For many real-world applications, labeled data can be costly to obtain. Semi-supervised learning methods make use of substantially available unlabeled data along with few labeled samples. Most of the latest work on semi-supervised learning for image classification show performance on standard machine learning datasets like MNIST, SVHN, etc. In this work, we propose a convolutional adversarial a...

In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the boolean operations (complementation, finite unions and finite intersections). We ...

In this paper we investigate continuous and upper and lower semi-continuous real functions in the framework of TTE, Type-2 Theory of EEectivity. First some basic facts about TTE are summarized. For each of the function spaces, we introduce several natural representations based on diierent intiuitive concepts of \eeectivity" and prove their equivalence. Computability of several operations on the...

In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post’s Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such i...

Semi-relativistic approach is employed to compute the differential and integrated cross sections, spin polarization P and the spin polarization parameters T and U for the scattering of electrons from barium and strontium atoms in the energy range from 2.0-300 eV. The projectile-target interaction is represented both by real and complex optical potential in the solution of Dirac equation for the...

We propose the study of query languages for databases involving real numbers as data (called semi-algebraic databases in the sequel). As main new aspect our approach is based on real number complexity theory as introduced in 8] and descriptive complexity for the latter developed in 17]. Using this formal framework a uniform treatment of semi-algebraic query languages is obtained. Precise result...

A non-commutative polynomial which is positive on a bounded semi-algebraic set of operators has a weighted sum of squares representation. This Positivstellensatz parallels similar results in the commutative case. A broader issue is to what extent does real semi-algebraic geometry extend to non-commutative polynomials? Our ”strict” Positivstellensatz is positive news, on the opposite extreme fro...