Architecture-aware Precision Tuning with Multiple Number Representation Systems

2021 ◽  
Author(s):  
Daniele Cattaneo ◽  
Michele Chiari ◽  
Nicola Fossati ◽  
Stefano Cherubin ◽  
Giovanni Agosta
Keyword(s):  
Number Representation ◽  
Representation Systems

scholarly journals Novel Binary Signed-Digit Addition Algorithm for FPGA Implementation

2019 ◽  
Vol 29 (09) ◽  
pp. 2050136
Author(s):  
Yuuki Tanaka ◽  
Yuuki Suzuki ◽  
Shugang Wei
Keyword(s):  
Field Programmable Gate Array ◽  
High Speed ◽  
Number System ◽  
Logic Circuit ◽  
Fpga Implementation ◽  
Number Representation ◽  
Representation System ◽  
Representation Systems ◽  
Field Programmable ◽  
Gate Array

Signed-digit (SD) number representation systems have been studied for high-speed arithmetic. One important property of the SD number system is the possibility of performing addition without long carry chain. However, many numbers of logic elements are required when the number representation system and such an adder are realized on a logic circuit. In this study, we propose a new adder on the binary SD number system. The proposed adder uses more circuit area than the conventional SD adders when those adders are realized on ASIC. However, the proposed adder uses 20% less number of logic elements than the conventional SD adder when those adders are realized on a field-programmable gate array (FPGA) which is made up of 4-input 1-output LUT such as Intel Cyclone IV FPGA.

scholarly journals Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

Heliyon ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. e06580
Author(s):  
Berenice Rojo-Garibaldi ◽  
Costanza Rangoni ◽  
Diego L. González ◽  
Julyan H.E. Cartwright
Keyword(s):  
Number Representation ◽  
Representation Systems

An arithmetical-training regime improves number representation and broad mathematical performance

2010 ◽  
Author(s):  
Arava Y. Kallai ◽  
Andrea L. Ponting ◽  
Christian D. Schunn ◽  
Julie A. Fiez
Keyword(s):  
Number Representation ◽  
Mathematical Performance

Neural Underpinnings of Numerical and Spatial Cognition: An fMRI Meta-Analysis of Brain Regions Associated with Symbolic Number, Arithmetic, and Mental Rotation

2019 ◽  
Author(s):  
Zachary Hawes ◽  
H Moriah Sokolowski ◽  
Chuka Bosah Ononye ◽  
Daniel Ansari
Keyword(s):  
Mental Rotation ◽  
Parietal Lobe ◽  
Meta Analysis ◽  
Likelihood Estimation ◽  
Brain Regions ◽  
Angular Gyrus ◽  
Number Representation ◽  
Neural Underpinnings ◽  
The Right ◽  
Symbolic Number

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger
Keyword(s):  
Sixth Grade ◽  
Number Line ◽  
Number Representation ◽  
Large Numbers ◽  
Position Task ◽  
Sigmoidal Curve ◽  
Anchor Points ◽  
The Right ◽  
Line P ◽  
Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

Default Logic Models of Certain Inheritance Systems with Exceptions

1993 ◽  
Vol 18 (2-4) ◽  
pp. 129-149
Author(s):  
Serge Garlatti
Keyword(s):  
Hierarchical Structure ◽  
Formal Semantics ◽  
Sufficient Conditions ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Representation Systems ◽  
The Hierarchical Structure ◽  
Necessary And Sufficient ◽  
Structure Of Knowledge ◽  
Made In

Representation systems based on inheritance networks are founded on the hierarchical structure of knowledge. Such representation is composed of a set of objects and a set of is-a links between nodes. Objects are generally defined by means of a set of properties. An inheritance mechanism enables us to share properties across the hierarchy, called an inheritance graph. It is often difficult, even impossible to define classes by means of a set of necessary and sufficient conditions. For this reason, exceptions must be allowed and they induce nonmonotonic reasoning. Many researchers have used default logic to give them formal semantics and to define sound inferences. In this paper, we propose a survey of the different models of nonmonotonic inheritance systems by means of default logic. A comparison between default theories and inheritance mechanisms is made. In conclusion, the ability of default logic to take some inheritance mechanisms into account is discussed.

Presidentialism and the Effect of Electoral Law in Postcommunist Systems

2005 ◽  
Vol 38 (2) ◽  
pp. 171-188 ◽  
Author(s):  
Terry D. Clark ◽  
Jill N. Wittrock
Keyword(s):  
Party System ◽  
Electoral Systems ◽  
New Democracies ◽  
Representation Systems ◽  
Legislative Agenda ◽  
Majority Control ◽  
Election Results ◽  
Duverger's Law ◽  
Electoral Law ◽  
Mixed Systems

Efforts to test Duverger’s law in the new democracies of postcommunist Europe have had mixed results. Research argues that mixed systems have an effect on the number of effective parties that is distinct from that of single-mandate district and proportional representation systems. Less attention has been given to the effect of other institutions on the party system, particularly strong presidents. Analyzing election results in postcommunist Europe, the authors find support for Duverger’s law after controlling for the strength of the executive. They argue that strong presidents substantially reduce the incentive for parties to seize control of the legislative agenda. Hence, the restraint that electoral systems exercise on the proliferation of parties and independent candidates is weakened. The authors find that a further consequence of strong presidents is that the incentive for majority control of committees and the legislative agenda is weakened.

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