1,710 research outputs found
Mechanism design for aggregating energy consumption and quality of service in speed scaling scheduling
We consider a strategic game, where players submit jobs to a machine that
executes all jobs in a way that minimizes energy while respecting the given
deadlines. The energy consumption is then charged to the players in some way.
Each player wants to minimize the sum of that charge and of their job's
deadline multiplied by a priority weight. Two charging schemes are studied, the
proportional cost share which does not always admit pure Nash equilibria, and
the marginal cost share, which does always admit pure Nash equilibria, at the
price of overcharging by a constant factor
Span programs and quantum algorithms for st-connectivity and claw detection
We introduce a span program that decides st-connectivity, and generalize the
span program to develop quantum algorithms for several graph problems. First,
we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries
to the n x n adjacency matrix to decide if vertices s and t are connected,
under the promise that they either are connected by a path of length at most d,
or are disconnected. We also show that if T is a path, a star with two
subdivided legs, or a subdivision of a claw, its presence as a subgraph in the
input graph G can be detected with O(n) quantum queries to the adjacency
matrix. Under the promise that G either contains T as a subgraph or does not
contain T as a minor, we give O(n)-query quantum algorithms for detecting T
either a triangle or a subdivision of a star. All these algorithms can be
implemented time efficiently and, except for the triangle-detection algorithm,
in logarithmic space. One of the main techniques is to modify the
st-connectivity span program to drop along the way "breadcrumbs," which must be
retrieved before the path from s is allowed to enter t.Comment: 18 pages, 4 figure
Reciprocity in Social Networks with Capacity Constraints
Directed links -- representing asymmetric social ties or interactions (e.g.,
"follower-followee") -- arise naturally in many social networks and other
complex networks, giving rise to directed graphs (or digraphs) as basic
topological models for these networks. Reciprocity, defined for a digraph as
the percentage of edges with a reciprocal edge, is a key metric that has been
used in the literature to compare different directed networks and provide
"hints" about their structural properties: for example, are reciprocal edges
generated randomly by chance or are there other processes driving their
generation? In this paper we study the problem of maximizing achievable
reciprocity for an ensemble of digraphs with the same prescribed in- and
out-degree sequences. We show that the maximum reciprocity hinges crucially on
the in- and out-degree sequences, which may be intuitively interpreted as
constraints on some "social capacities" of nodes and impose fundamental limits
on achievable reciprocity. We show that it is NP-complete to decide the
achievability of a simple upper bound on maximum reciprocity, and provide
conditions for achieving it. We demonstrate that many real networks exhibit
reciprocities surprisingly close to the upper bound, which implies that users
in these social networks are in a sense more "social" than suggested by the
empirical reciprocity alone in that they are more willing to reciprocate,
subject to their "social capacity" constraints. We find some surprising linear
relationships between empirical reciprocity and the bound. We also show that a
particular type of small network motifs that we call 3-paths are the major
source of loss in reciprocity for real networks
Femtosecond x-ray absorption spectroscopy of spin and orbital angular momentum in photoexcited Ni films during ultrafast demagnetization
We follow for the first time the evolution of the spin and orbital angular
momentum of a thin Ni film during ultrafast demagnetization, by means of x-ray
magnetic circular dichroism. Both components decrease with a 130 +/- 40 fs time
constant upon excitation with a femtosecond laser pulse. Additional x-ray
absorption measurements reveal an increase in the spin-orbit interaction by 6
+/- 2 % during this process. This is the experimental demonstration quantifying
the importance of spin-orbit mediated processes during the demagnetization
Combination of a magnetic Feshbach resonance and an optical bound-to-bound transition
We use laser light near resonant with an optical bound-to-bound transition to
shift the magnetic field at which a Feshbach resonance occurs. We operate in a
regime of large detuning and large laser intensity. This reduces the
light-induced atom-loss rate by one order of magnitude compared to our previous
experiments [D.M. Bauer et al. Nature Phys. 5, 339 (2009)]. The experiments are
performed in an optical lattice and include high-resolution spectroscopy of
excited molecular states, reported here. In addition, we give a detailed
account of a theoretical model that describes our experimental data
Localization of cold atoms in state-dependent optical lattices via a Rabi pulse
We propose a novel realization of Anderson localization in non-equilibrium
states of ultracold atoms trapped in state-dependent optical lattices. The
disorder potential leading to localization is generated with a Rabi pulse
transfering a fraction of the atoms into a different internal state for which
tunneling between lattice sites is suppressed. Atoms with zero tunneling create
a quantum superposition of different random potentials, localizing the mobile
atoms. We investigate the dynamics of the mobile atoms after the Rabi pulse for
non-interacting and weakly interacting bosons, and we show that the evolved
wavefunction attains a quasi-stationary profile with exponentially decaying
tails, characteristic of Anderson localization. The localization length is seen
to increase with increasing disorder and interaction strength, oppositely to
what is expected for equilibrium localization.Comment: 4 pages, 4 figure
Bohmian Mechanics and Quantum Information
Many recent results suggest that quantum theory is about information, and
that quantum theory is best understood as arising from principles concerning
information and information processing. At the same time, by far the simplest
version of quantum mechanics, Bohmian mechanics, is concerned, not with
information but with the behavior of an objective microscopic reality given by
particles and their positions. What I would like to do here is to examine
whether, and to what extent, the importance of information, observation, and
the like in quantum theory can be understood from a Bohmian perspective. I
would like to explore the hypothesis that the idea that information plays a
special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
The quantum query complexity of Boolean matrix multiplication is typically
studied as a function of the matrix dimension, n, as well as the number of 1s
in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values
of \ell. This is an improvement over previous algorithms for all values of
\ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps
n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing
that our algorithm is essentially tight.
We first reduce Boolean matrix multiplication to several instances of graph
collision. We then provide an algorithm that takes advantage of the fact that
the underlying graph in all of our instances is very dense to find all graph
collisions efficiently
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