Langtons type Theorem on Algebraic Orbifolds

In this paper, we show Langtons type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k

Malware Evasion Attack and Defense

Machine learning (ML) classifiers are vulnerable to adversarial examples. An adversarial example is an input sample which is slightly modified to induce misclassification in an ML classifier. In this work, we investigate white-box and grey-box evasion attacks to an ML-based malware detector and conduct performance evaluations in a real-world setting. We compare the defense approaches in mitigating the attacks. We propose a framework for deploying grey-box and black-box attacks to malware detection systems.

Non-Embedding Theorems of Nilpotent Lie groups and Sub-Riemannian Manifolds

We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the RCD(0,N), with N > 1. In fact, we can prove that a subRiemannian manifold whose generic degree of nonholonomy is not smaller than 2 can not be biLipschitzly embedded in any Banach space with the Radon-Nikodym property. We also get that every regular sub-Riemannian manifold do not satisfy the CD(K,N) with N > 1. We also prove that the subRiemannian manifold is infinitesimally Hilbert space.