Algorithms, Volume 15, Issue 12 (December 2022) – 45 articles

Capturing long-term statistics of signals and time series is important for modeling recurrent phenomena, especially when such recurrences are a-periodic and can be characterized by the approximate repetition of variable length motifs, such as patterns in human gestures and trends in financial time series or musical melodies. Regressive and auto-regressive models that are common in such problems, both analytically derived and neural network-based, often suffer from limited memory or tend to accumulate errors, making them sensitive during training. Moreover, such models often assume stationary signal statistics, which makes it difficult to deal with switching regimes or conditional signal dynamics. In this paper, we describe a method for time series modeling that is based on adaptive symbolization that maximizes the predictive information of the resulting sequence. Using approximate string-matching methods, the initial vectorized sequence is quantized into a discrete representation with a variable quantization threshold. Finding an optimal signal embedding is formulated in terms of a predictive bottleneck problem that takes into account the trade-off between representation and prediction accuracy. Several downstream applications based on discrete representation are described in this paper, which includes an analysis of the symbolic dynamics of recurrence statistics, motif extraction, segmentation, query matching, and the estimation of transfer entropy between parallel signals. Full article

Unweighted Pair Group Method with Arithmetic Mean (UPGMA) is one of the most popular distance-based methods to reconstruct an equidistant phylogenetic tree from a distance matrix computed from an alignment of sequences. Since we use equidistant trees as gene trees for phylogenomic analyses under the multi-species coalescent model and since an input distance matrix computed from an alignment of each gene in a genome is estimated via the maximum likelihood estimators, it is important to conduct a robust analysis on UPGMA. Stochastic safety radius, introduced by Steel and Gascuel, provides a lower bound for the probability that a phylogenetic tree reconstruction method returns the true tree topology from a given distance matrix. In this article, we compute the stochastic safety radius of UPGMA for a phylogenetic tree with n leaves. Computational experiments show an improved gap between empirical probabilities estimated from random samples and the true tree topology from UPGMA, increasing confidence in phylogenic results. Full article

In this paper, the procedure of finding the coefficients of an equation to describe the thermal conductivity of refrigerants low in global warming potential (GWP) is transformed into a multi-objective optimization problem by constructing a multi-objective mathematical model based on the Pareto approach. For the first time, the NSGAII algorithm was used to describe a thermophysical property such as thermal conductivity. The algorithm was applied to improve the performance of existing equations. Two objective functions were optimized by using the NSGAII algorithm. The average absolute relative deviation was minimized, while the coefficient of determination was maximized. After the minimization process, the optimal solution located on the Pareto frontier was chosen through a comparative analysis between ten selection methods available in the literature. The procedure generated a new set of coefficients of the studied equation that decreased its average absolute relative deviation by 0.24%, resulting in better performance over the entire database and for fluids with a high number of points. Finally, the system model was compared with existing literature models to evaluate its suitability for predicting the thermal conductivity of low-GWP refrigerants. Full article

Connectivity in large-scale data center networks is a critical indicator to evaluate network state. A feasible and performance-guaranteed algorithm enables us to find disjoint paths between network vertices to ensure effective data transfer and to maintain the normal operation of network in case of faulty nodes. As an important data center network, BCube Connected Crossbars (BCCC) has many excellent properties that have been widely studied. In this paper, we first propose a vertex disjoint path algorithm with the time complexity of $O\left(nk\right)$ in BCCC, where n denotes a switch connected to n servers and k denotes dimension. Then, we prove that the restricted connectivity of $BCCC\left(n,k\right)$. Finally, we present an $O\left(kn{\kappa }^1\left(G\right)\right)$ fault-free algorithm in BCCC, where ${\kappa }^1\left(G\right)$ is the restricted connectivity. This algorithm can obtain a fault-free path between any two distinct fault-free vertices under the condition that each vertex has at least one fault-free neighbor in the BCCC and a set of faulty vertices F with $\left|F\right|<{\kappa }^1\left(G\right)$. Full article

The evaluation of the fault diagnosis capability of a data center network (DCN) is important research in measuring network reliability. The g-extra diagnosability is defined under the condition that every component except the fault vertex set contains at least g+1 vertices. The t/k diagnosis strategy is that the number of fault nodes does not exceed t, and all fault nodes can be isolated into a set containing up to k fault-free nodes. As an important data center network, BCube Connected Crossbars (BCCC) has many excellent properties that have been widely studied. In this paper, we first determine that the g-extra connectivity of $B{C}_{n,k}$ for $0\le g\le n-1$. Based on this, we establish the g-extra conditional diagnosability of $B{C}_{n,k}$ under the MM* model for $1\le g\le n-1$. Next, based on the conclusion of the largest connected component in g-extra connectivity, we prove that the t/k-diagnosability of $B{C}_{n,k}$ under the MM* model for $1\le k\le n-1$. Finally, we present a t/k diagnosis algorithm on BCCC under the MM* model. The algorithm can correctly identify all nodes at most k nodes undiagnosed. So far, t/k-diagnosability and diagnosis algorithms for most networks in the MM* model have not been studied. Full article

It has been proven that extended resolution (ER) has more powerful reasoning than general resolution for the pigeonhole principle in Cook’s paper. This fact indicates the possibility that a solver based on extended resolution can exceed Boolean satisfiability problem solvers (SAT solvers for short) based on general resolution. However, few studies have provided practical evidence of this assumption. This paper explores how extended resolution can improve SAT solvers by using the pigeonhole principle, which was the first problem solved by ER in polynomial steps. In fact, although Cook’s paper introduced how to add auxiliary variables, there is no evidence that these variables are really useful for practical solvers. We try to answer the question: If the SAT solver can add appropriate auxiliary variables as proposed in Cook’s paper, can the solver enhance its performance by utilizing these variables? Experimental results show that if the solver properly prioritizes the extended variables in the search, the solver can end the search in a shorter time. Full article

The problem of wildfire spread prediction presents a high degree of complexity due in large part to the limitations for providing accurate input parameters in real time (e.g., wind speed, temperature, moisture of the soil, etc.). This uncertainty in the environmental values has led to the development of computational methods that search the space of possible combinations of parameters (also called scenarios) in order to obtain better predictions. State-of-the-art methods are based on parallel optimization strategies that use a fitness function to guide this search. Moreover, the resulting predictions are based on a combination of multiple solutions from the space of scenarios. These methods have improved the quality of classical predictions; however, they have some limitations, such as premature convergence. In this work, we evaluate a new proposal for the optimization of scenarios that follows the Novelty Search paradigm. Novelty-based algorithms replace the objective function by a measure of the novelty of the solutions, which allows the search to generate solutions that are novel (in their behavior space) with respect to previously evaluated solutions. This approach avoids local optima and maximizes exploration. Our method, Evolutionary Statistical System based on Novelty Search (ESS-NS), outperforms the quality obtained by its competitors in our experiments. Execution times are faster than other methods for almost all cases. Lastly, several lines of future work are provided in order to significantly improve these results. Full article

The Theta* algorithm is a path planning algorithm based on graph search, which gives the optimal path with more flexibility than A* algorithm in terms of routes. The traditional Theta* algorithm is difficult to take into account with the global and details in path planning and traverses more nodes, which leads to a large amount of computation and is not suitable for path planning in large scenarios directly by the Theta* algorithm. To address this problem, this paper proposes an improved Theta* algorithm, namely the W-Theta* algorithm. The heuristic function of Theta* is improved by introducing a weighting strategy, while the default Euclidean distance calculation formula of Theta* is changed to a diagonal distance calculation formula, which finally achieves a reduction in computation time while ensuring a shorter global path; the trajectory optimization is achieved by curve fitting of the generated path points to make the motion trajectory of the mobile robot smoother. Simulation results show that the improved algorithm can quickly plan paths in large scenarios. Compared with other path planning algorithms, the algorithm has better performance in terms of time and computational cost. In different scenarios, the W-Theta* algorithm reduces the computation time of path planning by 81.65% compared with the Theta* algorithm and 79.59% compared with the A* algorithm; the W-Theta* algorithm reduces the memory occupation during computation by 44.31% compared with the Theta* algorithm and 29.33% compared with the A* algorithm. Full article

We propose an agent-based model of financial markets with only one asset. Thirty-two agents follow very simple rules inspired by Wolfram’s Rule 110. They engage in buying, selling, and/or holding. Each agent is endowed with a starting balance sheet marked-to-market in each iteration. The simulation allows for margin calls for both buying and selling. During each iteration, the number of buy, hold, and sell positions is aggregated into a market price with the help of a simple, linear formula. The formula generates a price depending on the number of buy and sell positions. Various results are obtained by altering the pricing formula, the trading algorithm, and the initial conditions. When applying commonly used statistical tools, we find processes that are essentially indistinguishable from the price of real assets. They even display bubbles and crashes, just like real market data. Our model is remarkable because it can apparently generate a process of equivalent complexity to that of a real asset price, but it starts from a handful of initial conditions and a small number of very simple linear algorithms in which randomness plays no part. We contend our results have far-reaching implications for the debate around investor behavior and the regulation of financial markets. Full article

Parkinson’s disease (PD) is a neurodegenerative disorder that is more common in elderly people and affects motor control, flexibility, and how easily patients adapt to their walking environments. PD is progressive in nature, and if undetected and untreated, the symptoms grow worse over time. Fortunately, PD can be detected early using gait features since the loss of motor control results in gait impairment. In general, techniques for capturing gait can be categorized as computer-vision-based or sensor-based. Sensor-based techniques are mostly used in clinical gait analysis and are regarded as the gold standard for PD detection. The main limitation of using sensor-based gait capture is the associated high cost and the technical expertise required for setup. In addition, the subjects’ consciousness of worn sensors and being actively monitored may further impact their motor function. Recent advances in computer vision have enabled the tracking of body parts in videos in a markerless motion capture scenario via human pose estimation (HPE). Although markerless motion capture has been studied in comparison with gold-standard motion-capture techniques, it is yet to be evaluated in the prediction of neurological conditions such as PD. Hence, in this study, we extract PD-discriminative gait features from raw videos of subjects and demonstrate the potential of markerless motion capture for PD prediction. First, we perform HPE on the subjects using AlphaPose. Then, we extract and analyse eight features, from which five features are systematically selected, achieving up to 93% accuracy, 96% precision, and 92% recall in arbitrary views. Full article

One of the most critical issues that the marine surveillance system has to address is the accuracy of its ship detection. Since it is responsible for identifying potential pirate threats, it has to be able to perform its duties efficiently. In this paper, we present a novel deep learning approach that combines the capabilities of a Graph Neural Network (GNN) and a You Only Look Once (YOLOv7) deep learning framework. The main idea of this method is to provide a better understanding of the ship’s presence in harbor areas. The three hyperparameters that are used in the development of this system are the learning rate, batch sizes, and optimization selection. The results of the experiments show that the Adam optimization achieves a 93.4% success rate when compared to the previous generation of the YOLOv7 algorithm. The High-Resolution Satellite Image Dataset (HRSID), which is a high-resolution image of a synthetic aperture radar, was used for the test. This method can be further improved by taking into account the various kinds of neural network architecture that are commonly used in deep learning. Full article

Significant progress has been achieved in text generation due to recent developments in neural architectures; nevertheless, this task remains challenging, especially for low-resource languages. This study is centered on developing a model for abstractive summarization in Romanian. A corresponding dataset for summarization is introduced, followed by multiple models based on the Romanian GPT-2, on top of which control tokens were considered to specify characteristics for the generated text, namely: counts of sentences and words, token ratio, and n-gram overlap. These are special tokens defined in the prompt received by the model to indicate traits for the text to be generated. The initial model without any control tokens was assessed using BERTScore (${\mathrm{F}}_1$ = 73.43%) and ROUGE (ROUGE-L accuracy = 34.67%). Control tokens improved the overall BERTScore to 75.42% using <LexOverlap>, while the model was influenced more by the second token specified in the prompt when performing various combinations of tokens. Six raters performed human evaluations of 45 generated summaries with different models and decoding methods. The generated texts were all grammatically correct and consistent in most cases, while the evaluations were promising in terms of main idea coverage, details, and cohesion. Paraphrasing still requires improvements as the models mostly repeat information from the reference text. In addition, we showcase an exploratory analysis of the generated summaries using one or two specific control tokens. Full article

Nowadays, digital transformation (DX) is the key concept to change and improve the operations in governments, companies, and schools. Therefore, any data should be digitized for processing by computers. Unfortunately, a lot of data and information are printed and handled on paper, although they may originally come from digital sources. Data on paper can be digitized using an optical character recognition (OCR) software. However, if the paper contains a table, it becomes difficult because of the separated characters by rows and columns there. It is necessary to solve the research question of “how to convert a printed table on paper into an Excel table while keeping the relationships between the cells?” In this paper, we propose a printed table digitization algorithm using image processing techniques and OCR software for it. First, the target paper is scanned into an image file. Second, each table is divided into a collection of cells where the topology information is obtained. Third, the characters in each cell are digitized by OCR software. Finally, the digitalized data are arranged in an Excel file using the topology information. We implement the algorithm on Python using OpenCV for the image processing library and Tesseract for the OCR software. For evaluations, we applied the proposal to 19 scanned and 17 screenshotted table images. The results show that for any image, the Excel file is generated with the correct structure, and some characters are misrecognized by OCR software. The improvement will be in future works. Full article

The work defines in a new way the different types of solutions of the inverse kinematics (IK) problem for planar robots with a serial topology and presents an algorithm for solving it. The developed algorithm allows the finding of solutions for a wide range of robots by using a geometric approach, representing points in a polar coordinate system. Inverse kinematics, which is one of the most important, most studied and challenging problems in robotics, aims to calculate the values of the joint variables, given the desired position and orientation of the robot’s end effector. Configuration space is defined by joint angles and is the basis of most motion planning algorithms. Areas in the working and configuration space are generated that are reachable with different types of solutions. Programs are created that use the proposed algorithm for robots with two and three rotational degrees of freedom, and graphically present the results in the workspace and configuration space. The possibility of transitioning from one type of solution to another by passing through a singular configuration is discussed. The results are important for planning motions in the workspace and configuration space, as well as for the design and kinematic analysis of robots. Full article

The article discusses the problem of visualization of complex multiparameter systems, defined by datasets on their structure, functional structure, and activity in the form of complex graphs and transition of traditional representation of the data acquired by graph mining to a compact image built by pictographic methods. In these situations, we propose using the Unified Graphic Visualization of Activity (UGVA) method for data concentration and structuring. The UGVA method allows coding in an anthropomorphic image of elements of graphs with data on structural and functional features of systems and overlaying these images with the data on the system’s activity using coloring and artifacts. The image can be composed in different ways: it can include the zone of integral evaluation parameters, segmented data axes of five types, and four types of symmetry. We describe the method of creating UGVA images, which consists of 13 stages: the parametric model is represented as a structural image that is converted to a basic image that is then detailed into the particular image by defining geometric parameters of the primitives and to the individualized image with the data about a particular object. We show how the individualized image can be overlaid with the operative data as color coding and artifacts and describe the principles of interpreting UGVA images. This allows solving tasks of evaluation, comparison, and monitoring of complex multiparameter systems by showing the decision-maker an anthropomorphic image instead of the graph. We describe a case study of using the UGVA method for visualization of data about an educational process: curricula and graduate students, including the data mined from the university’s learning management system at the Siberian Federal University for students majoring in “informatics and computing”. The case study demonstrates all stages of image synthesis and examples of their interpretation for situation assessment, monitoring, and comparison of students and curricula. It allowed for finding problematic moments in learning for individual students and their entire group by analyzing the development of their competence profiles and formulating recommendations for further learning. The effectiveness of the resulting images is compared to the other approaches: elastic maps and Chernoff faces. We discuss using graph mining to generate learning problems in order to lessen the workload of gathering raw data for the UGVA method and provide general recommendations for using the UGVA method based on our experience of supporting decision making. Full article

Vehicle safety risk can be decreased by diagnosing the lithium-ion battery system of electric road vehicles. Real-time cell diagnostics can avoid unexpected occurrences. However, lithium-ion batteries in electric vehicles can significantly differ in design, capacity, and chemical composition. In addition, the battery monitoring systems of the various vehicles are also diverse, so communication across the board is not available or can only be achieved with significant difficulty. Hence, unique type-dependent data queries and filtering are necessary in most cases. In this paper, a Volkswagen e-Golf electric vehicle is investigated; communication with the vehicle was implemented via an onboard diagnostic port (so-called OBD), and the data stream was recorded. The goal of the research is principally to filter out, identify, and localize defective/weak battery cells. Numerous test cycles (constant and dynamic measurements) were carried out to identify cell abnormalities (so-called deviations). A query and data filtering process was designed to detect defective battery cells. The fault detection procedure is based on several cell voltage interruptions at various loading levels. The methodology demonstrated in this article uses a fault diagnosis technique based on voltage abnormalities. In addition, it employs a hybrid algorithm that executes calculations on measurement and recorded data. In the evaluation, a status line comprising three different categories was obtained by parametrizing and prioritizing (weighting) the individual measured values. It allows the cells to be divided into the categories green (adequate region), yellow (to be monitored), and red (possible error). In addition, several querying strategies were developed accordingly to clarify and validate the measurement results. The several strategies were examined individually and analyzed for their strengths and weaknesses. Based on the results, a data collection, processing, and evaluation strategy for an electric vehicle battery system have been developed. The advantage of the developed algorithm is that the method can be adapted to any electric or hybrid vehicle battery. Full article

Deep learning and additive manufacturing have progressed together in the previous couple of decades. Despite being one of the most promising technologies, they have several flaws that a collaborative effort may address. However, digital manufacturing has established itself in the current industrial revolution and it has slowed down quality control and inspection due to the different defects linked with it. Industry 4.0, the most recent industrial revolution, emphasizes the integration of intelligent production systems and current information technologies. As a result, deep learning has received a lot of attention and has been shown to be quite effective at understanding image data. This review aims to provide a cutting-edge deep learning application of the AM approach and application. This article also addresses the current issues of data privacy and security and potential solutions to provide a more significant dimension to future studies. Full article

Small perturbations can make deep models fail. Since deep models are widely used in face recognition systems (FRS) such as surveillance and access control, adversarial examples may introduce more subtle threats to face recognition systems. In this paper, we propose a practical white-box adversarial attack method. The method can automatically form a local area with key semantics on the face. The shape of the local area generated by the algorithm varies according to the environment and light of the character. Since these regions contain major facial features, we generated patch-like adversarial examples based on this region, which can effectively deceive FRS. The algorithm introduced the momentum parameter to stabilize the optimization directions. We accelerated the generation process by increasing the learning rate in segments. Compared with the traditional adversarial algorithm, our algorithms are very inconspicuous, which is very suitable for application in real scenes. The attack was verified on the CASIA WebFace and LFW datasets which were also proved to have good transferability. Full article

Researchers have explored multiple Wi-Fi features to estimate user locations in indoor environments in the past decade, such as Received Signal Strength Indication (RSSI), Channel State Information (CSI), Time of Arrival (TOA), and Angle of Arrive (AoA). Fine Time Measurement (FTM) is a protocol standardized by IEEE 802.11-2016, which can estimate the distance between the initiator and the station using Wi-Fi Round-Trip Time (RTT). Promoted by Google, such a protocol has been explored in many mobile localization algorithms, which can provide meter-level positioning accuracy between Wi-Fi RTT-enabled smartphones and access points (APs). However, previous studies have shown that the Wi-Fi RTT measurements are sensitive to environmental changes, which leads to significant errors in the localization algorithms. Such an error usually varies according to different environments and settings. Therefore, this paper investigates the error in Wi-Fi RTT distance measurements by setting multiple experiments with different hardware, motion status, and signal path loss conditions. The experiment results show that four categories of errors are found in RTT distance measurements, including hardware-dependent bias, blocker-dependent bias, fluctuations, and outliers. Comparison and analysis are carried out to illustrate the impact of the different errors on Wi-Fi RTT distance. Full article

A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients. However, multistep composition schemes are much less-known and investigated in the literature due to their complex nature. In this paper, we propose several novel schemes for solving ordinary differential equations based on the composition of adjoint multistep methods. Numerical stability, energy preservation, and performance of proposed schemes are investigated theoretically and experimentally using a set of differential problems. The applicability and efficiency of the proposed composition multistep methods are discussed. Full article

In this article, we explore a new extended Lienard-type planar system with “corrections” of the second kind Chebyshev’s polynomial $U_n$. The number and type of limit cycles are also studied. The discussion on the $y\left(t\right)$—component of the solution of the Lienard system is connected to searching for the solution of the synthesis of filters and electrical circuits. Numerical experiments, depicting our outcomes using CAS MATHEMATICA, are presented. Full article

Adversarial attacks hamper the functionality and accuracy of deep neural networks (DNNs) by meddling with subtle perturbations to their inputs. In this work, we propose a new mask-based adversarial defense scheme (MAD) for DNNs to mitigate the negative effect from adversarial attacks. Our method preprocesses multiple copies of a potential adversarial image by applying random masking, before the outputs of the DNN on all the randomly masked images are combined. As a result, the combined final output becomes more tolerant to minor perturbations on the original input. Compared with existing adversarial defense techniques, our method does not need any additional denoising structure or any change to a DNN’s architectural design. We have tested this approach on a collection of DNN models for a variety of datasets, and the experimental results confirm that the proposed method can effectively improve the defense abilities of the DNNs against all of the tested adversarial attack methods. In certain scenarios, the DNN models trained with MAD can improve classification accuracy by as much as $90\%$ compared to the original models when given adversarial inputs. Full article

The method of alternating projections for extracting low-rank signals is considered. The problem of decreasing the computational costs while keeping the estimation accuracy is analyzed. The proposed algorithm consists of alternating projections on the set of low-rank matrices and the set of Hankel matrices, where iterations of weighted projections with different weights are mixed. For algorithm justification, theory related to mixed alternating projections to linear subspaces is studied and the limit of mixed projections is obtained. The proposed approach is applied to the problem of Hankel low-rank approximation for constructing a modification of the Cadzow algorithm. Numerical examples compare the accuracy and computational cost of the proposed algorithm and Cadzow iterations. Full article

Tandem repeats (TRs) are important components of eukaryotic genomes; they have both structural and functional roles: (i) they form essential chromosome structures such as centromeres and telomeres; (ii) they modify chromatin structure and affect transcription, resulting in altered gene expression and protein abundance. There are established links between variations in TRs and incompatibilities between species, evolutionary development, chromosome mis-segregation, aging, cancer outcomes and different diseases. Given the importance of TRs, it seemed essential to develop an efficient, sensitive and automated application for the identification of all kinds of TRs in various genomic sequences. Here, we present our new GRM application for identifying TRs, which is designed to overcome all the limitations of the currently existing algorithms. Our GRM algorithm provides a straightforward identification of TRs using the frequency domain but avoiding the mapping of the symbolic DNA sequence into numerical sequence, and using key string matching, but avoiding the statistical methods of locally optimizing individual key strings. Using the GRM application, we analyzed human, chimpanzee and mouse chromosome 19 genome sequences (RefSeqs), and showed that our application was very fast, efficient and simple, with a powerful graphical user interface. It can identify all types of TRs, from the smallest (2 bp) to the very large, as large as tens of kilobasepairs. It does not require any prior knowledge of sequence structure and does not require any user-defined parameters or thresholds. In this way, it ensures that a full spectrum of TRs can be detected in just one step. Furthermore, it is robust to all types of mutations in repeat copies and can identify TRs with various complexities in the sequence pattern. From this perspective, we can conclude that the GRM application is an efficient, sensitive and automated method for the identification of all kinds of TRs. Full article

As the double carbon target continues to be promoted and the installed capacity of gas-fired power generation gradually expands, whether and when gas-fired power generation should enter the market is a major concern for the industry. This paper analyzes the change in power generation cost and the characteristics of bidding behavior of the power generation group with the fluctuation of primary energy price to study the timing and role of gas power generation entering the market. The evolutionary game model for gas- and coal-fired power generation groups based on the influence of multiple factors takes into account factors such as generation costs, the number of power generation groups, generation capacity, supply, and demand. The equilibrium states of the power generation groups under various scenarios and the conditions that need to be satisfied for the equilibrium states are analyzed, and a method for determining the stable equilibrium point of the evolving market game is proposed. Examples use the actual price fluctuations of coal and natural gas as input data to validate the rationality of the paper’s model and the stable equilibrium approach. Full article

Parathyroid scintigraphy with 99mTc-sestamibi (MIBI) is an established technique for localising abnormal parathyroid glands (PGs). However, the identification and localisation of PGs require much attention from medical experts and are time-consuming. Artificial intelligence methods can offer an assisting solution. This retrospective study enrolled 632 patients who underwent parathyroid scintigraphy with double-phase and thyroid subtraction techniques. The study proposes a three-path approach, employing the state-of-the-art convolutional neural network called VGG19. Images input to the model involved a set of three scintigraphic images in each case: MIBI early phase, MIBI late phase, and 99mTcO4 thyroid scan. A medical expert’s diagnosis provided the ground truth for positive/negative results. Moreover, the visualised suggested areas of interest produced by the Grad-CAM algorithm are examined to evaluate the PG-level agreement between the model and the experts. Medical experts identified 545 abnormal glands in 452 patients. On a patient basis, the deep learning (DL) model attained an accuracy of 94.8% (sensitivity 93.8%; specificity 97.2%) in distinguishing normal from abnormal scintigraphic images. On a PG basis and in achieving identical positioning of the findings with the experts, the model correctly identified and localised 453/545 glands (83.1%) and yielded 101 false focal results (false positive rate 18.23%). Concerning surgical findings, the expert’s sensitivity was 89.68% on patients and 77.6% on a PG basis, while that of the model reached 84.5% and 67.6%, respectively. Deep learning in parathyroid scintigraphy can potentially assist medical experts in identifying abnormal findings. Full article