Related papers: O'Mega: An Optimizing Matrix Element Generator
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem was that of Brent and Kung (1978). Recently, we improved…
Capacity is an important tool in decision-making under risk and uncertainty and multi-criteria decision-making. When learning a capacity-based model, it is important to be able to generate uniformly a capacity. Due to the monotonicity…
Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach…
We present an open architecture for just-in-time code generation and dynamic code optimization that is flexible, customizable, and extensible. While previous research has primarily investigated functional aspects of such a system,…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The 'Quantum Product Algorithm' (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations…
Recently, program autotuning has become very popular especially in embedded systems, when we have limited resources such as computing power and memory where these systems run generally time-critical applications. Compiler optimization space…
The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated…
Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
The implementation of adaptive genetic algorithms (AGA) for optimization problems has proven to be superior than many other methods due to its nature of producing more robust and high quality solutions. Considering the complexity involved…
One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a micro-genetic…
This article presents two novel algorithms for generating random increasing trees. The first algorithm efficiently generates strictly increasing binary trees using an ad hoc method. The second algorithm improves the recursive method for…
The quality of mesh generation has long been considered a vital aspect in providing engineers with reliable simulation results throughout the history of the Finite Element Method (FEM). The element extraction method, which is currently the…
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…
A computer program has been developed which generates Feynman graphs automatically for scattering and decay processes in non-Abelian gauge theory of high-energy physics. A new acceleration method is presented for both generating and…
A basis of $N^2$ projectors, each an ${N^2}\times{N^2}$ matrix with constant elements, is implemented to construct a class of braid matrices $\hat{R}(\theta)$, $\theta$ being the spectral parameter. Only odd values of $N$ are considered…
Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…