81,498 research outputs found
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
We consider the problem of designing spectral graph filters for the
construction of dictionaries of atoms that can be used to efficiently represent
signals residing on weighted graphs. While the filters used in previous
spectral graph wavelet constructions are only adapted to the length of the
spectrum, the filters proposed in this paper are adapted to the distribution of
graph Laplacian eigenvalues, and therefore lead to atoms with better
discriminatory power. Our approach is to first characterize a family of systems
of uniformly translated kernels in the graph spectral domain that give rise to
tight frames of atoms generated via generalized translation on the graph. We
then warp the uniform translates with a function that approximates the
cumulative spectral density function of the graph Laplacian eigenvalues. We use
this approach to construct computationally efficient, spectrum-adapted, tight
vertex-frequency and graph wavelet frames. We give numerous examples of the
resulting spectrum-adapted graph filters, and also present an illustrative
example of vertex-frequency analysis using the proposed construction
Optimal pricing control in distribution networks with time-varying supply and demand
This paper studies the problem of optimal flow control in dynamic inventory
systems. A dynamic optimal distribution problem, including time-varying supply
and demand, capacity constraints on the transportation lines, and convex flow
cost functions of Legendre-type, is formalized and solved. The time-varying
optimal flow is characterized in terms of the time-varying dual variables of a
corresponding network optimization problem. A dynamic feedback controller is
proposed that regulates the flows asymptotically to the optimal flows and
achieves in addition a balancing of all storage levels.Comment: Submitted to 21st International Symposium on Mathematical Theory of
Networks and Systems (MTNS) in December 201
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