373,923 research outputs found
Minimal -crystals and isomorphism numbers of isosimple -crystals
In this paper we generalize minimal -divisible groups defined by Oort to
-crystal over an algebraically closed field of positive characteristic. We
prove a structural theorem and give an explicit formula of the Frobenius
endomorphism of the isosimple minimal -crystals that are the building blocks
of minimal -crystals. We then define an invariant called the minimal height
for -crystals using minimal -crystals and give an upper bound of the
isomorphism numbers of isosimple -crystals in terms of their ranks, Hodge
slopes and Newton slopes.Comment: Final accepted version at Math. Nach
Holographic Representation of Local Operators In De Sitter Space
Assuming the existence of the dS/CFT correspondence, we construct local
scalar fields with in de Sitter space by
smearing over conformal field theory operators on the future/past boundary. To
maintain bulk micro-causality and recover the bulk Wightman function in the
Euclidean vacuum, the smearing prescription must involve two sets of
single--trace operators with dimensions and . Thus the local
operator prescription in de Sitter space differs from the analytic continuation
from the prescription in anti--de Sitter space. Pushing a local operator in the
global patch to future/past infinity is shown to lead to an operator relation
between single--trace operators in conformal field theories at
, which can be interpreted as a basis transformation, also
identified as the relation between an operator in CFT and its shadow operator.
Construction of spin gauge field operators is discussed, it is shown that
the construction of higher spin gauge fields in de Sitter space is equivalent
to constructing scalar fields with specific values of mass parameter
. An acausal higher spin bulk operator which
matches onto boundary higher spin current is constructed. Implementation of the
scalar operator constructions in AdS and dS with embedding formalism is briefly
described.Comment: 35 pages, 3 figures,published in Phys.Rev.D . Comments added,
reference fixe
Note on Adiabatic Modes and Ward Identities In A Closed Universe
As statements regarding the soft limit of cosmological correlation functions,
consistency relations are known to exist in any flat FRW universe. In this
letter we explore the possibility of finding such relations in a spatially
closed universe, where the soft limit does not exist
in any rigorous sense. Despite the absence of spatial infinity of the spatial
slices, we find the adiabatic modes and their associated consistency relations
in a toy universe with background topology . Flat FRW universe
adiabatic modes are recovered via taking the large radius limit , for which we are living in a small local patch of Hubble
size on the sphere. It is shown that both dilation and translation adiabatic
modes in the local patch are recovered by a global dilation on the sphere,
acting at different places.Comment: 4 page
Subtle Invariants of -crystals
Vasiu proved that the level torsion of an -crystal
over an algebraically closed field of characteristic is a
non-negative integer that is an effectively computable upper bound of the
isomorphism number of and expected that in fact
one always has . In this paper, we prove
that this equality holds.Comment: Final accepted version at J. Ramanujan Math. So
From Co-prime to the Diophantine Equation Based Sparse Sensing
With a careful design of sample spacings either in temporal and spatial
domain, co-prime sensing can reconstruct the autocorrelation at a significantly
denser set of points based on Bazout theorem. However, still restricted from
Bazout theorem, it is required O(M1 + M2) samples to estimate frequencies in
the case of co-prime sampling, where M1 and M2 are co-prime down-sampling
rates. Besides, for Direction-of-arrival (DOA) estimation, the sensors can not
be arbitrarily sparse in co-prime arrays. In this letter, we restrain our focus
on complex waveforms and present a framework under multiple samplers/sensors
for both frequency and DOA estimation based on Diophantine equation, which is
essentially to estimate the autocorrelation with higher order statistics
instead of the second order one. We prove that, given arbitrarily high
down-sampling rates, there exist sampling schemes with samples to estimate
autocorrelation only proportional to the sum of degrees of freedom (DOF) and
the number of snapshots required. In the scenario of DOA estimation, we show
there exist arrays of N sensors with O(N^3) DOF and O(N) minimal distance
between sensors.Comment: Sparse Sensing; Co-prime Sampling; Co-prime Arra
Multiplicative Iteration for Nonnegative Quadratic Programming
In many applications, it makes sense to solve the least square problems with
nonnegative constraints. In this article, we present a new multiplicative
iteration that monotonically decreases the value of the nonnegative quadratic
programming (NNQP) objective function. This new algorithm has a simple closed
form and is easily implemented on a parallel machine. We prove the global
convergence of the new algorithm and apply it to solving image super-resolution
and color image labelling problems. The experimental results demonstrate the
effectiveness and broad applicability of the new algorithm.Comment: 11 pages, 4 figure
On Degree-Based Decentralized Search in Complex Networks
Decentralized search aims to find the target node in a large network by using
only local information. The applications of it include peer-to-peer file
sharing, web search and anything else that requires locating a specific target
in a complex system. In this paper, we examine the degree-based decentralized
search method. Specifically, we evaluate the efficiency of the method in
different cases with different amounts of available local information. In
addition, we propose a simple refinement algorithm for significantly shortening
the length of the route that has been found. Some insights useful for the
future developments of efficient decentralized search schemes have been
achieved.Comment: 6 pages, 3 figs, shortly published by ECCS'0
On Intentional Attacks and Protections in Complex Communication Networks
Being motivated by recent developments in the theory of complex networks, we
examine the robustness of communication networks under intentional attack that
takes down network nodes in a decreasing order of their nodal degrees. In this
paper, we study two different effects that have been largely missed in the
existing results: (i) some communication networks, like Internet, are too large
for anyone to have global information of their topologies, which makes the
accurate intentional attack practically impossible; and (ii) most attacks in
communication networks are propagated from one node to its neighborhood
node(s), utilizing local network-topology information only. We show that
incomplete global information has different impacts to the intentional attack
in different circumstances, while local information-based attacks can be
actually highly efficient. Such insights would be helpful for the future
developments of efficient network attack/protection schemes.Comment: 5 pages, 11 figures, accepted by IEEE Globecom 2006 conferenc
On Solving Ambiguity Resolution with Robust Chinese Remainder Theorem for Multiple Numbers
Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity
resolution related problems such as undersampling frequency estimation and
phase unwrapping which are widely applied in localization. Recently, the
deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can
reconstruct multiple integers with unknown relationship of residue
correspondence via generalized CRT and achieves robustness to bounded errors
simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for
multiple objectives. In this paper, two open problems arising that how to
introduce statistical methods into RCRTMN and deal with arbitrary errors
introduced in residues are solved. We propose the extended version of RCRTMN
assisted with Maximum Likelihood Estimation (MLE), which can tolerate
unrestricted errors and bring considerable improvement in robustness
Instability and topological robustness of Weyl semimetals against Coulomb interaction
There is a close connection between various new phenomena in Weyl semimetals
and the existence of linear band crossings in the single particle description.
We show, by a full self-consistent mean-field calculation, how this picture is
modified in the presence of long-range Coulomb interactions. The chiral
symmetry breaking occurs at strong enough interactions and the internode
interband excitonic pairing channel is found to be significant, which
determines the gap-opened band profile varying with interaction strength.
Remarkably, in the resultant interacting phase, finite band Chern number jumps
in the three-dimensional momentum space are retained, indicating the robustness
of the topologically nontrivial features.Comment: 8 pages, 4 figures, accepted by Phys. Rev.
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