Related papers: "On the engineers' new toolbox" or Analog Circuit …
Quantum process tomography (QPT) is a fundamental tool for fully characterizing quantum systems. It relies on querying a set of quantum states as input to the quantum process. Previous QPT methods typically employ a straightforward strategy…
In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…
Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of…
This thesis proposes novel ternary circuits aiming to reduce energy to preserve battery consumption. The proposed designs include eight ternary logic gates, three ternary combinational circuits, and six Ternary Arithmetic Logic Units. This…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
This is a review paper updated from that presented for CAS 2004. Essentially, since then, commercial components have continued to extend their performance boundaries but the basic building blocks and the techniques for choosing the best…
Analog circuit topology synthesis is integral to Electronic Design Automation (EDA), enabling the automated creation of circuit structures tailored to specific design requirements. However, the vast design search space and strict constraint…
This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…
The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Analog IC design is a bottleneck due to its reliance on experience and inefficient simulations, as traditional formulas fail in advanced nodes. Applying Large Language Models (LLMs) directly to this problem risks mere "guessing" without…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
Analog and mixed-signal circuit design remains challenging due to the shortage of high-quality data and the difficulty of embedding domain knowledge into automated flows. Traditional black-box optimization achieves sampling efficiency but…
The automatic synthesis of analog circuits presents significant challenges. Most existing approaches formulate the problem as a single-objective optimization task, overlooking that design specifications for a given circuit type vary widely…
We construct a completely analog framework that emulates universal quantum gates and quantum algorithms. It is based on electronic circuits made of operational amplifiers, resistors and capacitors. In these circuits, input and output lines…