16,847 research outputs found
Convertible Codes: New Class of Codes for Efficient Conversion of Coded Data in Distributed Storage
Erasure codes are typically used in large-scale distributed storage systems to provide durability of data in the face of failures. In this setting, a set of k blocks to be stored is encoded using an [n, k] code to generate n blocks that are then stored on different storage nodes. A recent work by Kadekodi et al. [Kadekodi et al., 2019] shows that the failure rate of storage devices vary significantly over time, and that changing the rate of the code (via a change in the parameters n and k) in response to such variations provides significant reduction in storage space requirement. However, the resource overhead of realizing such a change in the code rate on already encoded data in traditional codes is prohibitively high.
Motivated by this application, in this work we first present a new framework to formalize the notion of code conversion - the process of converting data encoded with an [n^I, k^I] code into data encoded with an [n^F, k^F] code while maintaining desired decodability properties, such as the maximum-distance-separable (MDS) property. We then introduce convertible codes, a new class of code pairs that allow for code conversions in a resource-efficient manner. For an important parameter regime (which we call the merge regime) along with the widely used linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit low-field-size constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to the default approach of re-encoding
Predictive Modeling of the Non-Profit Sector in the US
The Non-Profit Sector contributes almost $1 trillion to the US economy, representing 5.4% of GDP, and generating over 12 million jobs in 2017. Yi (2010) suggests that a better understanding of the factors that affect fundraising should be of great interest to policy makers, and fundraisers. However, the workings of the sector are subject of much debate. Matsunaga, Yamauchi and Okuyama (2010) relate its size to the Theory of Government Failure. Sokolowski (2013) proposes that government funding does have a positive effect on revenues. Curry, Rodin and Carlson (2012) suggested they swing with GDP, but, Berman, Brooks and Murphy (2006) contend that macroeconomic variables do not affect short-run dynamics. List (2011) found that non-profit revenues react more to economic upswings than downturns. And the National Philanthropic Trust (2016) relates ups and downs to certain events and public awareness. Wallace (2016) points to the fact that predictive modeling has focused big-donor analytics, aimed at the identification of potential donors. We set out instead to define a working model. After locating complete time series for an emblematic segment, the environmental cause, Factor Analysis allowed us to pinpoint independent variables. We found that Non-Profit Revenues (NPR) depend largely on Public Awareness, as measured by TV coverage, and Disposable Personal Income (DPI), specifically: NPR = -4401.542 + 528.327(DPI) +23.121(TVCoverage) +
Smear correction of highly-variable, frame-transfer-CCD images with application to polarimetry
Image smear, produced by the shutter-less operation of frame transfer CCD
detectors, can be detrimental for many imaging applications. Existing
algorithms used to numerically remove smear, do not contemplate cases where
intensity levels change considerably between consecutive frame exposures. In
this report we reformulate the smearing model to include specific variations of
the sensor illumination. The corresponding desmearing expression and its noise
properties are also presented and demonstrated in the context of fast imaging
polarimetry.Comment: Article accepted for publication in Applied Optics on 08 Jun 201
A generalized Finch-Skea class one static solution
In the present article, we discuss relativistic anisotropic solutions of the
Einstein field equation for the spherically symmetric line element under the
class I condition. To do so we apply the embedding class one technique using
Eisland condition. Within this approach, one arrives at a particular
differential equation that links the two metric components and
. In order to obtain the full space-time description inside the
stellar configuration we ansatz the generalized form of metric component
corresponding to the Finch-Skea solution. Once the space-time geometry
is specified we obtain the complete thermodynamic description i.e. the matter
density , the radial, and tangential pressures and ,
respectively. Graphical analysis shows that the obtained model respects the
physical and mathematical requirements that all ultra-high dense collapsed
structures must obey. The diagram suggests that the solution yields
stiffer EoS as parameter increases. The graph is in agreement with
the concepts of Bejgar et al. \cite{bej} that the mass at is lesser
by few percent (for this solution ) from . This suggests
that the EoSs is without any strong high-density softening due to
hyperonization or phase transition to an exotic state.Comment: 14 figures, Accepted in European Physical Journal
A Chiellini type integrability condition for the generalized first kind Abel differential equation
The Chiellini integrability condition of the first order first kind Abel
equation is extended to the case of the general Abel
equation of the form , where
, and . In the case the generalized
Abel equations reduces to a Riccati type equation, for which a Chiellini type
integrability condition is obtained.Comment: 4 pages, no figure
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