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3D Normal Mode Functions (NMFs) of a Global Baroclinic Atmospheric Model
Characteristics of the atmospheric motions can be learned from the 3D normal modes of adiabatic, inviscid and linearized equations with respect to...
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Experimental Evaluation of Four Intermediate Filters to Improve the Motion Field Estimation
For the last 40 years, optical flow (OF) estimation has been challenging the computer vision community. OF is the apparent motion of the pixels in...
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Statistical Approaches for Forecasting Air pollution: A Review
With the rapid growth of energy consumption, acceleration of industrialization and urbanization, and the emission of automobile and industrial...
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Positive-instantaneous frequency and approximation
Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical...
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Multi-scaled Non-local Means Parallel Filters for Medical Image Denoising
In recent years, there has been an increased interest in denoising techniques that are applicable in various medical imaging fields. The...
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Approximation in the extended functional tensor train format
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product...
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A Short Introduction to Reduced Basis Method
In this chapter, we introduce the readers to the main notions regarding the Reduced Basis approximation based on Finite Element method for...
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Balanced Truncation Model Reduction for Lifted Nonlinear Systems
We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our...
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On Approximation Algorithm for Orthogonal Low-Rank Tensor Approximation
This work studies solution methods for approximating a given tensor by a sum of R rank-1 tensors with one or more of the latent factors being...
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Algebraic Structures and Social Processes
There has long been an interest among social scientists in the use of algebraic structures to analyze social data. Many popular approaches are...
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Global-local multiscale model reduction using GMsFEM
Our previous studies focused on local model reduction techniques. In these approaches, we develop local (space and time) reduced-order models to...
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Generalization error of GAN from the discriminator’s perspective
The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization...
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Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation
An energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The...
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Numerical Study of the Process of Gas Extraction from a Gas Hydrate Reservoir with Inhomogeneous Permeability
AbstractMathematical modeling of the process of gas extraction from a hydrate-containing reservoir, which is a cylindrical region of a porous medium,...
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Data-Driven Reduced Order Modelling for Patient-Specific Hemodynamics of Coronary Artery Bypass Grafts with Physical and Geometrical Parameters
In this work the development of a machine learning-based Reduced Order Model (ROM) for the investigation of hemodynamics in a patient-specific...
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3D Modal Variability and Energy Transformations on the Sphere
The three-dimensional (3D) normal-mode function (NMF) decomposition is derived in the system with pressure as the vertical coordinate followed by the...
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Post-Fourier Frequencies: Variations and Paradoxes
We address two questions related to the notion of frequency and its possible extensions in the case of evolutive situations, some of them leading to...
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Pipeline network design for gathering unconventional oil and gas production using mathematical optimization
The optimal design of gathering networks for the unconventional oil and gas production is a relevant problem, particularly with the shale boom. In...
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New Approaches and Methods of Adaptive Image Encoding
The author analyses new methods, approaches, and ideas for further development of image encoding to increase informativeness and reduce computational...
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Bayesian Estimation of Large Precision Matrix Based on Cholesky Decomposition
In this paper, we consider the estimation of a high dimensional precision matrix of Gaussian graphical model. Based on the re-parameterized...