One way of improving efficiency of Gentry’s fully homomorphic encryption from ideal lattices is controlling the number of operations, but our recollection is that any scheme which controls the bound has not proposed. In this paper, we propose a key generation algorithm for Gentry’s scheme that controls the bound of the circuit depth by using the relation between the circuit depth and the eigenv...

previous studies involving the ideal observer, the task considered has been that detection where it is assumed that there is complete a priori knowledge of the and of the possible object's shape, amplitude, and position. It is shown that the detection task to include the possibility of an unknown, slowly varying back._ _ ground reduces the importance of the low-frequency components in the image...

The object people perceive in an image can depend on its orientation relative to the scene it is in (its reference frame). For example, the images of the symbols × and + differ by a 45 degree rotation. Although real scenes have multiple images and reference frames, psychologists have focused on scenes with only one reference frame. We propose an ideal observer model based on nonparametric Bayes...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

In this paper, we present a new approach for computing normal forms in the quotient algebra A of a polynomial ring R by an ideal I. It is based on a criterion, which gives a necessary and suucient condition for a projection onto a set of polynomials, to be a normal form modulo the ideal I. This criterion does not require any monomial ordering and generalizes the Buchberger criterion of S-polyno...

We study computational aspects of the tight closure of a homogeneous primary ideal in a two-dimensional normal standard-graded domain. We show how to use slope criteria for the sheaf of syzygies for generators of the ideal to compute its tight closure. In particular, our method gives an algorithm to compute the tight closure of three elements under the condition that we are able to compute the ...

We re-examine a fixed-point algorithm proposed by Hyvarinen for independent component analysis, wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix. Here, we derive step-size bounds which ensure monotonic convergence to a local extremum for any initial condition. Our analysis does not assume an ideal signal model but appeals rather to pro...

We show that certain matrix approximation problems in the matrix 2-norm have uniquely defined solutions, despite the lack of strict convexity of the matrix 2-norm. The problems we consider are generalizations of the ideal Arnoldi and ideal GMRES approximation problems introduced by Greenbaum and Trefethen [SIAM J. Sci. Comput., 15 (1994), pp. 359–368]. We also discuss general characterizations ...

This article presents a novel adaptive bilateral control scheme for obtaining ideal responses for teleoperation systems with uncertainties. A condition that is equivalent to getting an ideal response in teleoperation has been found to be making the closed-loop dynamics of master and slave manipulators a similar form. An adaptive approach is applied to achieve similarity for the uncertain master...