Tag

Dimensionality Reduction

All articles tagged with #dimensionality reduction

physics1 year ago•7 min saved

"Expanding the Family of Quasi-Integrable Arrays in Physics"

Researchers have developed a new approach to solving arrays of two-dimensional differential equations, allowing for a drastic reduction in dimensionality and potentially enabling the investigation of complex systems such as arrays of spiking neurons. This quasi-integrable system could provide a promising strategy for tackling high-dimensional nonlinear systems, with implications for fields ranging from mathematical neuroscience to technology.

via Physics|

#arrays-of-oscillators #dimensionality-reduction #mathematical-neuroscience

science2 years ago•2 min saved

"Confirming the Low-Rank Hypothesis in Complex Systems"

Scientists have investigated the low-rank hypothesis in complex systems, finding that despite high-dimensional nonlinear dynamics, many real networks exhibit rapidly decreasing singular values, supporting the feasibility of effective dimension reduction for understanding and modeling complex system behaviors. The study, published in Nature Physics, aims to address the challenge of understanding large-scale behavior in complex systems by exploring the intrinsic simplicity of these systems and finding an optimal dimension for simplifying models. The researchers sought to validate the low-rank hypothesis using singular value decomposition, a powerful mathematical tool from linear algebra.

via Phys.org|

#complex-systems #dimensionality-reduction #emergent-phenomena