The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulat...

Customizing the precision of data can provide attractive trade-offs between accuracy and hardware resources. We propose a novel form of vector computing aimed at arrays of custom-precision floating point data. We represent these vectors in bitslice format. Bitwise instructions are used to implement arithmetic circuits in software that operate on customized bit-precision. Experiments show that t...

We consider logics on Z and N which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on Z and N which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by adding modulo and threshold counting predicates. 1991 Mathematics Subject Classification. 03B10, 68...

Recently, Grynkiewicz et al. [Israel J. Math. 193 (2013), 359–398], using tools from additive combinatorics and group theory, proved necessary and sufficient conditions under which the linear congruence a1x1+ · · ·+akxk ≡ b (mod n), where a1, . . . , ak, b, n (n ≥ 1) are arbitrary integers, has a solution 〈x1, . . . , xk〉 ∈ Z k n with all xi distinct modulo n. So, it would be an interesting pro...

This paper draws on findings from a study conducted in seven primary schools in Seychelles about pupils’ proficiency in one-step arithmetic word problems to discuss the roles of semantic structures of the problems on the pupils’ ability to identify the operation required to solve them. A sample of 530 pupils drawn from Primary 4, 5 and 6 responded to a 52 multiple choice item test in which they...

The main issue in this thesis is to minimize the energy consumption per operation for the arithmetic parts of DSP circuits, such as digital filters. More specific, the focus is on singleand multiple-constant multiplication using serial arithmetic. The possibility to reduce the complexity and energy consumption is investigated. The main difference between serial and parallel arithmetic, which is...

In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qmarithmetic one-to-one corresponds to decidable ...

Our algorithm combines the Reverse Polish Notation (RPN) and expression tree algorithms it is a novel method for efficiently evaluating arithmetic expressions. The benefits of Expression Trees to provide practical efficient solution expressions in both infix postfix notation. first converts notation RPN, which then used construct an tree. evaluated using recursive function that traverses perfor...

⎯The convergence of genetic algorithm is mainly determined by its core operation crossover operation. When the objective function is a multiple hump function, traditional genetic algorithms are easily trapped into local optimum, which is called premature convergence. In this paper, we propose a new genetic algorithm with improved arithmetic crossover operation based on gradient method. This cro...

BACKGROUND Calculation deficits are a common early manifestation of Alzheimer disease (AD). OBJECTIVE To investigate oral and written calculation skills in AD patients using quantitative and qualitative methods. DESIGN Comparison among controls, patients with mild AD, and patients with moderate AD on measures of arithmetic skill. SETTING Tertiary care university medical center. PARTICIP...