We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.

Value functions are a core component of reinforcement learning systems. The main idea is to to construct a single function approximator V (s; θ) that estimates the long-term reward from any state s, using parameters θ. In this paper we introduce universal value function approximators (UVFAs) V (s, g; θ) that generalise not just over states s but also over goals g. We develop an efficient techni...

Chimeric antigen receptor engineered-T (CAR-T) cells also named as living drugs, have been recently known as a breakthrough technology and were applied as an adoptive immunotherapy against different types of cancer. They also attracted widespread interest because of the success of B-cell malignancy therapy achieved by anti-CD19 CAR-T cells. Current genetic toolbox enabled the synthesis of CARs ...

We calculate Betti numbers of the framed moduli space of instantons on Ĉ/Z2, under the assumption that the corresponding torsion free sheaves E have vanishing properties(Hom(E, E(−l∞)) = Ext (E, E(−l∞)) = 0). Moreover we derive the generating function of Betti numbers and obtain closed formulas. On the other hand, we derive a universal relation between the generating function of Betti numbers o...

We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for KacMoody groups. For a pair consisting of a surface and a curve on it, we consider a refined generating function (involving G-bundles with parabolic structures along the curve) which depends on the elliptic as well as modular variables and prove i...

We study mock and mixed mock modular forms in the lower half-plane. In particular, our results apply to Zwegers’ three-variable mock Jacobi form μ(u, v; τ), three-variable generalizations of the universal mock modular partition rank generating function, and the quantum and mock modular strongly unimodal sequence rank generating function. We do not rely upon the analytic properties of these func...