2,990 research outputs found
Decomposition and convergence for tree martingales
AbstractIn this paper, the authors firstly construct a graph-theoretic decomposition of an index set for tree martingales, and based on this decomposition, they give a locally finite tree martingale’s notion and a tree martingale decomposition theorem. Secondly, they establish some relations between the locally finite tree martingales and the multiparameter martingales, and furthermore the convergence of tree martingales is shown by using the multiparameter martingale theory of Cairoli–Walsh. Finally, with some mild conditions, two inequalities for tree martingales are obtained by using their decomposition theorem and multiparameter martingale theory
Hidden-bottom molecular states from interaction
In this work, we study possible hidden-bottom molecular pentaquarks
from coupled-channel interaction in
the quasipotential Bethe-Salpeter equation approach. In isodoublet sector with
, with the same reasonable parameters the interaction produces seven
molecular states, a state near threshold with spin parity
, a state near threshold with , two states near
threshold with and , and three states near
threshold with , , and . The results
suggest that three states near threshold and two states near
threshold are very close, respectively, which may be difficult
to distinguish in experiment without partial wave analysis. Compared with the
hidden-charm pentaquark, the states are relatively narrow with widths at
an order of magnitude of 1 MeV or smaller. The importance of each channel
considered is also discussed, and it is found that the channel
provides important contribution for the widths of those states. In isoquartet
sector with , cutoff should be considerably enlarged to achieve bound
states from the interaction, which makes the existence of such states
unreliable. The results in the current work are helpful for searching for
hidden-bottom molecular pentaquarks in future experiments, such as the COMPASS,
J-PARC, and the Electron Ion Collider in China (EicC).Comment: 8 pages, 3 figure
The Complexity of Distributed Edge Coloring with Small Palettes
The complexity of distributed edge coloring depends heavily on the palette
size as a function of the maximum degree . In this paper we explore the
complexity of edge coloring in the LOCAL model in different palette size
regimes.
1. We simplify the \emph{round elimination} technique of Brandt et al. and
prove that -edge coloring requires
time w.h.p. and time deterministically, even on trees.
The simplified technique is based on two ideas: the notion of an irregular
running time and some general observations that transform weak lower bounds
into stronger ones.
2. We give a randomized edge coloring algorithm that can use palette sizes as
small as , which is a natural barrier for
randomized approaches. The running time of the algorithm is at most
, where is the complexity of a
permissive version of the constructive Lovasz local lemma.
3. We develop a new distributed Lovasz local lemma algorithm for
tree-structured dependency graphs, which leads to a -edge
coloring algorithm for trees running in time. This algorithm
arises from two new results: a deterministic -time LLL algorithm for
tree-structured instances, and a randomized -time graph
shattering method for breaking the dependency graph into independent -size LLL instances.
4. A natural approach to computing -edge colorings (Vizing's
theorem) is to extend partial colorings by iteratively re-coloring parts of the
graph. We prove that this approach may be viable, but in the worst case
requires recoloring subgraphs of diameter . This stands
in contrast to distributed algorithms for Brooks' theorem, which exploit the
existence of -length augmenting paths
Possible molecular dibaryons with quarks and their baryon-antibaryon partners
In this work, we systematically investigate the charmed-strange dibaryon
systems with quarks and their baryon-antibaryon partners from the
interactions , ,
, and and
their baryon-antibaryon partners from interactions
, ,
, and
. The potential kernels are constructed with the
help of effective Lagrangians under SU(3), heavy quark, and chiral symmetries
to describe these interactions. To search for possible molecular states, the
kernels are inserted into the quasipotential Bethe-Salpeter equation, which is
solved to find poles from scattering amplitude. The results suggest that 36 and
24 bound states can be found in the baryon-baryon and baryon-antibaryon
interactions, respectively. However, much large values of parameter
are required to produce the bound states from the baryon-antibaryon
interactions, which questions the existence of these bound states. Possible
coupled-channel effect are considered in the current work to estimate the
couplings of the molecular states to the channels considered.Comment: 13 pages, 5 figures. arXiv admin note: text overlap with
arXiv:2208.1196
Y(4626) as a molecular state from interaction
Recently, a new structure was reported by the Belle Colloboration
in the process . In this work, we propose an
assignment of the as a molecular state,
which decays into the channel through a coupling between
and channels. With the
help of the heavy quark symmetry, the potential of the interaction
is constructed within the
one-boson-exchange model, and inserted into the quasipotential Bethe-Salpeter
equation. The pole of obtained scattering amplitude is searched for in the
complex plane, which corresponds to a molecular state from the interaction
. The results suggest that a
pole is produced near the threshold, which exhibits
as a peak in the invariant mass spectrum of the
channel at about 4626 MeV. It obviously favors the as a
molecular state. In the same model, other molecular
states from the interaction
are also predicted, which can be checked in future experiments.Comment: 7 pages, 2 figure
The Energy Complexity of Broadcast
Energy is often the most constrained resource in networks of battery-powered
devices, and as devices become smaller, they spend a larger fraction of their
energy on communication (transceiver usage) not computation. As an imperfect
proxy for true energy usage, we define energy complexity to be the number of
time slots a device transmits/listens; idle time and computation are free.
In this paper we investigate the energy complexity of fundamental
communication primitives such as broadcast in multi-hop radio networks. We
consider models with collision detection (CD) and without (No-CD), as well as
both randomized and deterministic algorithms. Some take-away messages from this
work include:
1. The energy complexity of broadcast in a multi-hop network is intimately
connected to the time complexity of leader election in a single-hop (clique)
network. Many existing lower bounds on time complexity immediately transfer to
energy complexity. For example, in the CD and No-CD models, we need
and energy, respectively.
2. The energy lower bounds above can almost be achieved, given sufficient
() time. In the CD and No-CD models we can solve broadcast using
energy and energy,
respectively.
3. The complexity measures of Energy and Time are in conflict, and it is an
open problem whether both can be minimized simultaneously. We give a tradeoff
showing it is possible to be nearly optimal in both measures simultaneously.
For any constant , broadcast can be solved in
time with
energy, where is the diameter of the network
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