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There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Object oriented approach is one of the popular software development approach for managing complex systems with massive set of requirements. Unlike procedural approach, this approach captures the requirements as set of data rather than…
In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Software engineering activities in the Industry has come a long way with various improve- ments brought in various stages of the software development life cycle. The complexity of modern software, the commercial constraints and the…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Systematic testing of object-oriented software turned out to be much more complex than testing conventional software. Especially the highly incremental and iterative development cycle demands both many more changes and partially implemented…
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Software complexity metrics is essential for minimizing the cost of software maintenance. Package level and System level complexity cannot be measured without class level complexity. This research addresses the class complexity metrics.…
Software code complexity is a well-studied property to determine software component health. However, the existing code complexity metrics do not directly take into account the fault-proneness aspect of the code. We propose a metric called…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
This work aims at discussing the complexity aspect of software while demonstrating its relationship with security. Complexity is an essential part of software; however, numerous studies indicate that they increase the vulnerability of the…
Processes tend to interact with other processes and operate on various objects of different types. These objects can influence each other creating dependencies between sub-processes. Analyzing the conformance of such complex processes…