Related papers: Mathematical Modeling of General Inaccurate Adders

We consider the problem of constructing fast and small parallel prefix adders for non-uniform input arrival times. This problem arises whenever the adder is embedded into a more complex circuit, e. g. a multiplier. Most previous results are…

Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…

The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…

How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…

We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…

Trade-off is one of the main design parameters in the field of electronic circuit design. Whereas smaller electronics devices which use less hardware due to techniques like hardware multiplexing or due to smaller devices created due to…

Regression Discontinuity (RD) designs rely on the continuity of potential outcome means at the cutoff, but this assumption often fails when other treatments or policies are implemented at this cutoff. We characterize the bias in sharp and…

Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…

Algorithmic fairness research often assumes a tradeoff between fairness and accuracy. Yet this tradeoff may not be universal. We test this assumption in the context of U.S. property tax assessment - a setting in which the output of…

In this paper, a simple heuristic is proposed for the design of uncertainty aware predictive controllers for nonlinear models involving uncertain parameters. The method relies on Machine Learning-based approximation of ideal deterministic…

The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…

Statistical uncertainties complicate engineering design -- confounding regulated design approaches, and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double loop simulation; a nested…

This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…

The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…

Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…

In high-stakes automated decision-making, access to predictive uncertainty is essential for enabling users -- human or downstream systems -- to accept or reject predictions based on application-specific cost trade-offs. Such…

The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…

The conflict between stiffness and toughness is a fundamental problem in engineering materials design. However, the systematic discovery of microstructured composites with optimal stiffness-toughness trade-offs has never been demonstrated,…