Related papers: Polynomial Methods for Ensuring Data Integrity in …
The method of two-dimensional control and assurance of data integrity with the possibility of their recovery for information systems operating under conditions of random errors as well as errors generated through deliberate actions of the…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
Data gaps are ubiquitous in spectral irradiance data, and yet, little effort has been put into finding robust methods for filling them. We introduce a data-adaptive and nonparametric method that allows us to fill data gaps in…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
Blockchain systems rely on decentralized ledgers and strong security guarantees. A key requirement is non-repudiation, which prevents denial of transaction authorship and supports integrity of recorded data. This work surveys digital…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
Maintaining data consistency among multiple parties requires nodes to repeatedly send data to all other nodes. For example, the nodes of a blockchain network have to disseminate the blocks they create across the whole network. The…
In this paper, we address the problem of secure distributed computation in scenarios where user data is not uniformly distributed, extending existing frameworks that assume uniformity, an assumption that is challenging to enforce in data…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…
Much research has been conducted to securely outsource multiple parties' data aggregation to an untrusted aggregator without disclosing each individual's data, or to enable multiple parties to jointly aggregate their data while preserving…
Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…