Many complex systems in Nature are multifractal, a feature closely related to scale invariance. Multifractality is ubiquitous and so it can be found in systems as diverse as marine turbulence, econometric series, heartbeat dynamics and the solar magnetic field. In recent years, there has been growing interest in modelling the multifractal structure in these systems. This has improved our understanding of certain phenomena and has opened the way for applications such as reduction of coding redundancy, reconstruction of data gaps and forecasting of multifractal variables. Exhaustive multifractal characterization of experimental data is needed for tuning parameters of the models. The design of appro- priate algorithms to achieve this purpose remains a major challenge, since discretization, gaps, noise and long-range correlations require ad- vanced processing, especially since multifractal signals are not smooth: due to scale invariance, they are intrinsically uneven and intermittent. In the present study, we introduce a formalism for multifractal data based on microcanonical cascades. We show that with appropri- ate selection of the representation basis, we greatly improve inference capabilities in a robust fashion. In addition, we show two applications of microcanonical cascades: first, forecasting of stock market series; and second, detection of interscale heat transfer in the ocean.

Mobile phones are becoming a primary platform for information access. More and more people use their mobile devices as one of their major communication access tools. Commuters are increasingly carrying their mobile devices with them almost everywhere. Mobile devices fit perfectly into an ideal environment for realizing ubiquitous computing. A major aspect of ubiquitous computing is context-aware applications where the applications collect information about the environment that the user is in and use this information to achieve their goals or improve performance. The location of the device is one of the most important pieces of context information. Location awareness makes certain applications possible, e.g., recommending nearby businesses and tracking estimated routes, and greatly improves the performance of other applications, for example it can be associated with automobile navigation devices. A feature available to mobile applications in the Android platform makes it possible to determine a device's location without any additional hardware or sensor mechanisms, by simply using the native capability of the built-in wireless network card. Since the release of Android systems, there have been numerous applications developed to introduce new ways of tracking locations. Recently, there have been many papers on location estimation leveraging ubiquitous wireless networks. In this thesis, we develop an Android application to collect useful Wi-Fi information without registering a location listener with a network-based provider, such as Wi-Fi connections or data connections. Therefore it provides a passive, privacy-preserving, non-intrusive and power-saving way of achieving location awareness to Android mobile users. Accurate estimation of the location information can bring a more contextual experience to mobile users. We save the passively collected data of the IDs of Wi-Fi access points and the received signal strengths to a database in order to help us structure the data and analyse it. We employ some heuristics to infer the location information from the data. Our work presents a location tracking technique mainly based on Basic Service Set identification (BSSID) and/or Received Signal Strength Indicator (RSSI) using Wi-Fi information. It falls into one of the most active fields in mobile application development --location-based or location-aware applications.