12,143 research outputs found
Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices
We give several characterizations of discrete Sugeno integrals over bounded
distributive lattices, as particular cases of lattice polynomial functions,
that is, functions which can be represented in the language of bounded lattices
using variables and constants. We also consider the subclass of term functions
as well as the classes of symmetric polynomial functions and weighted minimum
and maximum functions, and present their characterizations, accordingly.
Moreover, we discuss normal form representations of these functions
Efficient determination of alloy ground-state structures
We propose an efficient approach to accurately finding the ground-state
structures in alloys based on the cluster expansion method. In this approach, a
small number of candidate ground-state structures are obtained without any
information of the energy. To generate the candidates, we employ the convex
hull constructed from the correlation functions of all possible structures by
using an efficient algorithm. This approach is applicable to not only simple
lattices but also complex lattices. Firstly, we evaluate the convex hulls for
binary alloys with four types of simple lattice. Then we discuss the structures
on the vertices. To examine the accuracy of this approach, we perform a set of
density functional theory calculations and the cluster expansion for Ag-Au
alloy and compare the formation energies of the vertex structures with those of
all possible structures. As applications, the ground-state structures of the
intermetallic compounds CuAu, CuAg, CuPd, AuAg, AuPd, AgPd, MoTa, MoW and TaW
are similarly evaluated. Finally, the energy distribution is obtained for
different cation arrangements in MgAlO spinel, for which long-range
interactions are essential for the accurate description of its energetics.Comment: 8 pages, 7 figure
Associative polynomial functions over bounded distributive lattices
The associativity property, usually defined for binary functions, can be
generalized to functions of a given fixed arity n>=1 as well as to functions of
multiple arities. In this paper, we investigate these two generalizations in
the case of polynomial functions over bounded distributive lattices and present
explicit descriptions of the corresponding associative functions. We also show
that, in this case, both generalizations of associativity are essentially the
same.Comment: Final versio
Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks
In this paper, the output reachable estimation and safety verification
problems for multi-layer perceptron neural networks are addressed. First, a
conception called maximum sensitivity in introduced and, for a class of
multi-layer perceptrons whose activation functions are monotonic functions, the
maximum sensitivity can be computed via solving convex optimization problems.
Then, using a simulation-based method, the output reachable set estimation
problem for neural networks is formulated into a chain of optimization
problems. Finally, an automated safety verification is developed based on the
output reachable set estimation result. An application to the safety
verification for a robotic arm model with two joints is presented to show the
effectiveness of proposed approaches.Comment: 8 pages, 9 figures, to appear in TNNL
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