An official website of the United States government
Abstract Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.
more »
« less
Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds
In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next steps.
more »
« less
- Award ID(s):
- 1809011
- PAR ID:
- 10404630
- Date Published:
- Journal Name:
- Symmetry, Integrability and Geometry: Methods and Applications
- ISSN:
- 1815-0659
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case.more » « less
-
In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences.more » « less
-
Agrobacterium effector protein VirE2 is important for plant transformation. VirE2 likely coats transferred DNA (T-DNA) in the plant cell and protects it from degradation. VirE2 localizes to the plant cytoplasm and interacts with several host proteins. Plant-expressed VirE2 can complement a virE2 mutant Agrobacterium strain to support transformation. We investigated whether VirE2 could facilitate transformation from a nuclear location by affixing to it a strong nuclear localization signal (NLS) sequence. Only cytoplasmic-, but not nuclear-localized, VirE2 could stimulate transformation. To investigate the ways VirE2 supports transformation, we generated transgenic Arabidopsis plants containing a virE2 gene under the control of an inducible promoter and performed RNA-seq and proteomic analyses before and after induction. Some differentially expressed plant genes were previously known to facilitate transformation. Knockout mutant lines of some other VirE2 differentially expressed genes showed altered transformation phenotypes. Levels of some proteins known to be important for transformation increased in response to VirE2 induction, but prior to or without induction of their corresponding mRNAs. Overexpression of some other genes whose proteins increased after VirE2 induction resulted in increased transformation susceptibility. We conclude that cytoplasmically localized VirE2 modulates both plant RNA and protein levels to facilitate transformation.more » « less
-
Abstract Gauss–Legendre quadrature, Clenshaw–Curtis quadrature and the trapezoid rule are powerful tools for numerical integration of analytic functions. For nearly singular problems, however, these standard methods become unacceptably slow. We discuss and generalize some existing methods for improving on these schemes when the location of the nearby singularity is known. We conclude with an application to some nearly singular surface integrals that arise in three-dimensional viscous fluid flow.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3842/SIGMA.2020.104
