Increased Training Time Research Articles

Exploration on Automatic Management of GIS Using TL-CNN and IoT

The research aims to effectively monitor the state of complex industrial equipment in real time, diagnose the internal Partial Discharge (PD) pattern of Gas Insulated Metal Enclosed Switchgear (GIS), implement effective health management, and change the traditional model optimization route of increasing training time in exchange for performance improvement. This paper studies the complex equipment-oriented Health Management System (HMS) based on Internet of Things (IoT) technology and Transfer Learning. Firstly, the principles of Transfer Learning and Deep Learning (DL) technology are introduced. Secondly, the requirements of GIS internal status recognition and management are studied. Furthermore, a GIS-oriented HMS based on Transfer Learning-optimized Convolutional Neural Networks (CNN) is proposed, and the training dataset is constructed. Finally, the proposed model is tested. The results show that the complex equipment-oriented HMS based on IoT technology, CNN, and Transfer Learning can detect the internal status of GIS in real time. Compared with the traditional DL algorithm and expert system, the proposed model has a shorter training time of only 16min, faster convergence speed, high testing recognition rate, and over 96% recognition rate. Compared with other mainstream algorithms, it has higher identification, the storage parameter volume is 408, and the storage space is 12.8MB. Moreover, the proposed Transfer Learning-optimized CNN model can accurately detect the status of GIS, identify abnormal statuses, and help prolong the service life of GIS. The proposed complex equipment-oriented HMS contributes to the intelligent manufacturing industry and provides a new direction for applying emerging Computer Technology in the intelligent industry.

Depression Detection on COVID 19 Tweets Using Chimp Optimization Algorithm

The Covid-19 outbreak has an unprecedented effects on people's daily lives throughout the world, causing immense stress amongst individuals owing to enhanced psychological disorders like depression, stress, and anxiety. Researchers have used social media data to detect behaviour changes in individuals with depression, postpartum changes and stress detection since it reveals critical aspects of mental and emotional diseases. Considerable efforts have been made to examine the psychological health of people which have limited performance in accuracy and demand increased training time. To conquer such issues, this paper proposes an efficient depression detection framework named Improved Chimp Optimization Algorithm based Convolution Neural Network–Long Short Term Memory and Natural Language Processing for Covid-19 Twitter data. In the proposed method, the tweets are pre-processed, user's frequent tweet identification, and hash tag identification has been done. The processed tweets are then clustered through cluster head selection using Swap-Displacement-Reversion-Bull based Optimization Algorithm and cluster formation using the Bregman distance-based K-Means algorithm. Then, the psycholinguistic features are extracted from the clustered data and inputted to the Improved Chimp Optimization Algorithm-based-Convolution Neural Network-Long Short Term Memory network for depression classification. Preliminary results show that the proposed method provides greater performance with 97.7% efficiency and outperforms the existing methodologies.

Learning deficits occurs prior to memory retrieval impairment in female Senescence Accelerated Mouse (SAMP8)

AbstractBackgroundThe most regularly used mouse models of Alzheimer's disease in drug development include APP/PS1, 3xTg, and 5xFAD mice. This is a limitation as all these mice represent familial AD. Given sporadic AD accounts for the majority of the AD cases in human, there is an unmet need to validate potential rodent models to better represent sporadic AD. SAMP8 is a naturally‐occurring mouse line that displays many characteristics identified in Alzheimer’s disease (AD) patients, such as learning and memory deficits, and accumulation of beta‐amyloid. In people with preclinical AD, deficits in learning manifest faster than decline in memory retrieval. It is unclear if SAMP8 mice also exhibit this feature, and therefore the current study aims to determine if this feature can be observed in SAMP8, to support the use of SAMP8 as a mouse model of sporadic AD for drug development.MethodThe cognitive function of SAMP8 mice and their age‐matched non‐AD control SAMR1 mice (at various ages) were assessed using Y maze spatial memory test, with 3‐10 min training duration and 1.5‐3 h interval between training and testing session.ResultAt 3‐4 months old, SAMP8 but not SAMR1 failed to differentiate the novel arm from familiar arm in a standard Y maze test (3 min training, 3 h interval). When training time was increased to 10 min, SAMP8 passed the test, while increased training time did not affect the performance of SAMR1 mice. These data indicated that longer training time is required by SAMP8 than SAMR1 to achieve the expected performance, suggesting the presence of learning deficits in SAMP8. Interestingly, at 6‐7 months old, though both SAMP8 and SAMR1 received 10‐min training, only SAMR1 passed the test. The performance of SAMP8 mice was successfully improved by shortening the interval between training and testing (from 3 h to 1.5 hr). These data indicate a deteriorated memory retention capability and a possible impairment in memory retrieval in SAMP8.ConclusionOverall, this study has provided supportive evidence that learning deficits occurs prior to memory retrieval impairment in SAMP8, and the use of SAMP8 as mouse model for AD.

Autonomous Vehicle Path Planning using Q-Learning

Path planning is vital in autonomous vehicle technology, from robots to self-driving cars and driverless trucks, it is impossible to navigate without a proper path planning algorithm, various algorithms exist Q-learning being one of them. Q-learning is used extensively in discrete applications as it is effective in finding solutions to these problems. This research investigates the possibility of using Q-learning for solving the local path planning problem with obstacle avoidance. Q-learning is split into two phases, the first being the training phase, and the second being the application phase. During training, Q-learning requires exponentially increasing training time based on the system’s state space. However, when Q-learning is applied it becomes as simple as a lookup table which allows it to run on even the simplest microcontrollers. Two simulations are conducted with varying environments. One to showcase the ability to learn the optimal path, the other to showcase the ability for learning navigation in variable environments. The first simulation was run on a static environment with one obstacle, with enough training episodes, Q-learning could solve the path planning problem with minimal movement steps. The second simulation focuses on a randomized environment, obstacles and the agent’s starting position are randomly chosen at the start of every episode. During testing, Q-learning was able to find a path to the target when a path did exist, as It was possible in certain configurations for the vehicle to be stuck in between obstacles with no feasible path or solution.

Comparison of Standard and Pretrained CNN Models for Potato, Cotton, Bean and Banana Disease Detection

Plant diseases lead to a significant decrease in product efficiency and economic losses for producers. However, early detection of plant diseases plays an important role in preventing these losses. Today, Convolutional Neural Network (CNN) models are widely used for image processing in many fields such as face recognition, climate, health, and agriculture. But in these models, the weights of the layers are randomly initialized during training, which increases training time and decreases performance. With the method known as Transfer Learning in the literature, CNN models are trained on large databases such as ImageNet. Then, pretrained CNN models are created using the weights obtained in this training. Thus, training time decreases while performance improves. In this study, standard and pretrained versions of popular CNN models DarkNet-19, GoogleNet, Inception-v3, Resnet-18, and ShuffleNet have been used for automatic classification of diseases from leaf images of potato, cotton, bean, and banana. In the experimental study, the classification performances of all these standard and pretrained CNN models are presented comparatively. Experimental results have shown that the performance of CNN models is significantly improved by transfer learning, even in a small number of epochs.

Implementing FLS Training Protocol for Minimally Invasive GYN Surgery Training

Study Objective The number of minimally invasive surgeries required for residents has increased alongside the requirement of passing the Fundamentals of Laparoscopic Surgery (FLS) program for board certification in Obstetrics and Gynecology (OBGYN) programs. Simulation training has been proposed as a method to increase the proficiency of training surgeons; however, no gynecologic simulation models have been validated. We hypothesized that 24-hour access to the FLS trainer would improve the residents’ times to complete the standardized FLS tasks and improve first time pass rates, and that increased training time would increase resident confidence. Design We performed an observational prospective study. Each resident was timed on the FLS tasks and surveyed to assess confidence each quarter. We compared first time pass rates of the FLS exam for residents who took the exam prior to having access to the trainer to the first-time pass rates of the residents who did have access to the trainer. Setting N/A. Patients or Participants 20 residents were enrolled. During the study period, 1 resident left the program. Interventions N/A. Measurements and Main Results There was no statistical significance between first time pass rates for the FLS exam. Paired t-test was used and found no significant differences in timed task completion or survey question. Conclusion Voluntary simulation-based training was not an effective way to improve gynecologic surgical skills during this study. We suspect this to be a result of lack of defined structure, limited free time, and challenges due to the COVID 19 pandemic. There were low compliance rates of the residents using the FLS trainer and no significant improvement in the time required to finish the standardized FLS tasks, first time pass rates on the FLS exam, or resident confidence levels measured by survey results. More research is needed to evaluate barriers to simulation training to improve minimally invasive surgical skills The number of minimally invasive surgeries required for residents has increased alongside the requirement of passing the Fundamentals of Laparoscopic Surgery (FLS) program for board certification in Obstetrics and Gynecology (OBGYN) programs. Simulation training has been proposed as a method to increase the proficiency of training surgeons; however, no gynecologic simulation models have been validated. We hypothesized that 24-hour access to the FLS trainer would improve the residents’ times to complete the standardized FLS tasks and improve first time pass rates, and that increased training time would increase resident confidence. We performed an observational prospective study. Each resident was timed on the FLS tasks and surveyed to assess confidence each quarter. We compared first time pass rates of the FLS exam for residents who took the exam prior to having access to the trainer to the first-time pass rates of the residents who did have access to the trainer. N/A. 20 residents were enrolled. During the study period, 1 resident left the program. N/A. There was no statistical significance between first time pass rates for the FLS exam. Paired t-test was used and found no significant differences in timed task completion or survey question. Voluntary simulation-based training was not an effective way to improve gynecologic surgical skills during this study. We suspect this to be a result of lack of defined structure, limited free time, and challenges due to the COVID 19 pandemic. There were low compliance rates of the residents using the FLS trainer and no significant improvement in the time required to finish the standardized FLS tasks, first time pass rates on the FLS exam, or resident confidence levels measured by survey results. More research is needed to evaluate barriers to simulation training to improve minimally invasive surgical skills

Risk of hospitalization, technique failure, and death with increased training duration in 3-days-a-week home hemodialysis.

Quality training is a core component of successful home hemodialysis (HHD) and training duration varies significantly between dialysis centers as well as at the patient level. This study aimed to assess the adverse outcomes associated with HHD training duration. All HHD patients successfully trained in a single dialysis center between January 2005 and July 2017 were included. A multivariable multiple-events (Andersen-Gill) survival model was built to evaluate the association between training time and main adverse events, including hospitalizations, technique failure, and death on HHD. Potential confounding factors were defined a priori (age, diabetes, coronary artery disease, and year of training start). Adjusted risk of vascular interventions (arteriovenous fistula angioplasties and central venous catheter replacements) was assessed as the secondary outcome in a negative binomial regression. Forty-eight patients were included in the study. Median HHD training duration was 86 (67-108) days, using a thrice weekly training schedule. Over a follow-up median time of 2.0 (0.7-3.3) years, three patients died while on HHD, 10 had a definitive transfer to HD, and 18 experienced a least 1 hospitalization (38 hospitalizations in total). Training duration was associated with a higher risk of hospitalization, technique failure, and death in unadjusted (hazard ratio [HR] 1.16 per month, 95% confidence interval [CI] 1.08-1.24) and adjusted multiple events model (HR 1.21, 95% CI 1.04-1.43). Risk of vascular access intervention was also significantly higher with increased training time (adjusted incidence rate ratio 1.31, 95% CI 1.03-1.64, per training month). In this single-center observational study, HHD training duration was associated with a higher risk of adverse events including, death, technique failure, hospitalizations, and vascular access intervention. Enhanced clinical follow-up and home support should be offered to these more vulnerable patients to mitigate this heightened risk.

Deep Learning Driven Noise Reduction for Reduced Flux Computed Tomography.

Deep neural networks have received considerable attention in clinical imaging, particularly with respect to the reduction of radiation risk. Lowering the radiation dose by reducing the photon flux inevitably results in the degradation of the scanned image quality. Thus, researchers have sought to exploit deep convolutional neural networks (DCNNs) to map low-quality, low-dose images to higher-dose, higher-quality images, thereby minimizing the associated radiation hazard. Conversely, computed tomography (CT) measurements of geomaterials are not limited by the radiation dose. In contrast to the human body, however, geomaterials may be comprised of high-density constituents causing increased attenuation of the X-rays. Consequently, higher-dose images are required to obtain an acceptable scan quality. The problem of prolonged acquisition times is particularly severe for micro-CT based scanning technologies. Depending on the sample size and exposure time settings, a single scan may require several hours to complete. This is of particular concern if phenomena with an exponential temperature dependency are to be elucidated. A process may happen too fast to be adequately captured by CT scanning. To address the aforementioned issues, we apply DCNNs to improve the quality of rock CT images and reduce exposure times by more than 60%, simultaneously. We highlight current results based on micro-CT derived datasets and apply transfer learning to improve DCNN results without increasing training time. The approach is applicable to any computed tomography technology. Furthermore, we contrast the performance of the DCNN trained by minimizing different loss functions such as mean squared error and structural similarity index.

Feature optimization using Backward Elimination and Support Vector Machines (SVM) algorithm for diabetes classification

Diabetes is a disease that occurs when the blood glucose level is higher than normal and also leads to health problems. Early and accurate diagnosis needs to be carried out on individuals affected by this disease. Furthermore, excellent treatment needs to be provided to prevent worse situations. Some studies have used several machine learning methods to diagnose diabetes. Furthermore, in this study, the Backward Elimination and Support Vector Machine (SVM) algorithm was used to classify the PIMA Indians diabetes dataset. It consisted of 268 diabetic and 500 non-diabetic patients with eight attributes. Backward Elimination is a feature selection method used to remove irrelevant features based on the linear regression model. Using this method, the right features for the model was expected. This method has some advantages which include increasing training time, decreasing complexity and improving performance and accuracy. Therefore, the performance of SVM improved. Based on the experiments, it was discovered that by combining feature selection algorithm (backward elimination) and SVM, the highest accuracy obtained was 85.71% using 90% data training. Therefore, it was concluded that Backward Elimination combined with SVM algorithm is an excellent method to classify diabetes by using the PIMA Indians diabetes dataset.

Maximal Strength, Sprint, and Jump Performance in High-Level Female Football Players Are Maintained With a Customized Training Program During the COVID-19 Lockdown.

IntroductionThe COVID-19 outbreak with partial lockdown has inevitably led to an alteration in training routines for football players worldwide. Thus, coaches had to face with the novel challenge of minimizing the potential decline in fitness during this period of training disruption.MethodsIn this observational pre- to posttest study involving Norwegian female football players (18.8 ± 1.9 years, height 1.68 ± 0.4 m, mass 61.3 ± 3.7 kg), we investigated the effects of a prescribed home-based and group-based intervention, implemented during the COVID-19 lockdown, on maximal muscular force production and high velocity variables. Specifically, maximal partial squat strength one repetition maximum (1RM), counter movement jump (CMJ) and 15 m sprint time were assessed 1 week prior to the lockdown and 12 weeks after the onset of lockdown. We also collected training content and volume from the prescribed training program and self-reported perceived training quality and motivation toward training.ResultsWe observed no change in 1RM [pretest: 104 ± 12 kg, posttest: 101 ± 11 kg (P = 0.28)], CMJ height [pretest: 28.1 ± 2.3 cm, posttest: 26.8 ± 1.9 (P = 0.09)], and 15 m sprint time [pretest: 2.60 ± 0.08 s, posttest: 2.61 ± 0.07 s (P = 0.52)].ConclusionOur findings suggest that a prescribed home-based and group-based intervention with increased training time devoted to strength, jump, and sprint ability, and regulated to obtain a sufficient infection control level is feasible and effective to preserve strength, jumping, and sprinting abilities of high-level female football players during a ∼ 3-month period of a pandemic-induced lockdown.

Optimization of Drilling Cost Using Artificial Intelligence

Drilling operations in the oil and gas industry takes most of the well cost and how fast the drilling bit penetrate and bore the formation is termed the Rate of penetration (ROP). Since most of the cost incurred during drilling is related to the drilling operations, there is need not only to drill carefully, but also to optimize the drilling process. A lot of parameters are related to the rate of penetration which are actually interdependent on each other. This makes it difficult to predict the influence of every single parameter Drilling optimization techniques have been used recently to reduce drilling operation costs. There are different approaches to optimizing the cost of drilling oil and gas wells, some of which include static and /or real time optimization of drilling parameters. A potential area for optimization of drilling cost is through bit run in the well but this is particularly difficult due to its significance in both drilling time and bit cost. In this sense, as a particular bit gets used, it gets dull as its footage increases, resulting from the reduction in the bit penetration rate. The reduction in penetration rate increases total drill time. In order to optimize bit cost, it is desirable to find a trade-off between the two by a bit change policy This study is aimed at minimizing drilling time by use of artificial intelligent for the bit program. Data obtained from a well in the Niger delta region of Nigeria was used in this study and the cost optimization modelled as a Markov decision process where the intelligent agent was to learn the optimal timings for bit change by reinforcement policy Iteration learning. This study was able to achieve its objectives as the reinforcement learning optimization process performed very well with time as the computer agent was able to figure out how to improve drilling cost over time. Better results could be obtained with a better hardware and increased training time.

Global Optimization: Combining Local Loss With Result Ranking Loss in Remote Sensing Image Retrieval

With the explosive growth of remote sensing big data, large-scale remote sensing image retrieval (RSIR) has become one of the most challenging tasks in data mining, attracting more and more attention from researchers. In recent years, deep learning has achieved fruitful results in RSIR. However, there are three major problems. The first problem is due to the imbalanced categories in RSIR data sets. Accordingly, a novel sample mining method is proposed. This method is based on top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> “misplaced” samples (Top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> MS) along the top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> nearest neighbor decision boundary, rather than setting boundary threshold of sample mining and reducing the impact of artificial and objective factors on network training as usual. The second problem comes from the inconsistency between the loss reduction direction and the optimization direction. In response, we additionally propose a novel result ranking loss (RRL) according to the retrieval results in a batch. RRL is used as a plug-in and combined with other local losses. As a result, the retrieval accuracy improved significantly. For the third problem, processing a large number of high-resolution images will increase training time and cause network freeze. To solve the problem, this article proposes a global optimization model based on feature space and retrieval results (FSRR). More specifically, FSRR consists of local loss based on feature space and RRL based on retrieval results, and can be optimized in an end-to-end manner. Experimental results show that our proposed algorithm achieves the best performance when compared with other state-of-the-art deep RSIR algorithms on two benchmark data sets.

A novel method for speed training acceleration of recurrent neural networks

Although recurrent neural networks (RNNs) perfectly solve many difficult problems, their computational complexity significantly increases training time. Therefore, the primary problem with applying RNNs is to shorten the time needed to train and operate a network. An effective solution to this problem is to use parallel processing. In the paper, a particular approach for the Jordan network will be shown, however, the presented idea is applicable to other RNN structures. This type of network is characterized by natural parallelism, and in the paper, this feature is used to significantly accelerate the learning process. High-performance learning has been achieved using a novel parallel three-dimensional architecture. The presented solutions can be implemented in digital hardware.

Handheld robotic needle holder training: slower but better.

Handheld robotic laparoscopic instruments fill the gap between robotic and conventional instruments, combining the advantages of degrees of freedom and low price. The difficulty and value in learning these new instruments require detailed investigation. Forty novice surgeons with no laparoscopic experience were randomly assigned to two groups: conventional instrument group (Group Conv) and robotic instrument group (Group Rob). The same training protocol was used in both groups: after viewing a standard operation film, laparoscopic suture training was administered using the corresponding instruments. After each training period, surgeons were tested using a force-sensing test platform. Maximum force (MF) and impulse (IMP) of operators through each ring were recorded. Learning curves based on MF and IMP for both instruments were compared. Institutional review board approval is not needed for this study. MF and IMP of both groups decreased with increased training time; the learning curve of Group Conv decreased faster than that of Group Rob. When training time reached 13h, the MF of Group Rob was significantly lower than that of Group Conv (P < 0.05), while IMP showed no significant difference between the two groups. Effective training reduces operator MF and IMP, possibly decreasing damage to tissues with both conventional and handheld robotic needle holders. Group Rob took longer to reach a plateau, but subsequently had lower suture tension than did Group Conv. MF is more sensitive than IMP for measuring performance progress.

Toward Communication-Efficient Federated Learning in the Internet of Things With Edge Computing

Federated learning is an emerging concept that trains the machine learning models with the local distributed data sets, without sending the raw data to the data center. But, in the Internet of Things (IoT) where the wireless network resource is constrained, the key problem of federated learning is the communication overhead for parameter synchronization, which wastes bandwidth, increases training time, and even impacts the model accuracy. Gradient sparsification has received increasing attention, which only updates significant gradients and accumulates insignificant gradients locally. However, how to preserve the accuracy after a high ratio sparsification has been ignored in the literature. In this article, a general gradient sparsification (GGS) framework is proposed for adaptive optimizers, to correct the sparse gradient update process. It consists of two important mechanisms: 1) gradient correction and 2) batch normalization (BN) update with local gradients. With gradient correction, the optimizer can properly treat the accumulated insignificant gradients, which makes the model converge better. Furthermore, updating the BN layer with local gradients can relieve the impact of delayed gradients without increasing the communication overhead. We have conducted experiments on LeNet-5, CifarNet, DenseNet-121, and AlexNet with adaptive optimizers. Results show that when 99.9% gradients are sparsified, validation data sets are maintained with top-1 accuracy.

Outlier Guided Optimization of Abdominal Segmentation.

Abdominal multi-organ segmentation of computed tomography (CT) images has been the subject of extensive research interest. It presents a substantial challenge in medical image processing, as the shape and distribution of abdominal organs can vary greatly among the population and within an individual over time. While continuous integration of novel datasets into the training set provides potential for better segmentation performance, collection of data at scale is not only costly, but also impractical in some contexts. Moreover, it remains unclear what marginal value additional data have to offer. Herein, we propose a single-pass active learning method through human quality assurance (QA). We built on a pre-trained 3D U-Net model for abdominal multi-organ segmentation and augmented the dataset either with outlier data (e.g., exemplars for which the baseline algorithm failed) or inliers (e.g., exemplars for which the baseline algorithm worked). The new models were trained using the augmented datasets with 5-fold cross-validation (for outlier data) and withheld outlier samples (for inlier data). Manual labeling of outliers increased Dice scores with outliers by 0.130, compared to an increase of 0.067 with inliers (p<0.001, two-tailed paired t-test). By adding 5 to 37 inliers or outliers to training, we find that the marginal value of adding outliers is higher than that of adding inliers. In summary, improvement on single-organ performance was obtained without diminishing multi-organ performance or significantly increasing training time. Hence, identification and correction of baseline failure cases present an effective and efficient method of selecting training data to improve algorithm performance.

SoftMemoryBox II: A Scalable, Shared Memory Buffer Framework for Accelerating Distributed Training of Large-Scale Deep Neural Networks

Distributed processing using high-performance computing resources is essential for developers to train large-scale deep neural networks (DNNs). The major impediment to distributed DNN training is the communication bottleneck during the parameter exchange among the distributed DNN training workers. The communication bottleneck increases training time and decreases the utilization of the computational resources. Our previous study, SoftMemoryBox (SMB1) presented considerably superior performance compared to message passing interface (MPI) in the parameter communication of distributed DNN training. However, SMB1 had disadvantages such as the limited scalability of the distributed DNN training due to the restricted communication bandwidth from a single memory server, inability to provide a synchronization function for the shared memory buffer, and low portability/usability as a consequence of the kernel-level implementation. This paper proposes a scalable, shared memory buffer framework, called SoftMemoryBox II (SMB2), which overcomes the shortcomings of SMB1. With SMB2, distributed training processes can easily share virtually unified shared memory buffers composed of memory segments provided from remote memory servers and can exchange DNN parameters at high speed through the shared memory buffer. The scalable communication bandwidth of the SMB2 framework facilitates the reduction of DNN distributed training times compared to SMB1. According to intensive evaluation results, the communication bandwidth of the proposed SMB2 is 6.3 times greater than that of SMB1 when the SMB2 framework is scaled out to use eight memory servers. Moreover, the training time of SMB2-based asynchronous distributed training of five DNN models is up to 2.4 times faster than SMB1-based training.

Ants’ Mental Positioning of Amounts on a Number Line

Myrmica sabuleti ants have a mental number line on which numbers (non-symbolic displayed amounts) are ranked, the smaller on the left and the larger on the right. Here we try to know if the difference between two successive numbers is identically estimated all along this line or is less and less well estimated with increasing number magnitude. Ants were trained to distinguish two successive numbers differing by one unit (1 vs 2, 2 vs 3, &amp;hellip;, 6 vs 7) during 72 hours and tested after 7, 24, 31, 48, 55 and 72 h. The ants responded less well for larger numbers (e.g. their response to 6 vs 7 was weaker than that to 1 vs 2). The relation between the ants&amp;rsquo; ability in discriminating two successive numbers according to their size, ratio or relative difference was best described by a non-linear, power function and somewhat less well by a logarithmic function. A linear function could only significantly better fit the data when large fluctuations in the ants&amp;rsquo; discrimination score appeared in the course of increasing training time. The ants&amp;rsquo; mental positioning of numerosity on their number line appears thus to be compressed along a non-linear scale, most likely according to a power function of the numbers&amp;rsquo; magnitude characteristics.

Ants’ Mental Positioning of Amounts on a Number Line

Myrmica sabuleti ants have a mental number line on which numbers (non-symbolic displayed amounts) are ranked, the smaller on the left and the larger on the right. Here we try to know if the difference between two successive numbers is identically estimated all along this line or is less and less well estimated with increasing number magnitude. Ants were trained to distinguish two successive numbers differing by one unit (1 vs 2, 2 vs 3, &amp;hellip;, 6 vs 7) during 72 hours and tested after 7, 24, 31, 48, 55 and 72 h. The ants responded less well for larger numbers (e.g. their response to 6 vs 7 was weaker than that to 1 vs 2). The relation between the ants&amp;rsquo; ability in discriminating two successive numbers according to their size, ratio or relative difference was best described by a non-linear, power function and somewhat less well by a logarithmic function. A linear function could only significantly better fit the data when large fluctuations in the ants&amp;rsquo; discrimination score appeared in the course of increasing training time. The ants&amp;rsquo; mental positioning of numerosity on their number line appears thus to be compressed along a non-linear scale, most likely according to a power function of the numbers&amp;rsquo; magnitude characteristics.

Ants’ Mental Positioning of Amounts on a Number Line

Myrmica sabuleti ants have a mental number line on which numbers (non-symbolic displayed amounts) are ranked, the smaller on the left and the larger on the right. Here we try to know if the difference between two successive numbers is identically estimated all along this line or is less and less well estimated with increasing number magnitude. Ants were trained to distinguish two successive numbers differing by one unit (1 vs 2, 2 vs 3, &amp;hellip;, 6 vs 7) during 72 hours and tested after 7, 24, 31, 48, 55 and 72 h. The ants responded less well for larger numbers (e.g. their response to 6 vs 7 was weaker than that to 1 vs 2). The relation between the ants&amp;rsquo; ability in discriminating two successive numbers according to their size, ratio or relative difference was best described by a non-linear, power function and somewhat less well by a logarithmic function. A linear function could only significantly better fit the data when large fluctuations in the ants&amp;rsquo; discrimination score appeared in the course of increasing training time. The ants&amp;rsquo; mental positioning of numerosity on their number line appears thus to be compressed along a non-linear scale, most likely according to a power function of the numbers&amp;rsquo; magnitude characteristics.