35,034 research outputs found
Two-layer Locally Repairable Codes for Distributed Storage Systems
In this paper, we propose locally repairable codes (LRCs) with optimal
minimum distance for distributed storage systems (DSS). A two-layer encoding
structure is employed to ensure data reconstruction and the designated repair
locality. The data is first encoded in the first layer by any existing maximum
distance separable (MDS) codes, and then the encoded symbols are divided into
non-overlapping groups and encoded by an MDS array code in the second layer.
The encoding in the second layer provides enough redundancy for local repair,
while the overall code performs recovery of the data based on redundancy from
both layers. Our codes can be constructed over a finite field with size growing
linearly with the total number of nodes in the DSS, and facilitate efficient
degraded reads.Comment: This paper has been withdrawn by the author due to inaccuracy of
Claim
A decades-long fast-rise-exponential-decay flare in low-luminosity AGN NGC 7213
We analysed the four-decades-long X-ray light curve of the low-luminosity
active galactic nucleus (LLAGN) NGC 7213 and discovered a
fast-rise-exponential-decay (FRED) pattern, i.e. the X-ray luminosity increased
by a factor of within 200d, and then decreased exponentially with
an -folding time d ( yr). For the theoretical
understanding of the observations, we examined three variability models
proposed in the literature: the thermal-viscous disc instability model, the
radiation pressure instability model, and the tidal disruption event (TDE)
model. We find that a delayed tidal disruption of a main-sequence star is most
favourable; either the thermal-viscous disk instability model or radiation
pressure instability model fails to explain some key properties observed, thus
we argue them unlikely.Comment: Accepted for publication in MNRAS, updated version after proof
correction
Vertex operator algebras of Argyres-Douglas theories from M5-branes
We study aspects of the vertex operator algebra (VOA) corresponding to
Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type
on a punctured sphere. We denote the AD theories as , where
and represent an irregular and a regular singularity respectively.
We restrict to the `minimal' case where has no associated mass
parameters, and the theory does not admit any exactly marginal deformations.
The VOA corresponding to the AD theory is conjectured to be the W-algebra
, where with being
the dual Coxeter number of . We verify this conjecture by showing that the
Schur index of the AD theory is identical to the vacuum character of the
corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of
the Higgs branch. We also find that the Schur and Hall-Littlewood index for the
AD theory can be written in a simple closed form for . We also test the
conjecture that the associated variety of such VOA is identical to the Higgs
branch. The M5-brane construction of these theories and the corresponding TQFT
structure of the index play a crucial role in our computations.Comment: 35 pages, 1 figure, v2: minor corrections, referenced adde
The 2016 global and national burden of diabetes mellitus attributable to PM2·5 air pollution
Associations of ambient coarse particulate matter, nitrogen dioxide, and carbon monoxide with the risk of kidney disease: A cohort study
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