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Metal energy carriers recently gained growing interest in research as a promising storage and transport material for renewable electricity. Within the development of a metal-fueled circular energy economy, research involves a model…
Discrete chemical reaction networks formalize the interactions of molecular species in a well-mixed solution as stochastic events. Given their basic mathematical and physical role, the computational power of chemical reaction networks has…
We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real…
Recent research into analog computing has introduced new notions of computing real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion of computing real numbers in real-time with chemical reaction networks (CRNs), introducing the…
Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the…
The Chemical Reaction Network (CRN) is a well-studied model that describes the interaction of molecules in well-mixed solutions. In 2014, Qian and Winfree [22] proposed the abstract surface chemical reaction network model (sCRN), which…
In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…
We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism $(X,S)\twoheadrightarrow(Y,T)$, we can establish emulation by a…
Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
We show that some natural output conventions for error-free computation in chemical reaction networks (CRN) lead to a common level of computational expressivity. Our main results are that the standard consensus-based output convention have…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
The fundamental decomposition of a chemical reaction network (CRN) is induced by partitioning the reaction set into "fundamental classes". It was the basis of the Higher Deficiency Algorithm for mass action systems of Ji and Feinberg, and…
The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…
The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…
Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a…
We present a novel framework for chemical learning based on Competitive Dimerization Networks (CDNs) - systems in which multiple molecular species, e.g. proteins or DNA/RNA oligomers, reversibly bind to form dimers. We show that these…
Reaction mechanisms are often presented as sequences of elementary steps, such as codified by arrow pushing. We propose an approach for representing such mechanisms using graph transformation. In this framework, each elementary step is a…
Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as…