We show that the (2 × 2)-subpermanents of a generic matrix generate an ideal whose height, unmixedness, primary decomposition, the number and structure of the minimal components, resolutions, radical, integral closure and Gröbner bases all depend on the characteristic of the underlying subfield: if the characteristic of the subfield is two, this ideal is the determinantal ideal for which all of...

Detection of intensity flashes in the blowfly photoreceptor is limited by photon noise in the input signal as well as noise contributed by transduction components within the photoreceptor. Our analysis uses an ideal observer and a model of blowfly phototransduction to compute the threshold for optimal detection of intensity flashes as background intensity varies. We find that detection threshol...

Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was later improved by Langlois, Stehlé and Steinfeld who proposed GGHLite which offers smaller parameter sizes. In this work, we provide the first implementation of such approximate multilinear maps based ...

Let R be a Noetherian ring and I an ideal. We prove that there exists an integer k such that for all n ≥ 1 there exists an irredundant primary decomposition I = q1 ∩ · · · ∩ ql such that √ qi nk ⊆ qi whenever ht (qi/I) ≤ 1. In particular, if R is a local ring with maximal ideal m and I is a prime ideal of dimension 1, then mI ⊆ I, where I denotes the n’th symbolic power of I . We study some asy...

BACKGROUND We hypothesized that the American Heart Association's metric of ideal cardiovascular health (CVH) predicts improved long-term functional status after adjusting for incident stroke and myocardial infarction. METHODS AND RESULTS In the prospective, multiethnic Northern Manhattan Study, stroke-free individuals in northern Manhattan aged ≥40 years had annual assessments of the primary ...

the concept of  -semihyperring is a generalization of semiring, a generalization of semihyperring and a generalization of      -semiring. since the theory of ideals plays an important role in the theory of  - semihyperring, in this paper, we will make an intensive study of the notions of noetherian, artinian, simple and   regular      -semihyperrings. the bulk of this paper...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...