We introduce the Non-commutative Subset Convolution – a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. We prese...

One of the key objectives of Universal Mobile Telecommunications System (UMTS) is the realization of enhanced end-user experience through the provision of rich multimedia services, ensuring in parallel an economical delivery cost for service providers. Multimedia Broadcast/Multicast Services (MBMS) framework of UMTS epitomizes the increasing popularity of such applications by efficiently delive...

Aggregation against distinct objects has been involved in many real applications with the presence of duplicates, including real-time monitoring moving objects. In this paper, we investigate the problem of counting distinct objects over sliding windows with arbitrary lengths. We present novel, time and space efficient, one scan algorithms to continuously maintain a sketch so that the counting c...

An algorithm for recognizing banknotes is required in many fields, such as banknote-counting machines and automatic teller machines (ATM). Due to the size and cost limitations of banknote-counting machines and ATMs, the banknote image is usually captured by a one-dimensional (line) sensor instead of a conventional two-dimensional (area) sensor. Because the banknote image is captured by the line...

This study provided a longitudinal assessment of skill development in addition for 26 normal and 12 mathematically disabled firstor second-grade children. At the first time of measurement, the children solved 40 simple addition problems. Ten months later, all subjects were readministered the addition task and a measure of working memory resources. Across times of measurement, the normal group s...

In this paper we propose an easy algorithm for real time hand finger counting involving one or more than one hand. Hand finger counting is a simple medium for Human-Computer Interface which can prove to be a convenient input method for driving interactive menus, small applications and interactive games. Here, we also calculate the orientation of the hand which can be used to provide inputs for ...

We introduce the Non-commutative Subset Convolution – a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. We prese...

Several researchers have proposed that skilled adults may solve single-digit addition problems (e.g. 3+1=4, 4+3=7) using a fast counting procedure. Practicing a procedure often leads to transfer of learning and faster performance of unpracticed items. Such transfer has been demonstrated using a counting-based alphabet arithmetic task (e.g., B+4 = C D E F) that indicated robust RT gains when unt...

Non linear devices such as amplifiers and electro-optical transducers introduce spurious signals known as intermodulations, especially when multiple signals at different frequencies access the system. In this paper an extension to the well known Fast Counting Algorithm (FCA) for the intermodulations is presented and a comparison with slow counting algorithms is done. Carrier configuration is re...