Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, re...

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this questio...

Chemical reaction rate and diffusion rate were defined. The concomitant advances in theory, measuring systems and computer simulation bring the new perspectives to the chemical reaction with diffusion studying. The obtained results shows effect the chemical reaction rate and diffusion. The obtained results demonstrate characterization of the dynamic and steady state conditions of the chemical s...

It is useful to have complete lists of nonisomorphic chemical reaction networks (CRNs) of a given size, with or without various restrictions. One may, for example, be interested in exploring how often certain dynamical behaviours occur in small CRNs, or wish to find examples to illustrate some aspect of the theory. In such cases, it is natural to examine one representative from each isomorphism...

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in n...

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 definition of error-free CRNs have equivalent computational power to 1) asymmetric and 2) democratic CRNs. The former have only “yes” voters, with the interpretation that the CRN’s output is yes i...

In undergoing this life, many people always try to do and get the best. New knowledge, experience, lesson, and everything that can improve the life will be done. However, many people sometimes feel confused to get those things. Feeling the limited of experience and sources to be better is one of the lacks to own. However, there is a very simple thing that can be done. This is what your teacher ...

In this paper we investigate the complexity of model selection and model testing in chemical reaction networks by formulating them as Euclidean distance problems. We determine closed form expressions for the Euclidean distance degree of the steady state varieties associated to several different families of toric chemical reaction networks with arbitrarily many reaction sites. We show how our re...

Directed hypercycles have recently been used to model chemical reaction networks. We present an NP-completeness proof for the problem of finding a hypercycle in a directed hypergraph. This sheds some light to some open questions posed by Zeigarnik [A.V. Zeigarnik, On hypercycles and hypercircuits in hypergraphs, in: Discrete Mathematical Chemistry, in: DIMACS Series in, Discrete Mathematics and...

The dynamics of bimolecular chemical reactions can be examined in liquid solutions using infrared absorption spectroscopy with picosecond time resolution. On such short time scales, the transient absorption spectra reveal vibrational mode and quantum-state-specific energy disposal, followed by vibrational relaxation as the energy is dissipated to the surrounding solvent. Comparison with energy ...