified using the extended conditions. The proposed projection rule improves the noise tolerance by a reduction in self-feedback. Computer simulations support that the proposed projection rule improves the noise tolerance of KHNNs.

Dual connections (DCs) utilize the noncommutativity of quaternions and improve the noise tolerance of quaternion Hopfield neural networks (QHNNs). In this article, we introduce DCs to twin-multistate QHNNs. We conduct computer simulations to investigate the noise tolerance. The QHNNs with DCs were weak against an increase in the number of training patterns, but they were robust against increased resolution factor. The simulation results can be explained from the standpoints of storage capacities and rotational invariance.

A rotor Hopfield neural network (RHNN) is an extension of a complex-valued Hopfield neural network (CHNN) and has excellent noise tolerance. The RHNN decomposition theorem says that an RHNN decomposes into a CHNN and a symmetric CHNN. For a large number of training patterns, the projection rule for RHNNs generates large self-feedbacks, which deteriorates the noise tolerance. To remove self-feedbacks, we propose a projection rule using quaternions based on the decomposition theorem. Using computer simulations, we show that the quaternion projection rule improves noise tolerance.

In multistate neural associative memories, some neurons have small noise and the others have large noise. If we know which neurons have small noise, the noise tolerance could be improved. In this brief, we provide a novel method to reinforce neurons with small noise and apply our new method to images with the Gaussian noise. A complex-valued multistate neuron is decomposed to two neurons, referred to as high and low neurons. For the Gaussian noise, the high neurons are expected to have small noise. The noise tolerance is improved by reinforcement of high neurons. The computer simulations support the efficiency of reinforced neurons.

At disaster response, it is essential to grab whole picture of damage situation quickly and early after disaster occurrence in order to make disaster response effective and efficient. However, it takes much time to understand damage situation because there is not enough information about it. Against this issue, we proposed implementation of CyborgCrowd for situation awareness in disaster response. In order to validate its possibility, we planned the first international disaster drill in October, 2019. In this drill, we simulated to detect flooded area by West Japan Flood occurred in 2018 from aerial photos by collaboration between crowdsourcing and AIs following Human-in-the-Loop process. Especially, in this drill, AIs were also crowdsourced. In this research, we validated the transition of the efforts from crowdsourcing and AIs to detecting flooded area, and verified the accuracy of result by comparing with the actual flooded area published by Geospatial Information Authority of Japan. Furthermore, we found some suggestion about features of detection results by humans and AIs. For example, some humans detected flooded area roughly, however AIs detected it much closely. Based on those features, we proposed the way to decrease the difference between results by humans and AIs. This was essential for local responders to understand the whole picture of damage situation after disaster occurrence urgently. In this paper, we introduced the framework of international disaster drill, clarified the result of validation, and mentioned the possibility of effective collaboration between crowdsourcing and AIs for quick situation awareness in disaster response.

For most multistate Hopfield neural networks, the stability conditions in asynchronous mode are known, whereas those in synchronous mode are not. If they were to converge in synchronous mode, recall would be accelerated by parallel processing. Complex-valued Hopfield neural networks (CHNNs) with a projection rule do not converge in synchronous mode. In this work, we provide stability conditions for hyperbolic Hopfield neural networks (HHNNs) in synchronous mode instead of CHNNs. HHNNs provide better noise tolerance than CHNNs. In addition, the stability conditions are applied to the projection rule, and HHNNs with a projection rule converge in synchronous mode. By computer simulations, we find that the projection rule for HHNNs in synchronous mode maintains a high noise tolerance.

A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Computer simulations support that the noise tolerance of CHNN with a bicomplex projection rule is equal to or even better than that of quaternion- and bicomplex-valued Hopfield neural networks. By computer simulations, we find that the projection rule for hyperbolic-valued Hopfield neural networks in synchronous mode maintains a high noise tolerance.

A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. Low noise tolerance is the main disadvantage of CHNNs. The hyperbolic Hopfield neural network (HHNN) is a noise robust multistate Hopfield model. In HHNNs employing the projection rule, noise tolerance rapidly worsened as the number of training patterns increased. This result was caused by the self-loops. The projection rule for CHNNs improves noise tolerance by removing the self-loops, however, that for HHNNs cannot remove them. In this brief, we extended the stability condition for the self-loops of HHNNs and modified the projection rule. Thus, the HHNNs had improved noise tolerance.

The most typical approach today to data processing which does not have proven algorithms is to first request humans to provide labels to a small set of data and then develop artificial intelligences (AIs) with the data to perform all the remaining tasks. This development is sometimes crowdsourced through platforms such as Kaggle. The approach, however, is not always effective; if the AI does not meet the quality requirement, we may have to give up the development and all the data items have to be done manually. In order to avoid this all-or-nothing situation, “selective” AI programs that perform tasks which they are confident to do will be effective. This study addresses the problem of designing an incentive structure for crowdsourcing the development of such selective AI programs. This paper shows the results of our real-world experiment with a stair-step incentive structure and the behavior of a worker who developed the AI agent under the incentive. This paper also discusses the limitations of the proposed incentive design.

This paper reports the result of a preliminary experiment on active learning strategies for the hierarchical labeling microtasks. A typical example of hierarchical labeling microtask consists of a set of labeling tasks for partitions of a large image; starting from the whole image, the workers choose to give a label or divide it into smaller ones. This paper shows the result of an experiment to compare several strategies for active learning in the setting. The result suggests that the difference in the strategies affects the performance in the early stage.

In complex-valued Hopfield neural networks (CHNNs), the neuron states are complex numbers whose amplitudes are: 1) they can also be described in special orthogonal matrices of order and 2) here, we propose a new Hopfield model, the O(2) -valued Hopfield neural network [ O(2) -HNN], whose neuron states are extended to orthogonal matrices. Its neuron states are embedded in 4-D space, while those of CHNNs are embedded in 2-D space. Computer simulations were conducted to compare the noise tolerance (NT) and storage capacity (SC) of CHNNs, O(2) -HNNs, and rotor Hopfield neural networks. In terms of SC, O(2) -HNNs outperformed the others, while in NT, they outdid CHNNs.

Can people learn from machines behavior in microtask based crowdsourcing? Can we train the machines as our mentor even without domain expertise? In this paper, we investigate how the task results improve concerning quality during and after presenting machine prediction as a reference answer in self-correction. Four reference types were examined in the experiment; Correct, Random, Machine prediction trained by correct answers, and that trained by human answers. Learning effects were observed only in presenting machine prediction, although those accuracy rates were far from correct (100%). Moreover, there were no learning effects in "Correct" and "Random". This suggests the following hypothesis: Since machine learners make some "models" for the problem, it is easier for humans to interpret the outputs of machine learners than the results without via them; it is more difficult to interpret not only random answers but also the correct answers in a case where the perfect interpretation of the problem is difficult. Furthermore, some workers answered with higher accuracy rate than machines in the post-test. Therefore, this strategy can be expected to be useful for bootstrapping solutions in the situation where unknown problems occur without expertise or at a low cost.

Self-correction for crowdsourced tasks is a two-stage setting that allows a crowd worker to review the task results of other workers; the worker is then given a chance to update his/her results according to the review.Self-correction was proposed as an approach complementary to statistical algorithms in which workers independently perform the same task. It can provide higher-quality results with few additional costs. However, thus far, the effects have only been demonstrated in simulations, and empirical evaluations are needed. In addition, as self-correction gives feedback to workers, an interesting question arises: whether perceptual learning is observed in self-correction tasks. This paper reports our experimental results on self-corrections with a real-world crowdsourcing service.The empirical results show the following: (1) Self-correction is effective for making workers reconsider their judgments. (2) Self-correction is more effective if workers are shown task results produced by higher-quality workers during the second stage. (3) Perceptual learning effect is observed in some cases. Self-correction can give feedback that shows workers how to provide high-quality answers in future tasks.The findings imply that we can construct a positive loop to improve the quality of workers effectively.We also analyze in which cases perceptual learning can be observed with self-correction in crowdsourced microtasks.

A complex-valued Hopfield neural network (CHNN) is a model of a Hopfield neural network using multistate neurons. The stability conditions of CHNNs have been widely studied. A CHNN with a synchronous mode will converge to a fixed point or a cycle of length 2. A rotor Hopfield neural network (RHNN) is also a model of a multistate Hopfield neural network. RHNNs have much higher storage capacity and noise tolerance than CHNNs. We extend the theories regarding the stability of CHNNs to RHNNs. In addition, we investigate the stability of RHNNs with the projection rule. Although a CHNN with projection rule can be trapped at a cycle, an RHNN with projection rule converges to a fixed point. This is one of the great advantages of RHNNs.

A complex-valued Hopfield neural network (CHNN) is a multistate model of a Hopfield neural network. It has the disadvantage of low noise tolerance. Meanwhile, a symmetric CHNN (SCHNN) is a modification of a CHNN that improves noise tolerance. Furthermore, a rotor Hopfield neural network (RHNN) is an extension of a CHNN. It has twice the storage capacity of CHNNs and SCHNNs, and much better noise tolerance than CHNNs, although it requires twice many connection parameters. In this brief, we investigate the relations between CHNN, SCHNN, and RHNN; an RHNN is uniquely decomposed into a CHNN and SCHNN. In addition, the Hebbian learning rule for RHNNs is decomposed into those for CHNNs and SCHNNs.

There are three important concepts related to learning processes in neural networks: reducibility, nonminimality, and singularity. Although the definitions of these three concepts differ, they are equivalent in real-valued neural networks. This is also true of complex-valued neural networks (CVNNs) with hidden neurons not employing biases. The situation of CVNNs with hidden neurons employing biases, however, is very complicated. Exceptional reducibility was found, and it was shown that reducibility and nonminimality are not the same. Irreducibility consists of minimality and exceptional reducibility. The relationship between minimality and singularity has not yet been established. In this paper, we describe our surprising finding that minimality and singularity are independent. We also provide several examples based on exceptional reducibility.

This paper proposes an improved version of sub-band adaptive notch (SAN) filters for detecting and eliminating multiple unknown sinusoids embedded in the broadband (in fact, white) signals. The proposed SAN filters enhance both the convergence speed and estimation accuracy especially when sinusoids have close angular frequencies, under which circumstances the original SAN filters suffer from convergence and accuracy problems. Several simulations are included illustrating the superiority of the proposed SAN filters over their original counterparts, in terms of considerably better estimation accuracy and faster convergence speed.

Complex-valued neural networks, which are extensions of ordinary neural networks, have been studied as interesting models by many researchers. Especially, complex-valued Hopfield neural networks (CHNNs) have been used to process multilevel data, such as gray-scale images. CHNNs with Hermitian connection weights always converge using asynchronous update. The noise tolerance of CHNNs deteriorates extremely as the resolution increases. Noise tolerance is one of the most controversial problems for CHNNs. It is known that rotational invariance reduces noise tolerance. In this brief, we propose symmetric CHNNs (SCHNNs), which have symmetric connection weights. We define their energy function and prove that the SCHNNs always converge. In addition, we show that the SCHNNs improve noise tolerance through computer simulations and explain this improvement from the standpoint of rotational invariance.

In this paper, we propose a Hopfield Associative Memory with Complex-valued and Real-valued neurons (CRHAM). CRHAM is an associative memory which can perform storing and recalling multi-valued patterns. A part of neurons in the network are complex-valued neurons, and the rest of neurons are conventional (real-valued) neurons. Spurious patterns that degrade the retrieval performance can be reduced by the combination of those two types of neurons. The experimental results show that high robustness for noisy inputs is achieved by CRHAM as compared with conventional complex-valued associative memories, such as Complex-valued Hopfield Associative Memory (CHAM) and Complex-valued Bipartite Auto-Associative Memory (CBAAM).

This paper presents Quaternionic Bidirectional Auto-Associative Memory (QBAAM) that is an associative memory network storing patterns with multiple levels. A part of neurons in the network are quaternionic neurons, where their states are encoded by quaternion, which is a four-dimensional hypercomplex number system. These neurons can represent three kinds of discretized phases, i.e., three-dimensional multilevel values. The rest of neurons are conventional (real-valued) neurons. QBAAM is expected to have a rich representation ability by employing quaternionic neurons, as well as to have fewer spurious patterns in the network by a combination of real-valued and quaternionic neurons. The experimental results show that high robustness of noisy inputs is achieved by QBAAM, as compared with Quaternionic Hopfield Associative Memory where all neurons in the network are quaternionic neurons.

A rotor Hopfield neural network (RHNN) is an extension of a complex-valued Hopfield neural network (CHNN). RHNNs have some excellent properties. For example, the storage capacity of an RHNN is twice that of a CHNN. The most important property of an RHNN is that it does not store rotated patterns of training patterns, unlike CHNNs, which have less noise robustness because they store rotated patterns. However, conventional learning methods for RHNNs, such as Hebbian learning rule and gradient descent learning rules, present difficulties with regard to, for example, storage capacity, noise robustness, and learning time. In this paper, we propose a projection rule for RHNN and demonstrate that the noise robustness of RHNN is better than that of CHNN. The proposed algorithm improves the noise robustness of RHNN. As the number of training patterns increases, the noise robustness of CHNN rapidly deteriorates. On the other hand, the noise robustness of RHNN reduces less rapidly for the same case. Moreover, RHNN can easily recover from rotated patterns, unlike CHNN. We show this ability by computer simulation.

Complex-valued Hopfield Associative Memory (CHAM) can store multi-valued patterns. But CHAM stores not only given training patterns but also many spurious patterns, such as their rotated patterns, at the same time. These rotated patterns and spurious patterns reduce the noise robustness of the CHAM. In the present work, we propose Complex-valued Bidirectional Auto-Associative Memory (CBAAM) as a model of auto-associative memory which improves the noise robustness. CBAAM consists of two layers. Although the structure of CBAAM is a Bidirectional Associative Memory (BAM), CBAAM works as an auto-associative memory, because the one layer is a visible layer and the other one is an invisible layer. The visible layer consists of complex-valued neurons and can process multi-valued patterns. The invisible layer consists of real-valued neurons and can reduce pseudo-memory such as rotated patterns. Thus, CBAAM has strong noise robustness. In the computer simulations, we show that the noise robustness of CBAAM highly exceeds that of CHAM. Especially, we find that CBAAM maintains high noise robustness independent of the resolution factor.

In recent years, several neural networks using Clifford algebra have been studied. Clifford algebra is also called geometric algebra. Complex-valued Hopfield neural networks (CHNNs) are the most popular neural networks using Clifford algebra. The aim of this brief is to construct hyperbolic HNNs (HHNNs) as an analog of CHNNs. Hyperbolic algebra is a Clifford algebra based on Lorentzian geometry. In this brief, a hyperbolic neuron is defined in a manner analogous to a phasor neuron, which is a typical complex-valued neuron model. HHNNs share common concepts with CHNNs, such as the angle and energy. However, HHNNs and CHNNs are different in several aspects. The states of hyperbolic neurons do not form a circle, and, therefore, the start and end states are not identical. In the quantized version, unlike complex-valued neurons, hyperbolic neurons have an infinite number of states.

Complex-valued Associative Memory (CAM) can store multi-state patterns unlike Hopfield Associative Memory (HAM). CAM stores not only given training patterns but also many spurious patterns, such as their rotated patterns, at the same time. Rotor Associative Memory (RAM) can make the most of rotated patterns unstable but the reversed patterns remain stable. In the present work, we propose RAM with a Periodic Activation Function (PAF) to make the reversed patterns unstable. PAF is an activation function that Aizenberg introduced to CAM. We prove that RAM with a PAF has far fewer spurious patterns by using dynamic associative memories which can search the stored patterns.

Conventional adaptive notch filter based on an infinite impulse response (IIR) filter is well known. However, the IIR adaptive notch filter has a problem of stability due to an IIR filter and bias error due to disturbance. The adaptive notch filter using Fourier sine series (ANFF) is therefore proposed as a stable adaptive notch filter with bias free adaptive algorithm. However, there are problems of the constant delay and low convergence rate due to the large term numbers of series expansion. In this paper, the structure of the notch filter is proposed to decrease the constant delay and improve the convergence rate.

Filtered-x algorithm has a possibility of making an active noise control (ANC) unstable due to the modeling error of a secondary path. A pre-inverse type ANC is proposed in order to solve the problem. The proposed ANC uses the filter which has the inverse transfer function of a secondary path before the secondary path. Whereas the filtered-x algorithm controls a primary path and a secondary path simultaneously by an adaptive filter, the pre-inverse type ANC can control a primary path and a secondary path independently. Therefore the proposed ANC is always stable. However, the adaptive filter estimating a secondary path converges on a solution with bias due to disturbance. Thus, the bias free adaptive algorithm is also proposed. The proposed adaptive algorithm takes advantage of the independence between the input signal and disturbance.

A neural network is referred to as minimal if it cannot reduce the number of hidden neurons that maintain the input-output map. The condition in which the number of hidden neurons can be reduced is referred to as reducibility. Real-valued neural networks have only three simple types of reducibility. It can be naturally extended to complex-valued neural networks without bias terms of hidden neurons. However, general complex-valued neural networks have another type of reducibility, referred to herein as exceptional reducibility. In this paper, another type of reducibility is presented, and a method by which to minimize complex-valued neural networks is proposed.

In content-based image retrieval (CBIR), similarity measures vary according to the user, and it is difficult to build a retrieval system which reflects the user's similarity measures automatically. Regarding CBIR as consisting of feature extraction, coarse classification and detailed matching stages, this work aims at reflecting the user's similarity measures in coarse classification. After obtaining the user's evaluation to the initial retrieval, we transform the initial feature vectors using optimal linear associative memory (OLAM). This leads to the selection of important features from the user's relevance feedback. Experimental results show the effectiveness of the proposed method which reflects the user's similarity measures in the coarse classification.

HAM (Hopfield Associative Memory) and BAM (Bidirectinal Associative Memory) are representative associative memories by neural networks. The storage capacity by the Hebb rule, which is often used, is extremely low. In order to improve it, some learning methods, for example, pseudo-inverse matrix learning and gradient descent learning, have been introduced. Oh introduced pseudo-relaxation learning algorithm to HAM and BAM. In order to accelerate it, Hattori proposed quick learning. Noest proposed CAM (Complex-valued Associative Memory), which is complex-valued HAM. The storage capacity of CAM by the Hebb rule is also extremely low. Pseudo-inverse matrix learning and gradient descent learning have already been generalized to CAM. In this paper, we apply pseudo-relaxation learning algorithm to CAM in order to improve the capacity.

MOTIVATION: To find a correlation between the activities and structures of molecules is one of the most important subjects for molecular evaluation study. Traditional quantitative structure-activity relationship (QSAR) methodologies represent those attempts using physicochemical descriptors. Creating a new molecular description factor based on the results of a computational docking study will add new dimensions to molecular evaluation. RESULTS: We propose a new molecular description factor analysis system called the Comparative Molecular Interaction Profile Analysis (CoMIPA) system in which the AutoDock program is used for docking evaluation of small molecule compound-protein complexes. Interaction energies are calculated, and the data sets obtained are called interaction profiles (IPFs). Using the IPF as a scoring indicator, the system could be a powerful tool to cluster the interacting properties between small molecules and bio macromolecules such as ligand-receptor bindings. Further development of the system will enable us to predict the adverse effects of a drug candidate.

A new online algorithm for updating equation error IIR ADF is proposed. The proposed algorithm, which involves maintaining a constant power of the desired signal, is independent of the white disturbance signal, and hence there is no bias in the coefficient's estimate of the ADF. We also provide the analysis and simulation results which verify this kind of performance. Application of the proposed algorithm to an adaptive line enhancer (ALE) is also provided. When compared with the method which uses a cascaded notch filter, we observe a considerable improvement in performance due to the complete elimination of the effect of white noise under mean sense condition.

We propose a new method for updating units in the Hopfield model. With this method two or more units change at the same time, so as to become the lowest energy state among all possible states. Since this updating algorithm is based on the detailed balance equation, convergence to the Boltzmann distribution is guaranteed. If our algorithm is applied to finding the minimum energy in constraint satisfaction and combinatorial optimization problems, then there is a faster convergence than those with the usual algorithm in the neural network. This is shown by experiments with the travelling salesman problem, the four-color problem, the N-queen problem, and the graph bi-partitioning problem. In constraint satisfaction problems, for which earlier neural networks are effective in some cases, our updating scheme works fine. Even though we still encounter the problem of ending up in local minima, our updating scheme has a great advantage compared with the usual updating scheme used in combinatorial optimization problems. Also, we discuss parallel computing using our updating algorithm.

In this paper we propose a new algorithm for an adaptive notch filter implemented using an allpass filter, for elimination of multiple sinusoids. The notch filter is implemented using cascades of second order notch filters, each of which has been realized using a second order direct form allpass filter. We also present an analysis which indicates that the proposed algorithm has a reduced bias in the estimation of the input sinusoids. Simulation results that have been provided confirm this analysis.

In this paper, we present a new method for the implementation of pipelined finite impulse response (FIR) adaptive digital filter (ADF). The proposed method reduces the length of the critical path, while simultaneously limiting the latency and the maximum delay of the coefficients of the FIR ADF to two and a fourth of the order of the filter, respectively. The latency of the proposed method is also independent of the order of the filter. Furthermore, since the FIR filter portion of the ADF incorporates only a single delay element, the proposed pipelining method can also be applied to pipelined IIR ADF.