461,736 research outputs found
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
Transformational derivation of programs using the Focus system
A program derivation support system called Focus is being constructed. It will formally derive programs using the paradigm of program transformation. The following issues are discussed: (1) the integration of validation and program derivation activities in the Focus system; (2) its tree-based user interface; (3) the control of search spaces in program derivation; and (4) the structure and organization of program derivation records. The inference procedures of the system are based on the integration of functional and logic programming principles. This brings about a synthesis of paradigms that were heretofore considered far apart, such as logical and executable specifications and constructive and transformational approaches to program derivation. A great emphasis has been placed, in the design of Focus, on achieving small search spaces during program derivation. The program manipulation operations such as expansion, simplification and rewriting were designed with this objective. The role of operations that are expensive in search spaces, such as folding, has been reduced. Program derivations are documented in Focus in a way that the high level descriptions of derivations are expressed only using program level information. All the meta-level information, together with dependencies between derivations of program components, is automatically recorded by the system at a lower level of description for its own use in replay
Fidelity and leakage of Josephson qubits
The unit of quantum information is the qubit, a vector in a two-dimensional
Hilbert space. On the other hand, quantum hardware often operates in
two-dimensional subspaces of vector spaces of higher dimensionality. The
presence of higher quantum states may affect the accuracy of quantum
information processing. In this Letter we show how to cope with {\em quantum
leakage} in devices based on small Josephson junctions. While the presence of
higher charge states of the junction reduces the fidelity during gate
operations we demonstrate that errors can be minimized by appropriately
designing and operating the gates.Comment: 9 pages, Revtex, 2 eps figure
Distributionally Robust Games with Risk-averse Players
We present a new model of incomplete information games without private
information in which the players use a distributionally robust optimization
approach to cope with the payoff uncertainty. With some specific restrictions,
we show that our "Distributionally Robust Game" constitutes a true
generalization of three popular finite games. These are the Complete
Information Games, Bayesian Games and Robust Games. Subsequently, we prove that
the set of equilibria of an arbitrary distributionally robust game with
specified ambiguity set can be computed as the component-wise projection of the
solution set of a multi-linear system of equations and inequalities. For
special cases of such games we show equivalence to complete information finite
games (Nash Games) with the same number of players and same action spaces.
Thus, when our game falls within these special cases one can simply solve the
corresponding Nash Game. Finally, we demonstrate the applicability of our new
model of games and highlight its importance.Comment: 11 pages, 3 figures, Proceedings of 5th the International Conference
on Operations Research and Enterprise Systems ({ICORES} 2016), Rome, Italy,
February 23-25, 201
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