111,961 research outputs found
Master equations for finite state mean field games with nonlinear activations
We formulate a class of mean field games on a finite state space with
variational principles resembling those in continuous-state mean field games.
We construct a controlled continuity equation featuring a nonlinear activation
function on graphs induced by finite-state reversible continuous time Markov
chains. In these graphs, each edge is weighted by the transition probability
and invariant measure of the original process. Using these controlled dynamics
on the graph and the dynamic programming principle for the value function, we
derive several key components: the mean field game systems, the functional
Hamilton-Jacobi equations, and the master equations on a finite probability
space for potential mean field games. The existence and uniqueness of solutions
to the potential mean field game system are ensured through a convex
optimization reformulation in terms of the density-flux pair. We also derive
variational principles for the master equations of both non-potential games and
mixed games on a continuous state space. Finally, we offer several concrete
examples of discrete mean field game dynamics on a two-point space, complete
with closed-formula solutions. These examples include discrete Wasserstein
distances, mean field planning, and potential mean field games.Comment: 39 page
Wireless Scheduling with Power Control
We consider the scheduling of arbitrary wireless links in the physical model
of interference to minimize the time for satisfying all requests. We study here
the combined problem of scheduling and power control, where we seek both an
assignment of power settings and a partition of the links so that each set
satisfies the signal-to-interference-plus-noise (SINR) constraints.
We give an algorithm that attains an approximation ratio of , where is the number of links and is the ratio
between the longest and the shortest link length. Under the natural assumption
that lengths are represented in binary, this gives the first approximation
ratio that is polylogarithmic in the size of the input. The algorithm has the
desirable property of using an oblivious power assignment, where the power
assigned to a sender depends only on the length of the link. We give evidence
that this dependence on is unavoidable, showing that any
reasonably-behaving oblivious power assignment results in a -approximation.
These results hold also for the (weighted) capacity problem of finding a
maximum (weighted) subset of links that can be scheduled in a single time slot.
In addition, we obtain improved approximation for a bidirectional variant of
the scheduling problem, give partial answers to questions about the utility of
graphs for modeling physical interference, and generalize the setting from the
standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore
the utility of graph models in capturing wireless interference.Comment: Revised full versio
EEG sleep stages identification based on weighted undirected complex networks
Sleep scoring is important in sleep research because any errors in the scoring of the patient's sleep electroencephalography (EEG) recordings can cause serious problems such as incorrect diagnosis, medication errors, and misinterpretations of patient's EEG recordings. The aim of this research is to develop a new automatic method for EEG sleep stages classification based on a statistical model and weighted brain networks.
Methods
each EEG segment is partitioned into a number of blocks using a sliding window technique. A set of statistical features are extracted from each block. As a result, a vector of features is obtained to represent each EEG segment. Then, the vector of features is mapped into a weighted undirected network. Different structural and spectral attributes of the networks are extracted and forwarded to a least square support vector machine (LS-SVM) classifier. At the same time the network's attributes are also thoroughly investigated. It is found that the network's characteristics vary with their sleep stages. Each sleep stage is best represented using the key features of their networks.
Results
In this paper, the proposed method is evaluated using two datasets acquired from different channels of EEG (Pz-Oz and C3-A2) according to the R&K and the AASM without pre-processing the original EEG data. The obtained results by the LS-SVM are compared with those by Naïve, k-nearest and a multi-class-SVM. The proposed method is also compared with other benchmark sleep stages classification methods. The comparison results demonstrate that the proposed method has an advantage in scoring sleep stages based on single channel EEG signals.
Conclusions
An average accuracy of 96.74% is obtained with the C3-A2 channel according to the AASM standard, and 96% with the Pz-Oz channel based on the R&K standard
- …