References in raw/Page_88.html

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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. ...