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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,…
This paired article aims to develop an automated and programmable biochemical fully connected neural network (BFCNN) with solid theoretical support. In Part I, a concrete design for BFCNN is presented, along with the validation of the…
Prediction of complete step-by-step chemical reaction mechanisms (CRMs) remains a major challenge. Whereas the traditional approaches in CRM tasks rely on expert-driven experiments or costly quantum chemical computations, contemporary deep…
We present a uniform method for translating an arbitrary nondeterministic finite automaton (NFA) into a deterministic mass action input/output chemical reaction network (I/O CRN) that simulates it. The I/O CRN receives its input as a…
This paper studies the (discrete) \emph{chemical reaction network (CRN)} computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under…
We prove that functions over the reals computable in polynomial time can be characterised using discrete ordinary differential equations (ODE), also known as finite differences. We also provide a characterisation of functions computable in…
While the treatment of chemically relevant systems containing hundreds or even thousands of electrons remains beyond the reach of quantum devices, the development of quantum-classical hybrid algorithms to resolve electronic correlation…
In this work, we propose a general inversion framework to non-uniquely invert a very large class of ordinary differential equations (ODEs) into chemical reaction networks. A thorough treatment of the relevant chemical reaction network…
Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet,…
Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is…
Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability…
Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A…
Inferring chemical reaction networks (CRN) from concentration time series is a challenge encouragedby the growing availability of quantitative temporal data at the cellular level. This motivates thedesign of algorithms to infer the…
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning…
Elementary function operations such as sin and exp cannot in general be computed exactly on today's digital computers, and thus have to be approximated. The standard approximations in library functions typically provide only a limited set…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this…