36,612 research outputs found
The Equivalence of Sampling and Searching
In a sampling problem, we are given an input x, and asked to sample
approximately from a probability distribution D_x. In a search problem, we are
given an input x, and asked to find a member of a nonempty set A_x with high
probability. (An example is finding a Nash equilibrium.) In this paper, we use
tools from Kolmogorov complexity and algorithmic information theory to show
that sampling and search problems are essentially equivalent. More precisely,
for any sampling problem S, there exists a search problem R_S such that, if C
is any "reasonable" complexity class, then R_S is in the search version of C if
and only if S is in the sampling version. As one application, we show that
SampP=SampBQP if and only if FBPP=FBQP: in other words, classical computers can
efficiently sample the output distribution of every quantum circuit, if and
only if they can efficiently solve every search problem that quantum computers
can solve. A second application is that, assuming a plausible conjecture, there
exists a search problem R that can be solved using a simple linear-optics
experiment, but that cannot be solved efficiently by a classical computer
unless the polynomial hierarchy collapses. That application will be described
in a forthcoming paper with Alex Arkhipov on the computational complexity of
linear optics.Comment: 16 page
On the discovery of social roles in large scale social systems
The social role of a participant in a social system is a label
conceptualizing the circumstances under which she interacts within it. They may
be used as a theoretical tool that explains why and how users participate in an
online social system. Social role analysis also serves practical purposes, such
as reducing the structure of complex systems to rela- tionships among roles
rather than alters, and enabling a comparison of social systems that emerge in
similar contexts. This article presents a data-driven approach for the
discovery of social roles in large scale social systems. Motivated by an
analysis of the present art, the method discovers roles by the conditional
triad censuses of user ego-networks, which is a promising tool because they
capture the degree to which basic social forces push upon a user to interact
with others. Clusters of censuses, inferred from samples of large scale network
carefully chosen to preserve local structural prop- erties, define the social
roles. The promise of the method is demonstrated by discussing and discovering
the roles that emerge in both Facebook and Wikipedia. The article con- cludes
with a discussion of the challenges and future opportunities in the discovery
of social roles in large social systems
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