104,502 research outputs found
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms
We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques
Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics
For many important network types (e.g., sensor networks in complex harsh
environments and social networks) physical coordinate systems (e.g.,
Cartesian), and physical distances (e.g., Euclidean), are either difficult to
discern or inapplicable. Accordingly, coordinate systems and characterizations
based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and
Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian
coordinates for many network algorithms. Herein, we present an approach to
recover geometric and topological properties of a network with a small set of
distance measurements. In particular, our approach is a combination of shortest
path (often called geodesic) recovery concepts and low-rank matrix completion,
generalized to the case of hop-distances in graphs. Results for sensor networks
embedded in 2-D and 3-D spaces, as well as a social networks, indicates that
the method can accurately capture the network connectivity with a small set of
measurements. TPM generation can now also be based on various context
appropriate measurements or VC systems, as long as they characterize different
nodes by distances to small sets of random nodes (instead of a set of global
anchors). The proposed method is a significant generalization that allows the
topology to be extracted from a random set of graph shortest paths, making it
applicable in contexts such as social networks where VC generation may not be
possible.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1712.1006
Sampled data systems passivity and discrete port-Hamiltonian systems
In this paper, we present a novel way to approach the interconnection of a continuous and a discrete time physical system first presented in [1][2] [3]. This is done in a way which preserves passivity of the coupled system independently of the sampling time T. This strategy can be used both in the field of telemanipulation, for the implementation of a passive master/slave system on a digital transmission line with varying time delays and possible loss of packets (e.g., the Internet), and in the field of haptics, where the virtual environment should `feel¿ like a physical equivalent system
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