Related papers: On the Complexity of Quadratization for Polynomial…
Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various…
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…
From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep…
Reservoir Computing Networks (RCNs) belong to a group of machine learning techniques that project the input space non-linearly into a high-dimensional feature space, where the underlying task can be solved linearly. Popular variants of RCNs…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…
The stochastic description of chemical reaction networks with the kinetic chemical master equation (CME) is important for studying biological cells, but it suffers from the curse of dimensionality: The amount of data to be stored grows…
It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…
The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
There has been significant recent interest in quantum neural networks (QNNs), along with their applications in diverse domains. Current solutions for QNNs pose significant challenges concerning their scalability, ensuring that the…
Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the…
Molecule representation learning (MRL) methods aim to embed molecules into a real vector space. However, existing SMILES-based (Simplified Molecular-Input Line-Entry System) or GNN-based (Graph Neural Networks) MRL methods either take…
The most fundamental abstraction underlying all modern computers is the Turing Machine, that is if any modern computer can simulate a Turing Machine, an equivalence which is called Turing completeness, it is theoretically possible to…
In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
In this paper, we will introduce a novel deep model named Reconciled Polynomial Network (RPN) for deep function learning. RPN has a very general architecture and can be used to build models with various complexities, capacities, and levels…
Reaction virtual screening and discovery are fundamental challenges in chemistry and materials science, where traditional graph neural networks (GNNs) struggle to model multi-reactant interactions. In this work, we propose ChemHGNN, a…
This is an expository note on large deviations, Hamilton-Jacobi-Bellman (HJB) equations, and the role of the Freidlin-Wentzell quasipotential in Chemical Reaction Networks (CRNs). The note was motivated by observations which identified…
Quadratization for partial differential equations (PDEs) is a process that transforms a nonquadratic PDE into a quadratic form by introducing auxiliary variables. This symbolic transformation has been used in diverse fields to simplify the…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…