Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining state a particular hyperplane in space. Contrary this, discrete-time sliding (DSMC) only drive representative point certain vicinity that hyperplane. In established literature on DSMC, width ...

Understanding the structure of indecomposable $n$-dimensional persistence modules is a difficult problem, yet foundational for studying multipersistence. To this end, Buchet and Escolar showed that any finitely presented rectangular $(n-1)$-dimensional module with finite support hyperplane restriction an module. We extend result to following: If $M$ support, then there exists $M'$ such hyperpla...

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric st...

We attempt to understand visual classification in humans using both psychophysical and machine learning techniques. Frontal views of human faces were used for a gender classification task. Human subjects classified the faces and their gender judgment, reaction time and confidence rating were recorded. Several hyperplane learning algorithms were used on the same classification task using the Pri...