High dimensionality and h-principle in PDEIn this note we would like to present "an analysts' point of view" on the\nNash-Kuiper theorem and in particular highlight the very close connection to\nsome aspects of turbulence -- a paradigm example of a high-dimensional\nphenomenon....
A key difficulty is that, without appropriate constraints, the high dimensionality of the data makes the model search space far too large for any purely data-driven approach to be tractable. In principle, machine learning can be used to construct suitable models (e.g., nonlinear partial ...
How could we have achieved a better fit in our synthetic data generation? Should we have balanced both classes equally or perhaps increase the representation of the minority class even higher? Could some feature transformation or dimensionality reduction helped the classification result? Should ...
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Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are, respectively, used to compute the value function and the optimal control fo...
transverse thermoelectric devices have several advantages, such as being able to modulate the dimensionality of the material independently to meet practical needs, having a wide spectral response range (from far infrared to ultraviolet), a large heat flux measurement range (10~108 W/m2), and fast...
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Introduction Emerging implantable biomedical systems need to transmit large amounts of data through skin/tissue to achieve high accuracy measurements, high dimensionality and real-time control of complex prosthetic devices like brain machine interfaces [1–3]. These systems require wireless biotelemetry ...
Among non-parametric methods, random forest (RF) is one of the most used classification methods in the field of image classification, as it is simple and does not require sophisticated parameter tuning [58,59]. RF can handle high data dimensionality (i.e., a small number of observations ...
After LDA, a canonical discriminant analysis was conducted to reduce the dimensionality of the variables included in the model to two canonical variates. The first canonical variate allowed the discrimination between the asymptomatic and the moderate and severe levels of disease, while the second variat...