References in raw/Page_88.html

• Verification of fixed-point datapaths with comparator units using Constrained Arithmetic Transform (CAT)
  O Sarbishei, K Radecka - 2012 IEEE International Symposium ..., 2012 - ieeexplore.ieee.org
  Arithmetic Transform (AT) [1, 16, 17] is an efficient spectral technique, to analyze range and precision of fixed-point polynomial datapaths, among other methods including AA [4, 15] and ...
  

• One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis
  G Muscolino, A Sofi, M Zingales - Computers & Structures, 2013 - Elsevier
  ... In the context of the stochastic analysis of structures with uncertain-but-bounded parameters, following the philosophy of the affine arithmetic, Muscolino and Sofi [15] proposed an ...
  

• Quadratic Underestimators of Differentiable McCormick Relaxations for Deterministic Global Optimization
  M Wilhelm, M Stuber - 2018 AIChE Annual Meeting, 2018 - psor.uconn.edu
  We commonly encounter problems that can be described by simulations. These simulations often haven a greatly reduced problem dimension compared to problems represented ...
  

• Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems
  C Fu, Y Liu, Z Xiao - Applied Mathematical Modelling, 2019 - Elsevier
  ... To remedy this issue, several different schemes including the generalized interval analysis [27], the affine arithmetic (AA) [28], the improved interval ... An introduction to affine arithmetic ...
  

• Discrete choice in the presence of numerical uncertainties
  D Lohar, E Darulova, S Putot... - IEEE Transactions on ..., 2018 - ieeexplore.ieee.org
  ... We do this by using affine arithmetic (AA), which we describe next. ... Probabilistic Affine
  

• Differentiable abstract interpretation for provably robust neural networks
  M Mirman, T Gehr, M Vechev - International Conference on ..., 2018 - proceedings.mlr.press
  We introduce a scalable method for training robust neural networks based on abstract interpretation. We present several abstract transformers which balance efficiency with precision ...
  

• Inverse propagation of uncertainties in finite element model updating through use of fuzzy arithmetic
  YS Erdogan, PG Bakir - Engineering Applications of Artificial Intelligence, 2013 - Elsevier
  A fuzzy finite element model updating (FFEMU) method is presented in this study for the damage detection problem. The uncertainty caused by the measurement noise in modal ...
  

• Computational vector-magnitude-based range determination for scientific abstract data types
  AB Kinsman, N Nicolici - IEEE Transactions on Computers, 2010 - ieeexplore.ieee.org
  ... Note that the DetermineRanges function (line 7) is based upon existing range analysis techniques, such as affine arithmetic or the computational method from [12]. The Partition function ...
  

• Uncertain geometry with dependencies
  Y Myers, L Joskowicz - Proceedings of the 14th ACM Symposium on ..., 2010 - dl.acm.org
  ... Affine arithmetic [11] improves interval estimation by tracking round-off and truncation errors, and allows for quantity interdependence. However, the primary concern of affine arithmetic ...
  

• Minimisation of voltage fluctuation resulted from renewable energy sources uncertainty in distribution systems
  AA Abou El-Ela, RA El-Sehiemy... - IET Generation ..., 2019 - Wiley Online Library
  ... A complex affine arithmetic based load flow was presented in [21] to study the impact of uncertainty in the unbalanced distribution systems. ...