31,024 research outputs found
Geometrical Realization of Beutler-Fano formulas appearing in eigenphase shifts and time delays in multichannel scattering
Recently, we showed that eigenphase shifts and eigentime delays near a
resonance for a system of one discrete state and two continua are functionals
of the Beutler-Fano formula using appropriate dimensionless energy units and
line profile indices and identified parameters responsible for the avoided
crossing of eigenphase shifts and eigentime delays and also identified
parameters responsible for the eigentime delays due to a change in frame
transformation.
In this paper, the geometrical realization of the Beutler-Fano formulas is
considered in the three-dimensional Liouville space spanned by the Pauli
matrices, where dynamic operators are vectors. Vectors corresponding to the
background scattering matrix, the S matrix, and the time delay matrix Q form a
spherical triangle whose vertex and edge angles are parameters pertaining to
the frame transformations among eigenchannels of those matrices and eigenphase
shifts of the scattering matrices and the phase shift due to a resonance
scattering. The cotangent laws of the spherical triangle yield Beutler-Fano
resonance formulas appearing in eigenphase shifts and time delays. Duality
holding for the spherical triangle explains the symmetry observed in the
relations among parameters and provides a systematic way of defining conjugate
dynamic parameters. The spherical triangle also shows the rule of combining the
channel-channel couplings in the background scattering with the resonant
interaction to give the avoided crossing interactions in the curves of
eigenphase shifts as functions of eneryg.
The theory developed in the previous and present papers is applied to the
vibrational predissociation of triatomic van der Waals molecules.Comment: 26 pages, 7 figures, RevTeX, will be submitted to Phys. Rev. A, Major
conceptual change
On the uniqueness of Ricci flow
In this note, we study the problem of uniqueness of Ricci flow on complete
noncompact manifolds. We consider the class of solutions with curvature bounded
above by C/t when t > 0. In paricular, we proved uniqueness if in addition the
initial curvature is of polynomial growth and Ricci curvature of the flow is
relatively small.Comment: All comments are welcome
Hermitian manifolds with quasi-negative curvature
In this work, we show that along a particular choice of Hermitian curvature
flow, the non-positivity of Chern-Ricci curvature will be preserved if the
initial metric has non-positive bisectional curvature. As an application, we
show that the canonical line bundle of a compact Hermitian manifold with
nonpositive bisectional curvature and quasi-negative Chern-Ricci curvature is
ample.Comment: final version to appear in Math. Ann. arXiv admin note: text overlap
with arXiv:1812.0461
Signal Space Alignment for an Encryption Message and Successive Network Code Decoding on the MIMO K-way Relay Channel
This paper investigates a network information flow problem for a
multiple-input multiple-output (MIMO) Gaussian wireless network with -users
and a single intermediate relay having antennas. In this network, each user
intends to convey a multicast message to all other users while receiving
independent messages from the other users via an intermediate relay. This
network information flow is termed a MIMO Gaussian -way relay channel. For
this channel, we show that degrees of freedom is achievable if
. To demonstrate this, we come up with an encoding and decoding strategy
inspired from cryptography theory. The proposed encoding and decoding strategy
involves a \textit{signal space alignment for an encryption message} for the
multiple access phase (MAC) and \textit{zero forcing with successive network
code decoding} for the broadcast (BC) phase. The idea of the \emph{signal space
alignment for an encryption message} is that all users cooperatively choose the
precoding vectors to transmit the message so that the relay can receive a
proper encryption message with a special structure, \textit{network code chain
structure}. During the BC phase, \emph{zero forcing combined with successive
network code decoding} enables all users to decipher the encryption message
from the relay despite the fact that they all have different self-information
which they use as a key.Comment: 5 pages, 3 figures, and submitted ICC 201
Negative Example Aided Transcription Factor Binding Site Search
Computational approaches to transcription factor binding site identification
have been actively researched for the past decade.
Negative examples have long been utilized in de novo motif discovery and have
been shown useful in transcription factor binding site search as well.
However, understanding of the roles of negative examples in binding site
search is still very limited.
We propose the 2-centroid and optimal discriminating vector methods, taking
into account negative examples. Cross-validation results on E. coli
transcription factors show that the proposed methods benefit from negative
examples, outperforming the centroid and position-specific scoring matrix
methods. We further show that our proposed methods perform better than a
state-of-the-art method. We characterize the proposed methods in the context of
the other compared methods and show that, coupled with motif subtype
identification, the proposed methods can be effectively applied to a wide range
of transcription factors. Finally, we argue that the proposed methods are
well-suited for eukaryotic transcription factors as well.
Software tools are available at: http://biogrid.engr.uconn.edu/tfbs_search/.Comment: 14 pages, 16 figure
The K\"ahler Ricci flow around complete bounded curvature K\"ahler metrics
We produce complete bounded curvature solutions to K\"ahler-Ricci flow with
existence time estimates, assuming only that the initial data is a smooth \K
metric uniformly equivalent to another complete bounded curvature \K metric. We
obtain related flow results for non-smooth as well as degenerate initial
conditions. We also obtain a stability result for complex space forms under the
flow.Comment: 22 pages; editions made to earlier version (including revision of
title, addition to Theorem 1.2 and correction in proof of Claim 2.2
Complex manifolds with negative curvature operator
We prove that compact complex manifolds with admitting metrics with negative
Chern curvature operator either admit a -exact positive (1,1) current, or
are K\"ahler with ample canonical bundle. In the case of complex surfaces we
obtain a complete classification. The proofs rely on a global existence and
convergence result for the pluriclosed flow
Individual Preference Aware Caching Policy Design in Wireless D2D Networks
Cache-aided wireless device-to-device (D2D) networks allow significant
throughput increase, depending on the concentration of the popularity
distribution of files. Many studies assume that all users have the same
preference distribution; however, this may not be true in practice. This work
investigates whether and how the information about individual preferences can
benefit cache-aided D2D networks. We examine a clustered network and derive a
network utility that considers both the user distribution and channel fading
effects into the analysis. We also formulate a utility maximization problem for
designing caching policies. This maximization problem can be applied to
optimize several important quantities, including throughput, energy efficiency
(EE), cost, and hit-rate, and to solve different tradeoff problems. We provide
a general approach that can solve the proposed problem under the assumption
that users coordinate, then prove that the proposed approach can obtain the
stationary point under a mild assumption. Using simulations of practical
setups, we show that performance can improve significantly with proper
exploitation of individual preferences. We also show that different types of
tradeoffs exist between different performance metrics and that they can be
managed through caching policy and cooperation distance designs.Comment: Accepted by IEEE Transactions on Wireless Communication
Chern-Ricci flows on noncompact complex manifolds
In this work, we obtain existence criteria for Chern-Ricci flows on
noncompact manifolds. We generalize a result by Tossati-Wienkove on Chern-Ricci
flows to noncompact manifolds and at the same time generalize a result for
Kahler-Ricci flows by Lott-Zhang to Chern-Ricci flows. Using the existence
results, we prove that any complete noncollapsed Kahler metric with nonnegative
bisectional curvature on a noncompact complex manifold can be deformed to a
complete Kahler metric with nonnegative and bounded bisectional curvature which
will have maximal volume growth if the initial metric has maximal volume.
Combining this result with the result of Chau-Tam, we give another proof that a
complete noncompact Kahler manifold with nonnegative bisectional curvature (not
necessarily bounded) and maximal volume growth is biholomorphic to the complex
Euclidean space. This last result has already been proved by Gang Liu recently
using other methods. This last result is partial confirmation of a
uniformization conjecture of Yau.Comment: some results added; printing mistakes correcte
Wrong-sign Kaons in B decays and New Physics
New physics can possibly emerge in the B decays into wrong-sign kaons for
which the standard model contributions are extremely suppressed. We analyze
two-body decays of and mesons involving the
() and () transitions in a model
independent way, and examine various wrong-sign kaon signals which are expected
to be observed in the future experiments. Our analysis shows that it would
be possible to identify the origin of new physics through the combined analysis
of several B decay modes involving one or two wrong-sign 's.Comment: 16 pages, revtex
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