Semi-supervised learning (SSL) has been a powerful strategy to incorporate few labels in better representations. In this paper, we focus on practical scenario that one aims apply SSL when unlabeled data may contain out-of-class samples - those cannot have one-hot encoded from closed-set of classes label data, i.e., the is an open-set. Specifically, introduce OpenCoS, simple framework for handli...

We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps. Introduction. In this paper we generalize the coincidence semi-index theory, introduced in [D-J] in the smooth case, to pairs of maps between topological manifolds. It will be based on the topological transversality lemma (...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f i...

This paper considers a machine as a pair (G5M) where G is a group or a semi group and where M is a state space. The first part of the paper called reversible-state machines considers the case where G is a locally compact group and M is any locally compact group and M is any locally compact space. The essential requirement is that (x,p)~>x(p) be continuous where XGG, peM and x(p)eM; i.e., we req...

By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point.

Let A be a bounded operator on a separable, infinite dimensional Hilbert space H. Moreover, assume that A is not in the set C + K(H) of operators expressible as a sum of a scalar multiple of identity and a compact operator. What is the smallest similarity invariant semigroup containing operator A? Equivalently, which operators can be expressed as products of operators, similar to A? A partial a...

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a new proof of the existence of universal Gröbner bases. 1. Orderings for semi-groups Given a semi-group G (ie. a set with an associative binary operation), a li...