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Functional Complexity Based on Topology (Hildegard Meyer-Ortmanns) Connections between Artificial Intelligence, Computational Complexity and the Complexity of Graphs (Angel Garrido) Selection Based Estimates of Complexity Unravel Some Mechanisms and Selective Pressures Underlying the Evolution of Complexity in Artificial Networks (Herve Le Nagard, Olivier Tenaillon) Three Types of Network Complexity Pyramid (Fang Jin-Qing, Li Yong, Liu Qiang) Computational Complexity of Graphs (Stasys Jukna) The Linear Complexity of a Graph (David L. Neel, Michael E. Orrison) Kirchhoff's Matrix Tree Theorem revisited: Counting Spanning Trees with the Quantum Relative Entropy (Vittorio Giovannetti, Simone Severini) Dimension Measure for Complex Networks (O. Shanker) Information Based Complexity of Networks (Russell K. Standish) Thermodynamic Depth in Undirected and Directed Networks (Francisco Escolano, Edwin R. Hancock) Circumscribed Complexity in Ecological Networks (Robert E. Ulanowicz) Metros as Biological Systems: Complexity in Small Real-life Networks (Sybil Derrible)

Purpose Nursing processes are complex and include quite a few nonlinear interrelationships that are difficult to discover. Moreover, the formal description, visualization, and analysis of these processes are nontrivial challenges. The purpose of this paper is to establish the term network nursing as synonym for using quantitative graph theory in nursing science and to discuss how network nursing can be used for tackling such complex challenges in nursing science. Methods In particular, methods from quantitative graph theory, divided into two major classes, comparative network analysis and network characterization, are employed to solve challenging problems in nursing. Findings We demonstrate by way of example that this mathematical apparatus is feasible to tackle research questions when modeling and analyzing nursing processes. Here we use a “NANDA-I” showcase to illustrate how nursing networks can be derived from nursing data and how these networks can be used to compare different patients regarding their nursing diagnoses. Conclusions Nursing networks can be used to characterize patients from a nursing perspective. Especially, they allow a process-based view and are able to map relationships or dependencies. One major advantage of a networking approach is that it can be applied independently from the underlying nursing classifications or terminologies. Implications for Nursing Practice Network nursing makes it possible to formally investigate the nursing process and thus opens up a so far little-known cosmos of possibilities and methods to expand nursing knowledge.

Control of Type I Error Rates for Oncology Biomarker Discovery with High-throughput Platforms (Jeffrey Miecznikowski, Dan Wang, Song Liu) Discovery of Expression Signatures in Chronic Myeloid Leukemia by Bayesian Model Averaging (Ka Yee Yeung) Bayesian Ranking and Selection Methods in Microarray Studies (Hisashi Noma, Shigeyuki Matsui) Multi-class Classification via Bayesian Variable Selection with Gene Expression Data (Yang Aijun, Song Xinyuan, Li Yunxian) Colorectal Cancer and its Molecular Subsystems: Construction, Interpretation, and Validation (Vishal N. Patel, Mark R. Chance) Semi-Supervised Methods for Analyzing High-Dimensional Genomic Data (Devin C. Koestler) Network Medicine: Disease Genes in Molecular Networks (Sreenivas Chavali, Kartiek Kanduri) Inference of Gene Regulatory Networks in Breast and Ovarian Cancer by Integrating Different Genomic Data (Binhua Tang, Fei Gu, Victor X. Jin) Network Module Based Approaches in Cancer Data Analysis (Guanming Wu, Lincoln D. Stein) Discriminant and Network Analysis to Study Origin Of Cancer (Yue Wang, Li Chen, Ye Tian, Guoqiang Yu, David J. Miller, Ie-Ming Shih) Intervention and Control of Gene Regulatory Net-Works: Theoretical Framework and Application to Human Melanoma Gene Regulation (Nidhal Bouaynaya, Roman Shterenberg, Dan Schonfeld, Hassan M. Fathallah-Shaykh) Identification of Recurrent DNA Copy Number Aberrations in Tumors (Vonn Walter, Andrew B. Nobel, D. Neil Hayes, Fred A. Wright) The Cancer Cell, its Entropy, and High-Dimensional Molecular Data (Wessel N. van Wieringen, Aad W. van der Vaart) Overview of Public Cancer Databases, Resources and Visualization Tools (Frank Emmert-Streib, Ricardo de Matos Simoes, Shailesh Tripathi, Matthias Dehmer)

Introduction to DNA Microarrays Comparative Analysis of Clustering Methods for Microarray Data Finding Verified Edges in Genetic/Gene Networks: Bilayer Verification for Network Recovery in the Presence Computational Inference of Biological Causal Networks - Analysis of Therapeutic Compound Effects Reverse Engineering Gene Regulatory Networks with Various Machine Learning Methods Statistical Methods for Inference of Genetic Networks and Regulatory Modules A Model of Genetic Networks with Delayed Stochastic Dynamics Probabilistic Boolean Networks as Models for Gene Regulation Structural Equation for Identification of Genetic Networks Detecting Pathological Pathways of a Complex Disease by a Comparative Analysis of Networks Predicting Functional Modules Using Microarray and Protein Interaction Data Computational Reconstruction of Transcriptional Regulatory Modules of the Yeast Cell Cycle Pathway-Based Methods for Analyzing Microarray Data The Most Probable Genetic Interaction Networks Inferred from Gene Expression Patterns

In the last decade, physics has been expanding to new research areas. In particular, life-related sciences (ecology, sociology, economics, and last but not least biology) have been showing striking analogies with complex systems arising from various physical areas. Such an approach has happened from both fronts: on the life sciences side, huge amounts of data have become available for detailed analysis, thanks also to the Internet, through which these data are nowadays easily collectable and queryable (e.g., stock market financial series, tables of social relationships from movie copart- nerships to e-mail fluxes, high-throughput biological data). On the other side, many physical and mathematical tools that had proven useful in explaining complex phenomena like polymer growth or spin glasses began to spread to other research areas like biological and social sciences in a broad sense. The common trait of these research fields can be found in the framework of network theory, such that focusing on the relationships among elements allows us to draw general conclusions even though the details of the system are not completely known or easily tractable from a mathematical point of view. Relaxing attention to the details of the specific interaction or element, network theory aims to provide tools for the characterization of a set of relationships, represented as edges or links, occurring among similar elements, referred to as vertices or nodes.