28,800 research outputs found
Hierarchical Codebook Design for Beamforming Training in Millimeter-Wave Communication
In millimeter-wave communication, large antenna arrays are required to
achieve high power gain by steering towards each other with narrow beams, which
poses the problem to efficiently search the best beam direction in the angle
domain at both Tx and Rx sides. As the exhaustive search is time consuming,
hierarchical search has been widely accepted to reduce the complexity, and its
performance is highly dependent on the codebook design. In this paper, we
propose two basic criteria for the hierarchical codebook design, and devise an
efficient hierarchical codebook by jointly exploiting sub-array and
deactivation (turning-off) antenna processing techniques, where closed-form
expressions are provided to generate the codebook. Performance evaluations are
conducted under different system and channel models. Results show superiority
of the proposed codebook over the existing alternatives.Comment: 13 pages, 11 figures. To appear in IEEE Trans. Wireless Commn. This
paper proposes the BMW-SS approach to design a fully-hierarchical codebook
for mmWave communication
Some symmetric -congruences
We prove some symmetric -congruences.Comment: 11 pages. This is a very very preliminary manuscript. And some
results will be added in the future verision
Divisibility of some binomial sums
With help of -congruence, we prove the divisibility of some binomial sums.
For example, for any integers , Comment: This is a very preliminary, which maybe contains some minor mistake
Information Theory of Data Privacy
By combining Shannon's cryptography model with an assumption to the lower
bound of adversaries' uncertainty to the queried dataset, we develop a secure
Bayesian inference-based privacy model and then in some extent answer Dwork et
al.'s question [1]: "why Bayesian risk factors are the right measure for
privacy loss".
This model ensures an adversary can only obtain little information of each
individual from the model's output if the adversary's uncertainty to the
queried dataset is larger than the lower bound. Importantly, the assumption to
the lower bound almost always holds, especially for big datasets. Furthermore,
this model is flexible enough to balance privacy and utility: by using four
parameters to characterize the assumption, there are many approaches to balance
privacy and utility and to discuss the group privacy and the composition
privacy properties of this model
Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
QCD at finite isospin chemical potential possesses a
positively definite fermion determinant and the lattice simulation can be
successfully performed. While the two-flavor effective models may be sufficient
to describe the phenomenon of pion condensation, it is interesting to study the
roles of the strangeness degree of freedom and the U anomaly. In
this paper, we present a systematic study of the three-flavor
Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that
mimics the U anomaly at finite isospin chemical potential. In the
mean-field approximation, the model predicts a phase transition from the vacuum
to the pion superfluid phase, which takes place at equal to the
pion mass . Due to the U anomaly, the strangeness degree of
freedom couples to the light quark degrees of freedom and the strange quark
effective mass depends on the pion condensate. However, the strange quark
condensate and the strange quark effective mass change slightly in the pion
superfluid phase, which verifies the validity of the two-flavor models. The
effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in
the presence of the pion condensation is constructed. Due to the U
anomaly, the pion condensation generally induces scalar-pseudoscalar
interaction. The Bethe-Salpeter equation for the mesonic excitations is
established and the meson mass spectra are obtained at finite isospin chemical
potential and temperature. Finally, the general expression for the topological
susceptibility at finite isospin chemical potential is
derived. In contrast to the finite temperature effect which suppresses ,
the isospin density effect leads to an enhancement of .Comment: Version punlished in PR
Viscous Dissipation, Helicity and Enstrophy of Bouncing Droplets undergoing Off-center Collision
The off-center collision of binary bouncing droplets of equal size was
studied numerically by a volume-of-fluid (VOF) method with two marker
functions, which has been validated by comparing with available experimental
results. A non-monotonic kinetic energy recovery with varying impact parameters
was found based on the energy budget analysis. This can be explained by the
prolonged entanglement time and the enhanced internal-flow-induced viscous
dissipation for bouncing droplets at intermediate impact parameters, compared
with those at smaller or larger impact parameters. The universality of this
non-monotonicity was numerically verified, and thereby an approximate fitting
formula was proposed to correlate the kinetic energy dissipation factor with
the impact parameter for various Weber numbers and Ohnesorge numbers. From the
vortex dynamics perspective, a helicity analysis of droplet internal flow
identifies a strong three-dimensional interaction between the "ring-shaped"
vortices and the "line-shaped" shear layers for off-center collisions.
Furthermore, we demonstrated theoretically and verified numerically that the
equivalence between the total enstrophy and the total viscous dissipation,
which holds for a single-phase flow system confined by stationary boundaries,
is not generally satisfied for the two-phase flow system containing gas-liquid
interfaces. This is attributed to the work done by the unbalanced viscous
stresses, which results from the interfacial flow and the vorticity associated
with the movement of the oscillating interface.Comment: 41 Pages, 12 figure
Realizing Fulde-Ferrell Superfluids via a Dark-State Control of Feshbach Resonances
We propose that the long-sought Fulde-Ferrell superfluidity with nonzero
momentum pairing can be realized in ultracold two-component Fermi gases of
K or Li atoms by optically tuning their magnetic Feshbach
resonances via the creation of a closed-channel dark state with a
Doppler-shifted Stark effect. In this scheme, two counterpropagating optical
fields are applied to couple two molecular states in the closed channel to an
excited molecular state, leading to a significant violation of Galilean
invariance in the dark-state regime and hence to the possibility of
Fulde-Ferrell superfluidity. We develop a field theoretical formulation for
both two-body and many-body problems and predict that the Fulde-Ferrell state
has remarkable properties, such as anisotropic single-particle dispersion
relation, suppressed superfluid density at zero temperature, anisotropic sound
velocity and rotonic collective mode. The latter two features can be
experimentally probed using Bragg spectroscopy, providing a smoking-gun proof
of Fulde-Ferrell superfluidity.Comment: Published version, typos in Supplemental Material correcte
On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index
The edge Szeged index and edge-vertex Szeged index of a graph are defined as
and
respectively, where
(resp., ) is the number of edges whose distance to
vertex (resp., ) is smaller than the distance to vertex (resp.,
), and (resp., ) is the number of vertices whose
distance to vertex (resp., ) is smaller than the distance to vertex
(resp., ), respectively. A cactus is a graph in which any two cycles have at
most one common vertex. In this paper, the lower bounds of edge Szeged index
and edge-vertex Szeged index for cacti with order and cycles are
determined, and all the graphs that achieve the lower bounds are identified.Comment: 12 pages, 5 figure
Constraining the anomalous couplings in off-shell Higgs region
We study the anomalous couplings in the golden channel in both on-shell and off-shell Higgs regions. Especially, the
interference between Higgs-mediated processes with anomalous couplings
and its continuum background is firstly calculated, which
is indispensable for constraining the anomalous couplings in off-shell
Higgs region. The analytic formulas and numerical results are given.Comment: 23 pages, 5 figure
Inherit Differential Privacy in Distributed Setting: Multiparty Randomized Function Computation
How to achieve differential privacy in the distributed setting, where the
dataset is distributed among the distrustful parties, is an important problem.
We consider in what condition can a protocol inherit the differential privacy
property of a function it computes. The heart of the problem is the secure
multiparty computation of randomized function. A notion \emph{obliviousness} is
introduced, which captures the key security problems when computing a
randomized function from a deterministic one in the distributed setting. By
this observation, a sufficient and necessary condition about computing a
randomized function from a deterministic one is given. The above result can not
only be used to determine whether a protocol computing differentially private
function is secure, but also be used to construct secure one. Then we prove
that the differential privacy property of a function can be inherited by the
protocol computing it if the protocol privately computes it. A composition
theorem of differentially private protocols is also presented. We also
construct some protocols to generate random variate in the distributed setting,
such as the uniform random variates and the inversion method. By using these
fundamental protocols, we construct protocols of the Gaussian mechanism, the
Laplace mechanism and the Exponential mechanism. Importantly, all these
protocols satisfy obliviousness and so can be proved to be secure in a
simulation based manner. We also provide a complexity bound of computing
randomized function in the distribute setting. Finally, to show that our
results are fundamental and powerful to multiparty differential privacy, we
construct a differentially private empirical risk minimization protocol
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