Computational Robustness Research Articles

A secured industrial wireless iot sensor network enabled quick transmission of data with a prototype study

The Wireless IoT sensor network (IWSN) has significant potential in industrial settings, but to fully realize its benefits, a robust and scalable computer system is required to handle the continuous influx of data from various applications. In this research study, we propose an IoT sensor-cloud architecture that integrates WSN with cloud technology, providing a unique data analytics framework for highly secure analysis of sensor data. The proposed architecture emphasizes effective interoperability mechanisms in the cloud, and provides an IPv6 extensible enterprise WSN design and simulation technique. To demonstrate the effectiveness of our proposed architecture, we track the pH, resistivity, and dissolved oxygen levels of industrial effluents that are discharged into water sources. We use AT instructions in conjunction with the HTTP GET technique to gather and upload detector data to the ThingSpeak cloud through a GPRS internet connection, enabling real-time online monitoring and control using IoT functionality. The proposed architecture uses a distributed approach to handle high volumes of incoming data from the IoT sensors, storing the data in a scalable and accessible way for analysis. Real-time analysis is performed using a combination of batch and stream processing frameworks and machine learning algorithms, and the results are visualized using a web-based dashboard that provides real-time updates on key metrics and allows users to explore the data in different ways. Security is a top priority in our proposed architecture, and we use encryption technologies such as SSL/TLS and access control mechanisms such as OAuth2 to ensure the secure transmission and storage of sensitive industrial IoT data. The architecture is designed to be scalable and adaptable to handle a wide range of IoT use cases in industrial settings. The proposed IoT sensor-cloud architecture provides a robust and scalable solution for the collection, analysis, and exchange of significant amounts of IoT sensor information, enabling real-time monitoring and control of critical environmental parameters in industrial settings.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Brain-inspired methods for achieving robust computation in heterogeneous mixed-signal neuromorphic processing systems

Abstract Neuromorphic processing systems implementing spiking neural networks with mixed signal analog/digital electronic circuits and/or memristive devices represent a promising technology for edge computing applications that require low power, low latency, and that cannot connect to the cloud for off-line processing, either due to lack of connectivity or for privacy concerns. However, these circuits are typically noisy and imprecise, because they are affected by device-to-device variability, and operate with extremely small currents. So achieving reliable computation and high accuracy following this approach is still an open challenge that has hampered progress on the one hand and limited widespread adoption of this technology on the other. By construction, these hardware processing systems have many constraints that are biologically plausible, such as heterogeneity and non-negativity of parameters. More and more evidence is showing that applying such constraints to artificial neural networks, including those used in artificial intelligence, promotes robustness in learning and improves their reliability. Here we delve even more into neuroscience and present network-level brain-inspired strategies that further improve reliability and robustness in these neuromorphic systems: we quantify, with chip measurements, to what extent population averaging is effective in reducing variability in neural responses, we demonstrate experimentally how the neural coding strategies of cortical models allow silicon neurons to produce reliable signal representations, and show how to robustly implement essential computational primitives, such as selective amplification, signal restoration, working memory, and relational networks, exploiting such strategies. We argue that these strategies can be instrumental for guiding the design of robust and reliable ultra-low power electronic neural processing systems implemented using noisy and imprecise computing substrates such as subthreshold neuromorphic circuits and emerging memory technologies.

Don’t get lost in the crowd: Graph convolutional network for online animal tracking in dense groups

Tracking the behaviour of animals in group-housed situations is a critical area of study for precision livestock farming, but it poses challenges in diverse and crowded environments. Existing methods often struggle with false positives and false negatives due to the complexities of these scenarios. In this study, we propose a robust computer vision algorithm for long-term (>10mins) animal tracking, with a primary focus on group-housed pigs. Our method addresses the limitations of current approaches by effectively handling errors from the detector in challenging environments. Our approach integrates Graph Convolutional Networks.(GCNs) with deep learning-based object detection techniques. We represent the data as a graph structure, with nodes corresponding to multiple animal detections over several frames. Edges connect thedetections that do not appear in the same frame. The model's objective is to perform edge classification, where each edge is associated with a scalar representing the probability of being the same object. To enhance the robustness of edge classification, we combine the classifier withan ensemble predictor, enabling accurate tracking of animal identitiesfor extended periods. Notably, our graph convolutional model achievesaccurate re identification of non-consecutive animal detections inreal-time without the need for trajectory prediction or ID association. We evaluate our method by comparing its performance against othertracking methods, including DeepSORT—a state-of-the-art animal trackingmethod that relies on a Kalman filter, a deep appearance descriptor, and the Hungarian algorithm for trajectory prediction and ID association.Our comparison demonstrates the advantages of our method, as it (1)improves the IDF1 score, indicating enhanced ID association accuracy, by 1.72%; (2) mitigates 93% of errors resulting from ID-switch anddeviation; (3) extends the tracking duration of each animal byapproximately 66% in challenging conditions; and (4) achieves aprocessing speed that is 1000 times faster than DeepSORT when operatingat 22fps with the detector. The potential applications of our method extend to various aspects of livestock management. By accurately tracking individual animals, we can monitor behaviours such as feeding, drinking, and aggressive interactions. This information can lead to improvements in animal welfare, resource allocation, and breeding strategies. Follow-ups of this research are available at: https://gitlab.kuleuven.be/m3-biores/public/m3pig.

Beyond Honest Majority: The Round Complexity of Fair and Robust Multi-party Computation

Beyond Honest Majority: The Round Complexity of Fair and Robust Multi-party Computation

IPAD: Iterative pruning with activation deviation for sclera biometrics

The sclera has recently been gaining attention as a biometric modality due to its various desirable characteristics. A key step in any type of ocular biometric recognition, including sclera recognition, is the segmentation of the relevant part(s) of the eye. However, the high computational complexity of the (deep) segmentation models used in this task can limit their applicability on resource-constrained devices such as smartphones or head-mounted displays. As these devices are a common desired target for such biometric systems, lightweight solutions for ocular segmentation are critically needed. To address this issue, this paper introduces IPAD (Iterative Pruning with Activation Deviation), a novel method for developing lightweight convolutional networks, that is based on model pruning. IPAD uses a novel filter-activation-based criterion (ADC) to determine low-importance filters and employs an iterative model pruning procedure to derive the final lightweight model. To evaluate the proposed pruning procedure, we conduct extensive experiments with two diverse segmentation models, over four publicly available datasets (SBVPI, SLD, SMD and MOBIUS), in four distinct problem configurations and in comparison to state-of-the-art methods from the literature. The results of the experiments show that the proposed filter-importance criterion outperforms the standard L1 and L2 approaches from the literature. Furthermore, the results also suggest that: (i) the pruned models are able to retain (or even improve on) the performance of the unpruned originals, as long as they are not over-pruned, with RITnet and U-Net at 50% of their original FLOPs reaching up to 4% and 7% higher IoU values than their unpruned versions, respectively, (ii) smaller models require more careful pruning, as the pruning process can hurt the model’s generalization capabilities, and (iii) the novel criterion most convincingly outperforms the classic approaches when sufficient training data is available, implying that the abundance of data leads to more robust activation-based importance computation.

Designs of Two Quadruple-Node-Upset Self-Recoverable Latches for Highly Robust Computing in Harsh Radiation Environments

This paper proposes two quadruple-node-upset (QNU) recoverable latches, namely QRHIL and QRHIL-LC (low-cost version of the QRHIL), for highly robust computing in harsh radiation environments. First, the QRHIL that mainly consists of a 5×5 looped C-element matrix, is proposed. Then, to reduce overhead, the QRHIL-LC that mainly uses 24 interlocking C-elements, is proposed. Both latches can self-recover from any QNU, while the QRHIL-LC has low cost compared to the QRHIL. Simulation waveforms show the QNU-recoverability of the proposed QRHIL and QRHIL-LC latches. Moreover, compared with the QRHIL latch, the QRHIL-LC can approximately save power dissipation by 16% and silicon area by 5%.

Daily INSOLation (DINSOL-v1.0): an intuitive tool for classrooms and specifying solar radiation boundary conditions

Abstract. Climate modelling requires spending an extensive amount of time programming, which means reading, learning, testing, and evaluating source code. Fortunately, many climate models have been developed within the past decades, making it easier for climate studies to be conducted on a global scale. However, some climate models have millions of code lines, making the introduction of new parameterizations a laborious task that demands teamwork. While it is true that the high-complexity models perform realistic climate simulations, some researchers perform their studies using simplified climate models in the preliminary test phases. This realization motivated the development of Daily INSOLation (DINSOL-v1.0), a robust computer program to support the simplified climate models, performing solar radiation calculations while considering Milankovitch cycles and offering various simulation options for its users. DINSOL was intended to function as a program that supplies data (e.g. daily insolation, instantaneous solar radiation, orbital parameters of the Earth, and calendar dates), such as the Paleoclimate Modelling Intercomparison Project (PMIP). While preparing the boundary conditions of solar radiation for climate models, it was realized that the DINSOL model could also be a helpful tool for use in classrooms. Thus, it was decided that an intuitive graphical user interface would be required to cater to this educational purpose. The model was written in the Fortran 90 language, while its graphical user interface would be built using PyGTK, a Python application programming interface (API) based on GIMP ToolKit (GTK). Furthermore, the R language would also be used to generate a panel containing contour fields and sketches of the orbital parameters to support the graphical execution. The model evaluation made use of data from PMIP and other tools, and the data analysis was performed through statistical methods. Once all tests were concluded, an insignificant difference between the DINSOL-obtained results and the results obtained from other models validated the viability of DINSOL as a dependable tool.

Multilevel Robustness for 2D Vector Field Feature Tracking, Selection and Comparison

AbstractCritical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time‐varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time‐varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large‐scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real‐world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.

Polyaniline‐Based Memristive Devices as Key Elements of Robust Reservoir Computing for Image Classification

One of the remarkable features of the emerging neuromorphic systems is the ability of implementing in‐memory computing which is demonstrated using memristors to realize both memory and computation functionalities within a single element. However, biological neural systems exhibit many other outstanding computing capabilities, among which one is the sensitivity to temporal parameters of neural activity. The identification and the realization of systems able to imitate this ability is still a very challenging perspective. Herein, polyaniline‐based organic memristive devices endowed with volatile resistive switching, complex temporal behaviors and capable of processing 4‐bit sequences of data with reliable separation of states are demonstrated. Thanks to this ability, such devices can be key elements in a reservoir layer of a network to map high‐dimensional input signals to a lower‐dimensional feature space. Herein, it is demonstrated through simulations that this type of device could be a valuable element for the realization of a reservoir computing system for the classification of handwritten digits from MNIST dataset. The model suggests that the electrical properties of the polyaniline‐based organic memristive devices ensure the realization of a system able to correctly classify handwritten digits and to be tolerant to considerable overlapping of neighboring reservoir states.

CoSumNet: A video summarization-based framework for COVID-19 monitoring in crowded scenes

The outbreak of COVID-19 pandemic poses new challenges to research community to investigate novel mechanisms for monitoring as well as controlling its further spread via crowded scenes. Moreover, the contemporary methods of COVID-19 preventions are enforcing strict protocols in the public places. The emergence of robust computer vision-enabled applications leverages intelligent frameworks for monitoring of the pandemic deterrence in public places. The employment of COVID-19 protocols via wearing face masks by human is an effective procedure that is implemented in several countries across the world. It is a challenging task for authorities to manually monitor these protocols particularly in densely crowded public gatherings such as, shopping malls, railway stations, airports, religious places etc. Thus, to overcome these issues, the proposed research aims to design an operative method that automatically detects the violation of face mask regulation for COVID-19 pandemic. In this research work, we expound a novel technique for COVID-19 protocol desecration via video summarization in the crowded scenes (CoSumNet). Our approach automatically yields short summaries from crowded video scenes (i.e., with and without mask human). Besides, the CoSumNet can be deployed in crowded places that may assist the controlling agencies to take appropriate actions to enforce the penalty to the protocol violators. To evaluate the efficacy of the approach, the CoSumNet is trained on a benchmark “Face Mask Detection ∼12K Images Dataset” and validated through various real-time CCTV videos. The CoSumNet demonstrates superior performance of 99.98 % and 99.92 % detection accuracy in the seen and unseen scenarios respectively. Our method offers promising performance in cross-datasets environments as well as on a variety of face masks. Furthermore, the model can convert the longer videos to short summaries in nearly 5–20 s approximately.

Models for Generation of Proof Forest in zk-SNARK Based Sidechains

Sidechains are among the most promising scalability and extended functionality solutions for blockchains. Application of zero knowledge techniques (Latus, Mina) allows for reaching high level security and general throughput, though it brings new challenges on keeping decentralization where significant effort is required for robust computation of zk-proofs. We consider a simultaneous decentralized creation of various zk-proof trees that form proof-trees sequences in sidechains in the model that combines behavior of provers, both deterministic (mutually consistent) or stochastic (independent) and types of proof trees. We define the concept of efficiency of such process, introduce its quantity measure and recommend parameters for tree creation. In deterministic cases, the sequences of published trees are ultimately periodic and ensure the highest possible efficiency (no collisions in proof creation). In stochastic cases, we obtain a universal measure of prover efficiencies given by the explicit formula in one case or calculated by a simulation model in another case. The optimal number of allowed provers’ positions for a step can be set for various sidechain parameters, such as number of provers, number of time steps within one block, etc. Benefits and restrictions for utilization of non-perfect binary proof trees are also explicitly presented.

Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit

We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.

WE3DS: An RGB-D Image Dataset for Semantic Segmentation in Agriculture

Smart farming (SF) applications rely on robust and accurate computer vision systems. An important computer vision task in agriculture is semantic segmentation, which aims to classify each pixel of an image and can be used for selective weed removal. State-of-the-art implementations use convolutional neural networks (CNN) that are trained on large image datasets. In agriculture, publicly available RGB image datasets are scarce and often lack detailed ground-truth information. In contrast to agriculture, other research areas feature RGB-D datasets that combine color (RGB) with additional distance (D) information. Such results show that including distance as an additional modality can improve model performance further. Therefore, we introduce WE3DS as the first RGB-D image dataset for multi-class plant species semantic segmentation in crop farming. It contains 2568 RGB-D images (color image and distance map) and corresponding hand-annotated ground-truth masks. Images were taken under natural light conditions using an RGB-D sensor consisting of two RGB cameras in a stereo setup. Further, we provide a benchmark for RGB-D semantic segmentation on the WE3DS dataset and compare it with a solely RGB-based model. Our trained models achieve up to 70.7% mean Intersection over Union (mIoU) for discriminating between soil, seven crop species, and ten weed species. Finally, our work confirms the finding that additional distance information improves segmentation quality.

Mixed formulation for an easy and robust numerical computation of sorptivity

Abstract. Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation, while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic function – even with infinite hydraulic diffusivity or positive air-entry water pressure heads – and any boundary condition, including infinite initial water pressure head, h→-∞. Lastly, we show the benefits of using the proposed formulation for modeling water into soil with analytical models that use sorptivity.

Revealing the Origin of Time-Reversal Symmetry Breaking in Fe-Chalcogenide Superconductor FeTe_{1-x}Se_{x}.

Recently, evidence has emerged in the topological superconductor Fe-chalcogenide FeTe_{1-x}Se_{x} for time-reversal symmetry breaking (TRSB), the nature of which has strong implications on the Majorana zero modes (MZM) discovered in this system. It remains unclear, however, whether the TRSB resides in the topological surface state (TSS) or in the bulk, and whether it is due to an unconventional TRSB superconducting order parameter or an intertwined order. Here, by performing in superconducting FeTe_{1-x}Se_{x} crystals both surface-magneto-optic-Kerr effect measurements using a Sagnac interferometer and bulk magnetic susceptibility measurements, we pinpoint the TRSB to the TSS, where we also detect a Dirac gap. Further, we observe surface TRSB in nonsuperconducting FeTe_{1-x}Se_{x} of nominally identical composition, indicating that TRSB arises from an intertwined surface ferromagnetic (FM) order. The observed surface FM bears striking similarities to the two-dimensional (2D) FM found in 2D van der Waals crystals, and is highly sensitive to the exact chemical composition, thereby providing a means for optimizing the conditions for Majorana particles that are useful for robust quantum computing.

Crack detection and crack segmentation in concrete beams undergoing mode I fracture using computer vision and convolutional neural network

The study presents two crack detection techniques for a beam undergoing mode I fracture: (i) convolutional neural network approach and (ii) image processing using opensource computer vision library OpenCV and pixel count of cracks approach. The second method also includes crack segmentation and masking for visualization of the cracks. The study attempted to evaluate the accuracy of both methods at different crack mouth opening displacement of seven simply supported concrete beams being tested using three-point bend test. The novelty of the present work lies in quantification of the crack growth from captured images and evaluating the potential of applying computer vision techniques as a replacement for sensitive crack measuring instruments to create a robust computer vision based health monitoring system. Results suggest that both methods identified the cracks in the beam and are capable of generating a warning before the collapse.

Robust Grid-Based Computation of H-Matrix Blocks’ Low-Rank Approximation for Vector Basis Functions

A fast method to assess and correct the domain misrepresentation of impedance matrix blocks, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Z}^{\mathrm {os}}$ </tex-math></inline-formula> , based on their row- and column-sampling, to ensure the accuracy of their low-rank approximation (LRA), is presented. The misrepresentation arises when auxiliary grid-based interaction matrices, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {G}$ </tex-math></inline-formula> , of smaller dimensions are used to replace <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Z}^{\mathrm {os}}$ </tex-math></inline-formula> to accelerate their LRA. Specifically, a recently introduced fast multilevel LRA algorithm, which uses truncated singluar-value decompositions of matrices corresponding to interactions between basis-functions and proxy grids, is shown to lose error controllability when used for vector basis/testing functions. A pre-processing stage that correctly and automatically sets the algorithm’s truncation threshold, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau _{\mathcal {G}}$ </tex-math></inline-formula> , for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {G}$ </tex-math></inline-formula> , such that the domains of their truncated versions represent those of the blocks to the desired accuracy, is proposed. The method first analyzes small, randomly sampled portions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {G}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Z}^{\mathrm {os}}$ </tex-math></inline-formula> , increasing the sample size until their spectrums converge; it then uses the converged spectra to gradually increase the rank and lower the truncation threshold, until the desired error level is achieved. The resulting truncation threshold, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\bar {\tau }$ </tex-math></inline-formula> , is then used for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau _{\mathcal {G}}$ </tex-math></inline-formula> across all algorithm levels. Representative examples validate the method and show its effectiveness.

FRACTIONAL CALCULUS OPERATORS–BLOCH–TORREY PARTIAL DIFFERENTIAL EQUATION–ARTIFICIAL NEURAL NETWORKS–COMPUTATIONAL COMPLEXITY MODELING OF THE MICRO–MACROSTRUCTURAL BRAIN TISSUES WITH DIFFUSION MRI SIGNAL PROCESSING AND NEURONAL MULTI-COMPONENTS

Fractional calculus and fractional-order calculus are arranged in lineage as regards the mathematical models with complexity-theoretical tenets capable of capturing the subtle molecular dynamics by the integration of power-law convolution kernels into time- and space-related derivatives emerging in equations concerning the Magnetic Resonance Imaging (MRI) phenomena to which the fractional models of diffusion and relaxation are applied. Endowed with an intricate level of complexity and a unique physical and structural scaffolding at molecular and cellular levels with numerous synapses forming elaborate neural networks which entail in-depth probing and computing of patterns and signatures in individual cells and neurons, human brain as a heterogeneous medium is constituted of tissues with cells of different sizes and shapes, distributed across an extra-cellular space. Characterization of the unique brain cells is sought after to unravel the connections between different cells and tissues for accurate, reliable, robust and optimal models and computing. Accordingly, Diffusion Magnetic Resonance Imaging (DMRI), as a noninvasive and experimental imaging technique with clinical and research applications, provides a measure related to the diffusion characteristics of water in biological tissues, particularly in the brain tissues. Compatible with these aspects and beyond the diffusion coefficients’ measurement, DMRI technique aims to exceed the spatial resolution of the MRI images and draw inferences from the microstructural properties of the related medium. Thus, novel tools become essential for the description of the biological (organelles, membranes, macromolecules and so on) and neurological (axons, dendrites, neurons and so forth) tissues’ complexity. Mathematical model-based computational analyses with multifaceted methods to extract information from the DMRI with SpinDoctor into neuronal dynamics can provide quantitative parametric instruments in order to reflect the tissue properties focusing on the precise link between the tissue microstructure and signals acquired by employing advanced medical imaging technologies. Coalesced with accurate neuron geometry models as well as numerical DMRI simulations, a novel extended and multifaceted predictive mathematical model based on SpinDoctor and Bloch–Torrey partial differential equation (BTPDE) with the Caputo fractional-order derivative (FOD) with three-parameter [Formula: see text] Mittag-Leffler function (MLF) has been proposed and developed in our study by extending for the application on Brain Neuron Spin Unit dataset with the relevant multi-stage application-related steps. The feedforward neural networks (FFNNs) with BFGS Quasi-Newton equation, as one of the artificial neural network (ANN) algorithms, are applied on BTPDE with Caputo fractional-order derivative for the neurons and their algorithmic complexity is computed by building a BTPDE with Caputo FOD Neuron model based on different fractional orders. The fractional-order degree of the proposed and developed model is applied in relation to their corresponding complexity degrees. Consequently, experimentation and observations from the simulation-driven FFNN (with BFGS Quasi-Newton equation) learning scheme applied to the Bloch–Torrey PDE–Caputo FOD with MLF Neuron model (named as FFNN–BTPDE–CFODMLF Neuron model) proposed in this study, are made. Thus, by investigating whether the mathematical models based on the accurate neuron geometry models obtained can be optimized by comparing the errors in order to define the order parameter and identify to what optimal extent the errors are in relation to the prediction results with a particular focus on the neuron model, we have been able to estimate and predict brain microstructure through DMRI, accentuating mathematical and medical contributions based on the exploitation and corroboration of powerful modeling as well as computational capabilities.

Quantifying resilience and the risk of regime shifts under strong correlated noise.

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.