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We introduce the global recovery time of Gaver's parallel system supervised by a safety unit. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. As an application, we consider the particular case of Coxian distributions. [ABSTRACT FROM AUTHOR]

Toolpath generation (TPG) for multi-axis milling machines using vector fields (VF) and vector field analysis (VFA) is becoming increasingly popular in the manufacturing industry. Therefore, the paper presents a survey of algorithms and methods of TPG based on the vector fields of preferred directions (VFPD) for five-axis CNC machining. Two hundred relevant citations in top manufacturing and optimization journals during 1995–2021 have been presented and discussed. Additional 79 references in Appendices are related to a classification of five-axis machines, the theory and recent advances in the area of the vector and tensor fields. [ABSTRACT FROM AUTHOR]

Segmentation of tumors in the ultrasound (US) images of the breast is a critical problem in medical imaging. Due to the poor quality of the US images and varying specifications of the US machines, the segmentation and classification of the abnormalities present difficulties even for trained radiologists. Nevertheless, the US remains one of the most reliable and inexpensive tests. Recently, an artificial life (ALife) model based on tracing agents and fusion of the US and the elasticity images (F-ALife) has been proposed and analyzed. Under certain conditions, F-ALife outperforms state-of-the-art including the selected deep learning (DL) models, deformable models, machine learning, contour grouping and superpixels. Apart from the improved accuracy, F-ALife requires smaller training sets. The strongest competitors of the F-ALife are hybrids of the DL with conventional models. However, the current DL methods require a large amount of data (thousands of annotated images), which often is not available. Moreover, the hybrids require that the conventional model is properly integrated into the DL. Therefore, we offer a new DL-based hybrid with ALife. It is characterized by a high accuracy, requires a relatively small dataset, and is capable of handling previously unseen data. The new ideas include (1) a special image mask to guide ALife. The mask is generated using DL and the distance transform, (2) modification of ALife for segmentation of the US images providing a high accuracy. (These ideas are motivated by the “vehicles” of Braitenberg (Vehicles, experiments in synthetic psychology, MIT Press, Cambridge, 1984) and ALife proposed in Karunanayake et al. (Pattern Recognit 108838, 2022), (3) a two-level genetic algorithm which includes training by an individual image and by the entire set of images. The training employs an original categorization of the images based on the properties of the edge maps. The efficiency of the algorithm is demonstrated on complex tumors. The method combines the strengths of the DL neural networks with the speed and interpretability of ALife. The tests based on the characteristics of the edge map and complexity of the tumor shape show the advantages of the proposed DL-ALife. The model outperforms 14 state-of-the-art algorithms applied to the US images characterized by a complex geometry. Finally, the novel classification allows us to test and analyze the limitations of the DL for the processing of the unseen data. The code is applicable to breast cancer diagnostics (Automated Breast Ultra Sound), US-guided biopsies as well as to  projects related to automatic breast scanners. A video demo is at https://tinyurl.com/3xthedff. [ABSTRACT FROM AUTHOR]

Segmentation of tumors in ultrasound (US) images of the breast is a critical issue in medical imaging. Due to the poor quality of US images and the varying specifications of US machines, segmentation and classification of abnormalities present difficulties even for trained radiologists. The paper aims to introduce a novel AI-based hybrid model for US segmentation that offers high accuracy, requires relatively smaller datasets, and is capable of handling previously unseen data. The software can be used for diagnostics and the US-guided biopsies. A unique and robust hybrid approach that combines deep learning (DL) and multi-agent artificial life (AL) has been introduced. The algorithms are verified on three US datasets. The method outperforms 14 selected state-of-the-art algorithms applied to US images characterized by complex geometry and high level of noise. The paper offers an original classification of the images and tests to analyze the limits of the DL. The model has been trained and verified on 1264 ultrasound images. The images are in the JPEG and PNG formats. The age of the patients ranges from 22 to 73 years. The 14 benchmark algorithms include deformable shapes, edge linking, superpixels, machine learning, and DL methods. The tests use eight-region shape- and contour-based evaluation metrics. The proposed method (DL-AL) produces excellent results in terms of the dice coefficient (region) and the relative Hausdorff distance H3 (contour-based) as follows: the easiest image complexity level, Dice = 0.96 and H3 = 0.26; the medium complexity level, Dice = 0.91 and H3 = 0.82; and the hardest complexity level, Dice = 0.90 and H3 = 0.84. All other metrics follow the same pattern. The DL-AL outperforms the second best (Unet-based) method by 10–20%. The method has been also tested by a series of unconventional tests. The model was trained on low complexity images and applied to the entire set of images. These results are summarized below. (1) Only the low complexity images have been used for training (68% unknown images): Dice = 0.80 and H3 = 2.01. (2) The low and the medium complexity images have been used for training (51% unknown images): Dice = 0.86 and H3 = 1.32. (3) The low, medium, and hard complexity images have been used for training (35% unknown images): Dice = 0.92 and H3 = 0.76. These tests show a significant advantage of DL-AL over 30%. A video demo illustrating the algorithm is at http://tinyurl.com/mr4ah687.Graphical Abstract: Segmentation of tumors in ultrasound (US) images of the breast is a critical issue in medical imaging. Due to the poor quality of US images and the varying specifications of US machines, segmentation and classification of abnormalities present difficulties even for trained radiologists. The paper aims to introduce a novel AI-based hybrid model for US segmentation that offers high accuracy, requires relatively smaller datasets, and is capable of handling previously unseen data. The software can be used for diagnostics and the US-guided biopsies. A unique and robust hybrid approach that combines deep learning (DL) and multi-agent artificial life (AL) has been introduced. The algorithms are verified on three US datasets. The method outperforms 14 selected state-of-the-art algorithms applied to US images characterized by complex geometry and high level of noise. The paper offers an original classification of the images and tests to analyze the limits of the DL. The model has been trained and verified on 1264 ultrasound images. The images are in the JPEG and PNG formats. The age of the patients ranges from 22 to 73 years. The 14 benchmark algorithms include deformable shapes, edge linking, superpixels, machine learning, and DL methods. The tests use eight-region shape- and contour-based evaluation metrics. The proposed method (DL-AL) produces excellent results in terms of the dice coefficient (region) and the relative Hausdorff distance H3 (contour-based) as follows: the easiest image complexity level, Dice = 0.96 and H3 = 0.26; the medium complexity level, Dice = 0.91 and H3 = 0.82; and the hardest complexity level, Dice = 0.90 and H3 = 0.84. All other metrics follow the same pattern. The DL-AL outperforms the second best (Unet-based) method by 10–20%. The method has been also tested by a series of unconventional tests. The model was trained on low complexity images and applied to the entire set of images. These results are summarized below. (1) Only the low complexity images have been used for training (68% unknown images): Dice = 0.80 and H3 = 2.01. (2) The low and the medium complexity images have been used for training (51% unknown images): Dice = 0.86 and H3 = 1.32. (3) The low, medium, and hard complexity images have been used for training (35% unknown images): Dice = 0.92 and H3 = 0.76. These tests show a significant advantage of DL-AL over 30%. A video demo illustrating the algorithm is at http://tinyurl.com/mr4ah687. [ABSTRACT FROM AUTHOR]

A segmentation model of the ultrasound (US) images of breast tumors based on virtual agents trained using reinforcement learning (RL) is proposed. The agents, living in the edge map, are able to avoid false boundaries, connect broken parts, and finally, accurately delineate the contour of the tumor. The agents move similarly to robots navigating in the unknown environment with the goal of maximizing the rewards. The individual agent does not know the goal of the entire population. However, since the robots communicate, the model is able to understand the global information and fit the irregular boundaries of complicated objects. Combining the RL with a neural network makes it possible to automatically learn and select the local features. In particular, the agents handle the edge leaks and artifacts typical for the US images. The proposed model outperforms 13 state-of-the-art algorithms, including selected deep learning models and their modifications. [ABSTRACT FROM AUTHOR]

We analyse the availability of a general robot–safety device system characterised by the feature of cold standby and by an admissible risky state. In contrast to the previous literature, we allow a general failure-free time distribution for the robot and, as an example, we present computational results for Coxian failure and repair time distributions. In order to decide whether the risky state is admissible, we introduce a risk criterion based on the notion of rare events. The criterion is always satisfied in the case of fast repair. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new version of generalized gradient flow (GGVF) snakes involving multiple features of the vector field. [•] Polynomial diffusion based on prescribed clusters of the edge map. [•] A new, directional (orientation) feature integrated into the GGVF snake model. [•] Preprocessing based on hierarchical clustering. [•] A large series of numerical experiments with an in-depth analysis and tests against recent modifications of GGVF. [ABSTRACT FROM AUTHOR]

We introduce a robot–safety device system characterized by cold stand-by and by an admissible risky state. The system is attended by a single repairman and the robot has overall (break-in) priority in repair with regard to the safety device. We obtain an explicit formula for the point availability of the robot via an integral equation of the renewal-type. The explicit solution requires the notion of effective repair-versus-virtual repair. In order to decide whether the risky state is admissible, we also introduce a risk criterion. The criterion is always satisfied in the case of fast repair. As an example, we consider the case of Weibull–Gnedenko repair and we display a computer-plotted graph of the point availability obtained by a direct numerical solution of a convolution-type integral equation. [ABSTRACT FROM AUTHOR]

Abstract: We propose a modification of the generalized gradient vector flow field techniques based on a continuous force field analysis. At every iteration the generalized gradient vector flow method obtains a new, improved vector field. However, the numerical procedure always employs the original image to calculate the gradients used in the source term. The basic idea developed in this paper is to use the resulting vector field to obtain an improved edge map and use it to calculate a new gradient based source term. The improved edge map is evaluated by new continuous force field analysis techniques inspired by a preceding discrete version. The approach leads to a better convergence and better segmentation accuracy as compared to several conventional gradient vector flow type methods. [Copyright &y& Elsevier]

The paper presents a survey of five-axis computer numerical controlled (CNC) machining optimization methods employing adaptable geometric patterns. First, the survey introduces evolution of CNC interpolators from the simplest Taylor series-based routines to sophisticated procedures based on constraint minimization from dynamic systems control theory. Furthermore, a variety of methods based on spline interpolation, NURBS interpolation and Farouki’s Pythagorean–hodograph curves is presented and analyzed. Next, the survey deals with techniques to optimize the positions and orientations of the tool in a particular neighborhood of the part surface. The most important application of these techniques is cutting by a flat-end or a fillet mill while avoiding local overcuts or undercuts due to the curvature interference and rear gouging. This section is supplemented by detection of global interference using visibility cone schemes and their recent modifications and improvements. Solutions offered by solid modeling are presented as well. Finally, adaptable geometric patterns employed for tool path generation are considered and analyzed. The adaptation is performed using certain criteria of the tool path quality, such as kinematics error, scallops, possible undercuts or overcuts, and the continuity of the path. Also covered are complex pocket milling employing geometric patterns capable of following the boundary, such as the offset methods, regional milling, the potential path methods, and clustering. The chapter also presents tool path optimization based on the adaptable curvilinear grids connecting the cutter location points. Finally, navigation approaches and the shortest-path schemes are considered, along with the adaptive space-filling curve algorithms and their combinations with grid generation. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a new combination of two methods for tool path generation for five-axis machining proposed earlier by the authors. The first method is based on the grid generation technologies whereas the second method exploits the space-filling curve approach. Combination of the two techniques is superior with regard to the conventional methods and with regard to the case when the two methods are applied independently. In particular the algorithm allows us to generate tool paths for workpieces with complex boundaries as well as when the scallop and gouging constraints are changing sharply and irregularly. In this case the conventional methods are inefficient, whereas the proposed algorithms construct the required tool path and reduce the length of the path and the time of the machining. The numerical experiments are complemented by the real machining as well as by the test simulations on the Unigraphics 18. [Copyright &y& Elsevier]

We propose multiresolution filter bank techniques to construct rotationally invariant moments. The multiresolution pyramid motivates a simple but efficient feature selection procedure based on a combination of a pruning algorithm, a new version of the Apriori mining techniques and the partially supervised fuzzy C-mean clustering. The recognition accuracy of the proposed techniques has been tested with the reference to conventional methods. The numerical experiments, with more than 50,000 images taken from standard image datasets, demonstrate an accuracy increase ranging from 5% to 27% depending on the noise level. [Copyright &y& Elsevier]

Optimization of cutting operations is an active area of research in CNC-based manufacturing. The limited capabilities of the CAD/CAM systems require development of a new software and new numerical methods verified by practical machining. We formulate the problem of tool-path optimization in terms of interpolation of the required part surface in the curvilinear coordinate system associated with the cutter location points. Next, we present some introductory examples to demonstrate that the concept of adaptive curvilinear grid contains almost all the basic ingredients of tool-path planning, such as: adaptation to regions of large milling errors, conventional zigzag/spiral patterns and constraints related to the scallop height. Consequently, we propose a new grid based optimization procedure characterized by adaptation to a control function which depends on the rotations required to correctly position the tool. We also consider a particular but important optimization of the rotation angles near the stationary points based on the shortest path scheme. Finally, we present an application of the algorithms to tool-path planning and demonstrate the efficiency of the proposed scheme by methodological examples verified by practical machining. [Copyright &y& Elsevier]

The paper presents six new numerical finite-difference schemes to solve nonlinear parabolic initial boundary value problems with constraints imposed a priori on the solution. The first three proposed schemes are based on a special first-order approximation of the “diffusion” and “transport” terms combined with an unconditionally stable Gauss–Seidel-type iterative technique. We present a theoretical analysis of the method as applied to the diffusion wave equation and to the generalized diffusion wave approach. The fourth scheme allows for an accuracy enhancement at the expense of the computational cost. The scheme employs an adaptive grid which guarantees the second-order approximation or nearly so. An efficiency of the proposed techniques is demonstrated by the numerical simulations of flood in the eastern areas of Bangkok. Next, the first-order techniques are generalized to the Richard''s type model of unsaturated porous medium flows, representing the general case of a nonlinear parabolic equation endowed with the space dependent bilateral constraints. The fifth and the sixth schemes are designed for space independent and space dependent constraints, respectively. We present a theoretical analysis of the methods. Finally, we verify the proposed schemes by methodological applications and analyze the convergence rate. [Copyright &y& Elsevier]

Targeted magnetic drug delivery (TMDD) is a promising approach relevant to multimodal cancer therapy. A majority of the TMDD models represent a mixture of blood and nanoparticles as a one-phase solution. However, in many cases it is an oversimplistic assumption. The existing two-phase models are usually one-way coupled, i.e. the blood flow has an impact on the MN flow. However, the inverse impact of the MNs on the the blood is not included. To eliminate these drawbacks the model is governed by two–way coupled momentum and temperature equations for the blood flow and the MN. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical procedure. The model, validated by experimental results, has been applied to analyze the formation of vortices generated by a combination of the magnetic force (MF) and the drag force (DF). The model also simulates the zones of TMDD and the corresponding changes in the vorticity. Finally, the model includes the impact of the size and concentration of the MNs on the temperature of the blood. These important scenarios cannot be analyzed by the earlier models. [ABSTRACT FROM AUTHOR]

Due to significant advances in nanomedicine, magnetic nanoparticles (MNs) have emerged as a promising carrier in targeted magnetic drug delivery (TMDD) systems. Therefore, this paper presents a computational model for optimized magnetic navigation of MNs coated with the anticancer drugs inside the blood vessels. A mixture of blood and MNs is represented as a one-phase solution in the majority of TMDD models. The preceding two-phase models are usually one-way coupled, i.e., the blood flow has a significant influence on the MNs flow. However, the inverse effect of the MNs on the blood flow is not taken into account. To overcome these limitations, the MNs in a blood vessel are simulated by a two-phase (solid–liquid) flow governed by two-way coupled momentum and temperature equations for the blood flow and the MNs. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical method on a finite-difference grid. The model, validated by the experimental results, has been applied to analyze the formation of vortices relative to the magnetic force and the drag force and the zones of TMDD, where the velocity of the blood flow is low and the velocity of the MNs is high toward the magnet. The model has been verified against the existing models and the experimental data. The numerical results show that the magnetohydrodynamics slows down the blood flow and smooths vortices created by Ferrohydrodynamics. The size of the drug-loaded MNs on the velocity and the temperature of the blood has been evaluated. [ABSTRACT FROM AUTHOR]

• A new method of segmentation medical images which combines AI, fusion and artificial life. • A new variant of fusion of the US and the elastography images. • Artificial agents with the ability to find strong edges and close the boundary gaps. • Testing against 85 preceding segmentation methods. • Video demo at http://shorturl.at/htBW9. Segmentation of cancerous tumors in ultrasound (US) images of human organs is one of the critical problems in medical imaging. The US images are characterized by low contrast, irregular shapes, high levels of speckle-noise and acoustic shadows, making it difficult to segment the tumor. Yet, US imaging is considered one of the most inexpensive and safe imaging tests available to detect cancer in its early stages. However, an automatic segmentation method applicable to all types of US imagery does not exist. This paper proposes a novel segmentation method that combines image fusion, artificial life (AL) and a genetic algorithm (GA). The new algorithm has been applied to US images of breast cancer. The method is based on tracing agents (TA), which are artificial organisms with memory and the ability to communicate. They live inside a fusion image generated from the US and the elastography (EL) images. The TA can recognize the patterns of strong edges and boundary gaps allowing to outline the tumor. The new model has been tested against six types of segmentation models, i.e., machine learning, active contours, level set models, superpixel models, edge linking models and selected hybrid methods. The experiments include 16 state-of-the-art methods, which outperform 69 recent and classical segmentation routines. The tests were run on 395 breast cancer images from http://onlinemedicalimages.com and https://www.ultrasoundcases.info/. TA training employs a GA. The model has been verified on "hard" cases (complex shapes, boundary leakage, and noisy edge maps). The proposed algorithm produces more accurate results than the reference methods on high complexity images. A video demo of the algorithm is at http://shorturl.at/htBW9. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a novel segmentation method based on the scale space techniques endowed with a feature stability approach. The novelty of the paper is the lifetime of the space-scale blobs measured not only by their presence and disappearance but by the stability of the features characterizing the objects of interest as well. Our numerical experiments show that the algorithm outperforms the conventional space scale algorithm applied to variable size and variable shape objects. The proposed algorithm can be used as a preprocessing step in object or pattern recognition applications to produce seeds for more accurate image segmentation methods such as the snakes or the level set techniques. [Copyright &y& Elsevier]

Abstract: The paper presents a simple, parameter-free method to detect the optic disc in retinal images. It works efficiently for blurred and noisy images with a varying ratio OD/image size. The method works equally well on images with different characteristics which often cause standard methods to fail or require a new round of training. The proposed method has been tested on 214 infant and adult retinal images and has been compared against hand-drawn ground truths generated by experts. It displays consistently high OD detection rates without any prior training or adjustment of the parameters. [Copyright &y& Elsevier]

• A new active contour initialization method based on the fusion of a conventional ultrasound with elasticity and Doppler images has been proposed and analyzed. • Numerical tests against four state-of-the-art initialization methods methods are presented to demonstrate the advantages of the proposed techniques. • The proposed algorithm is applicable to similar ultrasound images without any modifications. Active contours (snakes) are an efficient method for segmentation of ultrasound (US) images of breast cancer. However, the method produces inaccurate results if the seeds are initialized improperly (far from the true boundaries and close to the false boundaries). Therefore, we propose a novel initialization method based on the fusion of a conventional US image with elasticity and Doppler images. The proposed fusion method (FM) has been tested against four state-of-the-art initialization methods on 90 ultrasound images from a database collected by the Thammasat University Hospital of Thailand. The ground truth was hand-drawn by three leading radiologists of the hospital. The reference methods are: center of divergence (CoD), force field segmentation (FFS), Poisson Inverse Gradient Vector Flow (PIG), and quasi-automated initialization (QAI). A variety of numerical tests proves the advantages of the FM. For the raw US images, the percentage of correctly initialized contours is: FM-94.2%, CoD-0%, FFS-0%, PIG-26.7%, QAI-42.2%. The percentage of correctly segmented tumors is FM-84.4%, CoD-0%, FFS-0%, PIG-16.67%, QAI-22.44%. For reduced field of view US images, the percentage of correctly initialized contours is: FM-94.2%, CoD-0%, FFS-0%, PIG-65.6%, QAI-67.8%. The correctly segmented tumors are FM-88.9%, CoD-0%, FFS-0%, PIG-48.9%, QAI-44.5%. The accuracy, in terms of the average Hausdorff distance, is respectively 2.29 pixels, 33.81, 34.71, 7.7, and 8.4, whereas in terms of the Jaccard index, it is 0.9, 0.18, 0.19, 0.63, and 0.48. [ABSTRACT FROM AUTHOR]

We propose a novel initialization method designed for active contours (AC) and the level set method (LSM), based on walking particles. The algorithm defines the seeds at converging and diverging configurations of the corresponding vector field. Next, the seeds “explode”, generating a set of walking particles designed to differentiate between the seeds located inside and outside the object. The exploding seeds method (ESM) has been tested against five state-of-the-art initialization methods on 180 ultrasound images from a database collected by Thammasat University Hospital of Thailand. The set of images was additionally partitioned into malignant tumors, fibroadenomas and cysts. The method has been tested for each of those cases using the ground truth hand-drawn by leading radiologists of the hospital. The competing methods were: the trial snake (TS), centers of divergence (CoD), force field segmentation (FFS), Poisson Inverse Gradient Vector Flow (PIG), and quasi-automated initialization (QAI). The numerical tests demonstrated that CoD and FFS failed on the selected test images, whereas the average accuracy of PIG and QAI were lower than that achieved by the proposed method for both AC and the LSM. The LSM combined with the ESM provides the best results. [ABSTRACT FROM AUTHOR]

Gradient vector flow (GVF) snakes are an efficient method for segmentation of ultrasound images of breast cancer. However, the method produces inaccurate results if the seeds are initialized improperly (far from the true boundaries and close to the false boundaries). Therefore, we propose a novel initialization method designed for GVF-type snakes based on walking particles. At the first step, the algorithm locates the seeds at converging and diverging configurations of the vector field. At the second step, the seeds “explode,” generating a set of random walking particles designed to differentiate between the seeds located inside and outside the object. The method has been tested against five state-of-the-art initialization methods on sixty ultrasound images from a database collected by Thammasat University Hospital of Thailand (http://onlinemedicalimages.com). The ground truth was hand-drawn by leading radiologists of the hospital. The competing methods were: trial snake method (TS), centers of divergence method (CoD), force field segmentation (FFS), Poisson Inverse Gradient Vector Flow (PIG), and quasi-automated initialization (QAI). The numerical tests demonstrated that CoD and FFS failed on the selected test images, whereas the average accuracy of PIG and QAI was 73 and 87%, respectively, versus 97% achieved by the proposed method. Finally, TS has shown a comparable accuracy of about 93%; however, the method is about ten times slower than the proposed exploding seeds. A video demonstration of the algorithm is at http://onlinemedicalimages.com/index.php/en/presentations. [ABSTRACT FROM AUTHOR]