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Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches…

The design of quantum circuits is often still done manually, for instance by following certain patterns or rule of thumb. While this approach may work well for some problems, it can be a tedious task and present quite the challenge in other…

Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…

We describe modeling approaches to a "network" of connected enzyme-catalyzed reactions, with added (bio)chemical processes that introduce biochemical filtering steps into the functioning of such a biocatalytic cascade. Theoretical…

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

For simple digital circuits, conventional method of designing circuits can easily be applied. But for complex digital circuits, the conventional method of designing circuits is not fruitfully applicable because it is time-consuming. On the…

We advance here an algorithm of a synthesis of an electric circuit based on prescribed quadratic Lagrangian. That is the circuit evolution equations are equivalent to the relevant Euler-Lagrange equations. The proposed synthesis is a…

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…

This article exhibits a particular encoding of logic circuits into a sheaf formalism. The central result of this article is that there exists strictly more information available to a circuit designer in this setting than exists in static…

Logic synthesis is a crucial phase in the circuit design process, responsible for transforming hardware description language (HDL) designs into optimized netlists. However, traditional logic synthesis methods are computationally intensive,…

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…

Rule-based systems remain central in safety-critical domains but often struggle with scalability, brittleness, and goal misspecification. These limitations can lead to reward hacking and failures in formal verification, as AI systems tend…

Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding…

Genetic Programming is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use Genetic Programming to develop surrogate models to mitigate…

We present new techniques for synthesizing programs through sequences of mutations. Among these are (1) a method of local scoring assigning a score to each expression in a program, allowing us to more precisely identify buggy code, (2)…

Demonstrating quantum advantage using conventional quantum algorithms remains challenging on current noisy gate-based quantum computers. Automated quantum circuit synthesis via quantum machine learning has emerged as a promising solution,…

Many natural systems exhibit cyclo-stationary behavior characterized by periodic forcing such as annual and diurnal cycles. We present a data-driven method leveraging recent advances in score-based generative modeling to construct…

Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…

A central goal of evolutionary biology is to explain the origins and distribution of diversity across life. Beyond species or genetic diversity, we also observe diversity in the circuits (genetic or otherwise) underlying complex functional…