Unsupervised open-set domain adaptation (UODA) is a realistic problem where unlabeled target data contain unknown classes. Prior methods rely on the coexistence of both source and to perform alignment, which greatly limits their applications when are restricted due privacy concerns. In this paper we address challenging hypothesis transfer setting for UODA, from no longer available during domain...

We present a 2-step optimal transport approach that performs mapping from source distribution to target distribution. Here, the has particularity new classes not in domain. The first step of aims at rejecting samples issued these using an plan. second solves (class ratio) shift still as problem. develop dual solve optimization problem involved each and we prove our results outperform recent sta...

Given a nondecreasing sequence $$\Lambda =\{\lambda _n>0\}$$ such that $$\displaystyle \lim _{n\rightarrow \infty } \lambda _n=\infty ,$$ we consider the $$\mathcal {N}_\Lambda :=\left\{ _ne^{i\theta _n},n\in \,\mathbb {N}\right\} $$ , where $$\theta _n$$ are independent random variables uniformly distributed on $$[0,2\pi ].$$ We discuss conditions under which N_\Lambda is zero set (a uniqness ...

For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

We introduce theta divisors for vector bundles and relate them to the ordinariness of curves in characteristic p > 0. We prove, following M. Raynaud, that the sheaf of locally exact differentials in characteristic p > 0 has a theta divisor, and that the generic curve in (any) genus g ≥ 2 and (any) characteristic p > 0 has a cover that is not ordinary (and which we explicitely construct). 1 Thet...