Journal of Computational Mathematics and Data Science最新文献

The Singular Value Decomposition (SVD) is one of the most used factorizations when it comes to Data Science applications. In particular, given the big size of the processed matrices, in most of the cases, a truncated SVD algorithm is employed. In the following manuscript, we review some of the state-of-the-art approaches considered for the selection of the number of components (i.e., singular values) to retain to apply the truncated SVD. Moreover, three new approaches based on the Kullback–Leibler divergence and on unsupervised anomaly detection algorithms, are introduced. The revised methods are then compared on some standard benchmarks in the image processing context.

In view of the dominant properties of hybrid nanofluid such as high thermal and electrical conductivity in addition to enhanced heat transfer rate, efforts had been strengthened by many researchers to upgrade the thermal behavior of the base fluid through different approaches. In this study, viscous dissipation and thermal radiation effects on unsteady incompressible squeezing flow conveying $CuO-A{l}_2{O}_3/$water hybrid nanoparticles between two aligned surfaces with variable viscosity is examined. The fluid model is transformed to ordinary differential equations by incorporating appropriate similarity transformation. The numerical simulation is carried out in MATLAB software package via shooting procedure coupled with $4th$ order Runge–Kutta integration scheme. The limiting case is found to be in accord relative to the preceding reports. The outcomes of the scrutiny are unveiled in tables and graphs. It was revealed that the velocity and temperature augment with increasing viscosity variation and squeezing fluid parameters. Meanwhile, increasing viscous dissipation and thermal radiation parameters decrease the temperature distribution with no significant change in the fluid velocity.

In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating functions and data, and we interpret it in the framework of persistent homology. We call them Variably Scaled Persistence Kernels (VSPKs). These new kernels are then tested in different classification experiments. The obtained results show that they can improve the performance and the efficiency of existing standard kernels.

It is a common practice in multimodal medical imaging to undersample the anatomically-derived segmentation images to measure the mean activity of a co-acquired functional image. This practice avoids the resampling-related Gibbs effect that would occur in oversampling the functional image. As sides effect, waste of time and efforts are produced since the anatomical segmentation at full resolution is performed in many hours of computations or manual work. In this work we explain the commonly-used resampling methods and give errors bound in the cases of continuous and discontinuous signals. Then we propose a Fake Nodes scheme for image resampling designed to reduce the Gibbs effect when oversampling the functional image. This new approach is compared to the traditional counterpart in two significant experiments, both showing that Fake Nodes resampling gives smaller errors at the cost of an higher computational time.

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most eigenvalues of the Hessian of the loss functions on the loss landscape of over-parametrized deep neural networks are close to zero, while only a small number of eigenvalues are large. Zero eigenvalues indicate zero diffusion along the corresponding directions. This indicates that the process of minima selection mainly happens in the relatively low-dimensional subspace corresponding to the top eigenvalues of the Hessian. Although the parameter space is very high-dimensional, these findings seems to indicate that the SGD dynamics may mainly live on a low-dimensional manifold. In this paper, we pursue a truly data driven approach to the problem of getting a potentially deeper understanding of the high-dimensional parameter surface, and in particular, of the landscape traced out by SGD by analyzing the data generated through SGD, or any other optimizer for that matter, in order to possibly discover (local) low-dimensional representations of the optimization landscape. As our vehicle for the exploration, we use diffusion maps introduced by R. Coifman and coauthors.

The seminal work of Chow and Liu (1968) shows that approximation of a finite probabilistic system by Markov trees can achieve the minimum information loss with the topology of a maximum spanning tree. Our current paper generalizes the result to Markov networks of tree-width $\le k$, for every fixed $k\ge 2$. In particular, we prove that approximation of a finite probabilistic system with such Markov networks has the minimum information loss when the network topology is achieved with a maximum spanning $k$-tree. While constructing a maximum spanning $k$-tree is intractable for even $k=2$, we show that polynomial algorithms can be ensured by a sufficient condition accommodated by many meaningful applications. In particular, we show an efficient algorithm for learning the optimal topology of higher order correlations among random variables that belong to an underlying linear structure. As an application, we demonstrate effectiveness of this efficient algorithm applied to biomolecular 3D structure prediction.

Equation-based and agent-based models are popular methods in understanding disease dynamics. Although there are many types of equation-based models, the most common is the SIR compartmental model that assumes homogeneous mixing and populations. One way to understand the effects of these assumptions is by agentization. Equation-based models can be agentized by creating a simple agent-based model that replicates the results of the equation-based model, then by adding complexity to these agentized models it is possible to break the assumptions of homogeneous mixing and populations and test how breaking these assumptions results in different outputs. We report a set of experiments comparing the outputs of an SEIR model and a set of agent-based models of varying levels of complexity, using as a case study a measles outbreak in a town in Ireland. We define and use a six level complexity hierarchy for agent-based models to create a set of progressively more complex variants of an agentized SEIR model for the spread of infectious disease. We then compare the results of the agent-based model at each level of complexity with results of the SEIR model to determine when the agentization breaks. Our analysis shows this occurs on the fourth step of complexity, when scheduled movements are added into the model. When agents networks and behaviours are complex the peak of the outbreak is shifted to the right and is lower than in the SEIR model suggesting that heterogeneous populations and mixing patterns lead to slower outbreaks compared homogeneous populations and mixing patterns.

The present analysis reports a computational study of Magnetohydrodynamic (MHD) flow behaviour of 2D Maxwell nanofluid across a stretched sheet in appearance of Brownian motion. The substantial term thermal radiation and chemical reactions have been employed extensively in the current research. Nanofluids are usually chosen by researchers because of their rheological properties, which are important in determining their appropriateness for convective heat transfer. The present research reveals that the fluid velocity augments for the enhanced values of all the parameters. Heat source, as well as the radiation parameters, ensure that there is enough heat in the fluid, which implies escalation of the thermal boundary layer thickness by accruing radiation parameter. Moreover, streamlines and isotherms have been investigated for the different parametric values. The suggested model is valuable because it has a wide range of applications in domains including medical sciences (treatment of cancer therapeutics), microelectronics, biomedicine, biology, and industrial production processes.

The current investigation is to examine the compound impact of electromagnetic induced force and internal heat source on a tangent hyperbolic fluid in quadratic Boussinesq approximation. The current hyperbolic tangent liquid flow and heat transport formulation model adequately predicts and characterizes the shear-stricken event. The nonlinear dimensionless heat transfer flow equations are solved completely using weighted residual solution procedures coupled with Galerkin approximation integration approach. The results in the table and graphs revealed that the magnetic field strength has a substantial impact on the fluid flow and heat propagation, as well as the internal heat source. Therefore, the entropy generation is optimized through an enhanced thermodynamic equilibrium and adequate control of heat generating terms and energy loss.

A point cloud describing a railway environment is considered in a case study aimed at presenting a workflow for the automatic detection of external objects that, coming too close to the railway infrastructure, may cause potential risks for its correct functioning. The approach combines classical semantic segmentation methodologies with a novel geometric and numerical procedure to define a region of interest, consisting of a lower tube enveloping the 3D space occupied by the train during its transit and an upper tube enclosing the overhead contact lines. One useful application could be automatic vegetation monitoring in the proximity of the railway structure, which would help with planning maintenance pruning activities.