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Network Utility Maximization (NUM) Theory
Published in Liansheng Tan, Resource Allocation and Performance Optimization in Communication Networks and the Internet, 2017
In terms of the utility theory (see, e.g., [137]), the utility function of the base station is a function that ranks all pairs of bandwidth allocations by order of preference (completeness) such that any set of three or more bandwidth combinations forms a transitive relation. This means that for each combination (x,y) there is a unique relation, U (x,y), representing the utility (satisfaction) relation associated with (x,y). The relation (x,y) → U (x,y) is called the utility function. The range of the function is a set of real numbers. The actual values of the function have no importance. Only the ranking of those values has implications in the theory. More specifically, if U(x,y) ≥ U(x′,y′), then the bandwidth combination (x,y) is described as at least as good as the the combination (x′,y′). If U (x,y) > U (x′,y′), the combination (x,y) is referred to be strictly preferred to the combination (x′,y′).
A note on the marginal instability rates of two-dimensional linear cocycles
Published in Dynamical Systems, 2023
Let us say that is locally constant if for the matrix is determined by the symbol only. In this case, if denotes the range of the function A, then one simply has The case in which A is locally constant has been studied extensively due to its relevance to marginally unstable discrete-time linear switching systems in control theory, and investigations of sequences of the above form may be found in numerous works such as Refs. [7,16,17,21,23,28–30]. The same problem has also been studied in Refs. [3,4] based on quite different motivations relating to the notion of k-regular sequences in symbolic dynamics. In the works just cited, the simpler formulation (1) corresponding to the locally constant case is the only case studied, but the more general case in which A is not assumed locally constant has been touched upon in the ergodic optimization literature, notably Ref. [5] in which criteria for to be a bounded sequence are investigated.
Dynamic analysis and active control of hard-magnetic soft materials
Published in International Journal of Smart and Nano Materials, 2021
where , and the function represents the rate of feedback of the errors. The , , are the proportional, integral, and differential of errors. The determines the linear range of the function. The output signal of the PID controller can be expressed as
Deep learning for identifying environmental risk factors of acute respiratory diseases in Beijing, China: implications for population with different age and gender
Published in International Journal of Environmental Health Research, 2020
Because DNN was a multilayer perceptron with multiple hidden layers, their weights were all linked, and initialized based on supervised pattern. In this study, we used supervised learning to train the DNN model. And the training process was developed by the Caffe framework and Python script. DNN model had rich expression ability, which was attributed to the activation function. We used the Rectified Liner Unit (ReLU) function as activation function in this study. The value range of ReLU function was (0, +∞). And it was an unsaturated activation function with fast convergence, as shown in Figure 4.