Topological Space

"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and properties, dynamic properties, and functionality-topology relationship, etc. There are some common mathematical foundations, theories and methodology for network analysis, in which graph theory, statistics, and operational research, etc., are the fundamental sciences of network analysis. Various emerging biological networks, at both micro- and macro- levels, will provide numerous sources for the development of general network theory and methodology and also facilitate the development of theory and methodology of biological networks.

Biological network analysis is a fast moving science. Many core scientific issues, for example, ecological structure, co-evolution, co-extinction and biodiversity conservation in ecology, and cancer development and metabolic regulation in health science, etc., are expected to be addressed by network approaches and network analysis. Network analysis is becoming the core methodology to treat complex biological systems. As the fast development of this area, more and more papers on biological networks are published.

At present explosive numbers of quality papers on biological networks are being published each year. The initiation of the journal, Network Biology, will provide a public and unified platform for the publication of these studies. From this integrated and unique journal, researchers, university teachers and students will thoroughly have an in-depth and complete insight on knowledge, methodology and recent advances of biological networks.

In the view of system dynamics, biological networks are always self-organized systems with emergent, autonomous and adaptive properties. Their dynamics can be represented by agent-based modeling, individual-based modeling and some other methodologies like neural network modeling. Therefore, agent-based modeling, individual-based modeling, self-organization of biological systems, and neural network modeling, etc., fall into the aims and scope of the journal, Network Biology.

The NETWORK BIOLOGY (ISSN 2220-8879) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of network biology. It is the transactions of the International Society of Network Biology.It dedicates to the latest advances in network biology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Network Biology include, but are not limited to:

•Theories, algorithms and programs of network analysis
•Innovations and applications of biological networks
•Dynamics, optimization and control of biological networks
•Ecological networks, food webs and natural equilibrium
•Co-evolution, co-extinction, biodiversity conservation
•Metabolic networks, protein-protein interaction networks, biochemical reaction networks, gene networks, transcriptional regulatory networks, cell cycle networks, phylogenetic networks, network motifs
•Physiological networks
•Network regulation of metabolic processes, human diseases and ecological systems
•Social networks, epidemiological networks
•System complexity, self-organized systems, emergence of biological systems, agent-based modeling, individual-based modeling, neural network modeling, and other network-based modeling, etc.
We are also interested in short communications that clearly address a specific issue or completely present a new ecological network, food web, or metabolic or gene network, etc.

Authors can submit their works to the email box of this journal, [email protected]. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts.

In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue.

Network Biology 
ISSN 2220-8879
URL: http://www.iaees.org/publications/journals/nb/online-version.asp
RSS feed: http://www.iaees.org/publications/journals/nb/rss.xml
E-mail: [email protected]
Editor-in-Chief: WenJun Zhang"

In this paper we introduce the classical form of Z-continuous functions under the fuzzy setting in the name of "Fuzzy Z-Pre-continuous functions in Fuzzy Topological Spaces". A weaker form of fuzzy Z-continuous function, called fuzzy Z-pre-continuous function is introduced and its properties and characterizations are discussed.

Overlap algebras are complete lattices enriched with an extra primitive relation, called ''overlap''. The new notion of overlap relation satisfies a set of axioms intended to capture, in a positive way, the properties which hold for two elements with non-zero infimum. For each set, its powerset is an example of overlap algebra where two subsets overlap each other when their intersection is inhabited. Moreover, atomic overlap algebras are naturally isomorphic to the powerset of the set of their atoms. Overlap algebras can be seen as particular open (or overt) locales and, from a classical point of view, they essentially coincide with complete Boolean algebras. Contrary to the latter, overlap algebras offer a negation-free framework suitable, among other things, for the development of pointfree topology. A lot of topology can be done ''inside'' the language of overlap algebra. In particular, we prove that the collection of all regular open subsets of a topological space is an example of overlap algebra which, under natural hypotheses, is atomless. Since they are a constructive counterpart to complete Boolean algebras and, at the same time, they have a more powerful axiomatization than Heyting algebras, overlap algebras are expected to turn out useful both in constructive mathematics and for applications in computer science.

In 1883 Arzelà (1983Arzelà ( /1984 [2] gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued continuous functions on a compact interval to be continuous. Arzelà's work paved the way for several outstanding papers. A milestone was the P.S. Alexandroff convergence introduced in 1948 to tackle the question for a sequence of continuous functions from a topological space (not necessarily compact) to a metric space. In 2009, in the realm of metric spaces, Beer and Levi (2009) [10] found another necessary and sufficient condition through the novel notion of strong uniform convergence on finite sets. We offer a direct proof of the equivalence of Arzelà, Alexandroff and Beer-Levi conditions. The proof reveals the internal gear of these important convergences and sheds more light on the problem. We also study the main properties of the topology of strong uniform convergence of functions on bornologies, initiated in Beer and Levi (2009) [10].