On the Computational Complexity of Covering Multi-Interface Networks

We have applied a shift-invariant back propagation neural network to the cells' boundary detection of human corneal endothelium photomicrographs. The interconnection patterns of the neural network are constrained to be spatially invariant. Our experiments demonstrated that the generalizing ability of the neural network is dependent on its connectivity or complexity, i.e., the number of connections. To get a better generalization, we have proposed a modified back propagation learning rule, which reduces the complexity of the neural network during the learning procedure. The measure of the complexity of the neural network was defined as a formal entropy of the connectivity pattern. Simulations showed that the neural network trained by this learning rule has better generalizing ability but more computational complexity. In this paper a simplified function is investigated as the measure of the complexity of the neural network. This simplified measure is a first order approximation of the formal entropy measure. Simulations show that the simplified measure is effective to get better generalization and has less computational complexity than the original formal entropy measure.

Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability. Most research in neural networks focuses on learning, yet it is important to understand the physical limitations of the network before the resources needed to solve a certain problem can be calculated. One of the aims of this book is to compare the complexity of neural networks and the complexity of conventional computers, looking at the computational ability and resources (neurons and time) that are a necessary part of the foundations of neural network learning. Circuit Complexity and Neural Networks contains a significant amount of background material on conventional complexity theory that will enable neural network scientists to learn about how complexity theory applies to their discipline, and allow complexity theorists to see how their discipline applies to neural networks.

Based on the theoretical basis of quantum computation, entanglement has been further explored as one of the key resources. An outstanding problem in quantum computation is the detecting of entanglement, but no closed-form algorithm exists. According to an advanced matrix rearrangement approach for detecting multipartite quantum states, we give some examples to verify the effectiveness and practicability of this new criterion. Meanwhile, this paper shows how techniques from the quantum neural network can be utilized to detect entanglement. Two models, known as the discrete-variable and the continuous-variable quantum neural network, are applied to solve the separability problem. We demonstrate the utility that such a discrete-variable quantum neural network can be trained to detect the entanglement with great exactness. And the complexity of network and computation is greatly reduced. Besides, the continuous-variable quantum neural network is applied for detecting two-qumode Gaussian state. Compared with the results of the traditional neural network, this deep quantum neural network demonstrates its capability and adaptability as well.

Hematopathology II, Abstract 99–107, Posters

This paper introduced a feature selection algorithm, used a random forest classifier for recursive feature elimination, and selected the top 49 features according to the order of feature importance ranking, then proposed an attack detection model based on LeNet-5 convolutional neural network and named it as LeNet-4 network model. In its network structure, the first pooling layer and the last fully connection layer of the original LeNet-5 network were removed, which reduced the model’s computational load and network complexity, and the network self-learning ability was strengthened through the structure of the double convolutional layer and the single pooling layer. This paper used the CICIDS2017 dataset to evaluate the proposed model, we used all instances in the dataset for comprehensive detection. The experimental results show that on the LeNet-4 network model, the introduction of a recursive feature elimination algorithm has improved the accuracy of attack detection while reducing the time cost. Multi-class attack classification achieved an accuracy rate of 97.8%, and the binary attack classification achieved an accuracy rate of 98.5%.

Network motif identification is significant in that motifs generally reflect functionalities. However, the task is greatly challenging due to diverse patterns of motifs possibly existent in a network and high computation complexity for large scale networks. In this study, we propose a network motif identification method, FCMD, based on clustering subgraphs according to their local structures. By modeling local-topological feature of a network with a feature vector, the approach maps motif identification problem into a clustering problem of feature vectors in a feature space, which greatly reduces computation complexity hence facilitates very large scale networks. Experiments on 8 real networks, including biochemical network, neural network, electronics circuit network, et al., indicates that the proposed method is very effective in motif detection with computation complexity approximately independent to the scale of the network.

For the path planning problem of autonomous underwater vehicles (AUVs) in 3-dimensional (3-D) estuary environments, traditional methods may encounter problems due to their high computational complexity. In this paper, we proposed a dynamic neural network to solve the AUV path planning problem. In the neural network, neurons get input from the environment, locally interact with the neighbors and update neural activities in real time. The AUV path is then generated according to the neural activity landscapes. Stability, computational complexity of the neural network, and optimality of the generated path are analyzed. AUV path planning in 3-D complex environments without currents, with constant currents, and with variable currents are studied through simulations, which demonstrate the effectiveness of this approach.

Nowadays, deep learning methods with high structural complexity and flexibility inevitably lean on the computational capability of the hardware. A platform with high-performance GPUs and large amounts of memory could support neural networks having large numbers of layers and kernels. However, naively pursuing high-cost hardware would probably drag the technical development of deep learning methods. In the article, we thus establish a new preprocessing method to reduce the computational complexity of the neural networks. Inspired by the band theory of solids in physics, we map the image space into a noninteraction physical system isomorphically and then treat image voxels as particle-like clusters. Then, we reconstruct the Fermi–Dirac distribution to be a correction function for the normalization of the voxel intensity and as a filter of insignificant cluster components. The filtered clusters at the circumstance can delineate the morphological heterogeneity of the image voxels. We used the BraTS 2019 datasets and the dimensional fusion U-net for the algorithmic validation, and the proposed Fermi–Dirac correction function exhibited comparable performance to other employed preprocessing methods. By comparing to the conventional z-score normalization function and the Gamma correction function, the proposed algorithm can save at least 38% of computational time cost under a low-cost hardware architecture. Even though the correction function of global histogram equalization has the lowest computational time among the employed correction functions, the proposed Fermi–Dirac correction function exhibits better capabilities of image augmentation and segmentation.

Deep learning is currently the state of the art algorithm for image classification. The complexity of these feedforward neural networks have overcome a critical point, resulting algorithmic breakthroughs in various fields. On the other hand their complexity makes them executable in tasks, where High-throughput computing powers are available. The optimization of these networks -considering computational complexity and applicability on embedded systems- has not yet been studied and investigated in details. In this paper I show some examples how this algorithms can be optimized and accelerated on embedded systems.

Equivalent discrete fracture networks for modelling fluid flow in highly fractured rock mass

Convolutional neural networks are promising tool for pattern recognition. Implementations of convolutional neural networks require a significant number of computations during training and processing. In this paper we propose to use Winograd method to reduce computational complexity in convolutional layers of convolutional neural networks. Theoretical analysis of the convolutional layer’s computational complexity of convolutional neural networks showed that the use of the Winograd method can reduce the computational complexity compared with direct method by 26,75%, 17,01%, with filter sizes of 3×3, 5×5, respectively. A promising area of further research is the hardware implementation of convolutional layers with Winograd calculations on modern computing devices, such as FPGA and ASIC.

Despite breakthrough advances in image super-resolution (SR) with convolutional neural networks (CNNs), SR has yet to enjoy ubiquitous applications due to the high computational complexity of SR networks. Quantization is one of the promising approaches to solve this problem. However, existing methods fail to quantize SR models with a bit-width lower than 8 bits, suffering from severe accuracy loss due to fixed bit-width quantization applied everywhere. In this work, to achieve high average bit-reduction with less accuracy loss, we propose a novel Content-Aware Dynamic Quantization (CADyQ) method for SR networks that allocates optimal bits to local regions and layers adaptively based on the local contents of an input image. To this end, a trainable bit selector module is introduced to determine the proper bit-width and quantization level for each layer and a given local image patch. This module is governed by the quantization sensitivity that is estimated by using both the average magnitude of image gradient of the patch and the standard deviation of the input feature of the layer. The proposed quantization pipeline has been tested on various SR networks and evaluated on several standard benchmarks extensively. Significant reduction in computational complexity and the elevated restoration accuracy clearly demonstrate the effectiveness of the proposed CADyQ framework for SR. Codes are available at https://github.com/Cheeun/CADyQ.

User association and resource allocation for downlink orthogonal frequency division multiplexing (OFDM) should be jointly optimized in small cells networks with limited backhaul in order to maximize the network utility. In general, the joint user association and per-band resource allocation problem is known as an integer NP-hard problem requiring exponential order of computational complexity to find the global optimal point. To obtain a solution with feasible computational complexity, most previous works solve this problem by relaxing the integer problem of the per-band resource allocation to a real-valued problem by assuming that channel gain is averaged out over all the frequency bands and that base stations allocate a real-valued proportion of the bandwidth. We propose two sub-optimal algorithms to solve the original integer problem with polynomial order of computational complexity in pursuit of maximizing the network utility with limited backhaul constraints. The network utility and geometric mean of receiving rates for the two proposed schemes are evaluated via numerical simulations. The computational complexity of the two schemes are also represented, respectively, showing the trade-off between the network utility and complexity.

This article make use of the XML-based metadata organization and management technology, massive data distribution and redundant storage and load balancing technology and designed an architecture of distributed spatial data server cluster, up to an point, solved the three problems which refer to complexity of storage, network and computation.

Smart objects have grown in popularity and acceptance over the past period due to their decreasing size, greater intelligence, and lower costs. The Internet of Things (IoT) connects physical devices, including actuators, sensors, and cameras, to a network via the Internet. The widespread use of IoT devices has led to an exponential rise in network traffic volume and complexity, creating new challenges for real-time network security and threat detection. This study attempts to design an intrusion detection system which is scalable and capable of handling the vast number and variety of IoT traffic. It is based on improving the scalability and precision of the detection of threats by employing machine learning (ML) and deep learning (DL) techniques and hybrid model. The model is trained and tested on the CIC IoT DIAD 2024 dataset, a large high-volume dataset consisting of diversified IoT traffic, benign and malicious activity. It includes extensive data preprocessing, feature selection, and training of various models. Features were selected using an Analysis of Variance (ANOVA)–based feature selection technique to reduce computational overhead and time complexity while mitigating the curse of dimensionality and enhancing model accuracy. The resulting optimal feature subset was then used to train and evaluate several classifiers, including Decision Trees, K-Nearest Neighbors (KNN), Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM) networks, and a hybrid CNN–LSTM model. The models are compared using typical measures of performance such as accuracy, precision, recall, F1-score, and confusion matrix. The results indicate that hybrid deep learning models specifically the CNN-LSTM outperformed the other models in recognizing binary attacks achieving the highest performance with accuracy of 94.08% followed by CNN and LSTM with accuracies of 93.37% and 93.24% respectively. In contrast, the traditional machine learning model, Decision trees demonstrated superior performance in multi-class classification, achieving an accuracy of 98.25% defeating KNN (90%) as well as the hybrid deep learning model (CNN-LSTM – 88.30%). This, work paves the foundation for the implementation of scalable intrusion detection models in real IoT infrastructures. The future of the work is to integrate the developed models using massive data streaming infrastructures in support of real-time intrusion detection in large-scale, dynamic IoT infrastructures.