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BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly…
Counterfeiting threatens human health, social equity, national security and global and local economies. Hardware-based cryptography that exploits physical unclonable functions (PUFs) provides the means for secure identification and…
Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn-Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…
Function association is a useful process for binary reverse engineers. Search tools exist to perform association at scale, but they do not utilize the full range of capabilities that AI-enabled search provides. Prior work has explored the…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
We have assessed mechanical bending as a powerful controlling tool for the electronic structure and optical properties of phosphorene nanoribbons. We use state-of-the-art density functional approximations in our work. The overall…
In the "Big Data" era, a lot of data must be processed and moved between processing and memory units. New technologies and architectures have emerged to improve system performance and overcome the memory bottleneck. The memristor is a…
A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…
Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain…
Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of…
Design exploration is an important step in the engineering design process. This involves the search for design/s that meet the specified design criteria and accomplishes the predefined objective/s. In recent years, machine learning-based…
Permutation equivariant neural networks employing parameter-sharing schemes have emerged as powerful models for leveraging a wide range of data symmetries, significantly enhancing the generalization and computational efficiency of the…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
Approximate functional dependencies (AFDs) are functional dependencies (FDs) that "almost" hold in a relation. While various measures have been proposed to quantify the level to which an FD holds approximately, they are difficult to compare…
Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. Quick generation of high-quality interatomic potentials is of urgent need under present circumstances,…
The logarithmic and anti-logarithmic converters are realized with the piecewise linear approximation method, which is implemented by the shift-and-add architecture. This brief utilizes the similarities of Log and Antilog functions so that…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously…