Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Tecniche per il controllo dinamico del consumo di potenza per piattaforme system-on-chip

Providing support for multimedia applications on low-power mobile devices remains a significant research challenge. This is primarily due to two reasons: • Portable mobile devices have modest sizes and weights, and therefore inadequate resources, low CPU processing power, reduced display capabilities, limited memory and battery lifetimes as compared to desktop and laptop systems. • On the other hand, multimedia applications tend to have distinctive QoS and processing requirementswhichmake themextremely resource-demanding. This innate conflict introduces key research challenges in the design of multimedia applications and device-level power optimization. Energy efficiency in this kind of platforms can be achieved only via a synergistic hardware and software approach. In fact, while System-on-Chips are more and more programmable thus providing functional flexibility, hardwareonly power reduction techniques cannot maintain consumption under acceptable bounds. It is well understood both in research and industry that system configuration andmanagement cannot be controlled efficiently only relying on low-level firmware and hardware drivers. In fact, at this level there is lack of information about user application activity and consequently about the impact of power management decision on QoS. Even though operating system support and integration is a requirement for effective performance and energy management, more effective and QoSsensitive power management is possible if power awareness and hardware configuration control strategies are tightly integratedwith domain-specificmiddleware services. The main objective of this PhD research has been the exploration and the integration of amiddleware-centric energymanagement with applications and operating-system. We choose to focus on the CPU-memory and the video subsystems, since they are the most power-hungry components of an embedded system. A second main objective has been the definition and implementation of software facilities (like toolkits, API, and run-time engines) in order to improve programmability and performance efficiency of such platforms. Enhancing energy efficiency and programmability ofmodernMulti-Processor System-on-Chips (MPSoCs) Consumer applications are characterized by tight time-to-market constraints and extreme cost sensitivity. The software that runs on modern embedded systems must be high performance, real time, and even more important low power. Although much progress has been made on these problems, much remains to be done. Multi-processor System-on-Chip (MPSoC) are increasingly popular platforms for high performance embedded applications. This leads to interesting challenges in software development since efficient software development is a major issue for MPSoc designers. An important step in deploying applications on multiprocessors is to allocate and schedule concurrent tasks to the processing and communication resources of the platform. The problem of allocating and scheduling precedenceconstrained tasks on processors in a distributed real-time system is NP-hard. There is a clear need for deployment technology that addresses thesemulti processing issues. This problem can be tackled by means of specific middleware which takes care of allocating and scheduling tasks on the different processing elements and which tries also to optimize the power consumption of the entire multiprocessor platform. This dissertation is an attempt to develop insight into efficient, flexible and optimalmethods for allocating and scheduling concurrent applications tomultiprocessor architectures. It is a well-known problem in literature: this kind of optimization problems are very complex even in much simplified variants, therefore most authors propose simplified models and heuristic approaches to solve it in reasonable time. Model simplification is often achieved by abstracting away platform implementation ”details”. As a result, optimization problems become more tractable, even reaching polynomial time complexity. Unfortunately, this approach creates an abstraction gap between the optimization model and the real HW-SW platform. The main issue with heuristic or, more in general, with incomplete search is that they introduce an optimality gap of unknown size. They provide very limited or no information on the distance between the best computed solution and the optimal one. The goal of this work is to address both abstraction and optimality gaps, formulating accurate models which accounts for a number of ”non-idealities” in real-life hardware platforms, developing novel mapping algorithms that deterministically find optimal solutions, and implementing software infrastructures required by developers to deploy applications for the targetMPSoC platforms. Energy Efficient LCDBacklightAutoregulation on Real-LifeMultimediaAp- plication Processor Despite the ever increasing advances in Liquid Crystal Display’s (LCD) technology, their power consumption is still one of the major limitations to the battery life of mobile appliances such as smart phones, portable media players, gaming and navigation devices. There is a clear trend towards the increase of LCD size to exploit the multimedia capabilities of portable devices that can receive and render high definition video and pictures. Multimedia applications running on these devices require LCD screen sizes of 2.2 to 3.5 inches andmore to display video sequences and pictures with the required quality. LCD power consumption is dependent on the backlight and pixel matrix driving circuits and is typically proportional to the panel area. As a result, the contribution is also likely to be considerable in future mobile appliances. To address this issue, companies are proposing low power technologies suitable for mobile applications supporting low power states and image control techniques. On the research side, several power saving schemes and algorithms can be found in literature. Some of them exploit software-only techniques to change the image content to reduce the power associated with the crystal polarization, some others are aimed at decreasing the backlight level while compensating the luminance reduction by compensating the user perceived quality degradation using pixel-by-pixel image processing algorithms. The major limitation of these techniques is that they rely on the CPU to perform pixel-based manipulations and their impact on CPU utilization and power consumption has not been assessed. This PhDdissertation shows an alternative approach that exploits in a smart and efficient way the hardware image processing unit almost integrated in every current multimedia application processors to implement a hardware assisted image compensation that allows dynamic scaling of the backlight with a negligible impact on QoS. The proposed approach overcomes CPU-intensive techniques by saving system power without requiring either a dedicated display technology or hardware modification. Thesis Overview The remainder of the thesis is organized as follows. The first part is focused on enhancing energy efficiency and programmability of modern Multi-Processor System-on-Chips (MPSoCs). Chapter 2 gives an overview about architectural trends in embedded systems, illustrating the principal features of new technologies and the key challenges still open. Chapter 3 presents a QoS-driven methodology for optimal allocation and frequency selection for MPSoCs. The methodology is based on functional simulation and full system power estimation. Chapter 4 targets allocation and scheduling of pipelined stream-oriented applications on top of distributed memory architectures with messaging support. We tackled the complexity of the problem by means of decomposition and no-good generation, and prove the increased computational efficiency of this approach with respect to traditional ones. Chapter 5 presents a cooperative framework to solve the allocation, scheduling and voltage/frequency selection problem to optimality for energyefficient MPSoCs, while in Chapter 6 applications with conditional task graph are taken into account. Finally Chapter 7 proposes a complete framework, called Cellflow, to help programmers in efficient software implementation on a real architecture, the Cell Broadband Engine processor. The second part is focused on energy efficient software techniques for LCD displays. Chapter 8 gives an overview about portable device display technologies, illustrating the principal features of LCD video systems and the key challenges still open. Chapter 9 shows several energy efficient software techniques present in literature, while Chapter 10 illustrates in details our method for saving significant power in an LCD panel. Finally, conclusions are drawn, reporting the main research contributions that have been discussed throughout this dissertation.

Spectrum shaping and its application: spread-spectrum clock generator and circuits for ultra wide band

Electromagnetic spectrum can be identified as a resource for the designer, as well as for the manufacturer, from two complementary points of view: first, because it is a good in great demand by many different kind of applications; second, because despite its scarce availability, it may be advantageous to use more spectrum than necessary. This is the case of Spread-Spectrum Systems, those systems in which the transmitted signal is spread over a wide frequency band, much wider, in fact, than the minimum bandwidth required to transmit the information being sent. Part I of this dissertation deals with Spread-Spectrum Clock Generators (SSCG) aiming at reducing Electro Magnetic Interference (EMI) of clock signals in integrated circuits (IC) design. In particular, the modulation of the clock and the consequent spreading of its spectrum are obtained through a random modulating signal outputted by a chaotic map, i.e. a discrete-time dynamical system showing chaotic behavior. The advantages offered by this kind of modulation are highlighted. Three different prototypes of chaos-based SSCG are presented in all their aspects: design, simulation, and post-fabrication measurements. The third one, operating at a frequency equal to 3GHz, aims at being applied to Serial ATA, standard de facto for fast data transmission to and from Hard Disk Drives. The most extreme example of spread-spectrum signalling is the emerging ultra-wideband (UWB) technology, which proposes the use of large sections of the radio spectrum at low amplitudes to transmit high-bandwidth digital data. In part II of the dissertation, two UWB applications are presented, both dealing with the advantages as well as with the challenges of a wide-band system, namely: a chaos-based sequence generation method for reducing Multiple Access Interference (MAI) in Direct Sequence UWB Wireless-Sensor-Networks (WSNs), and design and simulations of a Low-Noise Amplifier (LNA) for impulse radio UWB. This latter topic was studied during a study-abroad period in collaboration with Delft University of Technology, Delft, Netherlands.

Advanced CMOS Interfaces for Bio-Nanosensors

The improvement of devices provided by Nanotechnology has put forward new classes of sensors, called bio-nanosensors, which are very promising for the detection of biochemical molecules in a large variety of applications. Their use in lab-on-a-chip could gives rise to new opportunities in many fields, from health-care and bio-warfare to environmental and high-throughput screening for pharmaceutical industry. Bio-nanosensors have great advantages in terms of cost, performance, and parallelization. Indeed, they require very low quantities of reagents and improve the overall signal-to-noise-ratio due to increase of binding signal variations vs. area and reduction of stray capacitances. Additionally, they give rise to new challenges, such as the need to design high-performance low-noise integrated electronic interfaces. This thesis is related to the design of high-performance advanced CMOS interfaces for electrochemical bio-nanosensors. The main focus of the thesis is: 1) critical analysis of noise in sensing interfaces, 2) devising new techniques for noise reduction in discrete-time approaches, 3) developing new architectures for low-noise, low-power sensing interfaces. The manuscript reports a multi-project activity focusing on low-noise design and presents two developed integrated circuits (ICs) as examples of advanced CMOS interfaces for bio-nanosensors. The first project concerns low-noise current-sensing interface for DC and transient measurements of electrophysiological signals. The focus of this research activity is on the noise optimization of the electronic interface. A new noise reduction technique has been developed so as to realize an integrated CMOS interfaces with performance comparable with state-of-the-art instrumentations. The second project intends to realize a stand-alone, high-accuracy electrochemical impedance spectroscopy interface. The system is tailored for conductivity-temperature-depth sensors in environmental applications, as well as for bio-nanosensors. It is based on a band-pass delta-sigma technique and combines low-noise performance with low-power requirements.

Enabling Blocks for Integrated CMOS UWB Transceivers

The last decades have seen an unrivaled growth and diffusion of mobile telecommunications. Several standards have been developed to this purposes, from GSM mobile phone communications to WLAN IEEE 802.11, providing different services for the the transmission of signals ranging from voice to high data rate digital communications and Digital Video Broadcasting (DVB). In this wide research and market field, this thesis focuses on Ultra Wideband (UWB) communications, an emerging technology for providing very high data rate transmissions over very short distances. In particular the presented research deals with the circuit design of enabling blocks for MB-OFDM UWB CMOS single-chip transceivers, namely the frequency synthesizer and the transmission mixer and power amplifier. First we discuss three different models for the simulation of chargepump phase-locked loops, namely the continuous time s-domain and discrete time z-domain approximations and the exact semi-analytical time-domain model. The limitations of the two approximated models are analyzed in terms of error in the computed settling time as a function of loop parameters, deriving practical conditions under which the different models are reliable for fast settling PLLs up to fourth order. Besides, a phase noise analysis method based upon the time-domain model is introduced and compared to the results obtained by means of the s-domain model. We compare the three models over the simulation of a fast switching PLL to be integrated in a frequency synthesizer for WiMedia MB-OFDM UWB systems. In the second part, the theoretical analysis is applied to the design of a 60mW 3.4 to 9.2GHz 12 Bands frequency synthesizer for MB-OFDM UWB based on two wide-band PLLs. The design is presented and discussed up to layout level. A test chip has been implemented in TSMC CMOS 90nm technology, measured data is provided. The functionality of the circuit is proved and specifications are met with state-of-the-art area occupation and power consumption. The last part of the thesis deals with the design of a transmission mixer and a power amplifier for MB-OFDM UWB band group 1. The design has been carried on up to layout level in ST Microlectronics 65nm CMOS technology. Main characteristics of the systems are the wideband behavior (1.6 GHz of bandwidth) and the constant behavior over process parameters, temperature and supply voltage thanks to the design of dedicated adaptive biasing circuits.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Operating System Contribution to Composable Timing Behaviour in High-Integrity Real-Time Systems

The development of High-Integrity Real-Time Systems has a high footprint in terms of human, material and schedule costs. Factoring functional, reusable logic in the application favors incremental development and contains costs. Yet, achieving incrementality in the timing behavior is a much harder problem. Complex features at all levels of the execution stack, aimed to boost average-case performance, exhibit timing behavior highly dependent on execution history, which wrecks time composability and incrementaility with it. Our goal here is to restitute time composability to the execution stack, working bottom up across it. We first characterize time composability without making assumptions on the system architecture or the software deployment to it. Later, we focus on the role played by the real-time operating system in our pursuit. Initially we consider single-core processors and, becoming less permissive on the admissible hardware features, we devise solutions that restore a convincing degree of time composability. To show what can be done for real, we developed TiCOS, an ARINC-compliant kernel, and re-designed ORK+, a kernel for Ada Ravenscar runtimes. In that work, we added support for limited-preemption to ORK+, an absolute premiere in the landscape of real-word kernels. Our implementation allows resource sharing to co-exist with limited-preemptive scheduling, which extends state of the art. We then turn our attention to multicore architectures, first considering partitioned systems, for which we achieve results close to those obtained for single-core processors. Subsequently, we shy away from the over-provision of those systems and consider less restrictive uses of homogeneous multiprocessors, where the scheduling algorithm is key to high schedulable utilization. To that end we single out RUN, a promising baseline, and extend it to SPRINT, which supports sporadic task sets, hence matches real-world industrial needs better. To corroborate our results we present findings from real-world case studies from avionic industry.