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Solving the Inverse Magnetoencephalography Problem in the Multidipole Model
AbstractThe author considers ways of localizing the inverse problem of magnetoencephalography (MEG). Localization is important in real clinical...
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The Generalized Ellipsoid Method*
An algorithm with space dilation is presented, which is the circumscribed ellipsoid method under a certain choice of dilation coefficient. It is...
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Polynomial Optimization in Geometric Modeling
In this chapter, we review applications of Polynomial Optimization techniques to Geometric Modeling problems. We present examples of topical problems...
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Behavior of Trajectories in Localizing Sets
It is well known that simple and complex dynamics of a nonlinear system are separated by a localizing set that contains all compact invariant sets...
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Polynomial Optimization, Certificates of Positivity, and Christoffel Function
We briefly recall basics of the Moment-SOS hierarchy in polynomial optimization and the Christoffel-Darboux kernel (and the Christoffel function...
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Hausdorff distance between convex semialgebraic sets
In this paper, we proposed an approach for computing the Hausdorff distance between convex semialgebraic sets. We exploit the KKT conditions to...
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Connecting optimization with spectral analysis of tri-diagonal matrices
We show that the global minimum (resp. maximum) of a continuous function on a compact set can be approximated from above (resp. from below) by...
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Stokes, Gibbs, and Volume Computation of Semi-Algebraic Sets
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely...
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Localization of Invariant Compacts in Multidimensional Systems with Phase Control
We consider phase systems of order six, four, and three that admit chaotic attractors of various types. We apply a localization method that makes it...
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A utopia point method-based robust vector polynomial optimization scheme
In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By...
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Surface Applications
This chapter studies locally supported surface mollifier decorrelation of the Earth’s gravitational potential model (EGM), the gravity disturbances...
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Tensor Fields for Data Extraction from Chart Images: Bar Charts and Scatter Plots
Charts are an essential part of both graphicacy (graphical literacy), and statistical literacy. As chart understanding has become increasingly...
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Interior Transmission Resonance
In this chapter, we consider the interior transmission eigenvalue problem. Our focus is on justifying that the transmission eigenfunctions form a...
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Oscillatory integral operators with homogeneous phase functions
Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the L p – L p -estimat...
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Mixed Robustness: Analysis of Systems with Uncertain Deterministic and Random Parameters by the Example of Linear Systems
AbstractThe robustness of linear systems with constant coefficients is considered. There are methods and tools for analyzing the stability of...
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A Collection of Nonsmooth Riemannian Optimization Problems
Nonsmooth Riemannian optimization is still a scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or...
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Autonomous Vehicle Localization
For autonomous vehicles, one of the most critical tasks is localization, i.e., the accurate and real-time determination of the unit’s position. In...
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Some regularity results for Lorentz–Finsler spaces
We prove that for continuous Lorentz–Finsler spaces timelike completeness implies inextendibility. Furthermore, we prove that under suitable locally...
