8 papers
A curvature-based criterion for harmonic circadian waveforms
Yusuke Yamada, Yutaro Kabata, Ryoya Fukasaku +1
Experimental and theoretical studies of circadian rhythms have focused largely on the period, on mutants that alter it and on phase shifts, and this focus has driven the identifica…
At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture
Yutaro Kabata, Hirotaka Matsumoto, Akifumi Okuno
A Gaussian mixture density can have more modes than components. It has been conjectured that the maximum number of modes of a -variate -component Gaussian mixture density is…
On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes
Akifumi Okuno, Yutaro Kabata
It is known that a mixture of three homoscedastic multivariate Gaussian densities whose centers form an equilateral triangle can have four modes, owing to the emergence of a ``ghos…
Shapes of light: singularities of slant functions and the Gauss map of a surface
Shuhei Honda, Yutaro Kabata
The slant function on a regular surface in three-space, introduced by Koenderink, is the inner product of a fixed light direction with the unit normal; under the standard Lambertia…
Algebraic Approach to Ridge-Regularized Mean Squared Error Minimization in Minimal ReLU Neural Network
Ryoya Fukasaku, Yutaro Kabata, Akifumi Okuno
This paper investigates a perceptron, a simple neural network model, with ReLU activation and a ridge-regularized mean squared error (RR-MSE). Our approach leverages the fact that…
Visualization of curvature on curve and surface by tangential angle parametrization
Yutaro Kabata, Shigeki Matsutani, Yuta Ogata
We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal incr…