79 research outputs found
Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
The field equations associated with the Born-Infeld-Einstein action are
derived using the Palatini variational technique. In this approach the metric
and connection are varied independently and the Ricci tensor is generally not
symmetric. For sufficiently small curvatures the resulting field equations can
be divided into two sets. One set, involving the antisymmetric part of the
Ricci tensor , consists of the field equation for
a massive vector field. The other set consists of the Einstein field equations
with an energy momentum tensor for the vector field plus additional
corrections. In a vacuum with the field
equations are shown to be the usual Einstein vacuum equations. This extends the
universality of the vacuum Einstein equations, discussed by Ferraris et al.
\cite{Fe1,Fe2}, to the Born-Infeld-Einstein action. In the simplest version of
the theory there is a single coupling constant and by requiring that the
Einstein field equations hold to a good approximation in neutron stars it is
shown that mass of the vector field exceeds the lower bound on the mass of the
photon. Thus, in this case the vector field cannot represent the
electromagnetic field and would describe a new geometrical field. In a more
general version in which the symmetric and antisymmetric parts of the Ricci
tensor have different coupling constants it is possible to satisfy all of the
observational constraints if the antisymmetric coupling is much larger than the
symmetric coupling. In this case the antisymmetric part of the Ricci tensor can
describe the electromagnetic field, although gauge invariance will be broken.Comment: 12 page
Semi-Streaming Set Cover
This paper studies the set cover problem under the semi-streaming model. The
underlying set system is formalized in terms of a hypergraph whose
edges arrive one-by-one and the goal is to construct an edge cover with the objective of minimizing the cardinality (or cost in the weighted
case) of . We consider a parameterized relaxation of this problem, where
given some , the goal is to construct an edge -cover, namely, a subset of edges incident to all but an
-fraction of the vertices (or their benefit in the weighted case).
The key limitation imposed on the algorithm is that its space is limited to
(poly)logarithmically many bits per vertex.
Our main result is an asymptotically tight trade-off between and
the approximation ratio: We design a semi-streaming algorithm that on input
graph , constructs a succinct data structure such that for
every , an edge -cover that approximates
the optimal edge \mbox{(-)cover} within a factor of can be
extracted from (efficiently and with no additional space
requirements), where In particular for the traditional
set cover problem we obtain an -approximation. This algorithm is
proved to be best possible by establishing a family (parameterized by
) of matching lower bounds.Comment: Full version of the extended abstract that will appear in Proceedings
of ICALP 2014 track
Buyback Problem - Approximate matroid intersection with cancellation costs
In the buyback problem, an algorithm observes a sequence of bids and must
decide whether to accept each bid at the moment it arrives, subject to some
constraints on the set of accepted bids. Decisions to reject bids are
irrevocable, whereas decisions to accept bids may be canceled at a cost that is
a fixed fraction of the bid value. Previous to our work, deterministic and
randomized algorithms were known when the constraint is a matroid constraint.
We extend this and give a deterministic algorithm for the case when the
constraint is an intersection of matroid constraints. We further prove a
matching lower bound on the competitive ratio for this problem and extend our
results to arbitrary downward closed set systems. This problem has applications
to banner advertisement, semi-streaming, routing, load balancing and other
problems where preemption or cancellation of previous allocations is allowed
Complex transitions to synchronization in delay-coupled networks of logistic maps
A network of delay-coupled logistic maps exhibits two different
synchronization regimes, depending on the distribution of the coupling delay
times. When the delays are homogeneous throughout the network, the network
synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92,
144101 (2004)], which may be periodic or chaotic depending on the delay; when
the delays are sufficiently heterogeneous, the synchronization proceeds to a
steady-state, which is unstable for the uncoupled map [Masoller and Marti,
Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from
time-dependent to steady-state synchronization as the width of the delay
distribution increases. We also compare the two transitions to synchronization
as the coupling strength increases. We use transition probabilities calculated
via symbolic analysis and ordinal patterns. We find that, as the coupling
strength increases, before the onset of steady-state synchronization the
network splits into two clusters which are in anti-phase relation with each
other. On the other hand, with increasing delay heterogeneity, no cluster
formation is seen at the onset of steady-state synchronization; however, a
rather complex unsynchronized state is detected, revealed by a diversity of
transition probabilities in the network nodes
Stock mechanics: predicting recession in S&P500, DJIA, and NASDAQ
An original method, assuming potential and kinetic energy for prices and
conservation of their sum is developed for forecasting exchanges. Connections
with power law are shown. Semiempirical applications on S&P500, DJIA, and
NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock
Exchange index ISE-100 is found involving a potential to continue to rise.Comment: 14 pages, 4 figure
A mechanism for randomness
We investigate explicit functions that can produce truly random numbers. We
use the analytical properties of the explicit functions to show that certain
class of autonomous dynamical systems can generate random dynamics. This
dynamics presents fundamental differences with the known chaotic systems. We
present realphysical systems that can produce this kind of random time-series.
We report theresults of real experiments with nonlinear circuits containing
direct evidence for this new phenomenon. In particular, we show that a
Josephson junction coupled to a chaotic circuit can generate unpredictable
dynamics. Some applications are discussed.Comment: Accepted in Physics Letters A (2002). 11 figures (.eps
Dyonic BIon black hole in string inspired model
We construct static and spherically symmetric particle-like and black hole
solutions with magnetic and/or electric charge in the
Einstein-Born-Infeld-dilaton-axion system, which is a generalization of the
Einstein-Maxwell-dilaton-axion (EMDA) system and of the Einstein-Born-Infeld
(EBI) system. They have remarkable properties which are not seen for the
corresponding solutions in the EMDA and the EBI system.Comment: 13 pages, 15 figures, Final version in PR
Research Perspectives for Logic and Deduction
The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scientic research along the various di-mensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for repre-senting the chosen logic, and nally the issue of developing the most ecient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search. Often a key advance is a matter of applying a small change to a single formula. Ray Kurzweil [Kur05, p.5]
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