Many-one reductions between search problems (i.e. multi-valued functions) play a crucial part in both algorithmic game theory (via classes such as PLS or PPAD) and the study of incomputability in analysis. While the formal setting differs significantly, the present papers offers a unifying approach in terms of category theory that allows to deduce that any degree structure arising from such red...

Abstract We investigate the uniform computational content of open and clopen Ramsey theorems in Weihrauch lattice. While they are known to be equivalent $\mathrm {ATR_0}$ from point view reverse mathematics, there is not a canonical way phrase them as multivalued functions. identify eight different functions (five corresponding theorem three theorem) study their degree Weihrauch, strong arithme...

We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than homogeneity in spacetime. Furthermore, we show that the formation of structure is accompanied by the appearance of a multivalued cosmological constant, i.e., one ...

V1‡ is a declarative visual query language for schema-based property graphs. V1 supports property graphs with mixed (both directed and undirected) edges and half-edges, with multivalued and composite properties, and with empty property values. V1 supports temporal data types, operators, and functions, and can be extended to support additional data types, operators, and functions (one spatiotemp...

In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of o...