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A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
Accurate measurements of kinetic rate constants for interacting biomolecules is crucial for understanding the mechanisms underlying intracellular signalling pathways. The magnitude of binding rates plays a very important molecular…
Efficient capture and detection of minute amount of deoxyribonucleic acid (DNA) molecules are pivotal for an array of modern gene technologies which are widely utilized in medical, forensic and defense applications, including DNA…
The efficiency of water electrolysis in a photoelectrochemical cell is largely limited by the oxygen evolution reaction (OER) at its semiconductor photoanode. Reaction rate constants are key to investigating the slow kinetics of the…
Recent advances in biochemical computing, i.e., information processing with cascades of primarily enzymatic reactions realizing computing gates, such as AND, OR, etc., as well as progress in networking these gates and coupling of the…
In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The DEs are typically nonlinear and difficult to analyze,…
High-density afferents in the human hand have long been regarded as essential for human grasping and manipulation abilities. In contrast, robotic tactile sensors are typically used to provide low-density contact data, such as…
Chemical kinetics mechanisms are essential for understanding, analyzing, and simulating complex combustion phenomena. In this study, a Neural Ordinary Differential Equation (Neural ODE) framework is employed to optimize kinetics parameters…
Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…
Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles, limit cycle bifurcations and multistability. The results…
The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Organic molecules with nonlinear optical behavior have advanced a wide range of fields spanning from integrated photonics to biological imaging. With advances in microscopy, an emerging application is multifunctional nonlinear organic…
Two-dimensional (2D) materials have been used extensively in various fields due to their unique physical and chemical properties. Among their diverse applications, field-effect transistor biosensors (bio-FETs) promise a brilliant prospect…
Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate…
Dynamic optical sensors, as those based on the reflectivity of isotropic dielectrical interfaces, can be useful for measuring small changes in the refractive index of fluid media. Exact and approximated explicit formulas for their…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
A method for determination of the bimolecular recombination constant in working double-injection diodes such as organic light-emitting diodes (OLEDs) and organic photovoltaics (OPVs) using impedance spectroscopy is proposed. The proposed…