In this paper, two structural results concerning low degree polynomials over finite fields are given. The first states that over any finite field F, for any polynomial f on n variables with degree d ≤ log(n)/10, there exists a subspace of F with dimension Ω(d·n1/(d−1)) on which f is constant. This result is shown to be tight. Stated differently, a degree d polynomial cannot compute an affine di...

let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

Statistical Learning Theory is commonly regarded as a sound framework within which we handle a variety of learning problems in presence of small size data samples. It has become a rapidly progressing research area in machine learning. The theory is based on real random samples and as such is not ready to deal with the statistical learning problems involving complex fuzzy random samples, which w...

Different methods have been experimented for processing and detecting forgery in digital images. Image forgery involves various activities like copy-move forgery, image slicing, retouching, morphing etc. In copy-move forgery a portion within the image is copied and pasted on another part of the same image, generally to conceal or enhance certain portions of the image. This paper proposes a copy...

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with controllable dimension by making use of the Kaplan-Yo...

In this lecture we address some limitations of the analysis of Occam algorithms that limit their applicability. We first discuss the case where the target concept c is not in H which is known as the non-realizable case and as agnostic PAC learning. We then turn to the case where the number of examples m is fixed (i.e., we cannot ask for more examples as in the standard PAC model) and consider h...

Purpose: The quality of education and research is one of the concerns that academic systems always strive to achieve. Undoubtedly, the existence of leading professors with appropriate scientific and ethical competencies is one of the effective fundamental factors in the quality of higher education systems. Methodology: The general purpose of the present study is to examine the dimensions of le...

2014 The rationalistic denotational approach to semantics is not adequate for capturing the structural dimension of meaning, which is immanent in semiotic systems. The demand for a structural approach to semantics is intensified by a turn in Artificial Intelligence, introduced by Connectionism and Information Retrieval. This paper presents such a structural approach to semantics founded on the ...