Numerical Experiments Research Articles

The Shrinking Great Salt Lake May Exacerbate Droughts by Reducing Local Precipitation: A Case Study

Abstract The Great Salt Lake (GSL) is a shallow terminal lake located in Northern Utah, the United States. Over the years the water extent of the GSL has undergone substantial reduction due to water diversions and a changing climate – in particular rising temperatures. However, the potential impacts of the shrinking GSL water body on the local hydroclimate system is poorly understood. In this study, we utilized the Weather Research and Forecasting model version 4.2 coupled with a lake model to simulate a series of high-resolution numerical experiments; these experiments aimed to assess the effect of varying lake areal extents on a storm event that occurred on June 6, 2007. The results revealed a systematic decline in the quantity of precipitation over the GSL and downwind regions with declining areal coverage. In the event of complete disappearance, the regional average precipitation would experience an approximate 50% reduction relative to its 2004 base lake extent; this decrease is principally attributed to a diminished water vapor flux and moist static energy (MSE) above the lake. The research underscores the consequences of a shrinking GSL, not just for precipitation delivery downstream but that of a negative feedback loop within the hydroclimatic system of the GSL basin, i.e., water flow reductions into the basin.

Arctic summer precipitation variability and its association with Indian summer monsoon anomalies

In recent years, there has been an increased focus on changes in Arctic precipitation，however, dominant characteristics of Arctic summer precipitation variability and their relationship to atmospheric circulation anomalies in the mid-low latitudes remain debatable. Spatially, the leading mode of Arctic summer precipitation variability is positive in most regions of the Arctic, corresponding to a cold anomaly in the middle and lower troposphere of the Arctic. As the temperature gradient between the Arctic and high latitudes increases, the zonal westerlies over the Arctic enhanced and lead to increased local baroclinicity and moisture convergence over the Arctic. This creats favorable conditions for increased summer precipitation. Additionally, it is found that there is a robust correlation between the first mode of Arctic summer precipitation and the Indian summer monsoon. Specifically, the positive Arctic summer precipitation anomaly is accompanied by a systematic northward shift of the zonal westerlies in the mid-latitude. The northward shift of the Asian westerly jet stream is associated with the intensified tropical easterly jet in the upper-troposphere and low-stratosphere, resulting in the strengthening of the monsoon circulation over the Indian Peninsula and then facilitating the precipitation anomaly over India. Numerical experiments reproduce the major features of the observed Arctic-Indian summer monsoon association, implying that Arctic summer precipitation variability is dynamically linked to tropical atmospheric circulation anomalies.

Hybrid Machine Learning Algorithms to Evaluate Prostate Cancer

The adequacy and efficacy of simple and hybrid machine learning and Computational Intelligence algorithms were evaluated for the classification of potential prostate cancer patients in two distinct categories, the high- and the low-risk group for PCa. The evaluation is based on randomly generated surrogate data for the biomarker PSA, considering that reported epidemiological data indicated that PSA values follow a lognormal distribution. In addition, four more biomarkers were considered, namely, PSAD (PSA density), PSAV (PSA velocity), PSA ratio, and Digital Rectal Exam evaluation (DRE), as well as patient age. Seven simple classification algorithms, namely, Decision Trees, Random Forests, Support Vector Machines, K-Nearest Neighbors, Logistic Regression, Naïve Bayes, and Artificial Neural Networks, were evaluated in terms of classification accuracy. In addition, three hybrid algorithms were developed and introduced in the present work, where Genetic Algorithms were utilized as a metaheuristic searching technique in order to optimize the training set, in terms of minimizing its size, to give optimal classification accuracy for the simple algorithms including K-Nearest Neighbors, a K-means clustering algorithm, and a genetic clustering algorithm. Results indicated that prostate cancer cases can be classified with high accuracy, even by the use of small training sets, with sizes that could be even smaller than 30% of the dataset. Numerous computer experiments indicated that the proposed training set minimization does not cause overfitting of the hybrid algorithms. Finally, an easy-to-use Graphical User Interface (GUI) was implemented, incorporating all the evaluated algorithms and the decision-making procedure.

An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion

The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, real-world disturbances pose a significant challenge to a ZNN’s convergence. We design an accelerated dual-integral structure zeroing neural network (ADISZNN), which can enhance convergence and restrict linear noise, particularly in complex domains. Based on the Lyapunov principle, theoretical analysis proves the convergence and robustness of ADISZNN. We have selectively integrated the SBPAF activation function, and through theoretical dissection and comparative experimental validation we have affirmed the efficacy and accuracy of our activation function selection strategy. After conducting numerous experiments, we discovered oscillations and improved the model accordingly, resulting in the ADISZNN-Stable model. This advanced model surpasses current models in both linear noisy and noise-free environments, delivering a more rapid and stable convergence, marking a significant leap forward in the field.

Badania wielofunkcyjnych właściwości nowej kompozycji o nazwie AZ-1

This article presents the results of the study of multifunctional properties of a new composition, with the conventional name AZ-1, which was prepared from various reagents under laboratory conditions. For this purpose, the results of its effect on a number of rheological parameters of commodity oil and the corrosion rate in hydrogen sulphide formation water have been interpreted. Laboratory experiments were conducted using concentrations of 100, 300, 500, 700 and 900 g/t of the composition, all following established standard methods. For the research purposes, the oil sample was taken from Narimanov field of SOCAR, and the aggressive medium was hydrogen sulphide formation water taken from well No. 1082 of “Bibiheybatneft” OGPD. Numerous experiments have shown that the optimum consumption rate of AZ-1 composition is 700 g/t. AZ-1 composition reduces the freezing temperature from +14°C to –8°C by improving the fluidity of the studied oil sample at optimal viscosity. The value of the shear stress limit of the anomalous oil sample is also drastically reduced. During the experiments carried out using the “cold finger test” method, it was found that AZ-1 composition has a high effect on oil deposits. At the temperature of +5°C of the “cold finger test”, its efficiency was 90% at the optimal consumption rate. During the effect of AZ-1 composition on the corrosion rate in hydrogen sulphide formation water, the protection effect increases at the concentration of 100–700 g/t and varies between 85–98%. At 900 g/t, the value of the protective effect is relatively reduced to 82%, and this is an indicator that the optimum consumption rate of AZ-1 composition is 700 g/t.

Perturbation bounds for stable gyroscopic systems in motion about an unstable equilibrium position

Relative perturbation bounds for stable linear gyroscopic systems Mẍ(t)+Gẋ(t)+Kx(t)=0 are considered, where M,K∈Rn×n are symmetric, M is positive definite, K negative definite and G∈Rn×n is skew-symmetric such that |G|>kM−k−1K for some k>0. This means that all of the eigenvalues of the system are purely imaginary and semi-simple. For this kind of systems, we present an upper bound for the relative change in eigenvalues as well as the sinΘ type bound for the corresponding eigenvectors under the perturbation of the system matrices. The performance of obtained bounds is illustrated in numerical experiments.

Price and product innovation competition with network effects and consumers’ adaptive learning: A differential game approach

For many high-tech and Internet related products, the utility of consumers depends partly on the scale of user groups, which is called network effects. In this paper, we formulate a differential game model to investigate the joint price and product innovation competition in a market exhibiting network effects. In the spirit of behavior economics, the consumers’ adaptive learning about network size is considered. The unique steady-state equilibrium is analytically characterized under both committed and feedback information structures. Our analysis mainly shows that (i) the network effects have negative influence on the result of price competition but have nothing to do with the result of product innovation competition under the premise of low market density; (ii) the marginal impact of network effects on the steady-state price is decreasing with the consumers’ learning speed; (iii) in the long-run, the product price converges to the level either higher or lower than the stationary price, depending on the strength of network effects; (iv) in a market where the consumers are extremely sensitive to the product price, the quality provision is insufficient compared with the first-best optimal level regardless of the choice of solution concept. The dynamic evolution patterns of the price and product innovation competition are illustrated by numerical experiments.

A discontinuous Galerkin method for a coupled Stokes–Biot problem

The interaction between fluid and poroelastic structure is a complex problem that couples the Stokes equations with the Biot system. In this work, we rewrite the poroelastic equations using three fields (displacement, fluid pressure, and total pressure) to account for locking phenomenon in fluid–structure interaction and the oscillation of numerical solutions. Then, in order to solve the coupled system, we use the weighted discontinuous Galerkin finite element method for spatial discretisation and propose a semi-discrete scheme. In addition, we propose a fully discrete scheme using the backward Euler’s method for temporal discretisation. In the framework of the Galerkin approximation, the stability and errors of semi- and fully discrete schemes are analysed using the theory of differential algebraic equations and weak compactness arguments. Through numerical experiments, we validate the theoretical rate of convergence, explain the behaviour of the method in modeling the interaction between surface and groundwater hydrological systems, investigate the robustness of the method with respect to physical parameters, and simulate channel filtering. In particular, the numerical results are free of locking features, reducing non-physical numerical oscillations.

The twin peaks of learning neural networks

Recent works demonstrated the existence of a double-descent phenomenon for the generalization error of neural networks, where highly overparameterized models escape overfitting and achieve good test performance, at odds with the standard bias-variance trade-off described by statistical learning theory. In the present work, we explore a link between this phenomenon and the increase of complexity and sensitivity of the function represented by neural networks. In particular, we study the Boolean mean dimension (BMD), a metric developed in the context of Boolean function analysis. Focusing on a simple teacher-student setting for the random feature model, we derive a theoretical analysis based on the replica method that yields an interpretable expression for the BMD, in the high dimensional regime where the number of data points, the number of features, and the input size grow to infinity. We find that, as the degree of overparameterization of the network is increased, the BMD reaches an evident peak at the interpolation threshold, in correspondence with the generalization error peak, and then slowly approaches a low asymptotic value. The same phenomenology is then traced in numerical experiments with different model classes and training setups. Moreover, we find empirically that adversarially initialized models tend to show higher BMD values, and that models that are more robust to adversarial attacks exhibit a lower BMD.

Sensitivity to intensity and distribution of the temperature field in the nonlinear thermo-mechanical analysis of laminated glass plates

Glass laminates consist of stiff glass plies permanently shear-coupled by polymeric interposed layers. When an external temperature rise occurs, the interlayers undergo a dramatic stiffness decay. As a consequence, not only the sectional warping typical of alternating stiff/soft composites is intensified, but also the overall behavior may evolve counter-intuitively. When slender elements prone to geometric nonlinearities are involved, even small thermal variations in intensity or distribution may act as uncertainty factors, strongly affecting the outcome. This paper proposes an efficient, robust, and accurate numerical framework to perform the sensitivity analysis to thermo-mechanical actions in glass plates. A large deformation isogeometric Kirchhoff-Love shell model enriched with through-the-thickness warping is employed, together with a generalized arc-length method involving a suitable temperature parameter as an additional unknown, namely the thermal amplifier or a spatial distribution coefficient. Numerical experiments are presented to highlight the effects that even small temperature variations produce on the equilibrium paths and the influence of the stiffness loss in the interlayer on the structural behavior and the accuracy of the models.

Stationary Landweber method with momentum acceleration for solving least squares problems

In this article, we proposed an enhancement to the convergence rate of Landweber’s method by incorporating the concept of momentum acceleration. Landweber’s method is commonly used to solve least squares problems of the form minx‖Ax−b‖. Our approach is based on Landweber’s method, which is acknowledged as a particular case of the methodologies outlined in Ding and Chen (2006). Through optimizing the momentum parameter, we were able to demonstrate the superior performance of the momentum-accelerated Landweber method. Specifically, we established that when A is a nonsquare m×n matrix with Rank(A)=n and σmin(A)≠σmax(A), the momentum-accelerated Landweber method with the optimal parameter consistently outperforms the standard Landweber method. Our numerical experiments have confirmed the theoretical findings, demonstrating a notable improvement in the convergence rate of the Landweber method.

Pinpointing the microbiota of tardigrades: What is really there?

Microbiota are considered significant in the biology of tardigrades, yet their diversity and distribution remain largely unexplored. This is partly due to the methodological challenges associated with studying the microbiota of small organisms that inhabit microbe-rich environments. In our study, we characterized the microbiota of 31 species of cultured tardigrades using 16S rRNA amplicon sequencing. We employed various sample preparation strategies and multiple types of controls and estimated the number of microbes in samples using synthetic DNA spike-ins. We also reanalysed data from previous tardigrade microbiome studies. Our findings suggest that the microbial communities of cultured tardigrades are predominantly composed of bacterial genotypes originating from food, medium, or reagents. Despite numerous experiments, we found it challenging to identify strains that were enriched in certain tardigrades, which would have indicated likely symbiotic associations. Putative tardigrade-associated microbes rarely constituted more than 20% of the datasets, although some matched symbionts identified in other studies. We also uncovered serious contamination issues in previous tardigrade microbiome studies, casting doubt on some of their conclusions. We concluded that tardigrades are not universally dependent on specialized microbes. Our work underscores the need for rigorous safeguards in studies of the microbiota of microscopic organisms and serves as a cautionary tale for studies involving samples with low microbiome abundance.

Asymptotic preserving semi-Lagrangian discontinuous Galerkin methods for multiscale kinetic transport equations

We propose a new family of asymptotic preserving (AP) discontinuous Galerkin (DG) schemes for kinetic transport equations under a diffusive scaling. They are built upon a characteristics-based model reformulation proposed in Zhang et al. (2023) [27]. The reformulated model comprises a convection-diffusion-like equation for the macroscopic density and another evolution equation for the distribution function. We employ the equations in a weak form to enjoy the advantages of a DG method. We also leverage a semi-Lagrangian (SL) approach to achieve higher efficiency than a fully implicit scheme without loss of unconditional stability. A damping technique is introduced to control spurious numerical oscillations for high-order DG methods. We establish formal AP and Fourier stability analyses for fully discrete schemes in a linear scenario. Numerical experiments, covering one-dimensional to three-dimensional in space problems, confirm the accuracy, AP property, uniformly unconditional stability, and high parallel efficiency of the proposed methods.

Nonlinear Response of Summertime Synoptic-Scale Disturbance Intensity over the Tropical Western North Pacific to ENSO Amplitude

Abstract El Niño–Southern Oscillation (ENSO) exhibits nonlinearity in its amplitude and impacts. This study investigates the dependence of summertime synoptic-scale disturbance (SSD) intensity over the tropical western North Pacific (TWNP) on the ENSO amplitude. A tendency of nonlinearity exists in the observed response of the TWNP SSD intensity to the amplitude of tropical central-eastern Pacific (CEP) sea surface temperature (SST) anomalies in boreal summer. Numerical experiments are conducted with an atmospheric general circulation model with linearly varying tropical CEP SST anomalies imposed to illustrate the nonlinearity exclusively induced by changes in the ENSO amplitude. A linear increase in the amplitude of El Niño–like SST anomalies results in a nonlinear enhancement of SSD intensity over the TWNP, manifested as the increase in SSD intensity at a rate larger than expected by linear response with an eastward shift. This is attributed to the nonlinear intensification of anomalous ascent over the TWNP induced by tropical convection response to positive tropical CEP SST anomalies and the nonlinear effect of anomalous convection on the synoptic-scale activity. In contrast, as La Niña–like SST anomalies increase linearly, the SSD intensity over the TWNP decreases at a rate slower than expected from a linear response and even reaches saturation with little longitudinal shift. Due to the thermodynamic control on the occurrence of deep convection in the tropics, enhanced negative SST anomalies do not induce additional changes in anomalous descent over the tropical CEP. Thus, the TWNP SSD intensity no longer decreases with further increase in tropical CEP cold SST anomalies. Significance Statement Synoptic-scale disturbances (SSDs) over the tropical western North Pacific (TWNP) play an important role in weather and climate over East and Southeast Asia. Impacts of those SSDs are contingent on their intensity. El Niño–Southern Oscillation (ENSO) has substantial impacts on weather and climate worldwide, including the SSDs over the TWNP. ENSO displays a diversity in amplitude, spatial pattern, and temporal evolution. The present study investigates the response of the TWNP SSD intensity to varying ENSO amplitude during boreal summer and reveals a distinctive nonlinear response of the TWNP SSD intensity to the amplitude of El Niño and La Niña, which has important implication for understanding the impacts of ENSO on climate over the TWNP and Asia.

Non-Blind Image Deblurring via Shear Total Variation Norm

In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation (TV) norm to the shear total variation (STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks (BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers (ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.

Modeling an on-demand meal delivery system with human couriers and autonomous vehicles in a spatial market

This paper investigates the impacts of introducing autonomous vehicles (AVs) into an on-demand meal delivery system at a strategic level. The proposed model consists of (i) a microscopic physical model describing the delivery process for bundled orders and (ii) a macroscopic network equilibrium model characterizing the interactions among customers, human couriers (HCs), and AVs, as well as couriers’ repositioning behaviors in the market. A tailored algorithm based on the Alternating Direction Method of Multiplier (ADMM) is developed to solve the platform’s optimal pricing and maximize its profit. To investigate the impact of AV operations, we test three AV distribution rules, i.e., distributing AVs evenly in the space (Rule 0), proportional to demand (Rule 1), and inversely proportional to demand (Rule 2). The numerical experiments show that Rule 2 archives the maximum platform profit, along with the highest service throughput and the hourly earning rate of HCs. Nevertheless, the numerical experiments adopting the parameters calibrated by current market conditions show that the employment of AVs does not show significant benefits to the platform or other stakeholders. It can only generate a higher platform profit when the AV operation cost is lower than HCs’ hourly earnings in a purely labor-based MDS system. As the AV fleet size expands, the improvement of service quality is rather minor meanwhile the hourly earning of HCs drops substantially.

Emotions recognition in audio signals using an extension of the latent block model

Emotion detection in human speech is a significant area of research, crucial for various applications such as affective computing and human–computer interaction. Despite advancements, accurately categorizing emotional states in speech remains challenging due to its subjective nature and the complexity of human emotions. To address this, we propose leveraging Mel frequency cepstral coefficients (MFCCS) and extend the latent block model (LBM) probabilistic clustering technique with a Gaussian multi-way latent block model (GMWLBM). Our objective is to categorize speech emotions into coherent groups based on the emotional states conveyed by speakers. We employ MFCCS from time-series audio data and utilize a variational Expectation Maximization method to estimate GMWLBM parameters. Additionally, we introduce an integrated Classification Likelihood (ICL) model selection criterion to determine the optimal number of clusters, enhancing robustness. Numerical experiments on real data from the Berlin Database of Emotional Speech (EMO-DB) demonstrate our method’s efficacy in accurately detecting and classifying emotional states in human speech, even in challenging real-world scenarios, thereby contributing significantly to affective computing and human–computer interaction applications.

Numerical energy dissipation for time fractional volume-conserved Allen–Cahn model based on the ESAV and R-ESAV approaches

In this study, we consider volume-conserved numerical schemes for the volume-conserved time fractional Allen–Cahn equation. We start with the L1 scheme based on a modified exponential scalar auxiliary variable (ESAV) approach for handling the nonlinear potential term. Then we introduce the fast L1 scheme to significantly reduce the CPU time and to make the long-term computation possible. Further to reduce the error between the discrete energy and the original energy of the ESAV approach, we introduce the fast L1 scheme based on a relaxed modified ESAV (R-ESAV) idea. We rigorously show the discrete energy dissipation properties for the above three schemes, including the discrete energy boundedness law, the discrete fractional energy dissipation law, and the discrete weighted energy dissipation law. Theoretical findings are validated by a few numerical experiments.

Quantum hitting time according to a given distribution

In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of classical hitting time: this quadratic speedup is a remarkable example of the computational advantages associated with quantum approaches. Our purpose here is twofold. On one hand, we provide a detailed proof of quadratic speedup for time-reversible walks within the Szegedy framework, in a language that should be familiar to the linear algebra community. Moreover, we explore the use of a general distribution in place of the stationary distribution in the definition of quantum hitting time, through theoretical considerations and numerical experiments.

Centrifugal pump performance improvement using back cavity filling

Centrifugal pumps consume majority of energy used by the electric motor driven systems among all end users of the industrial sector. Only in European region, a 1% improvement in efficiency (η) of the centrifugal pump is capable enough to reduce CO2 emissions by at least 572 tons per day. The prime motive of this research is to assess the applicability of the novel back cavity filling (BCF) in reducing the disk friction losses of centrifugal pumps without changing the pump's original design. By adding a solid ring to the bearing housing's back-cover plate, the BCF was applied to a medium specific speed pump (Ns = 54 rpm), resulting in a 1 mm back axial clearance from 13 mm. Numerical simulations and experiments were carried out to investigate the effect of BCF on pump performance under two conditions: with and without BCF at best efficient point (BEP) and various partload conditions for 1450 rpm (rated) as well as 1000 rpm. Pump performance characteristics were enhanced by BCF at both rpms for the whole flow rate range. At 1450 rpm, BCF resulted in an average 0.74% increment in total head, 2.08% reduction in input torque, and 2.70% increment in overall efficiency over the flow rate range. While an average 2.04% improvement in total head, 1.33% reduction in input torque, a 3.30% enhancement in overall efficiency were obtained at 1000 rpm. Performance parameter enhancement was higher at lowest part load compared to the BEP on rated rpm.