911,434 research outputs found
Vertex similarity in networks
We consider methods for quantifying the similarity of vertices in networks.
We propose a measure of similarity based on the concept that two vertices are
similar if their immediate neighbors in the network are themselves similar.
This leads to a self-consistent matrix formulation of similarity that can be
evaluated iteratively using only a knowledge of the adjacency matrix of the
network. We test our similarity measure on computer-generated networks for
which the expected results are known, and on a number of real-world networks
Computing matrix inversion with optical networks
With this paper we bring about a discussion on the computing potential of
complex optical networks and provide experimental demonstration that an optical
fiber network can be used as an analog processor to calculate matrix inversion.
A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber
network containing three nodes and operating at telecomm wavelength. For an NxN
matrix, the overall solving time (including setting time of the matrix elements
and calculation time of inversion) scales as O(N^2), whereas matrix inversion
by most advanced computer algorithms requires ~O(N^2.37) computational time.
For well-conditioned matrices, the error of the inversion performed optically
is found to be less than 3%, limited by the accuracy of measurement equipment.Comment: 5 page
Satellite-matrix-switched, time-division-multiple-access network simulator
A versatile experimental Ka-band network simulator has been implemented at the NASA Lewis Research Center to demonstrate and evaluate a satellite-matrix-switched, time-division-multiple-access (SMS-TDMA) network and to evaluate future digital ground terminals and radiofrequency (RF) components. The simulator was implemented by using proof-of-concept RF components developed under NASA contracts and digital ground terminal and link simulation hardware developed at Lewis. This simulator provides many unique capabilities such as satellite range delay and variation simulation and rain fade simulation. All network parameters (e.g., signal-to-noise ratio, satellite range variation rate, burst density, and rain fade) are controlled and monitored by a central computer. The simulator is presently configured as a three-ground-terminal SMS-TDMA network
Towards concept analysis in categories: limit inferior as algebra, limit superior as coalgebra
While computer programs and logical theories begin by declaring the concepts
of interest, be it as data types or as predicates, network computation does not
allow such global declarations, and requires *concept mining* and *concept
analysis* to extract shared semantics for different network nodes. Powerful
semantic analysis systems have been the drivers of nearly all paradigm shifts
on the web. In categorical terms, most of them can be described as
bicompletions of enriched matrices, generalizing the Dedekind-MacNeille-style
completions from posets to suitably enriched categories. Yet it has been well
known for more than 40 years that ordinary categories themselves in general do
not permit such completions. Armed with this new semantical view of
Dedekind-MacNeille completions, and of matrix bicompletions, we take another
look at this ancient mystery. It turns out that simple categorical versions of
the *limit superior* and *limit inferior* operations characterize a general
notion of Dedekind-MacNeille completion, that seems to be appropriate for
ordinary categories, and boils down to the more familiar enriched versions when
the limits inferior and superior coincide. This explains away the apparent gap
among the completions of ordinary categories, and broadens the path towards
categorical concept mining and analysis, opened in previous work.Comment: 22 pages, 5 figures and 9 diagram
Strategic Investment in Protection in Networked Systems
We study the incentives that agents have to invest in costly protection
against cascading failures in networked systems. Applications include
vaccination, computer security and airport security. Agents are connected
through a network and can fail either intrinsically or as a result of the
failure of a subset of their neighbors. We characterize the equilibrium based
on an agent's failure probability and derive conditions under which equilibrium
strategies are monotone in degree (i.e. in how connected an agent is on the
network). We show that different kinds of applications (e.g. vaccination,
malware, airport/EU security) lead to very different equilibrium patterns of
investments in protection, with important welfare and risk implications. Our
equilibrium concept is flexible enough to allow for comparative statics in
terms of network properties and we show that it is also robust to the
introduction of global externalities (e.g. price feedback, congestion).Comment: 32 pages, 3 figure
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