Increase In Model Size Research Articles

ECTFormer: An efficient Conv-Transformer model design for image recognition

Since the success of Vision Transformers (ViTs), there has been growing interest in combining ConvNets and Transformers in the computer vision community. While the hybrid models have demonstrated state-of-the-art performance, many of these models are too large and complex to be applied to edge devices for real-world applications. To address this challenge, we propose an efficient hybrid network called ECTFormer that leverages the strengths of ConvNets and Transformers while considering both model performance and inference speed. Specifically, our approach involves: (1) optimizing the combination of convolution kernels by dynamically adjusting kernel sizes based on the scale of feature tensors; (2) revisiting existing overlapping patchify to not only reduce the model size but also propagate fine-grained patches for the performance enhancement; and (3) introducing an efficient single-head self-attention mechanism, rather than multi-head self-attention in the base Transformer, to minimize the increase in model size and boost inference speed, overcoming bottlenecks of ViTs. In experimental results on ImageNet-1K, ECTFormer not only demonstrates comparable or higher top-1 accuracy but also faster inference speed on both GPUs and edge devices compared to other efficient networks.

Repmono: a lightweight self-supervised monocular depth estimation architecture for high-speed inference

Self-supervised monocular depth estimation has always attracted attention because it does not require ground truth data. Designing a lightweight architecture capable of fast inference is crucial for deployment on mobile devices. The current network effectively integrates Convolutional Neural Networks (CNN) with Transformers, achieving significant improvements in accuracy. However, this advantage comes at the cost of an increase in model size and a significant reduction in inference speed. In this study, we propose a network named Repmono, which includes LCKT module with a large convolutional kernel and RepTM module based on the structural reparameterisation technique. With the combination of these two modules, our network achieves both local and global feature extraction with a smaller number of parameters and significantly enhances inference speed. Our network, with 2.31MB parameters, shows significant accuracy improvements over Monodepth2 in experiments on the KITTI dataset. With uniform input dimensions, our network’s inference speed is 53.7% faster than R-MSFM6, 60.1% faster than Monodepth2, and 81.1% faster than MonoVIT-small. Our code is available at https://github.com/txc320382/Repmono.

CBin-NN: An Inference Engine for Binarized Neural Networks

Binarization is an extreme quantization technique that is attracting research in the Internet of Things (IoT) field, as it radically reduces the memory footprint of deep neural networks without a correspondingly significant accuracy drop. To support the effective deployment of Binarized Neural Networks (BNNs), we propose CBin-NN, a library of layer operators that allows the building of simple yet flexible convolutional neural networks (CNNs) with binary weights and activations. CBin-NN is platform-independent and is thus portable to virtually any software-programmable device. Experimental analysis on the CIFAR-10 dataset shows that our library, compared to a set of state-of-the-art inference engines, speeds up inference by 3.6 times and reduces the memory required to store model weights and activations by 7.5 times and 28 times, respectively, at the cost of slightly lower accuracy (2.5%). An ablation study stresses the importance of a Quantized Input Quantized Kernel Convolution layer to improve accuracy and reduce latency at the cost of a slight increase in model size.

Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation

Post-training quantization (PTQ) has emerged as a promising technique for mitigating memory consumption and computational costs in large language models (LLMs). However, a systematic examination of various quantization schemes, model families, and quantization bit precision has been absent from the literature. In this paper, we conduct a comprehensive analysis of these factors by investigating the effects of PTQ on weight-only, activation-only, and weight-and-activation quantization using diverse methods such as round-to-nearest (RTN), GPTQ, ZeroQuant, and their variants. We apply these methods to two distinct model families with parameters ranging from 125M to 176B. Our contributions include: (1) a sensitivity analysis revealing that activation quantization is generally more susceptible to weight quantization, with smaller models often outperforming larger models in terms of activation quantization; (2) an evaluation and comparison of existing PTQ methods to optimize model size reduction while minimizing the impact on accuracy, revealing that none of the current methods can achieve the original model quality for quantization with either INT4-weight or INT4-weight-and-INT8-activation; (3) based on these insights, we propose an optimized method called Low-Rank Compensation (LoRC), which employs low-rank matrices to enhance model quality recovery with a minimal increase in model size.

A Method of Body Condition Scoring for Dairy Cows Based on Lightweight Convolution Neural Network

Highlights A cow body condition scoring model (ShuffleNet-SEH) based on a lightweight convolutional neural network using ShuffleNetV2 was proposed. Introducing the SE attention mechanism and H-Swish activation function enhances the feature extraction capability of the model. Achieved over 98% classification accuracy rate on the cow datasets. The proposed method can be applied to mobile devices. Abstract. Body condition scoring is an essential tool for nutrition management in large-scale dairy farming. The traditional method of manual scoring is inefficient and prone to subjective error. With the advancement of deep learning algorithms and machine vision technology, automatic scoring methods have been proposed. In response to the current problems of large parameter sizes and poor robustness in deep learning models, this study proposes a cow body condition scoring model (ShuffleNet-SEH) based on a lightweight convolutional neural network using ShuffleNetV2 as a foundation. Firstly, tail area images of cows were collected to construct a diverse dataset that includes complex variations such as motion blur and different levels of illumination. Secondly, the ShuffleNet-SEH model was developed by integrating a Squeeze-and-Excitation Networks (SENet) module into the main branch of ShuffleNetV2 after 1×1 convolution to enhance the representation ability of the network and improve its accuracy in identifying the cow body condition. Additionally, the nonlinear activation function ReLU in SENet was replaced by H-Swish to reduce the computational data required for the model on mobile devices, making it suitable for quantization operations. ShuffleNet-SEH was comprehensively evaluated, including ablation experiments, confusion matrix analysis, and feature map analysis. Multiple complex test sets were constructed for validation purposes. Throughout these evaluations, ShuffleNet-SEH exhibited remarkable performance. Furthermore, the efficacy and interpretability of ShuffleNet-SEH in cow body condition scoring tasks were further substantiated through meticulous feature map analysis. The findings underscore the robustness and reliability of ShuffleNet-SEH across diverse experimental scenarios and assessments. In the constructed motion blur test set, ShuffleNet-SEH demonstrated outstanding performance. Specifically, it achieved an accuracy rate of 98.2%, a precision rate of 98.5%, and a recall rate of 98.3%. These results represent significant improvements of 2.3%, 2.4%, and 3.2%, respectively, compared to the performance of the ShuffleNetV2 model. In addition, it is noteworthy that the ShuffleNet-SEH model has a size of approximately 5.64 MB, while the original ShuffleNet model has a size of 4.97 MB. This indicates a modest increase in model size of approximately 13.5% with the incorporation of the ShuffleNet-SEH enhancements. Moreover, superior overall performance was displayed by ShuffleNet-SEH model compared to mainstream convolutional neural network classification models, including MobileNetV2, EfficientNetV1, and ConvNeXt. The success of ShuffleNet-SEH in accurately identifying cow body condition while maintaining a lightweight architecture makes it suitable for deployment on mobile devices and, thus, has the potential to promote the commercialization of cow body condition scoring. Keywords: Attention mechanism, Body condition score, Deep learning, ShuffleNetV2.

UAV-deployed deep learning network for real-time multi-class damage detection using model quantization techniques

Real-time damage detection algorithms deployed on Unmanned Aerial Vehicles (UAVs) can support flight control in real time, enabling the capture of higher quality inspection data. However, three challenges have hindered their wider application: 1) Existing anchor-based damage detectors cannot generalize well to real-world scenarios and degrade the detection speed; 2) Prior studies exhibit a low detection accuracy; 3) No previous study considers the energy consumption issue of the damage detector, limiting the UAVs' flight time. To meet these challenges, this paper presented the YOLOv6s-GRE-quantized method, which is an energy-efficient anchor free and real-time damage detection method built on top of the YOLOv6s algorithm. Firstly, the YOLOv6s-GRE method was presented, where a generalized feature pyramid network (GFPN), a reparameterization efficient layer aggregation network (RepELAN) and an efficient detection head were introduced into the YOLOv6s. Comparison experiments showed that the YOLOv6s-GRE method, in contrast to YOLOv6s, advanced 2.3 percentage points in the metric of mAP50, while maintaining comparable detection speed and without requiring an increase in model size. The YOLOv6s-GRE model was then reconstructed by the RepOptimizer (RepOpt) to equivalently transform the YOLOv6s-GRE into a quantization-friendly model for addressing the quantization difficulty of the reparameterization model. Finally, the YOLOv6s-GRE model with RepOpt was quantized by the partial quantization-aware training technique, expediting the detection speed by 83.5% and saving energy by 79.7% while still maintaining a comparable level of detection accuracy. Implementing of this proposed method can significantly boost bridge inspection productivity.

Fastensor: Optimise the Tensor I/O Path from SSD to GPU for Deep Learning Training

In recent years, benefiting from the increase in model size and complexity, deep learning has achieved tremendous success in computer vision (CV) and (NLP). Training deep learning models using accelerators such as GPUs often requires much iterative data to be transferred from NVMe SSD to GPU memory. Much recent work has focused on data transfer during the pre-processing phase and has introduced techniques such as multiprocessing and GPU Direct Storage (GDS) to accelerate it. However, tensor data during training (such as Checkpoints, logs, and intermediate feature maps), which is also time-consuming, is often transferred using traditional serial, long-I/O-path transfer methods. In this article, based on GDS technology, we built Fastensor, an efficient tool for tensor data transfer between the NVMe SSDs and GPUs. To achieve higher tensor data I/O throughput, we optimized the traditional data I/O process. We also proposed a data and runtime context-aware tensor I/O algorithm. Fastensor can select the most suitable data transfer tool for the current tensor from a candidate set of tools during model training. The optimal tool is derived from a dictionary generated by our adaptive exploration algorithm in the first few training iterations. We used Fastensor’s unified interface to test the read/write bandwidth and energy consumption of different transfer tools for different sizes of tensor blocks. We found that the execution efficiency of different tensor transfer tools is related to both the tensor block size and the runtime context. We then deployed Fastensor in the widely applicable Pytorch deep learning framework. We showed that Fastensor could perform superior in typical scenarios of model parameter saving and intermediate feature map transfer with the same hardware configuration. Fastensor achieves a 5.37x read performance improvement compared to torch.save () when used for model parameter saving. When used for intermediate feature map transfer, Fastensor can increase the supported training batch size by 20x, while the total read and write speed is increased by 2.96x compared to the torch I/O API.

F-ALBERT: A Distilled Model from a Two-Time Distillation System for Reduced Computational Complexity in ALBERT Model

Recently, language models based on the Transformer architecture have been predominantly used in AI natural language processing. These models, which have been proven to perform better with more parameters, have led to a significant increase in model size and computational load. ALBERT solves this problem by significantly reducing the number of parameters it retains by repeatedly reusing parameters. Although ALBERT significantly reduces the parameters it maintains, it requires a computational load similar to the original language model due to the reuse process. In this study, we develop a distillation system that decreases the number of times the ALBERT model reuses parameters and progressively reduces the parameters being reused. We propose a representation in this distillation system that can effectively distill the knowledge of the original model and develop a new architecture with reduced computation. Through this system, F-ALBERT, which had about half the computational load compared to the ALBERT model, restored about 98% of the performance of the original model on the GLUE benchmark.

Tomato Maturity Detection and Counting Model Based on MHSA-YOLOv8.

The online automated maturity grading and counting of tomato fruits has a certain promoting effect on digital supervision of fruit growth status and unmanned precision operations during the planting process. The traditional grading and counting of tomato fruit maturity is mostly done manually, which is time-consuming and laborious work, and its precision depends on the accuracy of human eye observation. The combination of artificial intelligence and machine vision has to some extent solved this problem. In this work, firstly, a digital camera is used to obtain tomato fruit image datasets, taking into account factors such as occlusion and external light interference. Secondly, based on the tomato maturity grading task requirements, the MHSA attention mechanism is adopted to improve YOLOv8's backbone to enhance the network's ability to extract diverse features. The Precision, Recall, F1-score, and mAP50 of the tomato fruit maturity grading model constructed based on MHSA-YOLOv8 were 0.806, 0.807, 0.806, and 0.864, respectively, which improved the performance of the model with a slight increase in model size. Finally, thanks to the excellent performance of MHSA-YOLOv8, the Precision, Recall, F1-score, and mAP50 of the constructed counting models were 0.990, 0.960, 0.975, and 0.916, respectively. The tomato maturity grading and counting model constructed in this study is not only suitable for online detection but also for offline detection, which greatly helps to improve the harvesting and grading efficiency of tomato growers. The main innovations of this study are summarized as follows: (1) a tomato maturity grading and counting dataset collected from actual production scenarios was constructed; (2) considering the complexity of the environment, this study proposes a new object detection method, MHSA-YOLOv8, and constructs tomato maturity grading models and counting models, respectively; (3) the models constructed in this study are not only suitable for online grading and counting but also for offline grading and counting.

Trap spaces of Boolean networks are conflict-free siphons of their Petri net encoding

Boolean network modeling of gene regulation but also of post-transcriptomic systems has proven over the years that it can bring powerful analyses and corresponding insight to the many cases where precise biological data is not sufficiently available to build a detailed quantitative model. Besides simulation, the analysis of such models is mostly based on attractor computation, since those correspond roughly to observable biological phenotypes. The recent use of trap spaces made a real breakthrough in that field allowing to consider medium-sized models that used to be out of reach. However, with the continuing increase in model size and complexity of Boolean update functions, the state-of-the-art computation of minimal trap spaces based on prime implicants shows its limits due to the difficulty of the prime-implicant computation.In this article we explore and prove for the first time a connection between trap spaces of a general Boolean network and siphons of its Petri net encoding. Besides important theoretical applications in studying properties of trap spaces, the connection enables us to propose an alternative approach to compute minimal trap spaces, and hence complex attractors, of a general Boolean network. It replaces the need for prime implicants by a completely different technique, namely the enumeration of maximal siphons in the Petri net encoding of the original model. We then demonstrate its efficiency and compare it to the state-of-the-art methods on a large collection of real-world and randomly generated models.

Detection of Bird Nests on Transmission Towers in Aerial Images Based on Improved YOLOv5s

To further improve the accuracy of bird nest model detection on transmission towers in aerial images without significantly increasing the model size and to make detection more suitable for edge-end applications, the lightweight model YOLOv5s is improved in this paper. First, the original backbone network is reconfigured using the OSA (One-Shot Aggregation) module in the VOVNet and the CBAM (Convolution Block Attention Module) is embedded into the feature extraction network, which improves the accuracy of the model for small target recognition. Then, the atrous rates and the number of atrous convolutions of the ASPP (Atrous Spatial Pyramid Pooling) module are reduced to effectively decrease the parameters of the ASPP. The ASPP is then embedded into the feature fusion network to enhance the detection of the targets in complex backgrounds, improving the model accuracy. The experiments show that the mAP (mean-Average Precision) of the fusion-improved YOLOv5s model improves from 91.84% to 95.18%, with only a 27.4% increase in model size. Finally, the improved YOLOv5s model is deployed into the Jeston Xavier NX, resulting in a model that runs well and has a substantial increase in accuracy and a speed of 10.2 FPS, which is only 0.7 FPS slower than the original YOLOv5s model.

Improved YOLOv5 for Aerial Images Based on Attention Mechanism

Object detection based on unmanned aerial vehicle(UAV) platforms is essential for both engineering and research. Complex scale problems in UAV application scenarios require strong regression localization capabilities from target detection algorithms. Nonetheless, due to the constraints of UAV platform, it is difficult to increase accuracy by deepening the network. Therefore, this paper presents an improved YOLOv5 with an attention mechanism, consisting a Convolution-Swin Transformer Block(CSTB) utilizing Swin Transformer as well as a Convolution-block Attention Module(CBAM) to improve network positioning accuracy. In addition, this paper incorporates Bidirectional Feature Pyramid Network(BiFPN) [1], Spatial Pyramid Pooling-Fast(SPPF) and some network components to increase the average precision while maintaining the limited size of the model. Experiments on Visdrone2019 dataset show that the proposed approach can raise the mean Average Precision(mAP) by 5.4% compared to YOLOv5, with only 18% increase in model size.

A Low Coupling and Lightweight Algorithm for Ship Detection in Optical Remote Sensing Images

In recent years, many ship detection algorithms based on convolutional neural networks (CNNs) have been proposed to improve the performance of ship detection. However, with the increase in model complexity and size, it is challenging to deploy these models to resource-constrained edge platforms. In this letter, a low coupling algorithm that belongs to anchor-free methods is proposed for ship detection to reduce the model complexity and still obtain a competitive performance. The proposed low coupling network (LCNet) is easy to deploy and contributes to speeding up the inference and improving memory utilization. In addition, we propose a model compression process consisting of the quantization-aware training (QAT) method and a structural pruning method based on Taylor expansion, which can effectively reduce the model size according to hardware resource constraints. Comparative experimental results demonstrate that LCNet outperforms the state-of-the-art ship detection and natural object detection algorithms, with a 95.27% mAP and 88.91% F1 score on the HRSC2016 dataset. Our proposed model compression method also achieves a compression ratio of at least 80% with a negligible loss of performance.

Region-Adaptive Dense Network for Efficient Motion Deblurring

In this paper, we address the problem of dynamic scene deblurring in the presence of motion blur. Restoration of images affected by severe blur necessitates a network design with a large receptive field, which existing networks attempt to achieve through simple increment in the number of generic convolution layers, kernel-size, or the scales at which the image is processed. However, these techniques ignore the non-uniform nature of blur, and they come at the expense of an increase in model size and inference time. We present a new architecture composed of region adaptive dense deformable modules that implicitly discover the spatially varying shifts responsible for non-uniform blur in the input image and learn to modulate the filters. This capability is complemented by a self-attentive module which captures non-local spatial relationships among the intermediate features and enhances the spatially varying processing capability. We incorporate these modules into a densely connected encoder-decoder design which utilizes pre-trained Densenet filters to further improve the performance. Our network facilitates interpretable modeling of the spatially-varying deblurring process while dispensing with multi-scale processing and large filters entirely. Extensive comparisons with prior art on benchmark dynamic scene deblurring datasets clearly demonstrate the superiority of the proposed networks via significant improvements in accuracy and speed, enabling almost real-time deblurring.

Dynamical energy analysis—An efficient mesh based simulation tool for mid-to-high frequency structure-borne sound calculations

Modelling the vibro-acoustic response of mechanical built-up structures is a challenging task—especially in the mid to high frequency regime—even with the computing powers available today. Standard modelling tools such as Finite Element Methods (FEM) are not scalable to high frequencies due to the prohibitive increase in model size. Typical high frequency methods such as the Statistical Energy Analysis (SEA) on the other hand, often lack details of the structure and require care in the setting up the model. In this talk, I will review the Dynamical Energy Analysis (DEA)—a method bridging the gap between the low and very high frequency range. DEA describes the energy flow in a complex structure keeping the directional information of energy propagation. It can be set up directly on meshed structures thus providing detailed spatial information about the vibrational energy of a built-up structure of high complexity. The response of coupling coefficients between sub-components are obtained through local wave models integrated into the global DEA treatment. The computational cost of DEA is frequency independent making it possible to get results from the mid-to-high frequency regime. The method can be extended to include sound radiation calculations in a post-processing step. The new method has been validated both using FEM computations and experiments in collaboration with Yanmar Co., Ltd., a Japanese tractor manufacturer. Further applications in the car, aerospace and ship building industry will be presented.Modelling the vibro-acoustic response of mechanical built-up structures is a challenging task—especially in the mid to high frequency regime—even with the computing powers available today. Standard modelling tools such as Finite Element Methods (FEM) are not scalable to high frequencies due to the prohibitive increase in model size. Typical high frequency methods such as the Statistical Energy Analysis (SEA) on the other hand, often lack details of the structure and require care in the setting up the model. In this talk, I will review the Dynamical Energy Analysis (DEA)—a method bridging the gap between the low and very high frequency range. DEA describes the energy flow in a complex structure keeping the directional information of energy propagation. It can be set up directly on meshed structures thus providing detailed spatial information about the vibrational energy of a built-up structure of high complexity. The response of coupling coefficients between sub-components are obtained through local wave m...

Mechanical Behavior and Its Influencing Factors on Engineered Cementitious Composite Linings

A 1/5-scale model test was used to analyze and compare the mechanical responses of engineered cementitious composite (ECC) lining and traditional concrete lining under vertically concentrated loading. Test results indicate that the major failure mode of the lining cross section is controlled by tensile stress. ECC linings express better cracking control capability and deformation performance than the traditional concrete tunnel linings. On this basis, the effects of loading direction, material tensile properties, soil stiffness, and model size on the mechanical behavior of ECC and R/ECC linings were analyzed by numerical calculation. Parametric analysis shows that the failure modes of ECC and R/ECC linings along different load directions are caused by the loss of bearing capacity due to the formation of three plastic hinges. Lining damage under horizontal loading is more concentrated than those under vertical and oblique loading. Improving the tensile properties of ECC materials can help enhance the load capacity and deformability of linings. Soil stiffness obviously affects the postpeak deformation behavior of ECC linings, as shown by the sharp increase of the load-displacement curve with the increase of soil stiffness. The peak load and corresponding displacement of linings demonstrate nonlinear increase with the increase in model size.

COBRAme: A computational framework for genome-scale models of metabolism and gene expression.

Genome-scale models of metabolism and macromolecular expression (ME-models) explicitly compute the optimal proteome composition of a growing cell. ME-models expand upon the well-established genome-scale models of metabolism (M-models), and they enable a new fundamental understanding of cellular growth. ME-models have increased predictive capabilities and accuracy due to their inclusion of the biosynthetic costs for the machinery of life, but they come with a significant increase in model size and complexity. This challenge results in models which are both difficult to compute and challenging to understand conceptually. As a result, ME-models exist for only two organisms (Escherichia coli and Thermotoga maritima) and are still used by relatively few researchers. To address these challenges, we have developed a new software framework called COBRAme for building and simulating ME-models. It is coded in Python and built on COBRApy, a popular platform for using M-models. COBRAme streamlines computation and analysis of ME-models. It provides tools to simplify constructing and editing ME-models to enable ME-model reconstructions for new organisms. We used COBRAme to reconstruct a condensed E. coli ME-model called iJL1678b-ME. This reformulated model gives functionally identical solutions to previous E. coli ME-models while using 1/6 the number of free variables and solving in less than 10 minutes, a marked improvement over the 6 hour solve time of previous ME-model formulations. Errors in previous ME-models were also corrected leading to 52 additional genes that must be expressed in iJL1678b-ME to grow aerobically in glucose minimal in silico media. This manuscript outlines the architecture of COBRAme and demonstrates how ME-models can be created, modified, and shared most efficiently using the new software framework.

Resource considerations for integrated planning of railway traffic and maintenance windows

This paper addresses the coordination of railway network maintenance and train traffic. The work extends a previously developed optimization model by considering maintenance resource constraints for crew availability and work time regulations. The aim is to find a long term tactical plan that minimizes the total cost of maintenance and train operations, where train services and train free windows are scheduled such that maintenance can be carried out by a pool of crew resources, which are divided into bases and have limitations on maximum working hours per day and minimum rest time between these working days. A mixed integer linear programming model along with computational experiments are presented which show that these resource considerations can be correctly handled with a moderate increase in model size and solution time.

LSTM Fully Convolutional Networks for Time Series Classification

Fully convolutional neural networks (FCN) have been shown to achieve state-of-the-art performance on the task of classifying time series sequences. We propose the augmentation of fully convolutional networks with long short term memory recurrent neural network (LSTM RNN) sub-modules for time series classification. Our proposed models significantly enhance the performance of fully convolutional networks with a nominal increase in model size and require minimal preprocessing of the dataset. The proposed Long Short Term Memory Fully Convolutional Network (LSTM-FCN) achieves state-of-the-art performance compared to others. We also explore the usage of attention mechanism to improve time series classification with the Attention Long Short Term Memory Fully Convolutional Network (ALSTM-FCN). Utilization of the attention mechanism allows one to visualize the decision process of the LSTM cell. Furthermore, we propose fine-tuning as a method to enhance the performance of trained models. An overall analysis of the performance of our model is provided and compared to other techniques.

Transverse propagation in an expanded PSpice model for cardiac muscle with gap-junction ion channels.

Transverse propagation was previously found to occur in a two-dimensional model of cardiac muscle using the PSpice software program for electronic circuit design and analysis. Longitudinal propagation within each chain, and transverse propagation between parallel chains, occurred even when there were no gap-junction (g-j) channels inserted between the simulated myocardial cells either longitudinally or transversely. In those studies, there were pronounced edge (boundary) effects and end-effects even within single chains. Transverse velocity increased with increase in model size. The present study was performed to examine boundary effects on transverse propagation velocity when the length of the chains was held constant at 10 cells and the number of parallel chains was varied from 3 to 5, to 7, to 10, and to 20. The number of g-j channels was either zero, both longitudinally and transversely (0/0), or 100/100. Some experiments were also made at 100/0, 1/1, and 10/10. Transverse velocity and overall velocity (both longitudinal and transverse components) was calculated from the measured total propagation time (TPT), i.e., the elapsed time between when the first action potential (AP) and the last AP crossed the zero potential level. The transverse g-j channels were placed only at the ends of each chain, such that propagation would occur in a zigzag pattern. Electrical stimulation was applied intracellularly between cells A1 and A2. It was found that, with no g-j channels (0/0), overall velocity increased almost linearly when more and more chains were placed in parallel. In contrast, with many g-j channels (100/100), there was a much flatter relationship between overall velocity and number of parallel chains. The difference in velocities with 0/0 channels and 100/100 channels was reduced as the number of chains was increased. In conclusion, edges have important effects on propagation velocity (overall and transverse) in cardiac muscle simulations.