The frequent breakdowns and malfunctions of industrial equipment have driven increasing interest in utilizing cost-effective and easy-to-deploy sensors, such as microphones, for effective condition monitoring of machinery. Microphones offer a low-cost alternative to widely used condition monitoring sensors with their high bandwidth and capability to detect subtle anomalies that other sensors might have less sensitivity. In this study, we investigate malfunctioning industrial machines to evaluate and compare anomaly detection performance across different machine types and fault conditions. Log-Mel spectrograms of machinery sound are used as input, and the performance is evaluated using the area under the curve (AUC) score for two different methods: baseline dense autoencoder (AE) and one-class deep Support Vector Data Description (deep SVDD) with different subspace dimensions. Our results over the MIMII sound dataset demonstrate that the deep SVDD method with a subspace dimension of 2 provides superior anomaly detection performance, achieving average AUC scores of 0.84, 0.80, and 0.69 for 6 dB, 0 dB, and -6 dB signal-to-noise ratios (SNRs), respectively, compared to 0.82, 0.72, and 0.64 for the baseline model. Moreover, deep SVDD requires 7.4 times fewer trainable parameters than the baseline dense AE, emphasizing its advantage in both effectiveness and computational efficiency.

Continuous long-term monitoring of motor health is crucial for the early detection of abnormalities such as bearing faults (up to 51% of motor failures are attributed to bearing faults). Despite numerous methodologies proposed for bearing fault detection, most of them require normal (healthy) and abnormal (faulty) data for training. Even with the recent deep learning (DL) methodologies trained on the labeled data from the same machine, the classification accuracy significantly deteriorates when one or few conditions are altered. Furthermore, their performance suffers significantly or may entirely fail when they are tested on another machine with entirely different healthy and faulty signal patterns. To address this need, in this pilot study, we propose a zero-shot bearing fault detection method that can detect any fault on a new (target) machine regardless of the working conditions, sensor parameters, or fault characteristics. To accomplish this objective, a 1D Operational Generative Adversarial Network (Op-GAN) first characterizes the transition between normal and fault vibration signals of (a) source machine(s) under various conditions, sensor parameters, and fault types. Then for a target machine, the potential faulty signals can be generated, and over its actual healthy and synthesized faulty signals, a compact, and lightweight 1D Self-ONN fault detector can then be trained to detect the real faulty condition in real time whenever it occurs. To validate the proposed approach, a new benchmark dataset is created using two different motors working under different conditions and sensor locations. Experimental results demonstrate that this novel approach can accurately detect any bearing fault achieving an average recall rate of around 89% and 95% on two target machines regardless of its type, severity, and location.

In a standard Turing test, a machine has to prove its humanness to the judges. By successfully imitating a thinking entity such as a human, this machine then proves that it can also think. Some objections claim that Turing test is not a tool to demonstrate the existence of general intelligence or thinking activity. A compelling alternative is the Lovelace test, in which the agent must originate a product that the agent's creator cannot explain. Therefore, the agent must be the owner of an original product. However, for this to happen the agent must exhibit the idea of self and distinguish oneself from others. Sustaining the idea of self within the Turing test is still possible if the judge decides to act as a textual mirror. Self-recognition tests applied on animals through mirrors appear to be viable tools to demonstrate the existence of a type of general intelligence. Methodology here constructs a textual version of the mirror test by placing the agent as the one and only judge to figure out whether the contacted one is an other, a mimicker, or oneself in an unsupervised manner. This textual version of the mirror test is objective, self-contained, and devoid of humanness. Any agent passing this textual mirror test should have or can acquire a thought mechanism that can be referred to as the inner-voice, answering the original and long lasting question of Turing "Can machines think?" in a constructive manner still within the bounds of the Turing test. Moreover, it is possible that a successful self-recognition might pave way to stronger notions of self-awareness in artificial beings.

Condition monitoring of induction machines is crucial to prevent costly interruptions and equipment failure. Mechanical faults such as misalignment and rotor issues are among the most common problems encountered in industrial environments. To effectively monitor and detect these faults, a variety of sensors, including accelerometers, current sensors, temperature sensors, and microphones, are employed in the field. As a non-contact alternative, thermal imaging offers a powerful monitoring solution by capturing temperature variations in machines with thermal cameras. In this study, we propose using 2-dimensional Self-Organized Operational Neural Networks (Self-ONNs) to diagnose misalignment and broken rotor faults from thermal images of squirrel-cage induction motors. We evaluate our approach by benchmarking its performance against widely used Convolutional Neural Networks (CNNs), including ResNet, EfficientNet, PP-LCNet, SEMNASNet, and MixNet, using a Workswell InfraRed Camera (WIC). Our results demonstrate that Self-ONNs, with their non-linear neurons and self-organizing capability, achieve diagnostic performance comparable to more complex CNN models while utilizing a shallower architecture with just three operational layers. Its streamlined architecture ensures high performance and is well-suited for deployment on edge devices, enabling its use also in more complex multi-function and/or multi-device monitoring systems.

Automating the constraint modelling process is one of the key challenges facing the constraints field, and one of the principal obstacles preventing widespread adoption of constraint solving. This paper focuses on the refinement-based approach to automated modelling, where a user specifies a problem in an abstract constraint specification language and it is then automatically refined into a constraint model. In particular, we revisit the Conjure system that first appeared in prototype form in 2005 and present a new implementation with a much greater coverage of the specification language Essence.

Magnetic Resonance Fingerprinting (MRF) enables simultaneous mapping of multiple tissue parameters such as T1 and T2 relaxation times. The working principle of MRF relies on varying acquisition parameters pseudo-randomly, so that each tissue generates its unique signal evolution during scanning. Even though MRF provides faster scanning, it has disadvantages such as erroneous and slow generation of the corresponding parametric maps, which needs to be improved. Moreover, there is a need for explainable architectures for understanding the guiding signals to generate accurate parametric maps. In this paper, we addressed both of these shortcomings by proposing a novel neural network architecture consisting of a channel-wise attention module and a fully convolutional network. The proposed approach, evaluated over 3 simulated MRF signals, reduces error in the reconstruction of tissue parameters by 8.88% for T1 and 75.44% for T2 with respect to state-of-the-art methods. Another contribution of this study is a new channel selection method: attention-based channel selection. Furthermore, the effect of patch size and temporal frames of MRF signal on channel reduction are analyzed by employing a channel-wise attention.

Purpose: The primary aim of this study is to enhance fault diagnosis in induction machines by leveraging the Padé Approximant Neuron (PAON) model. While accelerometers and microphones are standard in motor condition monitoring, deep learning models with nonlinear neuron architectures offer promising improvements in diagnostic performance. This research addresses the question: Can Padé Approximant Neural Networks (PadéNets) outperform conventional Convolutional Neural Networks (CNNs) and Self-Organized Operational Neural Networks (Self-ONNs) in diagnosing electrical and mechanical faults using vibration and acoustic data? Methods: We evaluate and compare the diagnostic capabilities of three deep learning architectures: one-dimensional CNNs, Self-ONNs, and PadéNets. These models are tested on the University of Ottawa's publicly available constant-speed induction motor datasets, which include both vibration and acoustic sensor data. The PadéNet model is designed to introduce enhanced nonlinearity and is compatible with unbounded activation functions such as Leaky ReLU. Results and Conclusion: PadéNets consistently outperformed the baseline models, achieving diagnostic accuracies of 99.96%, 98.26%, 97.61%, and 98.33% for accelerometers 1, 2, 3, and the acoustic sensor, respectively. The enhanced nonlinearity of PadéNets, together with their compatibility with unbounded activation functions, significantly improves fault diagnosis performance in induction motor condition monitoring.

Reinforcement Learning faces an important challenge in partial observable environments that has long-term dependencies. In order to learn in an ambiguous environment, an agent has to keep previous perceptions in a memory. Earlier memory based approaches use a fixed method to determine what to keep in the memory, which limits them to certain problems. In this study, we follow the idea of giving the control of the memory to the agent by allowing it to have memory-changing actions. This learning mechanism is supported by an intrinsic motivation to memorize rare observations that can help the agent to disambiguate its state in the environment. Our approach is experimented and analyzed on several partial observable tasks with long-term dependencies and compared with other memory based methods.

Croston's method is generally viewed as superior to exponential smoothing when demand is intermittent, but it has the drawbacks of bias and an inability to deal with obsolescence, in which an item's demand ceases altogether. Several variants have been reported, some of which are unbiased on certain types of demand, but only one recent variant addresses the problem of obsolescence. We describe a new hybrid of Croston's method and Bayesian inference called Hyperbolic-Exponential Smoothing, which is unbiased on non-intermittent and stochastic intermittent demand, decays hyperbolically when obsolescence occurs and performs well in experiments.

By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study, using shifts and element-wise summations. This machinery can be extended symbolically to continuous case by thinking each possible sum as a single frequency impulse on the frequency band. Multiplication with a cosine in this case corresponds to the shifting operation as modulation in communication systems. Preliminary experimentation suggests that signal generation thus solution space calculation can be done in polynomial time. However, reading the value at a specific frequency (sum value) is problematic, namely cannot be simulated in polynomial time currently. Dedicated hardware implementation might be a solution, where both circuit-based and wireless versions might be tried out. A polynomial representation is also given that is claimed to be analogous to a tape of a Turing machine. Both rational and real number versions of the subset sum problem are also discussed, where the rational version of the problem is mapped to 0-1 range with specific patterns of True values. Although this machinery may not be totally equivalent to a non-deterministic Turing machine, it may be helpful for non-deterministic universal Turing machine actualization. It may pave way to both theoretical and practical considerations that can help computing machinery, information processing, and pattern recognition domains in various ways.

To compare different forecasting methods on demand series we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable, some give counter-intuitive results, and there is no agreement on which is best. We argue that almost all known measures rank forecasters incorrectly on intermittent demand series. We propose several new error measures with wider applicability, and correct forecaster ranking on several intermittent demand patterns. We call these "mean-based" error measures because they evaluate forecasts against the (possibly time-dependent) mean of the underlying stochastic process instead of point demands.

Transforming non-orthogonal bases into orthogonal ones often sacrifices essential properties or physical meaning in quantum systems. Here, we demonstrate that Löwdin symmetric orthogonalization (LSO) outperforms the widely used Gram-Schmidt orthogonalization (GSO) in characterizing and quantifying quantum resources, with particular emphasis on coherence and superposition. We employ LSO both to construct an orthogonal basis from a non-orthogonal one and to obtain a non-orthogonal basis from an orthogonal set, thereby avoiding any ambiguity related to the basis choice for quantum coherence. Unlike GSO, which depends on the ordering of input states, LSO applies a symmetric transformation that treats all vectors equally and minimizes deviation from the original basis. This approach generates basis sets with enhanced stability and physical relevance, facilitating the analysis of superpositions in non-orthogonal quantum states. Building on LSO, we also introduce Löwdin weights -- probabilistic weights for non-orthogonal representations that provide a consistent measure of resource content. These weights further enable basis-independent quantification of coherence and state delocalization through information-theoretic measures such as entropy and participation ratios. Our theoretical and numerical analyses confirm LSO's superior preservation of quantum state symmetry and resource characteristics, underscoring the critical role of orthogonalization methods and Löwdin weights in resource theory frameworks.

Classification of polarimetric synthetic aperture radar (PolSAR) images is an active research area with a major role in environmental applications. The traditional Machine Learning (ML) methods proposed in this domain generally focus on utilizing highly discriminative features to improve the classification performance, but this task is complicated by the well-known "curse of dimensionality" phenomena. Other approaches based on deep Convolutional Neural Networks (CNNs) have certain limitations and drawbacks, such as high computational complexity, an unfeasibly large training set with ground-truth labels, and special hardware requirements. In this work, to address the limitations of traditional ML and deep CNN based methods, a novel and systematic classification framework is proposed for the classification of PolSAR images, based on a compact and adaptive implementation of CNNs using a sliding-window classification approach. The proposed approach has three advantages. First, there is no requirement for an extensive feature extraction process. Second, it is computationally efficient due to utilized compact configurations. In particular, the proposed compact and adaptive CNN model is designed to achieve the maximum classification accuracy with minimum training and computational complexity. This is of considerable importance considering the high costs involved in labelling in PolSAR classification. Finally, the proposed approach can perform classification using smaller window sizes than deep CNNs. Experimental evaluations have been performed over the most commonly-used four benchmark PolSAR images: AIRSAR L-Band and RADARSAT-2 C-Band data of San Francisco Bay and Flevoland areas. Accordingly, the best obtained overall accuracies range between 92.33 - 99.39% for these benchmark study sites.

The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behaviour and which generates a symbolic dynamics consisting of infinitely many different symbols. Here we introduce a generalization of the Gauss map which is given by $x_{t+1}=\frac{1}{x_t^\alpha} - \Bigl[\frac{1}{x_t^\alpha} \Bigr]$ where $\alpha \geq 0$ is a parameter and $x_t \in [0,1]$ ($t=0,1,2,3,\ldots$). The symbol $[\dots ]$ denotes the integer part. This map reduces to the ordinary Gauss map for $\alpha=1$. The system exhibits a sudden `jump into chaos' at the critical parameter value $\alpha=\alpha_c \equiv 0.241485141808811\dots$ which we analyse in detail in this paper. Several analytical and numerical results are established for this new map as a function of the parameter $\alpha$. In particular, we show that, at the critical point, the invariant density approaches a $q$-Gaussian with $q=2$ (i.e., the Cauchy distribution), which becomes infinitely narrow as $\alpha \to \alpha_c^+$. Moreover, in the chaotic region for large values of the parameter $\alpha$ we analytically derive approximate formulas for the invariant density, by solving the corresponding Perron-Frobenius equation. For $\alpha \to \infty$ the uniform density is approached. We provide arguments that some features of this transition scenario are universal and are relevant for other, more general systems as well.

Noise and low quality of ECG signals acquired from Holter or wearable devices deteriorate the accuracy and robustness of R-peak detection algorithms. This paper presents a generic and robust system for R-peak detection in Holter ECG signals. While many proposed algorithms have successfully addressed the problem of ECG R-peak detection, there is still a notable gap in the performance of these detectors on such low-quality ECG records. Therefore, in this study, a novel implementation of the 1D Convolutional Neural Network (CNN) is used integrated with a verification model to reduce the number of false alarms. This CNN architecture consists of an encoder block and a corresponding decoder block followed by a sample-wise classification layer to construct the 1D segmentation map of R- peaks from the input ECG signal. Once the proposed model has been trained, it can solely be used to detect R-peaks possibly in a single channel ECG data stream quickly and accurately, or alternatively, such a solution can be conveniently employed for real-time monitoring on a lightweight portable device. The model is tested on two open-access ECG databases: The China Physiological Signal Challenge (2020) database (CPSC-DB) with more than one million beats, and the commonly used MIT-BIH Arrhythmia Database (MIT-DB). Experimental results demonstrate that the proposed systematic approach achieves 99.30% F1-score, 99.69% recall, and 98.91% precision in CPSC-DB, which is the best R-peak detection performance ever achieved. Compared to all competing methods, the proposed approach can reduce the false-positives and false-negatives in Holter ECG signals by more than 54% and 82%, respectively. Results also demonstrate similar or better performance than most competing algorithms on MIT-DB with 99.83% F1-score, 99.85% recall, and 99.82% precision.

The local dependence function is important in many applications of probability and statistics. We extend the bivariate local dependence function introduced by Bairamov and Kotz (2000) and further developed by Bairamov et al. (2003) to three-variate and multivariate local dependence function characterizing the dependency between three and more random variables in a given specific point. The definition and properties of the three-variate local dependence function are discussed. An example of a three-variate local dependence function for underlying three-variate normal distribution is presented. The graphs and tables with numerical values are provided. The multivariate extension of the local dependence function that can characterize the dependency between multiple random variables at a specific point is also discussed.

High dynamic range (HDR) imaging enables to immortalize natural scenes similar to the way that they are perceived by human observers. With regular low dynamic range (LDR) capture/display devices, significant details may not be preserved in images due to the huge dynamic range of natural scenes. To minimize the information loss and produce high quality HDR-like images for LDR screens, this study proposes an efficient multi-exposure fusion (MEF) approach with a simple yet effective weight extraction method relying on principal component analysis, adaptive well-exposedness and saliency maps. These weight maps are later refined through a guided filter and the fusion is carried out by employing a pyramidal decomposition. Experimental comparisons with existing techniques demonstrate that the proposed method produces very strong statistical and visual results.

We consider systems whose lifetime is measured by the time of physical degradation of components, as well as the degree of power each component contributes to the system. The lifetimes of the components of the system are random variables. The power that each component contributes to the system is the product of a random variable and a time-decreasing stable function. The operational reliability of these systems is investigated and shown that it is determined by the joint lifetime functions of the order statistics and their concomitants. In addition to general formulas, examples are given using some known life distributions, and graphs of the operation life functions are shown.

Glaucoma leads to permanent vision disability by damaging the optical nerve that transmits visual images to the brain. The fact that glaucoma does not show any symptoms as it progresses and cannot be stopped at the later stages, makes it critical to be diagnosed in its early stages. Although various deep learning models have been applied for detecting glaucoma from digital fundus images, due to the scarcity of labeled data, their generalization performance was limited along with high computational complexity and special hardware requirements. In this study, compact Self-Organized Operational Neural Networks (Self- ONNs) are proposed for early detection of glaucoma in fundus images and their performance is compared against the conventional (deep) Convolutional Neural Networks (CNNs) over three benchmark datasets: ACRIMA, RIM-ONE, and ESOGU. The experimental results demonstrate that Self-ONNs not only achieve superior detection performance but can also significantly reduce the computational complexity making it a potentially suitable network model for biomedical datasets especially when the data is scarce.