2,241 research outputs found
Further Results on Geometric Properties of a Family of Relative Entropies
This paper extends some geometric properties of a one-parameter family of
relative entropies. These arise as redundancies when cumulants of compressed
lengths are considered instead of expected compressed lengths. These parametric
relative entropies are a generalization of the Kullback-Leibler divergence.
They satisfy the Pythagorean property and behave like squared distances. This
property, which was known for finite alphabet spaces, is now extended for
general measure spaces. Existence of projections onto convex and certain closed
sets is also established. Our results may have applications in the R\'enyi
entropy maximization rule of statistical physics.Comment: 7 pages, Prop. 5 modified, in Proceedings of the 2011 IEEE
International Symposium on Information Theor
Can a gravitational wave and a magnetic monopole coexist?
We investigate the behavior of small perturbations around the Kaluza-Klein
monopole in the five dimensional space-time. We find that the even parity
gravitational wave does not propagate in the five dimensional space-time with
Kaluza-Klein monopole provided that the gravitational wave is constant in the
fifth direction. We conclude that a gravitational wave and a U(1) magnetic
monopole do not coexist in five dimensional Kaluza-Klein spacetime.Comment: 10 pages, LaTeX. To appear in Modern Physics Letters
Generalized Shifts on Cartesian Products
It is proved that if E, F are infinite dimensional strictly convex Banach spaces totally incomparable in a restricted sense, then the Cartesian product E×F with the sum or sup norm does not admit a forward shift. As a corollary it is deduced that there are no backward or forward shifts on the Cartesian product`p1×`p2,1\u3c p16=p2\u3c∞, with the supremum norm thus settling a problem left open in Rajagopalan and Sundaresan in J. Analysis 7 (1999(, 75-81 and also a problem stated as unsolved in Rassias and Sundaresan
A case for adaptive sub-carrier level power allocation in OFDMA networks
In today's OFDMA networks, the transmission power is typically fixed and the same for all the sub-carriers that compose a channel. The sub-carriers though, experience different degrees of fading and thus, the received power is different for different sub-carriers; while some frequencies experience deep fades, others are relatively unaffected. In this paper, we make a case of redistributing the power across the sub-carriers (subject to a fixed power budget constraint) to better cope with this frequency selectivity. Specifically, we design a joint power and rate adaptation scheme (called JPRA for short) wherein power redistribution is combined with sub-carrier level rate adaptation to yield significant throughput benefits. We further consider two variants of JPRA: (a) JPRA-CR where, the power is redistributed across sub-carriers so as to support a maximum common rate (CR) across sub-carriers and (b) JPRA-MT where, the goal is to redistribute power such that the transmission time of a packet is minimized. While the first variant decreases transceiver complexity and is simpler, the second is geared towards achieving the maximum throughput possible. We implement both variants of JPRA on our WARP radio testbed. Our extensive experiments demonstrate that our scheme provides a 35% improvement in total network throughput in testbed experiments compared to FARA, a scheme where only sub-carrier level rate adaptation is used. We also perform simulations to demonstrate the efficacy of JPRA in larger scale networks. © 2012 ACM
Interacting Qubit-Photon Bound States with Superconducting Circuits
Qubits strongly coupled to a photonic crystal give rise to many exotic
physical scenarios, beginning with single and multi-excitation qubit-photon
dressed bound states comprising induced spatially localized photonic modes,
centered around the qubits, and the qubits themselves. The localization of
these states changes with qubit detuning from the band-edge, offering an avenue
of in situ control of bound state interaction. Here, we present experimental
results from a device with two qubits coupled to a superconducting microwave
photonic crystal and realize tunable on-site and inter-bound state
interactions. We observe a fourth-order two photon virtual process between
bound states indicating strong coupling between the photonic crystal and
qubits. Due to their localization-dependent interaction, these states offer the
ability to create one-dimensional chains of bound states with tunable and
potentially long-range interactions that preserve the qubits' spatial
organization, a key criterion for realization of certain quantum many-body
models. The widely tunable, strong and robust interactions demonstrated with
this system are promising benchmarks towards realizing larger, more complex
systems of bound states
Minimization Problems Based on Relative -Entropy II: Reverse Projection
In part I of this two-part work, certain minimization problems based on a
parametric family of relative entropies (denoted ) were
studied. Such minimizers were called forward
-projections. Here, a complementary class of minimization
problems leading to the so-called reverse -projections
are studied. Reverse -projections, particularly on
log-convex or power-law families, are of interest in robust estimation problems
() and in constrained compression settings ().
Orthogonality of the power-law family with an associated linear family is first
established and is then exploited to turn a reverse
-projection into a forward
-projection. The transformed problem is a simpler
quasiconvex minimization subject to linear constraints.Comment: 20 pages; 3 figures; minor change in the title; revised manuscript.
Accepted for publication in IEEE Transactions on Information Theor
Minimization Problems Based on Relative -Entropy I: Forward Projection
Minimization problems with respect to a one-parameter family of generalized
relative entropies are studied. These relative entropies, which we term
relative -entropies (denoted ), arise as
redundancies under mismatched compression when cumulants of compressed lengths
are considered instead of expected compressed lengths. These parametric
relative entropies are a generalization of the usual relative entropy
(Kullback-Leibler divergence). Just like relative entropy, these relative
-entropies behave like squared Euclidean distance and satisfy the
Pythagorean property. Minimizers of these relative -entropies on closed
and convex sets are shown to exist. Such minimizations generalize the maximum
R\'{e}nyi or Tsallis entropy principle. The minimizing probability distribution
(termed forward -projection) for a linear family is shown
to obey a power-law. Other results in connection with statistical inference,
namely subspace transitivity and iterated projections, are also established. In
a companion paper, a related minimization problem of interest in robust
statistics that leads to a reverse -projection is
studied.Comment: 24 pages; 4 figures; minor change in title; revised version. Accepted
for publication in IEEE Transactions on Information Theor
Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
Condensed matter physics has been driven forward by significant experimental
and theoretical progress in the study and understanding of equilibrium phase
transitions based on symmetry and topology. However, nonequilibrium phase
transitions have remained a challenge, in part due to their complexity in
theoretical descriptions and the additional experimental difficulties in
systematically controlling systems out of equilibrium. Here, we study a
one-dimensional chain of 72 microwave cavities, each coupled to a
superconducting qubit, and coherently drive the system into a nonequilibrium
steady state. We find experimental evidence for a dissipative phase transition
in the system in which the steady state changes dramatically as the mean photon
number is increased. Near the boundary between the two observed phases, the
system demonstrates bistability, with characteristic switching times as long as
60 ms -- far longer than any of the intrinsic rates known for the system. This
experiment demonstrates the power of circuit QED systems for studying
nonequilibrium condensed matter physics and paves the way for future
experiments exploring nonequilbrium physics with many-body quantum optics
Drought Stress Results in a Compartment-Specific Restructuring of the Rice Root-Associated Microbiomes.
Plant roots support complex microbial communities that can influence plant growth, nutrition, and health. While extensive characterizations of the composition and spatial compartmentalization of these communities have been performed in different plant species, there is relatively little known about the impact of abiotic stresses on the root microbiota. Here, we have used rice as a model to explore the responses of root microbiomes to drought stress. Using four distinct genotypes, grown in soils from three different fields, we tracked the drought-induced changes in microbial composition in the rhizosphere (the soil immediately surrounding the root), the endosphere (the root interior), and unplanted soils. Drought significantly altered the overall bacterial and fungal compositions of all three communities, with the endosphere and rhizosphere compartments showing the greatest divergence from well-watered controls. The overall response of the bacterial microbiota to drought stress was taxonomically consistent across soils and cultivars and was primarily driven by an enrichment of multiple Actinobacteria and Chloroflexi, as well as a depletion of several Acidobacteria and Deltaproteobacteria While there was some overlap in the changes observed in the rhizosphere and endosphere communities, several drought-responsive taxa were compartment specific, a pattern likely arising from preexisting compositional differences, as well as plant-mediated processes affecting individual compartments. These results reveal that drought stress, in addition to its well-characterized effects on plant physiology, also results in restructuring of root microbial communities and suggest the possibility that constituents of the altered plant microbiota might contribute to plant survival under extreme environmental conditions.IMPORTANCE With the likelihood that changes in global climate will adversely affect crop yields, the potential role of microbial communities in enhancing plant performance makes it important to elucidate the responses of plant microbiomes to environmental variation. By detailed characterization of the effect of drought stress on the root-associated microbiota of the crop plant rice, we show that the rhizosphere and endosphere communities undergo major compositional changes that involve shifts in the relative abundances of a taxonomically diverse set of bacteria in response to drought. These drought-responsive microbes, in particular those enriched under water deficit conditions, could potentially benefit the plant as they could contribute to tolerance to drought and other abiotic stresses, as well as provide protection from opportunistic infection by pathogenic microbes. The identification and future isolation of microbes that promote plant tolerance to drought could potentially be used to mitigate crop losses arising from adverse shifts in climate
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