We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Introduction to linear and nonlinear programming

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

http://romisatriawahono.net/lecture/rm/survey/softcomputing/Boussaid%20-%20Optimization%20Metaheuristics%20-%202013.pdf

A survey on optimization metaheuristics

高等学校計算数学学報 = Numerical mathematics

The importance of communication networks increases with every new system and over the last 20 years these networks have become a critical infrastructure like the electricity network. Besides all cables and connections, the core of these networks are the information transfer systems with routers and switches. To guarantee the availability of these systems resilience is needed. The present paper evaluates possibilities to ensure resilience by the training for IT-Experts. For this purpose, typical errors and the way to fix these failures are inspected. A concept for combining the simulation of failures in systems and the mean time to restore (MTTR) was developed. Related to the information provided by the simulation, the concept was extended by details about the experts training level to specify the MTTR. Our approach is a possible way for providing information related to the field of training in context between experience and computer-generated information. Goal of our work is to enlarge the resilience of systems in critical infrastructures like communication networks by drawing conclusions about the IT-Experts training.

Analysis and Optimization of the Resilience Enhancement Circle via Data Farming

According to our System Dynamics model for international emissions trading the price of permits differs strongly between different countries as a function of national economic structure. A fair international emissions trading can only be conducted with the use of protective duties. A comparatively high price which evokes emission reduction inevitably has an inhibiting effect on economic growth.

International Emissions Trading: A Pricing Model Based on System Dynamical Simulations

When analyzing complex networks, statistical techniques such as resampling [15], bootstrapping [40], randomization [46] have been proven useful. For instance, typical network structures represent technical networks, biological networks, and social networks. Technical networks appear for example in communication technology, transportation, and energy. In computational biology, several biological networks such as gene networks have been investigated. Emmert-Streib et al. [16, 8] found that biological networks are often non-deterministic, that means they cannot be inferred deterministically. Therefore statistical methods to analyze such networks have been crucial, see [16, 8]. In complex network analysis, there are several problems to deal with. For example, it has been challenging to collect network data properly such that statistical methods become applicable. Another problem that has been often demanding relates to visualize and analyze networks meaningfully [17]. To analyze networks, structural graph measures have been often used, see, e.g., see [16, 8]. Examples are the clustering coefficient, cohesion measures, connectivity measures and other topological indices to map graphs to real numbers [10]. The latter method relates to determine the complexity of networks. By employing statistical methods, important applications in network theory such as subgraph sampling and link mining. Link mining techniques have been also applied in Web Structure Mining [7] and related disciplines. Another striking problem in statistical network analysis is network inference [3]. In the age of big data, analyzing massive data sets become more and more important. In case of structural data (networks), tackling the complexity of the data sets has been often challenging. Either the networks are very large or one needs to deal with a huge number of graphs, see [9]. In both cases, applying statistical methods has been fruitful. The main contribution of the paper is to survey recent work on statistical network analysis. The survey aims to highlight the interdisciplinary character of the field and, hence, the paper can be useful for those who want to tackle problems in statistical network analysis and related disciplines.

Recent Developments in Network Analysis and their Applications (Invited Paper)

The optimization of complex adaptive operating systems is certainly a challenge. Such a system exhibits emergent behavior through learning and adaption of the entities it is composed of. We propose the OR control tower concept to address the optimization problems going along with these systems. We introduce a dedicated entity, the OR control tower, which not only has full overview of the system but is also able to force the system’s behavior into an optimal direction. Besides an observation component, the OR control tower has implemented an, e.g. simulation based, optimization algorithm. The tower influences the system by a control stimulus or a system reconfiguration when the performance is not adequate anymore. Our concept could make complex adaptive operating systems more stable and even resilient.

Stefan Pickl

Papers

Analysis and Optimization of the Resilience Enhancement Circle via Data Farming

International Emissions Trading: A Pricing Model Based on System Dynamical Simulations

Recent Developments in Network Analysis and their Applications (Invited Paper)

OR Control Towers: A Concept for Optimizing the Performance of Complex Adaptive Operating Systems

An Algorithm for Solving Discrete Optimal Control Problems with Infinite Time Horizon - Determining the Minimal Mean Cost Cycles in a Directed Graph