This thesis lays the necessary groundwork for measuring the complexity of systems architecture models. We propose a set of complexity measures, which are usable with models defined using the Object-Process Model (OPM). In order to do this, we introduce a new concept of interface complexity multiplier for compensating the hidden information at interfaces. We also define a set of complexity metri...

24 Good estimates of ecosystem complexity are essential for a number 25 of ecological tasks: from biodiversity estimation, to forest structure 26 variable retrieval, to feature extraction by edge detection and genera27 tion of multifractal surface as neutral models for e.g. feature change 28 assessment. Hence, measuring ecological complexity over space be29 comes crucial in macroecology and geo...

Many studies have noted significant differences among human electroencephalograph (EEG) results when participants or patients are exposed to different stimuli, undertaking different tasks, or being affected by conditions such as epilepsy or Alzheimer's disease. Such studies often use only one or two measures of complexity and do not regularly justify their choice of measure beyond the fact that...

In this exploratory work we attempt to understand and to measure the notion of complex structure in networks. The first section discusses the ill-defined notion of complexity and describes the quantitative tools that we will use in an attempt to tie it down. In the second section we describe our attempts at relating these measures of structural complexity in networks to measures of dynamical co...

We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately c...

Software is among the most complex endeavors of the human mind; large scale systems can have tens of millions of lines of source code. However, seldom is complexity measured above the lowest level of code, and sometimes source code files or low level modules. In this paper a hierarchical approach is explored in order to find a set of metrics that can measure higher levels of organization. These...

In complexity measures for sequences over finite fields, such as the linear complexity and the k – error linear complexity is of great relevance to cryptology, in particular, to the area of stream ciphers. There are basically two types of requirements for suitability of a keystream generated by a stream cipher. One of the requirements is the keystream sequence must pass various statistical test...

We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made wi...

Quantitative graph analysis by using structural indices has been intricate in a sense that it often remains unclear which structural graph measures is the most suitable one, see [1, 12, 13]. In general, quantitative graph analysis deals with quantifying structural information of networks by using a measurement approach [5]. As special problem thereof is to characterize a graph quantitatively, t...

An algorithmic uniform method to measure the complexity of statements of finitely refutable statements [6, 7, 8], was used to classify fa-mous/interesting mathematical statements like Fermat's last theorem, Hilbert's tenth problem, the four colour theorem, the Riemann hypothesis, [9, 13, 14]. Working with inductive Turing machines of various orders [1] instead of classical computations, we prop...