In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.

We develop and test new machine learning methods for the prediction of topological representations of protein structures in the form of coarseor fine-grained contact or distance maps that are translation and rotation invariant. The methods are based on generalized input-output hidden Markov models (GIOHMMs) and generalized recursive neural networks (GRNNs). The methods are used to predict topol...

Biological brains can adapt and learn from past experience. In neuroevolution, i.e. evolving artificial neural networks (ANNs), one way that agents controlled by ANNs can evolve the ability to adapt is by encoding local learning rules. However, a significant problem with most such approaches is that local learning rules for every connection in the network must be discovered separately. This pap...

In this paper another version of Gowers’ dichotomy for Banach spaces, involving topologies of special type on the Cartesian product of Banach spaces, is presented. These topologies are closely related to the game used by W. T. Gowers in his proof of the dichotomy.

We present some results about the class of Alexandroff topologies (i.e. topologies where the intersection of arbitrary many open sets is open) from the perspective obtained when they are viewed as closed subsets of the Cantor cuber 2 (the power set of X with the product topology).

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...