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With regard to the recently published article, ``Y.-Q. Wang, et al., Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: Analytical analyses of steady state evolving from initial state,…
We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance…
This paper has been withdrawn by the author, since now all four parts of the review are available as a single file 0804.1639. I also made some revision of the text in order to avoid misprints and some inaccurate expressions.
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…
Structured pruning compresses neural networks by reducing channels (filters) for fast inference and low footprint at run-time. To restore accuracy after pruning, fine-tuning is usually applied to pruned networks. However, too few remaining…
Versal deformation of a matrix A is a normal form to which all matrices A + E, close to A, can be reduced by similarity transformation smoothly depending on the entries of A + E. In this paper we discuss versal deformations and their use in…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
The original versions (1 and 2) of this paper paper contain a fatal error. All my attempts to patch the error have failed. As a service to the community I explain the error in some detail.
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…
Classical Bundle Adjustment (BA) is fundamentally limited by its reliance on precise metric initialization and prior camera intrinsics. While modern dense matchers offer high-fidelity correspondences, traditional Structure-from-Motion (SfM)…
In this paper, it is proved that certain stable rank-3 vector bundles can be written as extensions of line bundles and stable rank-2 bundles. As an application, we show the rationality of certain moduli spaces of stable rank-3 bundles over…
Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding functional can in turn be approximated in the sense of…
The original paper, as published in Nuclear Physics B in 1988, had a few factor-of-two errors. Some people got confused by those errors. The purpose of these errata is to make things clear. The revised version of the complete article is…
This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…
We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks,…
In section 8.3 of our paper "Duality and Flat Base Change on Formal Schemes" (http://arXiv.org/abs/alg-geom/9708006) some important results concerning localization of, and preservation of coherence by, basic duality functors, were based on…
The ability to store data in the DNA of a living organism has applications in a variety of areas including synthetic biology and watermarking of patented genetically-modified organisms. Data stored in this medium is subject to errors…
The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.
This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]