From Malware Samples to Fractal Images: A New Paradigm for Classification. (Version 2.0, Previous version paper name: Have you ever seen malware?)

To date, a large number of research papers have been written on the classification of malware, its identification, classification into different families and the distinction between malware and goodware. These works have been based on captured malware samples and have attempted to analyse malware and goodware using various techniques, including techniques from the field of artificial intelligence. For example, neural networks have played a significant role in these classification methods. Some of this work also deals with analysing malware using its visualisation. These works usually convert malware samples capturing the structure of malware into image structures, which are then the object of image processing. In this paper, we propose a very unconventional and novel approach to malware visualisation based on dynamic behaviour analysis, with the idea that the images, which are visually very interesting, are then used to classify malware concerning goodware. Our approach opens an extensive topic for future discussion and provides many new directions for research in malware analysis and classification, as discussed in conclusion. The results of the presented experiments are based on a database of 6 589 997 goodware, 827 853 potentially unwanted applications and 4 174 203 malware samples provided by ESET and selected experimental data (images, generating polynomial formulas and software generating images) are available on GitHub for interested readers. Thus, this paper is not a comprehensive compact study that reports the results obtained from comparative experiments but rather attempts to show a new direction in the field of visualisation with possible applications in malware analysis.Comment: This paper is under review; the section describing conversion from malware structure to fractal figure is temporarily erased here to protect our idea. It will be replaced by a full version when accepte

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

On partitioning multivariate self-affine time series

Given a multivariate time series, possibly of high dimension, with unknown and time-varying joint distribution, it is of interest to be able to completely partition the time series into disjoint, contiguous subseries, each of which has different distributional or pattern attributes from the preceding and succeeding subseries. An additional feature of many time series is that they display self-affinity, so that subseries at one time scale are similar to subseries at another after application of an affine transformation. Such qualities are observed in time series from many disciplines, including biology, medicine, economics, finance, and computer science. This paper defines the relevant multiobjective combinatorial optimization problem with limited assumptions as a biobjective one, and a specialized evolutionary algorithm is presented which finds optimal self-affine time series partitionings with a minimum of choice parameters. The algorithm not only finds partitionings for all possible numbers of partitions given data constraints, but also for self-affinities between these partitionings and some fine-grained partitioning. The resulting set of Pareto-efficient solution sets provides a rich representation of the self-affine properties of a multivariate time series at different locations and time scales

Applications of Dynamical Systems to Music Composition

Mathematics and music have long enjoyed a close working relationship: mathematicians have frequently taken an interest in the organisational principles used in music, while musicians often utilise mathematical formalisms and structures in their works. This relationship has thrived in recent years, particularly since the advent of the computer, which has allowed mathematicians and musicians alike to explore the creative aspects of various mathematical structures quickly and easily. One class of mathematical structure that is of particular interest to the technologically-minded musician is the class of dynamical systems - those that change some feature with time. This class includes fractal zooms, evolutionary computing techniques and cellular automata, each of which holds some potential as the basis of a composition algorithm. The studies that comprise this thesis were undertaken in order to further examine the relationship between mathematics and music. In particular we explore the notion that music can essentially be thought of as a type of pattern propagation: we begin with initial themes and motifs - the musical patterns - which, during the course of the composition, are subjected to certain transformations and developments according to the rules dictated by the composer or the musical form. This is exactly analogous to the process which occurs within a cellular automaton: initial configurations of cells are transformed and developed according to a set of evolution rules. We begin our study by describing the development of the CAMUS v2.0 composition software, which was based on an earlier system by Dr. Eduardo Miranda, and discuss how best to use the system to compose new musical works. The next step in our study is concerned with highlighting the limitations of CAMUS as it currently stands, and suggesting techniques for improving the capabilities of the system. We then chart the development of CAMUS 3D. At each stage we justify the changes made to the system using both aesthetic and technical arguments. We also provide a composition example, which illustrates not only the changes in operation, but also in interface. The system is then re-evaluated, and further developments are suggested