Singular Model Research Articles

Numerical treatment for the nonlinear fifth kind of multi-singular differential model: a neuro-swarming approach

In this study, a numerical scheme is proposed for the fifth order (FO) singular differential model (SDM), FO-SDM. The solutions of the singular form of the differential models are always considered difficult to solve and huge important in astrophysics. A neural network study together with the hybrid combination of global particle swarm optimization and local sequential quadratic programming schemes is provided to find the numerical simulations of the FO-SDM. An objective function is constructed using the differential FO-SDM along with the boundary conditions. The correctness of the scheme is observed by providing the comparison of the obtained and exact solutions. The justification of the proposed scheme is authenticated in terms of absolute error (AE), which is calculated in good measures for solving the FO-SDM. The efficiency and reliability of the stochastic approach are observed using the statistical performances to solve the FO-SDM.

In Silico Interactions of Morphine Opioids with TLR4 and TRPV1 Targets

By the importance of exploring new inhibitors or antagonists for the over-activity of each of Toll-Like Receptor 4 (TLR4) and Transient Receptor Potential Vanilloid 1 (TRPV1) targets, derivatives of morphine opioid were investigated in this work using the in silico methodology. The original morphine and three derivatives of oxymorphone, naloxone, and naltrexone were considered the parent ligands (L1-L4), and the C-3-O-Alky functionalized models were considered as functionalized ligands (L5-L8). The singular models of ligands were optimized to obtain the minimized energy structures, and molecular docking simulations were performed to examine their interactions with the targets. The optimizations indicated significant variations of the frontier electronic molecular orbital levels proposing different activities for the ligands. Next, molecular docking simulations showed that L1 (the original morphine) was at the lowest suitability of complex formation and L8 was at the highest suitability of complex formation with both TLR4 and TRPV1 targets. Consequently, optimizing the morphine lead compound for obtaining more suitable ligands was achieved for proposing new inhibitors or antagonists for the investigated TLR4 and TRPV1 targets.

Supersymmetric Wigner–Dunkl quantum mechanics

Wigner–Dunkl quantum mechanics can be viewed as deformed quantum mechanics, where the commutator between canonical momentum and position operators contains in addition a reflection operator. In the present work we carry over the general concepts of supersymmetric (SUSY) quantum mechanics to the Wigner–Dunkl quantum formulation. We investigate the SUSY ground states, the SUSY transformations and introduce a generalized shape invariance allowing for explicit solutions. In this way, exact solutions for a certain class of SUSY potentials can be provided. As example the harmonic oscillator is considered. We also take a look into a singular oscillator model, which does not belong to the shape-invariance class. Nevertheless, exact solutions can be provided, showing the peculiarities of that model in the SUSY Wigner–Dunkl quantum mechanics. A modification of that singular model is presented which restores shape invariance

Model stacking to improve prediction and variable importance robustness for soft sensor development

This paper presents an interpretable ensemble modelling method, in which the predictions of several individual base learners are combined together through Stacked generalisation, which makes use of a secondary layer model, or so called meta-learner, that is trained on the output cross-validation predictions of each base learner. To provide interpretability, the permutation variable importance (PVI) is computed on the ensemble, wherein variables are randomly shuffled and the reduction in predictive performance for the ensemble is calculated for each variable. This is a novel contribution, as no previous attempts have been made in the soft sensor literature to investigate the interpretability of ensemble models that use heterogeneous base learners. The Stacked ensemble model also avoids model selection, which is the process of choosing among many candidate models. Model selection is often based on cross-validation, which is not guaranteed to select the best model in terms of true generalisation performance on the test set. Instead, the proposed method combines multiple models instead of choosing a singular model, avoiding the need for model selection. The efficacy of the proposed methodology in terms of both variable importance and predictive performance is shown on a synthetic dataset, in which the variable importance is already known, and an industrial dataset of a refinery process provided by Dow. For the synthetic dataset, it is shown that the proposed method chooses the correct casual variables, whereas the in-built variable importance provided by the individual models, namely Partial least squares, Lasso, Random forests & XGBoost, can give increased importance to non-causal, randomly generated variables. For the industrial study, the combined ensemble is shown to outperform all individual base models in terms of predictive performance, whilst also providing a new perspective in terms of variable importance compared to previous studies.

Asymptotic behavior of free energy when optimal probability distribution is not unique

Bayesian inference is a widely used statistical method. The free energy and the generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal parameter. However, their characteristics have not yet been clarified when there are multiple optimal probability distributions. In this paper, we theoretically derive the asymptotic behaviors of the generalization loss and the free energy in the case that the optimal probability distributions are not unique and show that they contain asymptotically different terms from those of the conventional asymptotic analysis.

Tool wear prediction in face milling of stainless steel using singular generative adversarial network and LSTM deep learning models

During milling operations, wear of cutting tool is inevitable; therefore, tool condition monitoring is essential. One of the difficulties in detecting the state of milling tools is that they are visually inspected, and due to this, the milling process needs to be interrupted. Intelligent monitoring systems based on accelerometers and algorithms have been developed as a part of Industry 4.0 to monitor the tool wear during milling process. In this paper, acoustic emission (AE) and vibration signals captured through sensors are analyzed and the scalograms were constructed from Morlet wavelets. The relative wavelet energy (RWE) criterion was applied to select suitable wavelet functions. Due to the availability of less experimental data to train the LSTM model for the prediction of tool wear, SinGAN was applied to generate additional scalograms and later several image quality parameters were extracted to construct feature vectors. The feature vector is used to train three long short-term memory network (LSTM) models: vanilla, stacked, and bidirectional. To analyze the performance of LSTM models for tool wear prediction, five performance parameters were computed namely R2, adjusted R2, mean absolute error (MAE), root mean square error (RMSE), and mean square error (MSE). The lowest MAE, RMSE, and MSE values were observed as 0.005, 0.016, and 0.0002 and high R2 and Adj. R2 values as 0.997 are observed from the vibration signal. Results suggest that the stacked LSTM model predicts the tool wear better as compared to other LSTM models. The proposed methodology has given very less errors in tool wear predictions and can be extremely useful for the development of an online deep learning tool condition monitoring system.

An Improved Method to Estimate Savings from Thermal Comfort Control in Residences from Smart Wi-Fi Thermostat Data

The net-zero global carbon target for 2050 needs both expansion of renewable energy and substantive energy consumption reduction. Many of the solutions needed are expensive. Controlling HVAC systems in buildings based upon thermal comfort, not just temperature, uniquely offers a means for deep savings at virtually no cost. In this study, a more accurate means to quantify the savings potential in any building in which smart WiFi thermostats are present is developed. Prior research by Alhamayani et al. leveraging such data for individual residences predicted cooling energy savings in the range from 33 to 47%, but this research was based only upon a singular data-based model of indoor temperature. The present research improves upon this prior research by developing LSTM neural network models for both indoor temperature and humidity. Validation errors are reduced by nearly 22% compared to the prior work. Simulations of thermal comfort control for the residences considered yielded potential savings in the range of 29–43%, dependent upon both solar exposure and insulation characteristics of each residence. This research paves the way for smart Wi-Fi thermostat-enabled thermal comfort control in buildings of all types.

Characterising social-ecological drivers of landuse/cover change in a complex transboundary basin using singular or ensemble machine learning

Studies have focused on understanding land use/cover (LULC) change through regression techniques. However, machine learning (ML) techniques and their ensembles may provide more accurate results. Accurate determination of drivers of LULC can guide reliable land use planning and effective natural resource management. In this study, we tested the utility of ML techniques and ensemble modelling to explain the social-ecological drivers of LULC in the Okavango basin. The Deep Neural Network (DNN) coupled with climate-based regionalization of the study area were used for LULC classification of the years 2002, 2013 and 2020. Centroids of 22 LULC transitions of the same period were used to separately calibrate five (5) machine algorithms (namely Random Forests (RF), Gradient Boost Models (GBM) and Maximum Entropy (MaxEnt), Classification Tree Analysis (CTA) and their ensemble. Model performance was evaluated using the Receiver Operating Characteristic (ROC) and the True skill statistic (TSS). Variable importance was used to assess the contribution of social-ecological variables to each LULC transition. Variables that were determined to be driving LULC were then used to predict future LULC using the Artificial Neural Network and Cellular Automata (ANN-CA). Analysis results show that average LULC classification accuracy for the study period (2002, 2013 and 2020) was (Bsh Koppen zone; OA = 95.03, Kappa = 0.94), (Cwa Koppen zone; OA = 95.29, Kappa = 0.94), Cwb Koppen zone; OA = 96.04, Kappa = 0.95). The ML ensemble performed better (ROC> 95, TSS >87) than singular ML models based on two separate model evaluation metrics. The Random Forest classifier outperformed other singular ML (ROC = 90.41, TSS = 84.2). Based on the top-performing ensemble model, distance from rivers, population density, annual average temperature, drought severity, fire frequency and distance from towns influence the conversion of natural to anthropogenic LULC classes (importance >0.5). On the other hand, distance from rivers, soil organic carbon, precipitation, GDP, elevation, population density and annual average temperature importantly influenced conversion from one natural LULC class to another natural LULC class. The study revealed that natural classes (wetland, shrubland, water and woodlands) will gradually decrease at the expense of anthropogenic classes (built-up and cultivated) in future (2040). Despite proposing the necessity of a basin-wide land-use plan to minimise pressure on resources and ensure sustainable use, findings in this study illustrate the benefit of ensemble modelling in understanding LULC dynamics in transboundary basins.

Application of the novel circulant singular spectrum analysis ensemble model for forecasting of streamflow data

Application of the novel circulant singular spectrum analysis ensemble model for forecasting of streamflow data

Chinese Narrotologies

Chinese Narrotologies

Non-local gravity in bouncing cosmology scenarios

In this work, we analyzed the improved Deser-Woodard non-local gravity over the background of five different bouncing cosmologies, whose premise is avoid the initial singular state of the universe.We developed the numerical solution for the non-local distortion function, which encompass the modifications to the Einstein-Hilbert action, using the reconstruction procedure and we have found that they have a viable cosmological solution.Afterwards, we discussed the physical aspects and outcomes of the evolution of the distortion function throughout the bouncing point for these models, specifically: the symmetric bounce, oscillatory bounce, the matter bounce, finite time singularity model, and the pre-inflationary asymmetrical bounce.

Singular Function Model of Concentrated Mass-Cable Composite Structures

Singular Function Model of Concentrated Mass-Cable Composite Structures

On four-dimensional steady gradient Ricci solitons that dimension reduce

In this paper, we will study the asymptotic geometry of 4-dimensional steady gradient Ricci solitons under the condition that they dimension reduce to 3-manifolds. We will show that such solitons either strongly dimension reduce to a spherical space form S3/Γ or weakly dimension reduce to the 3-dimensional Bryant soliton. We also show that 4-dimensional steady gradient Ricci soliton singularity models with nonnegative Ricci curvature outside a compact set either are Ricci-flat ALE 4-manifolds or dimension reduce to 3-dimensional manifolds. As a further application, we prove that any steady gradient Kähler-Ricci soliton singularity models on complex surfaces with nonnegative Ricci curvature outside a compact set must be hyperkähler ALE 4-manifolds.

Singularity formation of complete Ricci flow solutions

We study singularity formation of complete Ricci flow solutions, motivated by two applications: (a) improving the understanding of the behavior of the essential blowup sequences of Enders–Müller–Topping [8] on noncompact manifolds, and (b) obtaining further evidence in favor of the conjectured stability of generalized cylinders as Ricci flow singularity models.

Dissecting the 2015 Chinese stock market crash

AbstractWe perform a novel analysis of the 2015 Chinese stock market crash by calibrating the log‐periodic power law singularity (LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early 2014 to June 2015. Our analysis indicates that the LPPLS model can readily detect the bubble behaviour of the faster‐than‐exponential increase corrected by the accelerating logarithm‐periodic oscillations in the crash. The existence of the log‐periodicity is identified by applying the Lomb spectral analysis on the detrended residuals. The Ornstein–Uhlenbeck property and the stationarity of the LPPLS fitting residuals are confirmed by the Phillips–Perron test and the Dickey–Fuller test. We find that the actual critical day of bubble crash can be well predicted by the LPPLS model as far back as 2 months before the actual crash. We have shown that the covariance matrix adaptation evolution strategy (CMA‐ES) can be used as an alternative optimization algorithm for the LPPLS model fit. Furthermore, the change rate of the prediction end time gap ( ) can be used as an additional indicator along with the key indicator to improve the prediction of bubble burst.

The Singular Evolution of Olea Genome Structure.

The current view of plant genome evolution proposes that genome size has mainly been determined by polyploidisation and amplification/loss of transposons, with a minor role played by other repeated sequences, such as tandem repeats. In cultivated olive (Olea europaea subsp. europaea var. europaea), available data suggest a singular model of genome evolution, in which a massive expansion of tandem-repeated sequences accompanied changes in nuclear architecture. This peculiar scenario highlights the importance of focusing on Olea genus evolution, to shed light on mechanisms that led to its present genomic structure. Next-generation sequencing technologies, bioinformatics and in situ hybridisation were applied to study the genomic structure of five related Olea taxa, which originated at different times from their last common ancestor. On average, repetitive DNA in the Olea taxa ranged from ~59% to ~73% of the total genome, showing remarkable differences in terms of composition. Among repeats, we identified 11 major families of tandem repeats, with different abundances in the analysed taxa, five of which were novel discoveries. Interestingly, overall tandem repeat abundance was inversely correlated to that of retrotransposons. This trend might imply a competition in the proliferation of these repeat classes. Indeed, O. paniculata, the species closest to the Olea common ancestor, showed very few tandem-repeated sequences, while it was rich in long terminal repeat retrotransposons, suggesting that the amplification of tandem repeats occurred after its divergence from the Olea ancestor. Furthermore, some tandem repeats were physically localised in closely related O. europaea subspecies (i.e., cultivated olive and O. europaea subsp. cuspidata), which showed a significant difference in tandem repeats abundance. For 4 tandem repeats families, a similar number of hybridisation signals were observed in both subspecies, apparently indicating that, after their dissemination throughout the olive genome, these tandem repeats families differentially amplified maintaining the same positions in each genome. Overall, our research identified the temporal dynamics shaping genome structure during Olea speciation, which represented a singular model of genome evolution in higher plants.

A Haredi Myth of Female Leadership: Rebbetzin Batsheva Kanievsky

Rebbetzin Batsheva Kanievsky (1932–2011) served as a spiritual guide for many; her prominence and influence were a unique phenomenon in the Haredi (Jewish ultra-Orthodox) community in which she grew up, where women, lacking Talmudic knowledge or other sources of authority, are generally found only at the margins of the public sphere. Her multi-faceted activity was focused on offering blessings and advice. She also innovated a few segulot (magical techniques) and religious rituals. Her leadership is characterized, on the one hand, by the preservation and even strengthening of the existing Lithuanian Haredi ethos, particularly in the context of the wife’s complete self-abnegation for her husband’s Torah study. On the other hand, it fostered emotional and experiential elements that are closer to the ethos of the Hasidic and Sephardi communities and are associated with folk piety and a quasi-magical orientation. Rebbetzin Kanievsky thus created a type of female religious leadership that can be characterized as anti-leadership, in which she embodied the Haredi conception of ideal womanhood. Consequently, she was not perceived as a threat to Haredi values but rather as their promoter. However, this model of leadership enabled her to break, almost despite herself, the limitations of the gender hierarchy of the Haredi community and serve as an almost singular female role model in that community’s pantheon.

High-Dimensional Dynamic Factor Models: A Selective Survey and Lines of Future Research

High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and applications of High-Dimensional Dynamic Factor Models is discussed. The emphasis is on model classes and their structure theory, rather than on estimation in the narrow sense. The survey is not comprehensive. Its aim is to point out promising lines of research and applications that have not yet been sufficiently developed.

A new numerical strategy for solving nonlinear singular Emden-Fowler delay differential models with variable order

The present study is related to the numerical solutions of new mathematical models based on the variable order Emden-Fowler delay differential equations. The shifted fractional Gegenbauer, C_{S,j}^{(alpha ,mu )}(t), operational matrices (OMs) of VO differentiation, in conjunction with the spectral collocation method are used to solve aforementioned models numerically. The VO operator of differentiation will be used in the Caputo sense. The proposed technique simplifies these models by reducing them to systems of algebraic equations that are easy to solve. To determine the effectiveness and accuracy of the sugested technique, the absolute errors and maximum absolute errors for four realistic models are studied and illustrated by several tables and graphs at different values of the VO and the SFG parameters; alpha and mu. Also numerical comparisons between the suggested technique with other numerical methods in the existing literature are held. The numerical results confirm that the suggested technique is accurate, computationally efficient and easy to implement.

Four-dimensional steady gradient Ricci solitons with 3-cylindrical tangent flows at infinity

In this paper we consider 4-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed 4-manifold. In particular, we study the geometry at infinity of such Ricci solitons under the assumption that their tangent flow at infinity is the product of R with a 3-dimensional spherical space form. We also classify the tangent flows at infinity of 4-dimensional steady soliton singularity models in general.