This paper addresses the task of anomaly diagnosis when underlying data generation process has a complex spatio-temporal (ST) dependency. The key technical challenge is to extract actionable insights from dependency tensor characterizing high-order interactions among temporal and spatial indices. We formalize problem as supervised discovery, where ST learned side product multivariate time-serie...

We introduce a notion of highly Kummer-faithful fields and study its relationship with the fields. also give some examples For example, if $k$ is number field finite degree over \mathbb{Q}, $g$ an integer $> 0$ $\mathbf{m}=(m_p)_p$ family non-negative integers, where $p$ ranges all prime numbers, then extension $k_{g,\mathbf{m}}$ obtained by adjoining to coordinates elements $p^{m_p}$-torsion s...

We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced in [KLS08]. We generalize the central extension theorem of Buhler and Reichstein, [BR97, Theorem 5.3] and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev [KM08] about the essential dimen...