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Traditional Statistical Process Control methodologies face several challenges when monitoring defects in complex geometries, such as those of products obtained via Additive Manufacturing techniques. Many approaches cannot be applied in…
Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space are usually used to study the solution structure such as…
Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…
We focus on the extension of bivariate causal learning methods into multivariate problem settings in a systematic manner via a novel framework. It is purposive to augment the scale to which bivariate causal discovery approaches can be…
Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
The curve-based lane representation is a popular approach in many lane detection methods, as it allows for the representation of lanes as a whole object and maximizes the use of holistic information about the lanes. However, the curves…
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…
Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then be used to "resum" series to obtain more efficient…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time…
We present a method to detect discontinuity curves, usually called faults, from a set of scattered data. The scheme first extracts from the data set a subset of points close to the faults. This selection is based on an indicator obtained by…
In this paper, a feature extraction approach for the deformable linear object is presented, which uses a Bezier curve to represent the original geometric shape. The proposed extraction strategy is combined with a parameterization technique,…
We use a continued fraction approach to compare two statistical ensembles of quadrangulations with a boundary, both controlled by two parameters. In the first ensemble, the quadrangulations are bicolored and the parameters control their…
Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally. Moreover, selecting a suitable model complexity requires a…
This work focuses on the detection of the buckling phenomena and bifurcation analysis of the parametric Von K\'arm\'an plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth…
We consider a two-dimensional sharp-interface model for solid-state dewetting of thin films with anisotropic surface energies on curved substrates, where the film/vapor interface and substrate surface are represented by an evolving and a…