Toward New Vision in Teaching Calculus

Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the prior fear of mathematics. The students today cant live without using computer technology. The uses of computer for teaching and learning can transform the boring traditional methodology of teach to more active and attractive method. In this paper, we will show how we can use Excel in teaching calculus to improve our students learning and understanding through different types of applications ranging from Business to Engineering. The effectiveness of the proposed methodology was tested on a random sample of 45 students from different majors over a period of two semesters.Comment: IERI Procedia, Elsevier. 201

Asymptotic vacua with higher derivatives

We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.Comment: v2: 17 pages, new author added, various improvements, new results on asymptotic stability of ekpyrosis, to appear in Phys. Lett.

Off-chain Transaction Routing in Payment Channel Networks: A Machine Learning Approach

Blockchain is a foundational technology that has the potential to create new prospects for our economic and social systems. However, the scalability problem limits the capability to deliver a target throughput and latency, compared to the traditional financial systems, with increasing workload. Layer-two is a collective term for solutions designed to help solve the scalability by handling transactions off the main chain, also known as layer one. These solutions have the capability to achieve high throughput, fast settlement, and cost efficiency without sacrificing network security. For example, bidirectional payment channels are utilized to allow the execution of fast transactions between two parties, thus forming the so-called payment channel networks (PCNs). Consequently, an efficient routing protocol is needed to find the payment path from the sender to the receiver, with the lowest transaction fees. This routing protocol needs to consider, among other factors, the unexpected online/offline behavior of the constituent payment nodes as well as payment channel imbalance. This study proposes a novel machine learning-based routing technique for fully distributed and efficient off-chain transactions to be used within the PCNs. For this purpose, the effect of the offline nodes and channel imbalance on the payment channels network are modeled. The simulation results demonstrate a good tradeoff among success ratio, transaction fees, routing efficiency, transaction overhead, and transaction maintenance overhead as compared to other techniques that have been previously proposed for the same purpose