762 research outputs found
A New Family of Solvable Self-Dual Lie Algebras
A family of solvable self-dual Lie algebras is presented. There exist a few
methods for the construction of non-reductive self-dual Lie algebras: an
orthogonal direct product, a double-extension of an Abelian algebra, and a
Wigner contraction. It is shown that the presented algebras cannot be obtained
by these methods.Comment: LaTeX, 12 page
Holography for Non-Critical Superstrings
We argue that a class of ``non-critical superstring'' vacua is
holographically related to the (non-gravitational) theory obtained by studying
string theory on a singular Calabi-Yau manifold in the decoupling limit . In two dimensions, adding fundamental strings at the singularity of the CY
manifold leads to conformal field theories dual to a recently constructed class
of vacua. In four dimensions, special cases of the construction
correspond to the theory on an NS5-brane wrapped around a Riemann surface.Comment: 29 pages, harvmac; minor changes, references adde
Topologically confined states at corrugations of gated bilayer graphene
We investigate the electronic and transport properties of gated bilayer
graphene with one corrugated layer, which results in a stacking AB/BA boundary.
When a gate voltage is applied to one layer, topologically protected gap states
appear at the corrugation, which reveal as robust transport channels along the
stacking boundary. With increasing size of the corrugation, more localized,
quantum-well-like states emerge. These finite-size states are also conductive
along the fold, but in contrast to the stacking boundary states, which are
gapless, they present a gap. We have also studied periodic corrugations in
bilayer graphene; our findings show that such corrugations between AB- and
BA-stacked regions behave as conducting channels that can be easily identified
by their shape
Interface States in Carbon Nanotube Junctions: Rolling up graphene
We study the origin of interface states in carbon nanotube intramolecular
junctions between achiral tubes. By applying the Born-von Karman boundary
condition to an interface between armchair- and zigzag-terminated graphene
layers, we are able to explain their number and energies. We show that these
interface states, costumarily attributed to the presence of topological
defects, are actually related to zigzag edge states, as those of graphene
zigzag nanoribbons. Spatial localization of interface states is seen to vary
greatly, and may extend appreciably into either side of the junction. Our
results give an alternative explanation to the unusual decay length measured
for interface states of semiconductor nanotube junctions, and could be further
tested by local probe spectroscopies
Controlling the layer localization of gapless states in bilayer graphene with a gate voltage
Experiments in gated bilayer graphene with stacking domain walls present
topological gapless states protected by no-valley mixing. Here we research
these states under gate voltages using atomistic models, which allow us to
elucidate their origin. We find that the gate potential controls the layer
localization of the two states, which switches non-trivially between layers
depending on the applied gate voltage magnitude. We also show how these bilayer
gapless states arise from bands of single-layer graphene by analyzing the
formation of carbon bonds between layers. Based on this analysis we provide a
model Hamiltonian with analytical solutions, which explains the layer
localization as a function of the ratio between the applied potential and
interlayer hopping. Our results open a route for the manipulation of gapless
states in electronic devices, analogous to the proposed writing and reading
memories in topological insulators
Almost Universal Anonymous Rendezvous in the Plane
Two mobile agents represented by points freely moving in the plane and
starting at two distinct positions, have to meet. The meeting, called
rendezvous, occurs when agents are at distance at most of each other and
never move after this time, where is a positive real unknown to them,
called the visibility radius. Agents are anonymous and execute the same
deterministic algorithm. Each agent has a set of private attributes, some or
all of which can differ between agents. These attributes are: the initial
position of the agent, its system of coordinates (orientation and chirality),
the rate of its clock, its speed when it moves, and the time of its wake-up. If
all attributes (except the initial positions) are identical and agents start at
distance larger than then they can never meet. However, differences between
attributes make it sometimes possible to break the symmetry and accomplish
rendezvous. Such instances of the rendezvous problem (formalized as lists of
attributes), are called feasible.
Our contribution is three-fold. We first give an exact characterization of
feasible instances. Thus it is natural to ask whether there exists a single
algorithm that guarantees rendezvous for all these instances. We give a strong
negative answer to this question: we show two sets and of feasible
instances such that none of them admits a single rendezvous algorithm valid for
all instances of the set. On the other hand, we construct a single algorithm
that guarantees rendezvous for all feasible instances outside of sets and
. We observe that these exception sets and are geometrically
very small, compared to the set of all feasible instances: they are included in
low-dimension subspaces of the latter. Thus, our rendezvous algorithm handling
all feasible instances other than these small sets of exceptions can be justly
called almost universal
Minimum and maximum against k lies
A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient,
and also necessary in the worst case, for finding both the minimum and the
maximum of an n-element totally ordered set. The set is accessed via an oracle
for pairwise comparisons. More recently, the problem has been studied in the
context of the Renyi-Ulam liar games, where the oracle may give up to k false
answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n
comparisons suffice. We improve on this by providing an algorithm with at most
(k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of
the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875,
and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure
Minimizing Flow Time in the Wireless Gathering Problem
We address the problem of efficient data gathering in a wireless network
through multi-hop communication. We focus on the objective of minimizing the
maximum flow time of a data packet. We prove that no polynomial time algorithm
for this problem can have approximation ratio less than \Omega(m^{1/3) when
packets have to be transmitted, unless . We then use resource
augmentation to assess the performance of a FIFO-like strategy. We prove that
this strategy is 5-speed optimal, i.e., its cost remains within the optimal
cost if we allow the algorithm to transmit data at a speed 5 times higher than
that of the optimal solution we compare to
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