Fractal Analysis

Receiving of remote sensed data's signals in urban space information reception centers is usually difficult, because of complex electromagnetic situation in cities and insufficient EMC. Traditional methods for digital reconstruction of images use smoothing and autoregressive forecasting. In this case anomalous spikes on the image are lost. Alternative method based on Kolmogorov-Wiener's filters and fractal properties of satellite images is

An iris recognition system is proposed in this paper. This system implements (a) the combination of proposed black hole search method and integro-differential operators for iris localization,(b) one-dimensional fractal analysis for feature extraction and (c) dissimilarity operator for matching. The black hole search method achieves 100% accuracy of pupil detection for both CASIA and MMU Iris databases. Experiment results show that the proposed system has an encouraging result with low EER to 4.63% in CASIA iris ...

Conditions during the formation of breccias in the Curnamona Province (eastern South Australia) have been investigated through a detailed fractal, microstructural, structural and fluid inclusion study of the breccias, syn-tectonic quartz veins and surrounding rocks. Fractal analysis of clast shapes and clast size distributions were able to distinguish two styles of breccia and indicate that fluid pressure fluctuations played a significant role, though to differing degrees, in the initiation of the brecciation process. Approximate palaeostress orientations prevalent during brecciation and their relationship to the deformational history of the terrane have been reconstructed by combining the orientations of microfractures (sealed microfractures and fluid inclusion planes) with structural field data. Fluid pressure fluctuations of w80 MPa during the brecciation process have been quantified by structurally constrained microthermometric analysis of syn-tectonic fluid inclusions coupled with an analysis of the metamorphic history of the area. Results from this study allow brecciation within the Curnamona Province to be placed within a structural framework and relate the process of brecciation to the interaction between regional hydrothermal alteration/fluid flow systems, shear zone formation and lithological contrasts within the upper crust during the Palaeoproterozoic Olarian Orogeny. These methods and findings provide a template for the study of brecciation processes in other terranes where fluid-induced brittle deformation is a controlling factor in the localisation of major ore deposits. q

Fractal analysis of the morphology of ice crystal particles in frozen food was attempted for frozen soybean curd (tofu). From a microscopic image analysis of the ice crystal particles, it was found that the perimeter of the ice crystal particles could be recognized as a fractal. Effects of the storage time and storage temperature on the fractal dimension (d p ) of the perimeter of the ice crystal particles were also investigated. As storage time was increased, the d p value tended to decrease. When the storage temperature was increased, the value of d p decreased more rapidly. The changes corresponded to the visual observation of the shape change for the ice crystal particles during storage reported by many researchers, suggesting that the fractal dimension d p could be used as a quantitative indicator reflecting the surface roughness of ice crystal particles.

Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: (1) The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). (2) Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. (3) Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis.

In pathological brain, a variety of morphological forms exist that reflect differences in functional requirements. To better understand microglia function in neurological disease, it is important to identify and quantify microglia morphology associated with specific neuropathologies. Traditional feature parameters such as area or cell diameter are not sufficient. In this study microglia were quantified by the box-counting fractal dimension (DB). One hundred and four cells from post-mortem tissue were analyzed comprising cells of controls, Alzheimer's disease, schizophrenia and affective disorder. The DB was significantly different from the control (1.36) compared to schizophrenia (1.41), Alzheimer's disease (1.41) and affective disorder (1.43) with p < 0.01. Thus fractal analysis provides a useful quantitative and objective measure of microglial form associated with normal function and diverse neuropathology. The distribution of fractal dimensions associated with microgli...

Epitaxially-grown Al x Ga 1−x As-GaAs heterostructures allow electron confinement to a thin sheet known as a two-dimensional electron gas (2DEG). Using negatively biased surface-gates to electrostatically deplete selected regions of the 2DEG, allows lateral confinement of the 2DEG to specific geometries smaller than the 2DEG electron mean free path. These confined regions are called billiards. Electron transport through billiards is ballistic. At millikelvin temperatures, the electron phase coherence length is sufficient that electron quantum interference effects produce reproducible magnetoconductance fluctuations (M CF). M CF act as a 'magneto-fingerprint' of the scattering dynamics of electrons traversing the billiard. It has been predicted and demonstrated experimentally that billiard M CF are fractal. Fractal M CF in mesoscopic semiconductor billiards is investigated. The M CF of a Sinai billiard (circle at the centre of a square) displayed exact self-similarity (ESS). Self-similarity is a property of fractal behaviour taking one of two forms: exact where precise structural features are repeated at different scales, and statistical where structure at different scales is linked by the same scaling relationship. A correlation function analysis is introduced to quantify the presence of ESS. A model for the Sinai billiard M CF based on a Weierstrass function is presented. Using a bridging interconnect, a continuous transition between the Sinai and an empty square geometry is achieved. The removal of the circle induces a transition from ESS to statistical self-similarity (SSS), suggesting that ESS is due to the presence of an obstacle at the centre of the billiard. A mechanism for the transition between ESS and SSS is proposed. Fractal behaviour is observed over 3.7 orders of magnitude for ESS and 2.1 orders for SSS. The physical dependencies of SSS are investigated and produce variations in the fractal dimension, rather than the fractal scaling range. SSS obeys a unified picture where the fractal dimension depends only on the ratio between the average spacing and broadening of billiard energy levels, irrespective of other billiard parameters. The semiclassical origin of SSS is demonstrated and the suppression of SSS is observed in both the quantum and classical limits. The influence of soft-wall potential profile on fractal M CF is investigated using double-2DEG billiards. i Acknowledgements So many people to thank. I just hope I don't miss anyone. First and foremost I would like to thank (enormously) my supervisors A/Prof. Richard Newbury and Dr Richard Taylor. I could never have hoped for two better people to work with over the last three and a half years. Without fail, they have always been helpful and supportive and have given me a lot of freedom to chase my own ideas and do things my way. They have also persevered with my stubbornness and occasional bouts of stupidity in that time. Secondly, I'd like to thank Prof. Jon Bird for allowing me to work on his phasebreaking studies in the early days, for providing me with a large amount of experimental data and for patiently answering all of my questions along the way. Dr M ark Fromhold and his Ph.D. student Chris Tench have provided theoretical support for this project since the beginning. I'd like to thank M ark also for answering many questions along the way and allowing me to use his results, diagrams and simulations over this time. Dr Giles Davies and Dr Linda M acks have been instrumental in the double-2DEG billiards project. I'd like to thank them for providing these samples, helping out with the experiments and freely giving their advice. I'd also like to thank Linda for proofreading the fabrication chapter in this thesis. Without these seven people, this thesis would not be.

Recently a large number of studies has been published in the area of Fractal Analysis. In this paper we review briefly the IFS (Iterated Function System) theory, and we show how this theoretical tool leads to new applications in Pattern Recognition and more precisely in the analysis of handwritten texts.

Many archaeological patterns are fractal. Fractal analysis, therefore, has much to contribute to archaeology. This article offers an introduction to fractal analysis for archaeologists. We explain what fractals are, describe the essential methods of fractal analysis, and present archaeological examples. Some examples have been published previously, while others are presented here for the first time. We also explain the connection between fractal geometry and nonlinear dynamical systems. Fractals are the geometry of complex nonlinear systems. Therefore, fractal analysis is an indispensable method in our efforts to understand nonlinearities in past cultural dynamics.

Horton's hierarchical and fractal analysis of channel circumference reveals that tidal-channel systems in the Dutch Wadden Sea have similar branching patterns. Channel systems have the same characteristics as three- to four-times branching networks. The branch lengths of these channels decrease logarithmically. The channel systems can be regarded as ‘statistical self-similar fractal’ networks, considering the natural variability in branch lengths and channel positions. Branching of channels does not continue below the 500 m scale. The channel-system circumference length is logarithmically related to the tidal prism and drainage area. The similarity of the channel systems, regardless of their size, relative amount of intertidal flats, and tidal amplitude, points to a self-organising nature. All processes depend on the feedback between morphology and hydrodynamics. At first sight, the channel systems can be regarded as an ebb-driven drainage network, governed by erosion. However, flood-dominated net sedimentation occurs in large parts of the drainage basins and modifies the ebb-driven network. The complex interaction of hydrodynamic and morphodynamic processes in tidal basins limits the applicability of process-based models. Behaviour-oriented modelling has a wide applicability and can be improved using the fractal geometry as the dynamical equilibrium morphology. The fractal-network geometry can also be used for stochastic reconstructions of fossil tidal-channel systems, when only limited observations are available.

В статье рассмотрены основные положения теорий динамики рынков, в частности, гипотезы эффективного рынка, гипотезы когерентного рынка, гипотезы фрактального рынка и гипотезы синергетического рынка. Проанализированы инструменты фрактального рынка для принятия на их основе обоснованных инвестиционных решений. Приведены и обоснованы инструменты технического анализа, основанного на игре за трендом для прогнозирования динамики рынка, согласно гипотезе фрактального рынка, в частности, волновую модель Эллиотта и применения нейро-нечетких моделей.
Ключевые слова: эффективный рынок, когерентный рынок, фрактальный рынок, синергетический рынок, технический анализ

Several destructive earthquakes have occurred in the Kachchh region of Gujarat during the past two centuries, among them Allah Bund earthquake (M7.8) in 1819, Anjar earthquake (M6) in 1956 and the recent Bhuj earthquake (M7.6) in 2001. The Anjar earthquake was on KMF (Kachchh Mainland Fault) and the recent Bhuj events were caused by a hidden fault north of KMF. The present study discusses the fractal analysis of tectonics governing seismic activity in the region. The region has been divided into five blocks and the fractal dimension of each block has been calculated using the box-counting technique. The results show significantly low value of fractal dimension of the Kachchh rift block consisting of the KMF compared to the other surrounding blocks, which also contain faults and rifts of higher fractal dimension. This indicates that the cause of earthquakes in this block may be asperities and barriers. However, the predominance of aftershocks over foreshocks signifies that barriers may be the main cause. The other results, such as the lower value of dimension of fault clustering show that the Kachchh rift block has faults which are distributed in a clustered manner. In this context, the seismicity of this block seems to be high.

In this manuscript, we review fractal calculus and random processes. Random variables and processes on totally disconnected fractal sets are defined. Random walks on fractal middle-ξ Cantor sets are suggested and corresponding variances are given which are power laws. The mean square stochastic calculus is generalized on fractal sets, which can lead to the standard case by setting dimension α = 1. Furthermore , we solve a fractal stochastic differential equation using the Frobenius method. Graphs are presented to give more details. ARTICLE HISTORY

The theory of space-charge-limited currents for trap-free insulator, insulator with single trap level and exponential trap distribution in energy is presented using fractal analysis. It is shown that independent of the electrode configuration it is possible to write a general equation for current-voltage characteristic changing only the parameter of fractal dimension. On the basis of cylindrical electrode configuration the expression for the current-voltage dependence on the surface gap sample was derived.

The rheological properties and fractal dimensions of flaxseed gum gels were analyzed in various ionic strength values ranging between 0 and 1000 mM. The rheological properties of flaxseed gum were significantly influenced by the ionic strength. The gel strength first increased then decreased with the increasing of ionic strength and the strongest gel was obtained when the ionic strength was 400 mM. The calculated fractal dimensions of the flaxseed gum gels were 2.06–2.49 or 1.42–2.18, based on the model selected and the ionic strength applied. These results would help to understand the microstructure of the flaxseed gum gels and the influence of ionic strength on that. However, the difference in results between the two models implied that further study is needed to find suitable model for flaxseed gum gels.► The fractal structure of flaxseed gum was analyzed using two Rheological model. ► The fractal dimension of flaxseed gum was calculated to be 2.06–2.49 or 1.42–2.18. ► Ionic strength has significant effect on the fractal dimension of flaxseed gum.

In this paper a fractal analysis study of VoIP traffic is presented. The characteristics of measured VoIP traffic on both call and packet level have been investigated. The results support the popular Poisson process for VoIP call arrival modeling but we argue that the call holding times follow heavy-tailed distributions rather than exponential distributions. We propose the generalized Pareto distribution for modeling the call holding times. At the packet level we have found that the exponential modeling of On and Off periods is also inappropriate and heavy-tailed characteristics have been identified in case of all the investigated VoIP codecs. The generalized Pareto distribution can be used as an accurate model for the On and Off periods too. In the analysis we revealed that the aggregated VoIP traffic has fractal characteristics and we suggest the fractional Gaussian noise model for the aggregated VoIP traffic.

Streszczenie Wprowadzenie: w procesie reinkluzji ząb wyrzynający się lub wyrznięty ponownie zagłębia się w kości stwarzając różne problemy kliniczne. Etiopatogeneza tej anomalii nie została dotychczas wyjaśniona. Rozpoznanie reinkluzji opiera się głównie na ustalonych objawach klinicznych i radiologicznych. Cechą radiologiczną zębów reinkludowanych jest nieprawidłowa resorpcja korzeni oraz zmiany struktury tkanki kostnej w ich otoczeniu. Ilościowej oceny zmian w tkance kostnej można dokonać za pomocą wymiaru fraktalnego obrazów radiologicznych w regionach danej patologii. Cel pracy: ocena wartości wymiaru fraktalnego obrazów radiologicznych kości żuchwy w obszarze zębów reinkludowanych. Materiał i metody: materiał badawczy obejmował 10 pantomogramów, na których wybierano 45 regionów patologicznych i tyle samo kontrolnych. Analizę fraktalną wykonano metodą Fouriera. Wyniki: stwierdzono istotnie wyższe wartości wymiaru fraktalnego ocenianych obrazów radiologicznych w regionach zębów reinkludowanych. Wnioski: tkanka kostna części zębodołowej żuchwy w obszarze zębów reinkludowanych wykazuje duży stopień nieregularności. Analiza fraktalna poszerza możliwości oceny obrazów radiologicznych.

Запропоновано методику передпрогнозного фрактального аналізу часових рядів, яка базується на послідовному R/S-аналізі. На основі цієї методики можна визначати рівень персистентності, розраховувати середню величину неперіодичного циклу часових рядів, а також встановлювати інвестиційну якість (дохідність) активів, які представляються фінансовими часовими рядами. В рамках цієї методики запропоновано критерій визначення середньої довжини періодичного і неперіодичного циклів, на основі згладжування V-статистики за допомогою звичайних плинних середніх та адаптивної плинної Кауфмана.

Ключові слова: послідовний R/S-аналіз, показник Херста, часовий ряд, середня довжина неперіодичного циклу, інвестиційна якість фінансових активів

Предложена методика предпрогнозного фрактального анализа временных рядов, основанная на последовательном R/S-анализе. На основе этой методики можно определять уровень персистентности, рассчитывать среднюю длину непериодического цикла временных рядов, а также определять инвестиционное качество (доходность) активов, которые задаются финансовыми временными рядами. В рамках этой методики предложен критерий определения средней длины периодического и непериодического циклов на основе сглаживания V-статистики с помощью обычных скользящих средних и адаптивной средней Кауфмана.

Ключевые слова: последовательный R/S-анализ, показатель Херста, временной ряд, средняя длина непериодического цикла, инвестиционное качество финансовых активов.

The method of pre-forecasting fractal time series analysis, based on the sequential R/S-analysis is offered. Based on this technique it is possible to determine to the level of persistence, to calculate the average length of non-time series periodic cycle, and to establish investment quality (yield) of assets which are represented by financial time series. Under this method the criterion for the average length of periodic and non-periodic cycles determining, based on smoothing the V-statistics using simple moving average and Kaufman adaptive moving average is proposed.

Keywords: sequential R/S-analysis, Hurst index, time series, average length of non-time series periodic cycle, investment quality of assets

In this paper, point pattern analysis, fractal analysis and Fry analysis were employed to study the spatial pattern of known occurrences of mineral deposits of the type sought, whereas distance distribution method was applied to study the spatial associations between various geological features and known occurrences of mineral deposits of the type sought. In the Aroroy district (Philippines), the results of the applications of these spatial analytical techniques support a conceptual model of district-scale mechanism of geologic controls on low-sulphidation epithermal Au mineralization, which involves a more-or-less regular mesh of interlinked zones of extension faults/fractures at and/or around intersections of NNW-and NW-trending strike-slip faults/fractures. Integration of spatial evidential data layers representing these structural controls and surficial geochemical anomalies, via knowledge-guided application of data-driven evidential belief functions, results in delineation of prospective areas occupying about 25% of the district, in which there is about 70% likelihood of undiscovered occurrences of low-sulphidation epithermal Au deposits.

In the southwestern part of the Ashanti Belt, the results of fractal and Fry analyses of the spatial pattern of 51 known mines/prospects of (mostly lode) gold deposits and the results of analysis of their spatial associations with faults and fault intersections suggest different predominant structural controls on lode gold mineralisation at local and district scales. Intersections of NNE-and NW-trending faults were likely predominantly involved in local-scale structural controls on lode gold mineralisation, whilst NNEtrending faults were likely predominantly involved in district-scale structural controls on lode gold mineralisation. The results of the spatial analyses facilitate the conceptualisation and selection of spatial evidence layers for lode gold prospectivity mapping in the study area. The applications of the derived map of lode gold prospectivity and a map of radial density of spatially coherent lode gold mines/ prospects results in a one-level prediction of 37 undiscovered lode gold prospects. The applications of quantified radial density fractal dimensions of the spatial pattern of spatially coherent lode gold mines/prospects result in an estimate of 40 undiscovered lode gold prospects. The study concludes finally that analysis of the spatial pattern of discovered mineral deposits is the key to a strong link between mineral prospectivity mapping and assessment of undiscovered mineral deposits.

The approach taken in this paper, namely synthesising a wealth of previous information with new data and a genetic model, in combination with integrated numerical analyses, led to new insights into the geological controls on the localisation of auriferous veins and residual prospectivity of the Charters Towers goldfield, NE Australia. The method also has implications for the assessment of other "mature" goldfields worldwide.

Fractal geometry is being used in diverse research areas and it is proving to be an increasingly useful tool. Since there is a growing interest in the applications of fractal geometry in many branches of science and art, questions about its methodology, underlying principles and meaningful use, become more and more current. The present paper deals with the conceptual and methodological aspects of fractal geometry. By means of the fractal analysis and calculus we discuss some basic concepts of fractal geometry using as an example the triadic Koch curve. We present a system of parametric equations for that fractal, and derive its capacity dimension and two main inverse-power laws. Since little evidence is available on the properties of the Koch surface, our main endeavour is directed toward investigating its characteristics. Starting from an experimentally stated hypothesis that interior of some natural objects is solid we support this hypothesis theoretically on the Koch surface. We show that the areas of that surface converge to a finite number whose value we calculated. Using the capacity dimension we demonstrate that the surface area of the limit Koch curve is structureless so that it does not belong to the ''first category'' of fractals.

The impact that progress in information technology has on the entire activity of humans has proportions and a complexity that are difficult to describe or summarize. On one hand, the objects built by humans become – more and more each day – “smart”, or at least capable of collecting, processing and transmitting information.  However, these objects are increasingly capable of making decisions, based on pre-programmed algorithms or based on heuristic “learning” techniques – through progressive exposure to the environment and the preferences and options of the user. On the other hand, all of the intellectual and even emotional activity of modern man is increasingly assisted and dependent on instruments developed through information technology: databases, search engines, communication devices, operational models, heuristic models. 

This progress in information technology has submitted the actual paradigm of scientific knowledge to revision pressures unprecedented from Karl Popper to the present day. The new debate has coagulated like a show around the confrontation between Noam Chomski, the illustrious American linguist and political scientist and Peter Norvig, the leader of the research department in Google company. This confrontation of ideas began in 2011, at the Brains, Minds, and Machines symposium hosted by the Massachusetts Institute of Technology, from „how one can obtain artificial intelligence” and, in a few months, through articles and relatively elaborate interventions [Norvig, 2012] became about „what human knowledge is”. Essentially, it is about knowledge understood as an explicative model, simple enough for every link to be logically comprehensible (Chomski) and, alternatively, knowledge as an informational model, a „black box”, capable of offering increasingly better predictions based on historical data and internal statistical search algorithms (Norvig). The question is: does the progress of knowledge still depend on models that are elegant in their simplicity, logically accessible – in integrity and in detail, models that are continually reviewed to approximate the available data as well as possible? Or are we entering a new era of statistical informational models, capable of continuously processing enormous quantities of data – historical or real time data and providing classifications, predictions, etc. – but without subjacent explanations: we find out how much, when, with associated probabilities, but the question „why?” loses its relevance.

In the applied medical sciences, the most significant reflection of this pressure to change the relationship paradigm between historical data – formalized knowledge – the practice of decisions and predictions is Evidence Based Medicine, EBM. It is not a new concept – its origins can be traced (at least) to the comparative clinical study on six groups of patients, through which the British physician James Lind, of the Royal Navy, established in 1747 what the foods than can prevent and treat scurvy – lemons and oranges – were. Isolating vitamin C and clarifying the pathogenesis of scurvy came about almost 200 years later, in 1932, but the prophylactic treatment had already been generalized by the Royal Navy as early as 1787, based on the evidence collected by Lind. The reference definition of EBM was settled in 1996:
„the conscious, explicit and judicious use of the best evidence in order to formulate decisions with regard to the treatment of individual patients” [Sackett, 1996]. Best evidence meaning proof (as certain as possible), not explanations (as plausible as possible). In the last few decades, the scope of medical research and the increasing pressure for the maximum but responsible use of the results of this research imposed EBM as a dominant technique for collecting, organizing, evaluating and using medical information; EBM procedures are now standardized at a national and international level, with specialized associations and regulation and certification organizations facilitating the development of work methods [Mayer, 2010].

In a good correlation with EBM, a direction of accelerated progress in applying new information techniques in medicine is that of prediction models capable of continuous development, through what is suggestively known as „learning” or „training”. Artificial neural networks are one of the forms that were intensely studied and tested in this context, as part of the research surrounding „artificial intelligence”. Promising results have been reported more and more frequently in applying neural networks to diagnosis [Ganesan, 2010], [Jiang, 2010], [Barwad, 2012], [Amato, 2013], but also to evaluating prognosis and prediction factors [Lundin, 1999]. The number of such factors under evaluation has risen exponentially lately, especially due to the progress in genomics and molecular biology, which gave rise to a necessity for new information instruments, capable of processing such a large data volume.  Prediction based on such information models supplied with huge databases is already transitioning into the current medical practice [Silva, 2015], [Prigg, 2015]: at Beth Israel Deaconess Hospital in Boston USA, Dr. Steven Horng recently announced the operational phase for of an information instrument that allows the formulation of a diagnosis, indicates recommended therapeutic procedures and estimates the prognosis for every patient in intensive therapy.  Dr. Horng, a physician specializing in both emergency medicine and biomedical IT, believes that the accuracy with which the program formulates, for example, the prediction for the imminence of the patient’s death in the next 30 days is over 96%.  The recent and historical clinical and paraclinical data of the patient are introduced into the information model based on similar historical data collected in the last 30 years from over 250000 patients. The database is augmented continuously through the regular collection of information, every 3 minutes, from the physiological data monitors installed for all the patients admitted into the ICU of the hospital. 

In the last 30 years, technological progress has brought about a true revolution in medical imagery [Dougherty, 2009]. On one hand, minimally invasive investigation techniques have become accessible for a very large number of patients, both in human and veterinary medicine: MRIs, computerized tomography, nuclear magnetic resonance, confocal reflection microscopy. On the other hand, the increased performance of information instruments facilitates new approaches in distinguishing useful information in medical images [Bubnov, 2014], [Lennon, 2015]. The digital format, practically generalized both for the results in new investigation techniques, as well as for classical microscopy and radiology, now facilitates processing for the extraction of useful information, storing and accessing images, as well as the comparison, morphometric and statistical analysis, identification of regions of interest/lesions etc. [Rangayyan, 2005].

The road towards semi-automated and even automated procedures that can be used directly in research, screening, pre-diagnosis or diagnosis is open and is beginning to be intensely exploited, including by the commercial component of medical activity. Using automated and semi-automated procedures also leads to an exponential increase in the volume of collected data which, in turn, reclaims information approaches such as neural networks for processes or such as EBM for testing and application. It is a progress spiral that is presently accelerating and in which man, the professional, the expert, can be centrifugally marginalized towards positions in which he only contributes punctually to ample, interdependent processes that he does not control anymore. It is possible that we are witnessing the dawn of a new historical era, in which the virtual reality created continuously by humans becomes as significant and autonomous as objective reality. Our attempt to know and change reality in its entirety for our own purposes shall inevitably adapt to the new situation. 

Simon Rosenfeld, from the National Cancer Institute – USA, considers that oncology and oncological research are at a critical crossroads with the dynamics of nonlinear systems and research regarding swarm intelligence in the contemporary attempt to offer a new, unifying vision with regard to the way in which systems as diverse as „biological networks, communities of social insects, robotic communities, microbial communities, communities of somatic cells, (…) social networks, and (…) many other systems” [Rosenfeld, 2015] appear and function. Rosenfeld’s unifying vision marks an essential link between carcinogenesis, fractal analysis – that was mainly developed as a modeling instrument for nonlinear dynamic systems and artificial neural networks – that are one of the best documented examples of man-made swarm intelligence.

Fractal analysis facilitates the obtaining of measurements, of numbers that quantify the non-periodical complexity that is so characteristic of biological structures, on all size scales in which life is manifested.  This research has investigated the possibility of including fractal analysis applied to histopathological or cytopathological microscopic images amongst the instruments used for diagnosing tumours in animals. I then tested the introduction of the fractal dimension amongst oncological prognostic factors. For this purpose, I developed statistical models and artificial neural network-type models for the survival duration, including the fractal dimension in the set of predictors based on which these models estimate the prognostic for cancer patients.

Regarding the foundations of matter as energy fields in a fractal gearing structure can redefine the foundations of quantum physics in a unique new way, while remaining consistent with modern probabilisitic theories.  Further, working experimental models of fractal gear arrays have created effects that cannot be explained with current theories, and they are described here in detail.  This theory is the only way to explain the experimental phenomenon, and it is an explanation to phenomenon which I have been able to create in the lab for the first time in physics history.  Fractal gear theory is a deterministic model of quantum fields that can be used simultaneously with the current standard model and they both can borrow concepts from each other without breaking the logical consistency.  An example is the double-slit experiment; fractal gear theory states that a harmonic field structure is created by the geometry of the matter (the slits) and the electron or photon rides on it in an oscillatory manner so it does not matter if one or many particles enter simultaneously through the slits.  Many of the modern theories provide quantitative answers to the questions that arise from this new deterministic unified field theory. A prime example is that strings from string theory can be understood as a line of contact thru time within a fractal gear field array.  Physicists today have obfuscated theories with statistical data , whereas most of the real advances in physics have arisen from thought experiments and theoretical and geometric analysis. This theory was devised with very little mathematics and a whole lot of 3D geometry and analysis with almost zero experimental data or references beyond the foundations of modern quantum physics.  It is a grass roots endeavor to start from scratch and rebuild quantum physics with a correct picture that almost any mechanically inclined person can understand; a picture that has eluded physicists for over 100 years.  I believe that if a picture is worth 1000 words, then a geometry is worth 1000 formulas, but geometry is much easier to work with.

Fractal gear fields are a quantum foam theory and provides means for transmitting information and by its explanation of emergent space time, it is directly implied that information is able to travel faster than the speed of light within a bound domain.  The speed of transmission dissipates at a rate proportional to the total energy within the domain.  Fractal gear theory is a geometrical foundation for a pilot-wave theory in the spirit of DeBroglie -Bohm theory.  Further, the 3D geometric form of fractal gear fields shows clearly that all bell inequality measurements using photon polarization is biased and in error, due to angular variations in density of the field structure.

La presente investigación sigue la línea de los estudios tecnológicos de la fabricación cerámica. No se pretende desarrollar un análisis de cadenas operatorias, pero se parte de la idea que una secuencia específica de acciones y gestos deja una huella en los materiales arqueológicos y que esa huella puede ser identificada y caracterizada. El proceso de producción de la cerámica es complejo y abarca un número considerable de etapas, desde la selección de la materia prima hasta la decoración posterior a la cocción. En este proceso se anidan varias cadenas operatorias que van a dejar rastro en la pasta cerámica, que es el objeto de esta investigación.  No es la intención identificar los gestos o acciones específicas que dieron como resultado una pasta particular. El objetivo es más modesto. Se trata simplemente de identificar sistemáticamente las distintas pastas presentes en una colección de tiestos arqueológicos.  En esta investigación se propone un método para hacer una caracterización sistemática de la pasta de la cerámica arqueológica que no se base primordialmente en aspectos naturales de la materia prima, sino que se desprenda de las huellas que dejaron los procesos de manufactura. El método que se propone es el análisis fractal del patrón de la pasta.

Over the last years, fractal and multifractal geometries were applied extensively in many medical signal (1D, 2D or 3D) analysis applications like pattern recognition, texture analysis and segmentation. Application of this geometry relies heavily on the estimation of the fractal features. Various methods were proposed to estimate the fractal dimension or multifractal spectral of a signal. This article presents an overview of these algorithms, the way they work, their benefits and their limits. The aim of this review is to explain and to categorize the various algorithms into groups and their application in the field of medical signal analysis.

Mapping of mineral prospectivity and assessment of undiscovered mineral deposits both aim to delineate prospective ground for mineral exploration, but the latter is usually carried out exclusive of the former. We propose that the spatial distribution of known mineral deposits of the type sought is the key to link mapping of mineral prospectivity and assessment of undiscovered deposits. We demonstrate this proposition in regional-scale mapping of prospectivity for volcanogenic massive sulphides (VMS) deposits and estimation of undiscovered VMS endowment in the Skellefte district (Sweden). The results of analyses of the spatial distribution of known VMS deposits and their spatial associations with geological features are consistent with existing knowledge of geological controls on VMS mineralization in the district, and we used them to define spatial recognition criteria of regional-scale VMS prospectivity. Integration of layers of evidence representing spatial recognition criteria of VMS prospectivity via application of data-driven evidential belief functions results in a regional-scale map of prospective areas occupying 15% of the district and having fittingand prediction-rates of 100%. We used the map of prospective areas and proxy measures for degrees of exploration based on the spatial distribution of known VMS deposits in one-level prediction of undiscovered mineral endowment. We obtained estimates of 709 Kt undiscovered Cu endowment, 3190 Kt undiscovered Zn endowment, 95 Mt undiscovered ore tonnage, and 48 undiscovered VMS deposits. These estimates are slightly (ca. 5% on average) lower than, and thus corroborated by, estimates obtained via radial-density fractal analysis of the spatial distribution of known VMS deposits. Therefore, mineral prospectivity mapping can be a part of mineral resource assessment if the spatial distribution of discovered deposits of the type sought is considered in both predictive modeling processes.

Palette images are widely used on the World Wide Web (WWW) and in game-cartridge applications. Many images used on the WWW are stored and transmitted after they are compressed losslessly with the standard graphics interchange format (GIF), or portable network graphics (PNG). Well-known 2-D compression schemes, such as JPEG-LS and JPEG-2000, fail to yield better compression than GIF or PNG due to the fact that the pixel values represent indices that point to color values in a look-up table. To improve the compression performance of JPEG-LS and JPEG-2000 techniques, several researchers have proposed various reindexing algorithms. We investigate various compression techniques for color palette images. We propose a new technique comprised of a traveling salesman problem (TSP)-based reindexing scheme, Burrows-Wheeler transformation, and inversion ranks. We show that the proposed technique yields better compression gain on average than all the other 1-D compressors and the reindexing schemes that utilize JPEG-LS or JPEG-2000.

Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems' behavior.

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at s1× ∼ 12 and s2× ∼ 130 months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second ones is approximately equal to the well known cycle of sun activity. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The value of Hurst exponent of the runoff water of rivers without the sinusoidal trend shows a long range correlation behavior. For the Daugava river the value of Hurst exponent is 0.52 ± 0.01 and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.

An experimental study on CH 4 -CO 2 -air flames at various pressures is conducted by using both laminar and turbulent Bunsen flame configurations. The aim of this research is to contribute to the characterization of fuel lean methane/carbon dioxide/air premixed laminar and turbulent flames at different pressures, by studying laminar and turbulent flame propagation velocities, the flame surface density and the instantaneous flame front wrinkling parameters. PREMIX computations and experimental results indicate a decrease of the laminar flame propagation velocities with increasing CO 2 dilution rate. Instantaneous flame images are obtained by Mie scattering tomography. The image analysis shows that although the height of the turbulent flame increases with the CO 2 addition rate, the flame structure is quite similar. This implies that the flame wrinkling parameters and flame surface density are indifferent to the CO 2 addition. However, the pressure increase has a drastic effect on both parameters. This is also confirmed by a fractal analysis of instantaneous images. It is also observed that the combustion intensity S T /S L increases both with pressure and the CO 2 rate. Finally, the mean fuel consumption rate decreases with the CO 2 addition rate but increases with the pressure.

Relationships between habitat structure and spatial variations in vegetation composition were determined in catenas of central Argentina salt marsh landscapes. Vegetation was classified following a multi-technique strategy. An analysis of species distributions along an environmental gradient was made and a redundancy analysis was used to relate the environmental variables to vegetation data. The spatial covariation was evaluated through fractal analysis. The vegetation can be divided into four discrete noda that correspond to different topographic positions (summit, backslope, footslope and toeslope, respectively): nodum of Stipa trichotoma + St. tenuissima, nodum of Distichlis scoparia, nodum of Distichlis spicata and nodum of Spartina densiflora. Each of these nodum is characterized by a definite combination of floristic groups. Symmetric aggregation of vegetation borders was observed in all three sites. The existence of vegetation discontinuities along the catenas depended largely on water table depth and salinity which in turn controlled the edaphic salinity. The arrangement of sites by multivariate analysis reflected the influence of a complex gradient representing halomorphic and hydromorphic factors. β-diversity was associated with abrupt changes in the physical structure of the catena for a reduced spatial dimension (300-m scale). Absolute diversity and evenness were higher on the summit and declined progressively toward the toeslope. The rate of change was higher on the backslope and the dominant species have different ecological amplitudes overlapping along the gradient. The main operational factors associated with the floristic differences are: (i) the variations in the chemical composition and the seasonal dynamics of the soil solution in the aerated layer of soils, (ii) the salinity and dynamics of groundwater, and (iii) the length of time that the soil is flooded during the rainy season (summer). The fractal dimension was close to 2, implying weak spatial dependence. Fractal dimension varied as a function of scale. The fractogram only revealed a significant spatial dependence on the summit. This spatial dependence was associated with short distances of gradient showing that the organizational pattern of Distichlis spp.- Spartina was related to combinations of underlying environmental factors rather than to a specific position in the catena. The catenas are highly structured spatially, floristic compositions are inextricably linked to this structure. Habitat complexity may directly affect associated vegetation by regulating the hydrohalomorphic conditions in the aerated layer of the soils. The relationships of the habitat-floristic groups are not simple, hydromorphism interacts in a complex way with halomorphism.