5,436 research outputs found
Extremal Reaches in Polynomial Time
Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM
Extremal Reaches in Polynomial Time
Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM
Minority Becomes Majority in Social Networks
It is often observed that agents tend to imitate the behavior of their
neighbors in a social network. This imitating behavior might lead to the
strategic decision of adopting a public behavior that differs from what the
agent believes is the right one and this can subvert the behavior of the
population as a whole.
In this paper, we consider the case in which agents express preferences over
two alternatives and model social pressure with the majority dynamics: at each
step an agent is selected and its preference is replaced by the majority of the
preferences of her neighbors. In case of a tie, the agent does not change her
current preference. A profile of the agents' preferences is stable if the
preference of each agent coincides with the preference of at least half of the
neighbors (thus, the system is in equilibrium).
We ask whether there are network topologies that are robust to social
pressure. That is, we ask if there are graphs in which the majority of
preferences in an initial profile always coincides with the majority of the
preference in all stable profiles reachable from that profile. We completely
characterize the graphs with this robustness property by showing that this is
possible only if the graph has no edge or is a clique or very close to a
clique. In other words, except for this handful of graphs, every graph admits
at least one initial profile of preferences in which the majority dynamics can
subvert the initial majority. We also show that deciding whether a graph admits
a minority that becomes majority is NP-hard when the minority size is at most
1/4-th of the social network size.Comment: To appear in WINE 201
Non-Einstein geometries in Chiral Gravity
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.Comment: 11 pages, 3 figures. v2: references and comments on linear stability
(Sect.2) adde
Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used
tool in theoretical computer sciences to obtain structural results about
computational problems and complexity classes by indirect proofs. The Uniform
Diagonalization Theorem allows the construction of problems outside complexity
classes while still being reducible to a specific decision problem. This paper
provides a generalization of the Uniform Diagonalization Theorem by extending
it to promise problems and the complexity classes they form, e.g. randomized
and quantum complexity classes. The theorem requires from the underlying
computing model not only the decidability of its acceptance and rejection
behaviour but also of its promise-contradicting indifferent behaviour - a
property that we will introduce as "total decidability" of promise problems.
Implications of the Uniform Diagonalization Theorem are mainly of two kinds:
1. Existence of intermediate problems (e.g. between BQP and QMA) - also known
as Ladner's Theorem - and 2. Undecidability if a problem of a complexity class
is contained in a subclass (e.g. membership of a QMA-problem in BQP). Like the
original Uniform Diagonalization Theorem the extension applies besides BQP and
QMA to a large variety of complexity class pairs, including combinations from
deterministic, randomized and quantum classes.Comment: 15 page
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