Anecdotal experience constructing proofs of correctness of code built from reusable software components reveals that they tend to be relatively trivial bookkeeping exercises: they rarely require a substantive mathematical deduction. A careful empirical analysis of hundreds of verification conditions (VCs) for a library of component-client code shows the level of sophistication each proof requir...

Deriving gradient algorithms for time-dependent neural network structures typically requires numerous chain rule expansions, diligent bookkeeping, and careful manipulation of terms. We show, however, that an eecient gradient descent algorithm may be formulated for any network structure with virtually no eeort using a set of simple block diagram manipulation rules. Examples are provided that ill...

Spreadsheets are important business tools. Increasingly they are being used for simulation e.g. to perform risk analysis. Such tasks have far greater computational demands than traditional spreadsheet bookkeeping applications. In this paper we show how spreadsheets can support supercomputing. This is achieved without requiring the spreadsheet user to have specialist tools or knowledge. The key ...

This article seeks to determine how much we understand of Pacioli's purpose, and clarify what he wrote justifying his preparation publication ‘bookkeeping treatise’ in 1494. The context that motivated Pacioli prepare treatise is identified: why published it for whom. A new critical translation the first chapter presented, revealing statements omitted from translations, terms misunderstood. Its ...

This study expects to find and portray the attributes of extortion that happen in public area computerized time foster models use Public Area Bookkeeping forestall misrepresentation happens advanced age. The exploration was a writing survey obtained from articles as per examination point for additional investigation. outcomes showed happened incorporate utilization confusions with respect job i...

This report discusses an implementation [1] of an Adaptive Mesh Refinement (AMR) Poisson solver which solves Poisson’s equation using multigrid relaxation. Local refinement introduces several added issues. Special care has been taken to match the solution across coarse/fine interfaces so that the solution maintains global second order accuracy. The nested mesh hierarchy can be defined by the us...

With the advances in e-Sciences and the growing complexity of scientific analyses, more and more scientists and researchers are relying on workflow systems for process coordination, derivation automation, provenance tracking, and bookkeeping. Workflows are not a new concept and have been around for decades [1][3][6][7][2]. In the scientific community, several systems for scientific programming ...

This paper discusses a method for the construction of nonlinear 2D wavelet decompositions using an adaptive update lifting scheme. A very interesting aspect is that the decomposition does not require any bookkeeping, i.e., it is nonredundant, but that it, nevertheless, allows perfect reconstruction. The major ingredient of the construction is the so-called decision map which triggers the choice...